Subgroups — #63013

Order 256.

3588 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3559	C₂	1	4	yes	maximal, complemented
2	#3554	C₂	1	2	yes	maximal, complemented
3	#3552	C₂	1	2	yes	maximal, complemented
4	#3548	C₂	1	1	yes	maximal, characteristic, complemented
5	#3544	C₂	1	2	yes	maximal, complemented
6	#3541	C₂	1	4	yes	maximal, complemented
7	#3536	C₂	1	4	yes	maximal, complemented
8	#3535	C₂	1	8	yes	maximal, complemented
9	#3522	C₂	1	2	yes	maximal, complemented
10	#3520	C₂	1	2	yes	maximal, complemented
11	#3520	C₂	1	2	yes	maximal, complemented
12	#3519	C₂	1	2	yes	maximal, complemented
13	#3515	C₂	1	2	yes	maximal, complemented
14	#3513	C₂	1	4	yes	maximal, complemented
15	#3511	C₂	1	1	yes	maximal, characteristic, complemented
16	#3503	C₂	1	1	yes	maximal, characteristic, complemented
17	#3501	C₂	1	2	yes	maximal, complemented
18	#3499	C₂	1	1	yes	maximal, characteristic, complemented
19	#3492	C₂	1	4	yes	maximal, complemented
20	#3489	C₂	1	4	yes	maximal, complemented
21	#3482	C₂	1	1	yes	maximal, characteristic, complemented
22	#3481	C₂	1	1	yes	maximal, characteristic, complemented
23	#3481	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#554	C₂	1	2	yes	maximal, complemented
25	D₄×#41	C₂	1	2	yes	maximal, complemented
26	C₂×#547	C₂	1	2	yes	maximal, complemented
27	C₂×2₋¹⁺⁴	C₂²	1	2	yes	complemented
28	C₂²×#41	C₂²	1	4	yes	complemented
29	#563	C₂²	1	8	yes	complemented
30	#563	C₂²	1	8	yes	complemented
31	#562	C₂²	1	4	yes	complemented
32	#562	C₂²	1	8	yes	complemented
33	#562	C₂²	1	8	yes	complemented
34	#559	C₂²	1	1	yes	characteristic, complemented
35	#559	C₂²	1	1	yes	characteristic, complemented
36	#559	C₂²	1	4	yes	complemented
37	Q₈²	C₂²	1	2	yes	complemented
38	#557	C₂²	1	1	yes	characteristic, complemented
39	#557	C₂²	1	2	yes	complemented
40	#556	C₂²	1	1	yes	characteristic, complemented
41	#556	C₂²	1	2	yes	complemented
42	#556	C₂²	1	2	yes	complemented
43	#555	C₂²	1	2	yes	complemented
44	#554	C₂²	1	1	yes	characteristic
45	#554	C₂²	1	4	yes	—
46	#554	C₂²	1	2	yes	—
47	#554	C₂²	1	1	yes	characteristic
48	#554	C₂²	1	4	yes	complemented
49	#554	C₂²	1	2	yes	complemented
50	#554	C₂²	1	8	yes	complemented
51	#554	C₂²	1	4	yes	complemented
52	#554	C₂²	1	2	yes	complemented
53	#554	C₂²	1	4	yes	complemented
