Subgroups — #63012

Order 256.

4025 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3558	C₂	1	4	yes	maximal, complemented
2	#3546	C₂	1	2	yes	maximal, complemented
3	#3543	C₂	1	1	yes	maximal, characteristic, complemented
4	#3542	C₂	1	4	yes	maximal, complemented
5	#3536	C₂	1	4	yes	maximal, complemented
6	#3534	C₂	1	8	yes	maximal, complemented
7	#3532	C₂	1	4	yes	maximal, complemented
8	#3520	C₂	1	2	yes	maximal, complemented
9	#3519	C₂	1	4	yes	maximal, complemented
10	#3514	C₂	1	2	yes	maximal, complemented
11	#3513	C₂	1	4	yes	maximal, complemented
12	#3508	C₂	1	1	yes	maximal, characteristic, complemented
13	#3496	C₂	1	2	yes	maximal, complemented
14	#3490	C₂	1	4	yes	maximal, complemented
15	#3488	C₂	1	4	yes	maximal, complemented
16	#3484	C₂	1	4	yes	maximal, complemented
17	#3481	C₂	1	2	yes	maximal, complemented
18	D₄×#41	C₂	1	2	yes	maximal, complemented
19	C₂×#546	C₂	1	4	yes	maximal, complemented
20	C₂×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×H(5,𝔽₂)	C₂²	1	4	yes	complemented
22	C₂²×#41	C₂²	1	4	yes	complemented
23	C₂³×D₄	C₂²	1	4	yes	complemented
24	#562	C₂²	1	8	yes	complemented
25	#562	C₂²	1	8	yes	complemented
26	H(3,𝔽₄)	C₂²	1	4	yes	complemented
27	#560	C₂²	1	8	yes	complemented
28	#560	C₂²	1	4	yes	complemented
29	#560	C₂²	1	4	yes	complemented
30	#559	C₂²	1	2	yes	complemented
31	#559	C₂²	1	4	yes	complemented
32	#559	C₂²	1	1	yes	characteristic, complemented
33	#556	C₂²	1	2	yes	complemented
34	#555	C₂²	1	4	yes	complemented
35	#554	C₂²	1	2	yes	complemented
36	#554	C₂²	1	4	yes	complemented
37	#554	C₂²	1	2	yes	complemented
38	#553	C₂²	1	2	yes	complemented
39	#553	C₂²	1	4	yes	complemented
40	#553	C₂²	1	2	yes	complemented
41	#553	C₂²	1	8	yes	complemented
42	#553	C₂²	1	4	yes	complemented
43	#552	C₂²	1	4	yes	complemented
44	#551	C₂²	1	4	yes	complemented
45	#551	C₂²	1	8	yes	complemented
46	#551	C₂²	1	4	yes	complemented
47	#551	C₂²	1	8	yes	complemented
48	#551	C₂²	1	8	yes	complemented
49	#551	C₂²	1	4	yes	complemented
50	#550	C₂²	1	4	yes	complemented
51	#550	C₂²	1	2	yes	complemented
52	#550	C₂²	1	4	yes	complemented
53	D₄×Q₈	C₂²	1	2	yes	complemented
54	#548	C₂²	1	4	yes	complemented
55	#548	C₂²	1	4	yes	complemented
56	#548	C₂²	1	4	yes	complemented
57	#547	C₂²	1	2	yes	complemented
58	#547	C₂²	1	2	yes	complemented
59	#547	C₂²	1	4	yes	complemented
60	#547	C₂²	1	4	yes	complemented
61	#546	C₂²	1	2	yes	complemented
62	#546	C₂²	1	4	yes	complemented
63	#546	C₂²	1	8	yes	complemented
64	#546	C₂²	1	4	yes	complemented
65	#546	C₂²	1	8	yes	complemented
66	#546	C₂²	1	4	yes	complemented
67	#546	C₂²	1	8	yes	complemented
68	#546	C₂²	1	4	yes	complemented
69	#546	C₂²	1	4	yes	complemented
70	#546	C₂²	1	4	yes	complemented
71	#546	C₂²	1	4	yes	complemented
72	#546	C₂²	1	4	yes	complemented
73	#546	C₂²	1	2	yes	complemented
74	#546	C₂²	1	8	yes	complemented
75	#546	C₂²	1	8	yes	complemented
76	#546	C₂²	1	8	yes	complemented
77	#546	C₂²	1	8	yes	complemented
78	#546	C₂²	1	8	yes	complemented
79	#546	C₂²	1	8	yes	complemented
80	#546	C₂²	1	4	yes	complemented
81	#546	C₂²	1	4	yes	complemented
82	#546	C₂²	1	4	yes	complemented
83	#546	C₂²	1	8	yes	complemented
84	#546	C₂²	1	4	yes	complemented
85	D₄²	C₂²	1	1	yes	characteristic, complemented
86	D₄²	C₂²	1	4	yes	complemented
87	D₄²	C₂²	1	2	yes	complemented
88	D₄²	C₂²	1	4	yes	complemented
89	D₄²	C₂²	1	4	yes	complemented
90	D₄²	C₂²	1	1	yes	characteristic, complemented
91	D₄²	C₂²	1	2	yes	complemented
92	D₄²	C₂²	1	8	yes	complemented
93	D₄²	C₂²	1	4	yes	complemented
94	D₄²	C₂²	1	4	yes	complemented
95	D₄²	C₂²	1	8	yes	complemented
96	D₄²	C₂²	1	4	yes	complemented
97	D₄²	C₂²	1	4	yes	complemented
98	D₄²	C₂²	1	1	yes	characteristic, complemented
99	#543	C₂²	1	4	yes	complemented
100	#542	C₂²	1	4	yes	complemented
101	#542	C₂²	1	4	yes	complemented
102	#542	C₂²	1	4	yes	complemented
103	#540	C₂²	1	8	yes	complemented
104	#540	C₂²	1	4	yes	complemented
105	#540	C₂²	1	4	yes	complemented
106	#539	C₂²	1	8	yes	complemented