54	#554	C₂²	1	1	yes	characteristic, complemented
55	#554	C₂²	1	1	yes	characteristic, complemented
56	#554	C₂²	1	8	yes	complemented
57	#554	C₂²	1	4	yes	complemented
58	#554	C₂²	1	2	yes	complemented
59	#554	C₂²	1	4	yes	complemented
60	#554	C₂²	1	4	yes	complemented
61	#553	C₂²	1	2	yes	complemented
62	#553	C₂²	1	2	yes	complemented
63	#553	C₂²	1	2	yes	complemented
64	#553	C₂²	1	2	yes	complemented
65	#553	C₂²	1	8	yes	complemented
66	#553	C₂²	1	4	yes	complemented
67	#553	C₂²	1	4	yes	complemented
68	#553	C₂²	1	4	yes	complemented
69	#552	C₂²	1	2	yes	complemented
70	#552	C₂²	1	4	yes	complemented
71	#552	C₂²	1	8	yes	complemented
72	#552	C₂²	1	4	yes	complemented
73	#552	C₂²	1	4	yes	complemented
74	#552	C₂²	1	4	yes	complemented
75	#551	C₂²	1	4	yes	complemented
76	#551	C₂²	1	4	yes	complemented
77	#551	C₂²	1	8	yes	complemented
78	#551	C₂²	1	8	yes	complemented
79	#550	C₂²	1	2	yes	complemented
80	#550	C₂²	1	2	yes	complemented
81	D₄×Q₈	C₂²	1	2	yes	—
82	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
83	D₄×Q₈	C₂²	1	4	yes	complemented
84	D₄×Q₈	C₂²	1	4	yes	complemented
85	D₄×Q₈	C₂²	1	2	yes	complemented
86	D₄×Q₈	C₂²	1	2	yes	complemented
87	#548	C₂²	1	4	yes	complemented
88	#548	C₂²	1	2	yes	complemented
89	#548	C₂²	1	4	yes	complemented
90	#548	C₂²	1	4	yes	complemented
91	#548	C₂²	1	4	yes	complemented
92	#547	C₂²	1	1	yes	characteristic
93	#547	C₂²	1	4	yes	complemented
94	#547	C₂²	1	4	yes	complemented
95	#547	C₂²	1	2	yes	complemented
96	#547	C₂²	1	2	yes	complemented
97	#547	C₂²	1	8	yes	complemented
98	#547	C₂²	1	4	yes	complemented
99	#547	C₂²	1	4	yes	complemented
100	#547	C₂²	1	2	yes	complemented
101	#547	C₂²	1	2	yes	complemented
102	#547	C₂²	1	4	yes	complemented
103	#547	C₂²	1	2	yes	complemented
104	#547	C₂²	1	8	yes	complemented
105	#547	C₂²	1	8	yes	complemented
106	#547	C₂²	1	4	yes	complemented
107	#547	C₂²	1	4	yes	complemented
108	#547	C₂²	1	2	yes	complemented
109	#546	C₂²	1	2	yes	—
110	#546	C₂²	1	2	yes	—
111	#546	C₂²	1	4	yes	complemented
112	#546	C₂²	1	8	yes	complemented
113	#546	C₂²	1	2	yes	complemented
114	#546	C₂²	1	2	yes	complemented
115	#546	C₂²	1	8	yes	complemented
116	#546	C₂²	1	8	yes	complemented
117	#546	C₂²	1	4	yes	complemented
118	D₄²	C₂²	1	1	yes	characteristic