107	#539	C₂²	1	8	yes	complemented
108	#538	C₂²	1	8	yes	complemented
109	#538	C₂²	1	8	yes	complemented
110	#538	C₂²	1	8	yes	complemented
111	#538	C₂²	1	8	yes	complemented
112	#538	C₂²	1	8	yes	complemented
113	#538	C₂²	1	8	yes	complemented
114	#537	C₂²	1	8	yes	complemented
115	#537	C₂²	1	4	yes	complemented
116	#537	C₂²	1	4	yes	complemented
117	#535	C₂²	1	2	yes	complemented
118	#535	C₂²	1	8	yes	complemented
119	#535	C₂²	1	4	yes	complemented
120	#535	C₂²	1	4	yes	complemented
121	#535	C₂²	1	4	yes	complemented
122	#534	C₂²	1	4	yes	complemented
123	#534	C₂²	1	8	yes	complemented
124	#534	C₂²	1	8	yes	complemented
125	#534	C₂²	1	8	yes	complemented
126	#533	C₂²	1	1	yes	characteristic, complemented
127	#532	C₂²	1	2	yes	complemented
128	#532	C₂²	1	4	yes	complemented
129	#532	C₂²	1	2	yes	complemented
130	#532	C₂²	1	2	yes	complemented
131	C₂×#127	C₂²	1	1	yes	characteristic, complemented
132	#529	C₂²	1	2	yes	complemented
133	#529	C₂²	1	4	yes	complemented
134	#529	C₂²	1	2	yes	complemented
135	#529	C₂²	1	4	yes	complemented
136	C₂×#124	C₂²	1	4	yes	complemented
137	#525	C₂²	1	4	yes	complemented
138	#525	C₂²	1	4	yes	complemented
139	#525	C₂²	1	4	yes	complemented
140	#525	C₂²	1	8	yes	complemented
141	#525	C₂²	1	8	yes	complemented
142	#525	C₂²	1	4	yes	complemented
143	C₂×#123	C₂²	1	8	yes	complemented
144	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
145	C₂×#121	C₂²	1	4	yes	complemented
146	C₂×#121	C₂²	1	8	yes	complemented
147	C₂×#121	C₂²	1	4	yes	complemented
148	C₂×#121	C₂²	1	4	yes	complemented
149	C₂×#120	C₂²	1	4	yes	complemented
150	C₂×#120	C₂²	1	8	yes	complemented
151	C₂×#120	C₂²	1	4	yes	complemented
152	#520	C₂²	1	4	yes	complemented
153	#518	C₂²	1	2	yes	complemented
154	#518	C₂²	1	4	yes	complemented
155	#518	C₂²	1	4	yes	complemented
156	C₄×#41	C₂²	1	1	yes	characteristic, complemented
157	C₄×#41	C₂²	1	2	yes	complemented
158	C₂×C₄×D₄	C₂²	1	2	yes	complemented
159	C₂×C₄×D₄	C₂²	1	4	yes	complemented
160	C₂×C₄×D₄	C₂²	1	4	yes	complemented
161	C₂×C₄×D₄	C₂²	1	2	yes	complemented
162	C₂²×C₂²⋊C₄	C₂²	1	4	yes	complemented
163	C₂⁵	C₂³	1	4	yes	—
164	H(5,𝔽₂)	—	4	16	no	—
165	C₂×#41	—	4	16	no	—
166	C₂×#41	C₂³	1	2	yes	—
167	C₂×#41	C₂³	1	4	yes	—
168	C₂×#41	C₂³	1	1	yes	characteristic
169	C₂×#41	C₂³	1	4	yes	complemented
170	C₂×#41	C₂³	1	8	yes	complemented
171	C₂×#41	C₂³	1	4	yes	complemented
172	C₂×#41	C₂³	1	4	yes	complemented
173	C₂×#41	C₂³	1	8	yes	complemented
174	C₂×#41	C₂³	1	4	yes	complemented
175	C₂×#41	C₂³	1	8	yes	complemented
176	C₂×#41	C₂³	1	4	yes	complemented
177	C₂²×Q₈	C₂³	1	4	yes	complemented
178	C₂²×D₄	—	4	16	no	—
179	C₂²×D₄	C₂³	1	4	yes	—
180	C₂²×D₄	C₂³	1	2	yes	—
181	C₂²×D₄	C₂³	1	2	yes	—
182	C₂²×D₄	C₂³	1	4	yes	—
183	C₂²×D₄	C₂³	1	4	yes	—
184	C₂²×D₄	C₂³	1	2	yes	—
185	C₂²×D₄	C₂³	1	4	yes	—
186	C₂²×D₄	C₂³	1	8	yes	—
187	C₂²×D₄	C₂³	1	8	yes	—
188	C₂²×D₄	C₂³	1	4	yes	—
189	C₂²×D₄	C₂³	1	4	yes	—
190	C₂²×D₄	C₂³	1	8	yes	—
191	C₂²×D₄	C₂³	1	4	yes	—
192	C₂²×D₄	C₂³	1	8	yes	complemented
193	C₂²×D₄	C₂³	1	8	yes	complemented
194	C₂²×D₄	C₂³	1	8	yes	complemented
195	C₂²×D₄	C₂³	1	8	yes	complemented
196	C₂²×D₄	C₂³	1	4	yes	complemented
197	C₂³×C₄	C₂³	1	4	yes	—
198	C₂³×C₄	C₂³	1	8	yes	complemented
199	C₂³×C₄	C₂³	1	4	yes	complemented
200	C₄⋊Q₈	C₂³	1	2	yes	complemented
201	C₄⋊Q₈	C₂³	1	2	yes	complemented
202	C₄⋊Q₈	C₂³	1	4	yes	complemented
203	#127	C₂³	1	1	yes	characteristic
204	#127	C₂³	1	1	yes	characteristic
205	#127	C₂³	1	4	yes	—
206	#127	C₂³	1	2	yes	—
207	#127	C₂³	1	2	yes	—
208	#127	C₂³	1	4	yes	complemented
209	#127	C₂³	1	4	yes	complemented
210	#127	C₂³	1	8	yes	complemented
211	#126	C₂³	1	8	yes	complemented
212	#126	C₂³	1	4	yes	complemented
213	#126	C₂³	1	4	yes	complemented
214	#126	C₂³	1	4	yes	complemented
215	#126	C₂³	1	4	yes	complemented
216	#126	C₂³	1	8	yes	complemented
217	#126	C₂³	1	8	yes	complemented
218	#126	C₂³	1	8	yes	complemented
219	#125	C₂³	1	2	yes	complemented
220	#125	C₂³	1	4	yes	complemented