119	D₄²	C₂²	1	4	yes	—
120	D₄²	C₂²	1	1	yes	characteristic
121	#544	C₂²	1	4	yes	complemented
122	#544	C₂²	1	4	yes	complemented
123	#544	C₂²	1	4	yes	complemented
124	#544	C₂²	1	2	yes	complemented
125	#543	C₂²	1	8	yes	complemented
126	#542	C₂²	1	4	yes	complemented
127	#542	C₂²	1	4	yes	complemented
128	#542	C₂²	1	4	yes	complemented
129	#542	C₂²	1	4	yes	complemented
130	#542	C₂²	1	8	yes	complemented
131	#542	C₂²	1	4	yes	complemented
132	#541	C₂²	1	4	yes	complemented
133	#540	C₂²	1	4	yes	complemented
134	#540	C₂²	1	4	yes	complemented
135	#539	C₂²	1	8	yes	complemented
136	#539	C₂²	1	8	yes	complemented
137	#539	C₂²	1	8	yes	complemented
138	#539	C₂²	1	8	yes	complemented
139	#539	C₂²	1	8	yes	complemented
140	#539	C₂²	1	8	yes	complemented
141	#538	C₂²	1	8	yes	complemented
142	#538	C₂²	1	8	yes	complemented
143	#537	C₂²	1	8	yes	complemented
144	#537	C₂²	1	4	yes	complemented
145	#537	C₂²	1	4	yes	complemented
146	#537	C₂²	1	2	yes	complemented
147	#536	C₂²	1	8	yes	complemented
148	#536	C₂²	1	4	yes	complemented
149	#536	C₂²	1	4	yes	complemented
150	#536	C₂²	1	2	yes	complemented
151	#533	C₂²	1	2	yes	complemented
152	#533	C₂²	1	1	yes	characteristic, complemented
153	#533	C₂²	1	2	yes	complemented
154	#533	C₂²	1	2	yes	complemented
155	#532	C₂²	1	2	yes	complemented
156	#532	C₂²	1	4	yes	complemented
157	#532	C₂²	1	1	yes	characteristic, complemented
158	#532	C₂²	1	1	yes	characteristic, complemented
159	#532	C₂²	1	2	yes	complemented
160	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
161	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
162	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
163	#529	C₂²	1	2	yes	complemented
164	#529	C₂²	1	2	yes	complemented
165	#529	C₂²	1	2	yes	complemented
166	#529	C₂²	1	2	yes	complemented
167	#529	C₂²	1	4	yes	complemented
168	#529	C₂²	1	2	yes	complemented
169	#529	C₂²	1	4	yes	complemented
170	C₂×#125	C₂²	1	4	yes	complemented
171	#525	C₂²	1	8	yes	complemented
172	#525	C₂²	1	4	yes	complemented
173	#525	C₂²	1	4	yes	complemented
174	#525	C₂²	1	4	yes	complemented
175	#525	C₂²	1	8	yes	complemented
176	#525	C₂²	1	4	yes	complemented
177	C₂×#123	C₂²	1	8	yes	complemented
178	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
179	C₂×C₂²⋊Q₈	C₂²	1	8	yes	complemented