221	#125	C₂³	1	2	yes	complemented
222	#125	C₂³	1	2	yes	complemented
223	#125	C₂³	1	8	yes	complemented
224	#124	C₂³	1	2	yes	—
225	#124	C₂³	1	4	yes	—
226	#124	C₂³	1	4	yes	complemented
227	#124	C₂³	1	4	yes	complemented
228	#124	C₂³	1	8	yes	complemented
229	#124	C₂³	1	8	yes	complemented
230	#124	C₂³	1	2	yes	complemented
231	#124	C₂³	1	4	yes	complemented
232	#124	C₂³	1	4	yes	complemented
233	#124	C₂³	1	4	yes	complemented
234	#124	C₂³	1	8	yes	complemented
235	#124	C₂³	1	8	yes	complemented
236	#124	C₂³	1	4	yes	complemented
237	#124	C₂³	1	8	yes	complemented
238	#124	C₂³	1	8	yes	complemented
239	#123	C₂³	1	4	yes	—
240	#123	C₂³	1	8	yes	—
241	#123	C₂³	1	4	yes	—
242	#123	C₂³	1	8	yes	complemented
243	#123	C₂³	1	8	yes	complemented
244	#123	C₂³	1	8	yes	complemented
245	#123	C₂³	1	8	yes	complemented
246	#123	C₂³	1	8	yes	complemented
247	#123	C₂³	1	8	yes	complemented
248	#123	C₂³	1	4	yes	complemented
249	#123	C₂³	1	8	yes	complemented
250	#123	C₂³	1	4	yes	complemented
251	#123	C₂³	1	4	yes	complemented
252	#123	C₂³	1	8	yes	complemented
253	#123	C₂³	1	8	yes	complemented
254	#123	C₂³	1	4	yes	complemented
255	#123	C₂³	1	8	yes	complemented
256	#123	C₂³	1	4	yes	complemented
257	#123	C₂³	1	4	yes	complemented
258	#123	C₂³	1	8	yes	complemented
259	#123	C₂³	1	4	yes	complemented
260	#123	C₂³	1	8	yes	complemented
261	#123	C₂³	1	8	yes	complemented
262	#123	C₂³	1	8	yes	complemented
263	#123	C₂³	1	4	yes	complemented
264	C₂²⋊Q₈	C₂³	1	2	yes	—
265	C₂²⋊Q₈	C₂³	1	4	yes	—
266	C₂²⋊Q₈	C₂³	1	8	yes	—
267	C₂²⋊Q₈	C₂³	1	4	yes	—
268	C₂²⋊Q₈	C₂³	1	4	yes	complemented
269	C₂²⋊Q₈	C₂³	1	4	yes	complemented
270	C₂²⋊Q₈	C₂³	1	8	yes	complemented
271	C₂²⋊Q₈	C₂³	1	4	yes	complemented
272	C₂²⋊Q₈	C₂³	1	4	yes	complemented
273	C₂²⋊Q₈	C₂³	1	8	yes	complemented
274	C₂²⋊Q₈	C₂³	1	4	yes	complemented
275	C₂²⋊Q₈	C₂³	1	4	yes	complemented
276	C₂²⋊Q₈	C₂³	1	8	yes	complemented
277	C₂²⋊Q₈	C₂³	1	8	yes	complemented
278	C₂²⋊Q₈	C₂³	1	4	yes	complemented
279	C₂²⋊Q₈	C₂³	1	2	yes	complemented
280	C₂²⋊Q₈	C₂³	1	4	yes	complemented
281	C₂²⋊Q₈	C₂³	1	8	yes	complemented
282	C₂²⋊Q₈	C₂³	1	8	yes	complemented
283	C₂²⋊Q₈	C₂³	1	8	yes	complemented
284	#121	C₂³	1	4	yes	—
285	#121	C₂³	1	4	yes	—
286	#121	C₂³	1	2	yes	—
287	#121	C₂³	1	4	yes	—
288	#121	C₂³	1	8	yes	—
289	#121	C₂³	1	4	yes	—
290	#121	C₂³	1	8	yes	—
291	#121	C₂³	1	4	yes	—
292	#121	C₂³	1	4	yes	—
293	#121	C₂³	1	8	yes	—
294	#121	C₂³	1	2	yes	—
295	#121	C₂³	1	4	yes	—
296	#121	C₂³	1	4	yes	—
297	#121	C₂³	1	2	yes	—
298	#121	C₂³	1	8	yes	complemented
299	#121	C₂³	1	4	yes	complemented
300	#121	C₂³	1	2	yes	complemented
301	#121	C₂³	1	4	yes	complemented
302	#121	C₂³	1	8	yes	complemented
303	#121	C₂³	1	8	yes	complemented
304	#121	C₂³	1	8	yes	complemented
305	#121	C₂³	1	8	yes	complemented
306	#121	C₂³	1	8	yes	complemented
307	#121	C₂³	1	4	yes	complemented
308	#121	C₂³	1	8	yes	complemented
309	#121	C₂³	1	8	yes	complemented
310	#121	C₂³	1	8	yes	complemented
311	#121	C₂³	1	8	yes	complemented
312	#121	C₂³	1	8	yes	complemented
313	#121	C₂³	1	8	yes	complemented
314	#121	C₂³	1	4	yes	complemented
315	#121	C₂³	1	4	yes	complemented
316	#121	C₂³	1	4	yes	complemented
317	#121	C₂³	1	4	yes	complemented
318	#121	C₂³	1	4	yes	complemented
319	#121	C₂³	1	8	yes	complemented
320	#121	C₂³	1	4	yes	complemented
321	#121	C₂³	1	4	yes	complemented
322	#121	C₂³	1	8	yes	complemented
323	#121	C₂³	1	8	yes	complemented
324	#121	C₂³	1	8	yes	complemented
325	#121	C₂³	1	8	yes	complemented
326	#121	C₂³	1	8	yes	complemented
327	#121	C₂³	1	8	yes	complemented
328	#121	C₂³	1	8	yes	complemented
329	#120	C₂³	1	4	yes	—
330	#120	C₂³	1	8	yes	—
331	#120	C₂³	1	4	yes	—
332	#120	C₂³	1	4	yes	—
333	#120	C₂³	1	4	yes	—
334	#120	C₂³	1	8	yes	—
335	#120	C₂³	1	8	yes	—
336	#120	C₂³	1	8	yes	—
337	#120	C₂³	1	8	yes	—
338	#120	C₂³	1	4	yes	—
339	#120	C₂³	1	4	yes	—
340	#120	C₂³	1	4	yes	—
341	#120	C₂³	1	8	yes	complemented
342	#120	C₂³	1	8	yes	complemented
343	#120	C₂³	1	8	yes	complemented
344	#120	C₂³	1	8	yes	complemented
345	#120	C₂³	1	8	yes	complemented
346	#120	C₂³	1	8	yes	complemented
347	#120	C₂³	1	8	yes	complemented
348	#120	C₂³	1	4	yes	complemented
349	#120	C₂³	1	4	yes	complemented
350	#120	C₂³	1	8	yes	complemented
351	#120	C₂³	1	4	yes	complemented
352	#120	C₂³	1	8	yes	complemented
353	C₄×Q₈	C₂³	1	2	yes	complemented
354	C₄×Q₈	C₂³	1	2	yes	complemented
355	C₄×Q₈	C₂³	1	2	yes	complemented
356	C₄×Q₈	C₂³	1	4	yes	complemented
357	C₄×Q₈	C₂³	1	4	yes	complemented
358	C₄×D₄	C₂³	1	2	yes	—
359	C₄×D₄	C₂³	1	2	yes	—
360	C₄×D₄	C₂³	1	2	yes	—
361	C₄×D₄	C₂³	1	4	yes	—
362	C₄×D₄	C₂³	1	4	yes	—
363	C₄×D₄	C₂³	1	2	yes	—
364	C₄×D₄	C₂³	1	4	yes	—
365	C₄×D₄	C₂³	1	4	yes	—
366	C₄×D₄	C₂³	1	2	yes	—
367	C₄×D₄	C₂³	1	4	yes	—
368	C₄×D₄	C₂³	1	4	yes	—
369	C₄×D₄	C₂³	1	2	yes	—
370	C₄×D₄	C₂³	1	2	yes	—
371	C₄×D₄	C₂³	1	2	yes	—
372	C₄×D₄	C₂³	1	8	yes	—
373	C₄×D₄	C₂³	1	4	yes	complemented
374	C₄×D₄	C₂³	1	8	yes	complemented
375	C₄×D₄	C₂³	1	4	yes	complemented
376	C₄×D₄	C₂³	1	4	yes	complemented
377	C₄×D₄	C₂³	1	2	yes	complemented
378	C₄×D₄	C₂³	1	4	yes	complemented
379	C₄×D₄	C₂³	1	4	yes	complemented
380	C₄×D₄	C₂³	1	2	yes	complemented
381	C₄×D₄	C₂³	1	4	yes	complemented
382	C₄×D₄	C₂³	1	8	yes	complemented
383	C₄×D₄	C₂³	1	4	yes	complemented
384	C₄×D₄	C₂³	1	4	yes	complemented
385	C₄×D₄	C₂³	1	4	yes	complemented
386	C₄×D₄	C₂³	1	2	yes	complemented
387	C₄×D₄	C₂³	1	4	yes	complemented
388	C₄×D₄	C₂³	1	4	yes	complemented
389	C₄×D₄	C₂³	1	8	yes	complemented
390	C₄×D₄	C₂³	1	8	yes	complemented
391	C₄×D₄	C₂³	1	8	yes	complemented
392	C₄×D₄	C₂³	1	8	yes	complemented
393	C₄×D₄	C₂³	1	8	yes	complemented
394	C₄×D₄	C₂³	1	4	yes	complemented
395	C₄×D₄	C₂³	1	4	yes	complemented
396	C₄×D₄	C₂³	1	4	yes	complemented
397	C₄×D₄	C₂³	1	8	yes	complemented
398	C₄×D₄	C₂³	1	8	yes	complemented
399	#117	C₂³	1	1	yes	characteristic
400	#117	C₂³	1	2	yes	—
401	#117	C₂³	1	4	yes	complemented
402	#117	C₂³	1	2	yes	complemented
403	#117	C₂³	1	2	yes	complemented
404	#117	C₂³	1	4	yes	complemented
405	#117	C₂³	1	4	yes	complemented
406	#117	C₂³	1	8	yes	complemented
407	#117	C₂³	1	4	yes	complemented
408	#117	C₂³	1	8	yes	complemented
409	C₂×C₄⋊C₄	C₂³	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³	1	4	yes	complemented
411	C₂×C₄⋊C₄	C₂³	1	4	yes	complemented
412	C₂×C₄⋊C₄	C₂³	1	2	yes	complemented
413	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
414	C₂×C₄⋊C₄	C₂³	1	4	yes	complemented
415	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
418	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
423	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
424	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
425	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
426	C₂×C₂²⋊C₄	C₂³	1	4	yes	complemented
427	C₂×C₂²⋊C₄	C₂³	1	4	yes	complemented
428	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
429	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
430	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
431	C₂×C₄²	C₂³	1	1	yes	characteristic
432	C₂×C₄²	C₂³	1	4	yes	complemented
433	C₂×C₄²	C₂³	1	2	yes	complemented
434	C₂⁴	—	4	16	no	—
435	C₂⁴	—	4	8	no	—
436	C₂⁴	C₂⁴	1	4	yes	—
437	C₂⁴	C₂⁴	1	4	yes	—
438	C₂⁴	C₂⁴	1	4	yes	—
439	C₂⁴	C₂⁴	1	8	yes	—
440	C₂⁴	C₂⁴	1	4	yes	—
441	C₂⁴	C₂⁴	1	4	yes	—
442	C₂⁴	C₂⁴	1	4	yes	—
443	#41	—	2	8	no	—
444	#41	—	2	16	no	—
445	#41	—	4	8	no	—
446	#41	—	4	16	no	—
447	#41	—	4	16	no	—
448	#41	—	4	2	no	—
449	#41	—	4	16	no	—
450	#41	—	4	8	no	—
451	#41	—	4	8	no	—
452	#41	—	4	8	no	—
453	#41	—	4	8	no	—
454	C₂×Q₈	—	4	8	no	—
455	C₂×Q₈	C₂⁴	1	2	yes	—
456	C₂×Q₈	C₂⁴	1	4	yes	—
457	C₂×Q₈	C₂⁴	1	1	yes	characteristic
458	C₂×Q₈	C₂⁴	1	4	yes	—
459	C₂×Q₈	C₂⁴	1	8	yes	—
460	C₂×D₄	—	2	8	no	—
461	C₂×D₄	—	2	16	no	—
462	C₂×D₄	—	2	16	no	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	4	8	no	—
465	C₂×D₄	—	4	8	no	—
466	C₂×D₄	—	4	8	no	—
467	C₂×D₄	—	4	8	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂×D₄	—	4	16	no	—
470	C₂×D₄	—	4	16	no	—
471	C₂×D₄	—	4	16	no	—
472	C₂×D₄	—	4	16	no	—
473	C₂×D₄	—	4	8	no	—