180	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
181	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
182	C₂×#121	C₂²	1	4	yes	complemented
183	#520	C₂²	1	2	yes	—
184	#520	C₂²	1	4	yes	complemented
185	#520	C₂²	1	2	yes	complemented
186	#520	C₂²	1	4	yes	complemented
187	#518	C₂²	1	4	yes	—
188	C₄×#41	C₂²	1	1	yes	characteristic
189	C₄×#41	C₂²	1	2	yes	complemented
190	C₄×#41	C₂²	1	1	yes	characteristic, complemented
191	C₄×#41	C₂²	1	1	yes	characteristic, complemented
192	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
193	C₂×C₄×D₄	C₂²	1	4	yes	—
194	C₂×C₄×D₄	C₂²	1	2	yes	—
195	C₂×C₄×D₄	C₂²	1	2	yes	—
196	C₂×C₄×D₄	C₂²	1	2	yes	complemented
197	C₂×C₄×D₄	C₂²	1	2	yes	complemented
198	C₂²×C₄⋊C₄	C₂²	1	4	yes	complemented
199	2₋¹⁺⁴	—	4	8	no	—
200	C₂×#41	—	4	16	no	—
201	C₂×#41	C₂³	1	1	yes	characteristic
202	C₂×#41	C₂³	1	1	yes	characteristic
203	C₂×#41	C₂³	1	2	yes	—
204	C₂×#41	C₂³	1	4	yes	—
205	C₂×#41	C₂³	1	1	yes	characteristic
206	C₂×#41	C₂³	1	2	yes	—
207	C₂×#41	C₂³	1	4	yes	—
208	C₂×#41	C₂³	1	2	yes	—
209	C₂×#41	C₂³	1	8	yes	—
210	C₂×#41	C₂³	1	4	yes	—
211	C₂×#41	C₂³	1	8	yes	—
212	C₂×#41	C₂³	1	4	yes	—
213	C₂×#41	C₂³	1	8	yes	—
214	C₂×#41	C₂³	1	4	yes	—
215	C₂²×Q₈	C₂³	1	2	yes	—
216	C₂²×Q₈	C₂³	1	4	yes	—
217	C₂²×Q₈	C₂³	1	4	yes	—
218	C₂²×Q₈	C₂³	1	4	yes	—
219	C₂²×Q₈	C₂³	1	2	yes	—
220	C₂²×D₄	C₂³	1	2	yes	—
221	C₂²×D₄	C₂³	1	2	yes	—
222	C₂²×D₄	C₂³	1	2	yes	—
223	C₂²×D₄	C₂³	1	2	yes	—
224	C₂²×D₄	C₂³	1	8	yes	—
225	C₂³×C₄	C₂³	1	4	yes	—
226	C₂³×C₄	C₂³	1	8	yes	—
227	C₂³×C₄	C₂³	1	4	yes	—
228	C₄⋊Q₈	C₂³	1	1	yes	characteristic
229	C₄⋊Q₈	C₂³	1	2	yes	—
230	C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₄⋊Q₈	C₂³	1	2	yes	—
232	C₄⋊Q₈	C₂³	1	2	yes	—
233	C₄⋊Q₈	C₂³	1	2	yes	—
234	C₄⋊Q₈	C₂³	1	4	yes	—
235	C₄⋊Q₈	C₂³	1	4	yes	—
236	C₄⋊Q₈	C₂³	1	4	yes	—
237	C₄⋊Q₈	C₂³	1	4	yes	—
238	C₄⋊Q₈	C₂³	1	4	yes	—
239	C₄⋊Q₈	C₂³	1	4	yes	—
240	C₄⋊Q₈	C₂³	1	1	yes	characteristic
241	C₄⋊Q₈	C₂³	1	4	yes	—
242	C₄⋊Q₈	C₂³	1	1	yes	characteristic
243	C₄⋊Q₈	C₂³	1	2	yes	—
244	C₄⋊Q₈	C₂³	1	2	yes	—
245	C₄⋊Q₈	C₂³	1	8	yes	—
246	C₄⋊Q₈	C₂³	1	8	yes	—
247	#127	C₂³	1	1	yes	characteristic
248	#127	C₂³	1	1	yes	characteristic
249	#127	C₂³	1	4	yes	—
250	#126	C₂³	1	4	yes	—
251	#126	C₂³	1	8	yes	—
252	#126	C₂³	1	4	yes	—
253	#126	C₂³	1	4	yes	—
254	#126	C₂³	1	4	yes	—