474	C₂×D₄	—	4	8	no	—
475	C₂×D₄	—	4	16	no	—
476	C₂×D₄	—	4	16	no	—
477	C₂×D₄	—	4	16	no	—
478	C₂×D₄	C₂⁴	1	2	yes	—
479	C₂×D₄	C₂⁴	1	4	yes	—
480	C₂×D₄	C₂⁴	1	4	yes	—
481	C₂×D₄	C₂⁴	1	2	yes	—
482	C₂×D₄	C₂⁴	1	8	yes	—
483	C₂×D₄	C₂⁴	1	8	yes	—
484	C₂×D₄	C₂⁴	1	4	yes	—
485	C₂×D₄	C₂⁴	1	4	yes	—
486	C₂×D₄	C₂⁴	1	8	yes	—
487	C₂×D₄	C₂⁴	1	4	yes	—
488	C₂×D₄	C₂⁴	1	4	yes	—
489	C₂×D₄	C₂⁴	1	2	yes	—
490	C₂×D₄	C₂⁴	1	2	yes	—
491	C₂×D₄	C₂⁴	1	4	yes	—
492	C₂×D₄	C₂⁴	1	2	yes	—
493	C₂×D₄	C₂⁴	1	4	yes	—
494	C₂×D₄	C₂⁴	1	4	yes	—
495	C₂×D₄	C₂⁴	1	8	yes	—
496	C₂×D₄	C₂⁴	1	1	yes	characteristic
497	C₂×D₄	C₂⁴	1	4	yes	—
498	C₂×D₄	C₂⁴	1	8	yes	—
499	C₂×D₄	C₂⁴	1	8	yes	—
500	C₂×D₄	C₂⁴	1	8	yes	—
501	C₂×D₄	C₂⁴	1	8	yes	—
502	C₂×D₄	C₂⁴	1	4	yes	—
503	C₂×D₄	C₂⁴	1	8	yes	—
504	C₂×D₄	C₂⁴	1	8	yes	—
505	C₂×D₄	C₂⁴	1	8	yes	—
506	C₂×D₄	C₂⁴	1	8	yes	—
507	C₂×D₄	C₂⁴	1	4	yes	—
508	C₂×D₄	C₂⁴	1	2	yes	—
509	C₂²×C₄	—	4	8	no	—
510	C₂²×C₄	—	4	8	no	—
511	C₂²×C₄	—	4	16	no	—
512	C₂²×C₄	C₂⁴	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴	1	2	yes	—
514	C₂²×C₄	C₂⁴	1	4	yes	—
515	C₂²×C₄	C₂⁴	1	4	yes	—
516	C₂²×C₄	C₂⁴	1	2	yes	—
517	C₂²×C₄	C₂⁴	1	2	yes	—
518	C₂²×C₄	C₂⁴	1	8	yes	—
519	C₂²×C₄	C₂⁴	1	4	yes	—
520	C₂²×C₄	C₂⁴	1	4	yes	—
521	C₂²×C₄	C₂⁴	1	4	yes	—
522	C₂²×C₄	C₂⁴	1	2	yes	—
523	C₂²×C₄	C₂⁴	1	4	yes	—
524	C₂²×C₄	C₂⁴	1	4	yes	—
525	C₂²×C₄	C₂⁴	1	8	yes	—
526	C₂²×C₄	C₂⁴	1	8	yes	—
527	C₂²×C₄	C₂⁴	1	8	yes	—
528	C₂²×C₄	C₂⁴	1	8	yes	—
529	C₂²×C₄	C₂⁴	1	4	yes	—
530	C₂²×C₄	C₂⁴	1	4	yes	—
531	C₂²×C₄	C₂⁴	1	4	yes	—
532	C₂²×C₄	C₂⁴	1	8	yes	—
533	C₂²×C₄	C₂⁴	1	4	yes	—
534	C₂²×C₄	C₂⁴	1	4	yes	—
535	C₄⋊C₄	C₂⁴	1	2	yes	—
536	C₄⋊C₄	C₂⁴	1	2	yes	—
537	C₄⋊C₄	C₂⁴	1	4	yes	—
538	C₄⋊C₄	C₂⁴	1	2	yes	—
539	C₄⋊C₄	C₂⁴	1	4	yes	—
540	C₄⋊C₄	C₂⁴	1	2	yes	—
541	C₄⋊C₄	C₂⁴	1	4	yes	—
542	C₄⋊C₄	C₂⁴	1	8	yes	—
543	C₄⋊C₄	C₂⁴	1	4	yes	—
544	C₄⋊C₄	C₂⁴	1	4	yes	—
545	C₄⋊C₄	C₂⁴	1	4	yes	—
546	C₄⋊C₄	C₂⁴	1	8	yes	—
547	C₄⋊C₄	C₂⁴	1	4	yes	—
548	C₄⋊C₄	C₂⁴	1	8	yes	—
549	C₄⋊C₄	C₂⁴	1	8	yes	—
550	C₄⋊C₄	C₂⁴	1	2	yes	—
551	C₄⋊C₄	C₂⁴	1	4	yes	—
552	C₄⋊C₄	C₂⁴	1	2	yes	—
553	C₄⋊C₄	C₂⁴	1	4	yes	—
554	C₄⋊C₄	C₂⁴	1	8	yes	—
555	C₄⋊C₄	C₂⁴	1	2	yes	—
556	C₄⋊C₄	C₂⁴	1	4	yes	—
557	C₄⋊C₄	C₂⁴	1	4	yes	—
558	C₄⋊C₄	C₂⁴	1	4	yes	—
559	C₄⋊C₄	C₂⁴	1	4	yes	—
560	C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
561	C₂²⋊C₄	C₂⁴	1	4	yes	—
562	C₂²⋊C₄	C₂⁴	1	4	yes	—
563	C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
564	C₂²⋊C₄	C₂⁴	1	4	yes	—
565	C₂²⋊C₄	C₂⁴	1	4	yes	—
566	C₂²⋊C₄	C₂⁴	1	8	yes	—
567	C₂²⋊C₄	C₂⁴	1	8	yes	—
568	C₂²⋊C₄	C₂⁴	1	8	yes	—
569	C₂²⋊C₄	C₂⁴	1	4	yes	—
570	C₂²⋊C₄	C₂⁴	1	4	yes	—
571	C₂²⋊C₄	C₂⁴	1	4	yes	—
572	C₂²⋊C₄	C₂⁴	1	8	yes	—
573	C₂²⋊C₄	C₂⁴	1	4	yes	—
574	C₂²⋊C₄	C₂⁴	1	4	yes	—
575	C₂²⋊C₄	C₂⁴	1	4	yes	—
576	C₂²⋊C₄	C₂⁴	1	4	yes	—
577	C₂²⋊C₄	C₂⁴	1	4	yes	—
578	C₂²⋊C₄	C₂⁴	1	8	yes	—
579	C₂²⋊C₄	C₂⁴	1	4	yes	—
580	C₂²⋊C₄	C₂⁴	1	4	yes	—
581	C₂²⋊C₄	C₂⁴	1	4	yes	—
582	C₂²⋊C₄	C₂⁴	1	8	yes	—
583	C₂²⋊C₄	C₂⁴	1	2	yes	—
584	C₂²⋊C₄	C₂⁴	1	4	yes	—
585	C₂²⋊C₄	C₂⁴	1	8	yes	—
586	C₂²⋊C₄	C₂⁴	1	4	yes	—
587	C₂²⋊C₄	C₂⁴	1	4	yes	—
588	C₂²⋊C₄	C₂⁴	1	8	yes	—
589	C₂²⋊C₄	C₂⁴	1	4	yes	—
590	C₂²⋊C₄	C₂⁴	1	8	yes	—
591	C₂²⋊C₄	C₂⁴	1	8	yes	—
592	C₂²⋊C₄	C₂⁴	1	8	yes	—
593	C₂²⋊C₄	C₂⁴	1	8	yes	—
594	C₂²⋊C₄	C₂⁴	1	4	yes	—
595	C₂²⋊C₄	C₂⁴	1	4	yes	—
596	C₂²⋊C₄	C₂⁴	1	2	yes	—
597	C₂²⋊C₄	C₂⁴	1	4	yes	—
598	C₂²⋊C₄	C₂⁴	1	4	yes	—
599	C₂²⋊C₄	C₂⁴	1	4	yes	—
600	C₄²	C₂⁴	1	1	yes	characteristic
601	C₄²	C₂⁴	1	2	yes	—
602	C₄²	C₂⁴	1	1	yes	characteristic
603	C₄²	C₂⁴	1	2	yes	—
604	C₄²	C₂⁴	1	2	yes	—
605	C₄²	C₂⁴	1	4	yes	—
606	C₄²	C₂⁴	1	4	yes	—
607	C₄²	C₂⁴	1	2	yes	—
608	C₄²	C₂⁴	1	4	yes	—
609	C₄²	C₂⁴	1	4	yes	—
610	C₄²	C₂⁴	1	8	yes	—
611	C₂³	—	2	16	no	—
612	C₂³	—	2	8	no	—
613	C₂³	—	2	8	no	—
614	C₂³	—	2	8	no	—
615	C₂³	—	2	16	no	—
616	C₂³	—	2	8	no	—
617	C₂³	—	4	4	no	—
618	C₂³	—	4	4	no	—
619	C₂³	—	4	4	no	—
620	C₂³	—	4	8	no	—
621	C₂³	—	4	8	no	—
622	C₂³	—	4	8	no	—
623	C₂³	—	4	4	no	—
624	C₂³	—	4	8	no	—
625	C₂³	—	4	4	no	—
626	C₂³	—	4	8	no	—
627	C₂³	—	4	4	no	—
628	C₂³	—	8	32	no	—
629	C₂³	C₂⁵	1	4	yes	—
630	C₂³	C₂⁵	1	4	yes	—
631	C₂³	C₂⁵	1	4	yes	—
632	C₂³	C₂⁵	1	4	yes	—
633	C₂³	C₂⁵	1	2	yes	—
634	C₂³	C₂⁵	1	4	yes	—
635	C₂³	C₂⁵	1	1	yes	characteristic
636	Q₈	—	2	4	no	—
637	Q₈	—	2	8	no	—
638	Q₈	—	4	8	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	4	4	no	—
641	D₄	—	2	8	no	—
642	D₄	—	2	16	no	—
643	D₄	—	2	16	no	—
644	D₄	—	2	8	no	—
645	D₄	—	2	16	no	—
646	D₄	—	2	8	no	—
647	D₄	—	2	8	no	—
648	D₄	—	2	4	no	—
649	D₄	—	2	4	no	—
650	D₄	—	2	8	no	—
651	D₄	—	2	8	no	—
652	D₄	—	2	4	no	—
653	D₄	—	4	8	no	—
654	D₄	—	4	8	no	—
655	D₄	—	4	8	no	—
656	D₄	—	4	4	no	—
657	D₄	—	4	8	no	—
658	D₄	—	4	4	no	—
659	D₄	—	4	4	no	—
660	D₄	—	4	8	no	—
661	D₄	—	4	8	no	—
662	D₄	—	4	2	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	4	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	8	no	—
667	D₄	—	4	4	no	—
668	D₄	—	4	8	no	—
669	D₄	—	4	8	no	—
670	D₄	—	4	1	no	—
671	D₄	H(5,𝔽₂)	1	8	yes	complemented
672	C₂×C₄	—	2	8	no	—
673	C₂×C₄	—	2	16	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	8	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	8	no	—
679	C₂×C₄	—	2	8	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	4	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	8	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	8	no	—
690	C₂×C₄	—	4	4	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	C₂⁵	1	1	yes	characteristic
696	C₂×C₄	C₂⁵	1	2	yes	—
697	C₂×C₄	C₂⁵	1	1	yes	characteristic
698	C₂×C₄	C₂⁵	1	4	yes	—
699	C₂×C₄	C₂⁵	1	2	yes	—
700	C₂×C₄	C₂⁵	1	4	yes	—
701	C₂×C₄	C₂⁵	1	2	yes	—
702	C₂×C₄	C₂⁵	1	4	yes	—
703	C₂×C₄	C₂⁵	1	8	yes	—
704	C₂×C₄	C₂⁵	1	4	yes	—
705	C₂×C₄	C₂⁵	1	2	yes	—
706	C₂×C₄	C₂⁵	1	4	yes	—
707	C₂×C₄	C₂⁵	1	2	yes	—
708	C₂²	—	2	4	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	4	no	—
713	C₂²	—	2	4	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	8	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	2	8	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	4	16	no	—
725	C₂²	—	4	16	no	—
726	C₂²	—	8	8	no	—
727	C₂²	—	8	8	no	—
728	C₂²	—	8	16	no	—
729	C₂²	—	8	8	no	—
730	C₂²	—	16	4	no	—
731	C₂²	C₂×H(5,𝔽₂)	1	8	yes	—
732	C₂²	#585	1	2	yes	—
733	C₂²	C₂⁶	1	1	yes	characteristic
734	C₄	—	2	2	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	4	no	—
738	C₄	—	2	4	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	8	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	1	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	4	no	—
745	C₄	—	2	2	no	—
746	C₄	C₂×H(5,𝔽₂)	1	4	yes	—
747	C₂	—	2	2	no	—
748	C₂	—	2	8	no	—
749	C₂	—	4	4	no	—
750	C₂	—	4	4	no	—
751	C₂	—	4	2	no	—
752	C₂	—	4	4	no	—
753	C₂	—	4	4	no	—
754	C₂	C₂²×H(5,𝔽₂)	1	2	yes	—
755	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #3558	C₂	semidirect
2. #3546	C₂	semidirect
3. #3543	C₂	semidirect
4. #3542	C₂	semidirect
5. #3536	C₂	semidirect
6. #3534	C₂	semidirect
7. #3532	C₂	semidirect
8. #3520	C₂	semidirect
9. #3519	C₂	semidirect
10. #3514	C₂	semidirect
11. #3513	C₂	semidirect
12. #3508	C₂	semidirect
13. #3496	C₂	semidirect
14. #3490	C₂	semidirect
15. #3488	C₂	semidirect
16. #3484	C₂	semidirect
17. #3481	C₂	semidirect
18. D₄×#41	C₂	semidirect
19. C₂×#546	C₂	semidirect
20. C₂×D₄²	C₂	semidirect
21. C₂×H(5,𝔽₂)	C₂²	semidirect
22. C₂²×#41	C₂²	semidirect
23. C₂³×D₄	C₂²	semidirect
24. #562	C₂²	semidirect
25. #562	C₂²	semidirect
26. H(3,𝔽₄)	C₂²	semidirect
27. #560	C₂²	semidirect
28. #560	C₂²	semidirect
29. #560	C₂²	semidirect
30. #559	C₂²	semidirect
31. #559	C₂²	semidirect
32. #559	C₂²	semidirect
33. #556	C₂²	semidirect
34. #555	C₂²	semidirect
35. #554	C₂²	semidirect
36. #554	C₂²	semidirect
37. #554	C₂²	semidirect
38. #553	C₂²	semidirect
39. #553	C₂²	semidirect
40. #553	C₂²	semidirect
41. #553	C₂²	semidirect
42. #553	C₂²	semidirect
43. #552	C₂²	semidirect
44. #551	C₂²	semidirect
45. #551	C₂²	semidirect
46. #551	C₂²	semidirect
47. #551	C₂²	semidirect
48. #551	C₂²	semidirect
49. #551	C₂²	semidirect
50. #550	C₂²	semidirect
51. #550	C₂²	semidirect
52. #550	C₂²	semidirect
53. D₄×Q₈	C₂²	semidirect