255	#126	C₂³	1	4	yes	—
256	#126	C₂³	1	4	yes	—
257	#126	C₂³	1	4	yes	—
258	#126	C₂³	1	8	yes	—
259	#126	C₂³	1	8	yes	—
260	#126	C₂³	1	8	yes	—
261	#126	C₂³	1	8	yes	—
262	#125	C₂³	1	2	yes	—
263	#125	C₂³	1	4	yes	—
264	#125	C₂³	1	8	yes	—
265	#125	C₂³	1	8	yes	—
266	#125	C₂³	1	4	yes	—
267	#125	C₂³	1	4	yes	—
268	#125	C₂³	1	4	yes	—
269	#125	C₂³	1	2	yes	—
270	#125	C₂³	1	2	yes	—
271	#125	C₂³	1	2	yes	—
272	#125	C₂³	1	2	yes	—
273	#125	C₂³	1	4	yes	—
274	#125	C₂³	1	4	yes	—
275	#125	C₂³	1	2	yes	—
276	#125	C₂³	1	8	yes	—
277	#125	C₂³	1	8	yes	—
278	#125	C₂³	1	8	yes	—
279	#124	C₂³	1	2	yes	—
280	#124	C₂³	1	2	yes	—
281	#124	C₂³	1	4	yes	—
282	#124	C₂³	1	2	yes	—
283	#124	C₂³	1	2	yes	—
284	#124	C₂³	1	2	yes	—
285	#124	C₂³	1	4	yes	—
286	#124	C₂³	1	2	yes	—
287	#124	C₂³	1	4	yes	—
288	#124	C₂³	1	8	yes	—
289	#124	C₂³	1	2	yes	—
290	#124	C₂³	1	8	yes	—
291	#124	C₂³	1	8	yes	—
292	#124	C₂³	1	8	yes	—
293	#123	C₂³	1	4	yes	—
294	#123	C₂³	1	8	yes	—
295	#123	C₂³	1	8	yes	—
296	#123	C₂³	1	8	yes	—
297	#123	C₂³	1	8	yes	—
298	#123	C₂³	1	8	yes	—
299	#123	C₂³	1	8	yes	—
300	#123	C₂³	1	8	yes	—
301	#123	C₂³	1	4	yes	—
302	#123	C₂³	1	8	yes	—
303	#123	C₂³	1	8	yes	—
304	#123	C₂³	1	8	yes	—
305	#123	C₂³	1	4	yes	—
306	#123	C₂³	1	4	yes	—
307	#123	C₂³	1	4	yes	—
308	#123	C₂³	1	8	yes	—
309	#123	C₂³	1	4	yes	—
310	#123	C₂³	1	4	yes	—
311	#123	C₂³	1	4	yes	—
312	#123	C₂³	1	4	yes	—
313	#123	C₂³	1	4	yes	—
314	#123	C₂³	1	4	yes	—
315	#123	C₂³	1	8	yes	—
316	#123	C₂³	1	8	yes	—
317	#123	C₂³	1	8	yes	—
318	#123	C₂³	1	8	yes	—
319	#123	C₂³	1	8	yes	—
320	C₂²⋊Q₈	C₂³	1	4	yes	—
321	C₂²⋊Q₈	C₂³	1	8	yes	—
322	C₂²⋊Q₈	C₂³	1	2	yes	—
323	C₂²⋊Q₈	C₂³	1	2	yes	—
324	C₂²⋊Q₈	C₂³	1	2	yes	—
325	C₂²⋊Q₈	C₂³	1	4	yes	—
326	C₂²⋊Q₈	C₂³	1	2	yes	—
327	C₂²⋊Q₈	C₂³	1	4	yes	—
328	C₂²⋊Q₈	C₂³	1	4	yes	—
329	C₂²⋊Q₈	C₂³	1	8	yes	—
330	C₂²⋊Q₈	C₂³	1	8	yes	—
331	C₂²⋊Q₈	C₂³	1	8	yes	—
332	C₂²⋊Q₈	C₂³	1	4	yes	—
333	C₂²⋊Q₈	C₂³	1	4	yes	—
334	C₂²⋊Q₈	C₂³	1	4	yes	—
335	C₂²⋊Q₈	C₂³	1	4	yes	—
336	C₂²⋊Q₈	C₂³	1	8	yes	—
337	C₂²⋊Q₈	C₂³	1	8	yes	—
338	C₂²⋊Q₈	C₂³	1	8	yes	—
339	C₂²⋊Q₈	C₂³	1	8	yes	—
340	C₂²⋊Q₈	C₂³	1	8	yes	—
341	C₂²⋊Q₈	C₂³	1	8	yes	—
342	C₂²⋊Q₈	C₂³	1	8	yes	—
343	C₂²⋊Q₈	C₂³	1	8	yes	—
344	C₂²⋊Q₈	C₂³	1	2	yes	—
345	C₂²⋊Q₈	C₂³	1	8	yes	—
346	C₂²⋊Q₈	C₂³	1	4	yes	—
347	C₂²⋊Q₈	C₂³	1	4	yes	—
348	C₂²⋊Q₈	C₂³	1	4	yes	—