54. #548	C₂²	semidirect
55. #548	C₂²	semidirect
56. #548	C₂²	semidirect
57. #547	C₂²	semidirect
58. #547	C₂²	semidirect
59. #547	C₂²	semidirect
60. #547	C₂²	semidirect
61. #546	C₂²	semidirect
62. #546	C₂²	semidirect
63. #546	C₂²	semidirect
64. #546	C₂²	semidirect
65. #546	C₂²	semidirect
66. #546	C₂²	semidirect
67. #546	C₂²	semidirect
68. #546	C₂²	semidirect
69. #546	C₂²	semidirect
70. #546	C₂²	semidirect
71. #546	C₂²	semidirect
72. #546	C₂²	semidirect
73. #546	C₂²	semidirect
74. #546	C₂²	semidirect
75. #546	C₂²	semidirect
76. #546	C₂²	semidirect
77. #546	C₂²	semidirect
78. #546	C₂²	semidirect
79. #546	C₂²	semidirect
80. #546	C₂²	semidirect
81. #546	C₂²	semidirect
82. #546	C₂²	semidirect
83. #546	C₂²	semidirect
84. #546	C₂²	semidirect
85. D₄²	C₂²	semidirect
86. D₄²	C₂²	semidirect
87. D₄²	C₂²	semidirect
88. D₄²	C₂²	semidirect
89. D₄²	C₂²	semidirect
90. D₄²	C₂²	semidirect
91. D₄²	C₂²	semidirect
92. D₄²	C₂²	semidirect
93. D₄²	C₂²	semidirect
94. D₄²	C₂²	semidirect
95. D₄²	C₂²	semidirect
96. D₄²	C₂²	semidirect
97. D₄²	C₂²	semidirect
98. D₄²	C₂²	semidirect
99. #543	C₂²	semidirect
100. #542	C₂²	semidirect
101. #542	C₂²	semidirect
102. #542	C₂²	semidirect
103. #540	C₂²	semidirect
104. #540	C₂²	semidirect
105. #540	C₂²	semidirect
106. #539	C₂²	semidirect
107. #539	C₂²	semidirect
108. #538	C₂²	semidirect
109. #538	C₂²	semidirect
110. #538	C₂²	semidirect
111. #538	C₂²	semidirect
112. #538	C₂²	semidirect
113. #538	C₂²	semidirect
114. #537	C₂²	semidirect
115. #537	C₂²	semidirect
116. #537	C₂²	semidirect
117. #535	C₂²	semidirect
118. #535	C₂²	semidirect
119. #535	C₂²	semidirect
120. #535	C₂²	semidirect
121. #535	C₂²	semidirect
122. #534	C₂²	semidirect
123. #534	C₂²	semidirect
124. #534	C₂²	semidirect
125. #534	C₂²	semidirect
126. #533	C₂²	semidirect
127. #532	C₂²	semidirect
128. #532	C₂²	semidirect
129. #532	C₂²	semidirect
130. #532	C₂²	semidirect
131. C₂×#127	C₂²	semidirect
132. #529	C₂²	semidirect
133. #529	C₂²	semidirect
134. #529	C₂²	semidirect
135. #529	C₂²	semidirect
136. C₂×#124	C₂²	semidirect
137. #525	C₂²	semidirect
138. #525	C₂²	semidirect
139. #525	C₂²	semidirect
140. #525	C₂²	semidirect
141. #525	C₂²	semidirect
142. #525	C₂²	semidirect
143. C₂×#123	C₂²	semidirect
144. C₂×C₂²⋊Q₈	C₂²	semidirect
145. C₂×#121	C₂²	semidirect
146. C₂×#121	C₂²	semidirect
147. C₂×#121	C₂²	semidirect
148. C₂×#121	C₂²	semidirect
149. C₂×#120	C₂²	semidirect
150. C₂×#120	C₂²	semidirect
151. C₂×#120	C₂²	semidirect
152. #520	C₂²	semidirect
153. #518	C₂²	semidirect
154. #518	C₂²	semidirect
155. #518	C₂²	semidirect
156. C₄×#41	C₂²	semidirect
157. C₄×#41	C₂²	semidirect
158. C₂×C₄×D₄	C₂²	semidirect
159. C₂×C₄×D₄	C₂²	semidirect
160. C₂×C₄×D₄	C₂²	semidirect
161. C₂×C₄×D₄	C₂²	semidirect
162. C₂²×C₂²⋊C₄	C₂²	semidirect
169. C₂×#41	C₂³	semidirect
170. C₂×#41	C₂³	semidirect
171. C₂×#41	C₂³	semidirect
172. C₂×#41	C₂³	semidirect
173. C₂×#41	C₂³	semidirect
174. C₂×#41	C₂³	semidirect
175. C₂×#41	C₂³	semidirect
176. C₂×#41	C₂³	semidirect
177. C₂²×Q₈	C₂³	semidirect
192. C₂²×D₄	C₂³	semidirect
193. C₂²×D₄	C₂³	semidirect
194. C₂²×D₄	C₂³	semidirect
195. C₂²×D₄	C₂³	semidirect
196. C₂²×D₄	C₂³	semidirect
198. C₂³×C₄	C₂³	semidirect
199. C₂³×C₄	C₂³	semidirect
200. C₄⋊Q₈	C₂³	semidirect
201. C₄⋊Q₈	C₂³	semidirect
202. C₄⋊Q₈	C₂³	semidirect
208. #127	C₂³	semidirect
209. #127	C₂³	semidirect
210. #127	C₂³	semidirect
211. #126	C₂³	semidirect
212. #126	C₂³	semidirect
213. #126	C₂³	semidirect
214. #126	C₂³	semidirect
215. #126	C₂³	semidirect
216. #126	C₂³	semidirect
217. #126	C₂³	semidirect
218. #126	C₂³	semidirect
219. #125	C₂³	semidirect
220. #125	C₂³	semidirect
221. #125	C₂³	semidirect
222. #125	C₂³	semidirect
223. #125	C₂³	semidirect
226. #124	C₂³	semidirect
227. #124	C₂³	semidirect
228. #124	C₂³	semidirect
229. #124	C₂³	semidirect
230. #124	C₂³	semidirect
231. #124	C₂³	semidirect
232. #124	C₂³	semidirect
233. #124	C₂³	semidirect
234. #124	C₂³	semidirect
235. #124	C₂³	semidirect
236. #124	C₂³	semidirect
237. #124	C₂³	semidirect
238. #124	C₂³	semidirect
242. #123	C₂³	semidirect
243. #123	C₂³	semidirect
244. #123	C₂³	semidirect
245. #123	C₂³	semidirect
246. #123	C₂³	semidirect
247. #123	C₂³	semidirect
248. #123	C₂³	semidirect
249. #123	C₂³	semidirect
250. #123	C₂³	semidirect
251. #123	C₂³	semidirect
252. #123	C₂³	semidirect
253. #123	C₂³	semidirect
254. #123	C₂³	semidirect
255. #123	C₂³	semidirect
256. #123	C₂³	semidirect
257. #123	C₂³	semidirect
258. #123	C₂³	semidirect
259. #123	C₂³	semidirect
260. #123	C₂³	semidirect
261. #123	C₂³	semidirect
262. #123	C₂³	semidirect
263. #123	C₂³	semidirect
268. C₂²⋊Q₈	C₂³	semidirect
269. C₂²⋊Q₈	C₂³	semidirect
270. C₂²⋊Q₈	C₂³	semidirect
271. C₂²⋊Q₈	C₂³	semidirect
272. C₂²⋊Q₈	C₂³	semidirect
273. C₂²⋊Q₈	C₂³	semidirect
274. C₂²⋊Q₈	C₂³	semidirect
275. C₂²⋊Q₈	C₂³	semidirect
276. C₂²⋊Q₈	C₂³	semidirect
277. C₂²⋊Q₈	C₂³	semidirect
278. C₂²⋊Q₈	C₂³	semidirect
279. C₂²⋊Q₈	C₂³	semidirect
280. C₂²⋊Q₈	C₂³	semidirect
281. C₂²⋊Q₈	C₂³	semidirect
282. C₂²⋊Q₈	C₂³	semidirect
283. C₂²⋊Q₈	C₂³	semidirect
298. #121	C₂³	semidirect
299. #121	C₂³	semidirect
300. #121	C₂³	semidirect
301. #121	C₂³	semidirect
302. #121	C₂³	semidirect
303. #121	C₂³	semidirect
304. #121	C₂³	semidirect
305. #121	C₂³	semidirect
306. #121	C₂³	semidirect
307. #121	C₂³	semidirect
308. #121	C₂³	semidirect
309. #121	C₂³	semidirect
310. #121	C₂³	semidirect
311. #121	C₂³	semidirect
312. #121	C₂³	semidirect
313. #121	C₂³	semidirect
314. #121	C₂³	semidirect
315. #121	C₂³	semidirect
316. #121	C₂³	semidirect
317. #121	C₂³	semidirect
318. #121	C₂³	semidirect
319. #121	C₂³	semidirect
320. #121	C₂³	semidirect
321. #121	C₂³	semidirect
322. #121	C₂³	semidirect
323. #121	C₂³	semidirect
324. #121	C₂³	semidirect
325. #121	C₂³	semidirect
326. #121	C₂³	semidirect
327. #121	C₂³	semidirect
328. #121	C₂³	semidirect
341. #120	C₂³	semidirect
342. #120	C₂³	semidirect
343. #120	C₂³	semidirect
344. #120	C₂³	semidirect
345. #120	C₂³	semidirect
346. #120	C₂³	semidirect
347. #120	C₂³	semidirect
348. #120	C₂³	semidirect
349. #120	C₂³	semidirect
350. #120	C₂³	semidirect
351. #120	C₂³	semidirect
352. #120	C₂³	semidirect
353. C₄×Q₈	C₂³	semidirect
354. C₄×Q₈	C₂³	semidirect
355. C₄×Q₈	C₂³	semidirect
356. C₄×Q₈	C₂³	semidirect
357. C₄×Q₈	C₂³	semidirect
373. C₄×D₄	C₂³	semidirect
374. C₄×D₄	C₂³	semidirect
375. C₄×D₄	C₂³	semidirect
376. C₄×D₄	C₂³	semidirect
377. C₄×D₄	C₂³	semidirect
378. C₄×D₄	C₂³	semidirect
379. C₄×D₄	C₂³	semidirect
380. C₄×D₄	C₂³	semidirect
381. C₄×D₄	C₂³	semidirect
382. C₄×D₄	C₂³	semidirect
383. C₄×D₄	C₂³	semidirect
384. C₄×D₄	C₂³	semidirect
385. C₄×D₄	C₂³	semidirect
386. C₄×D₄	C₂³	semidirect
387. C₄×D₄	C₂³	semidirect
388. C₄×D₄	C₂³	semidirect
389. C₄×D₄	C₂³	semidirect
390. C₄×D₄	C₂³	semidirect
391. C₄×D₄	C₂³	semidirect
392. C₄×D₄	C₂³	semidirect
393. C₄×D₄	C₂³	semidirect
394. C₄×D₄	C₂³	semidirect
395. C₄×D₄	C₂³	semidirect
396. C₄×D₄	C₂³	semidirect
397. C₄×D₄	C₂³	semidirect
398. C₄×D₄	C₂³	semidirect
401. #117	C₂³	semidirect
402. #117	C₂³	semidirect
403. #117	C₂³	semidirect
404. #117	C₂³	semidirect
405. #117	C₂³	semidirect
406. #117	C₂³	semidirect
407. #117	C₂³	semidirect
408. #117	C₂³	semidirect
410. C₂×C₄⋊C₄	C₂³	semidirect
411. C₂×C₄⋊C₄	C₂³	semidirect
412. C₂×C₄⋊C₄	C₂³	semidirect
413. C₂×C₄⋊C₄	C₂³	semidirect
414. C₂×C₄⋊C₄	C₂³	semidirect
422. C₂×C₂²⋊C₄	C₂³	semidirect
423. C₂×C₂²⋊C₄	C₂³	semidirect
424. C₂×C₂²⋊C₄	C₂³	semidirect
425. C₂×C₂²⋊C₄	C₂³	semidirect
426. C₂×C₂²⋊C₄	C₂³	semidirect
427. C₂×C₂²⋊C₄	C₂³	semidirect
428. C₂×C₂²⋊C₄	C₂³	semidirect
429. C₂×C₂²⋊C₄	C₂³	semidirect
430. C₂×C₂²⋊C₄	C₂³	semidirect
432. C₂×C₄²	C₂³	semidirect
433. C₂×C₄²	C₂³	semidirect
671. D₄	H(5,𝔽₂)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#3558	2
#3546	2
#3543	2
#3542	2
#3536	2
#3534	2
#3532	2
#3520	2
#3519	2
#3514	2
#3513	2
#3508	2
#3496	2
#3490	2
#3488	2
#3484	2
#3481	2
D₄×#41	2
C₂×#546	2
C₂×D₄²	2