349	C₂²⋊Q₈	C₂³	1	8	yes	—
350	C₂²⋊Q₈	C₂³	1	4	yes	—
351	C₂²⋊Q₈	C₂³	1	8	yes	—
352	C₂²⋊Q₈	C₂³	1	2	yes	—
353	C₂²⋊Q₈	C₂³	1	4	yes	—
354	C₂²⋊Q₈	C₂³	1	2	yes	—
355	C₂²⋊Q₈	C₂³	1	2	yes	—
356	C₂²⋊Q₈	C₂³	1	2	yes	—
357	C₂²⋊Q₈	C₂³	1	4	yes	—
358	C₂²⋊Q₈	C₂³	1	4	yes	—
359	C₂²⋊Q₈	C₂³	1	8	yes	—
360	C₂²⋊Q₈	C₂³	1	8	yes	—
361	C₂²⋊Q₈	C₂³	1	8	yes	—
362	C₂²⋊Q₈	C₂³	1	8	yes	—
363	C₂²⋊Q₈	C₂³	1	8	yes	—
364	C₂²⋊Q₈	C₂³	1	8	yes	—
365	#121	C₂³	1	2	yes	—
366	#121	C₂³	1	4	yes	—
367	#121	C₂³	1	8	yes	—
368	#121	C₂³	1	4	yes	—
369	#121	C₂³	1	4	yes	—
370	#121	C₂³	1	8	yes	—
371	#121	C₂³	1	4	yes	—
372	#121	C₂³	1	2	yes	—
373	#121	C₂³	1	2	yes	—
374	#121	C₂³	1	8	yes	—
375	#121	C₂³	1	4	yes	—
376	#121	C₂³	1	4	yes	—
377	#121	C₂³	1	8	yes	—
378	#121	C₂³	1	4	yes	—
379	#121	C₂³	1	4	yes	—
380	#121	C₂³	1	8	yes	—
381	#121	C₂³	1	2	yes	—
382	#121	C₂³	1	4	yes	—
383	#121	C₂³	1	4	yes	—
384	#121	C₂³	1	2	yes	—
385	#121	C₂³	1	2	yes	—
386	#121	C₂³	1	2	yes	—
387	#121	C₂³	1	8	yes	—
388	#121	C₂³	1	4	yes	—
389	#121	C₂³	1	2	yes	—
390	#121	C₂³	1	2	yes	—
391	#121	C₂³	1	4	yes	—
392	#121	C₂³	1	8	yes	—
393	#121	C₂³	1	8	yes	—
394	#121	C₂³	1	8	yes	—
395	#121	C₂³	1	8	yes	—
396	#120	C₂³	1	4	yes	—
397	#120	C₂³	1	8	yes	—
398	#120	C₂³	1	4	yes	—
399	#120	C₂³	1	4	yes	—
400	#120	C₂³	1	8	yes	—
401	#120	C₂³	1	4	yes	—
402	C₄×Q₈	C₂³	1	1	yes	characteristic
403	C₄×Q₈	C₂³	1	2	yes	—
404	C₄×Q₈	C₂³	1	2	yes	—
405	C₄×Q₈	C₂³	1	4	yes	—
406	C₄×Q₈	C₂³	1	2	yes	—
407	C₄×Q₈	C₂³	1	4	yes	—
408	C₄×Q₈	C₂³	1	1	yes	characteristic
409	C₄×Q₈	C₂³	1	1	yes	characteristic
410	C₄×Q₈	C₂³	1	1	yes	characteristic
411	C₄×Q₈	C₂³	1	1	yes	characteristic
412	C₄×Q₈	C₂³	1	2	yes	—
413	C₄×Q₈	C₂³	1	1	yes	characteristic
414	C₄×Q₈	C₂³	1	2	yes	—
415	C₄×Q₈	C₂³	1	4	yes	—
416	C₄×Q₈	C₂³	1	4	yes	—
417	C₄×Q₈	C₂³	1	4	yes	—
418	C₄×Q₈	C₂³	1	4	yes	—
419	C₄×Q₈	C₂³	1	4	yes	—
420	C₄×D₄	C₂³	1	2	yes	—
421	C₄×D₄	C₂³	1	1	yes	characteristic
422	C₄×D₄	C₂³	1	1	yes	characteristic
423	C₄×D₄	C₂³	1	2	yes	—
424	C₄×D₄	C₂³	1	4	yes	—
425	C₄×D₄	C₂³	1	8	yes	—
426	C₄×D₄	C₂³	1	4	yes	—
427	C₄×D₄	C₂³	1	4	yes	—
428	C₄×D₄	C₂³	1	4	yes	—
429	C₄×D₄	C₂³	1	2	yes	—
430	C₄×D₄	C₂³	1	2	yes	—
431	C₄×D₄	C₂³	1	4	yes	—
432	C₄×D₄	C₂³	1	2	yes	—
433	C₄×D₄	C₂³	1	4	yes	—
434	C₄×D₄	C₂³	1	8	yes	—
435	C₄×D₄	C₂³	1	2	yes	—
436	C₄×D₄	C₂³	1	4	yes	—
437	C₄×D₄	C₂³	1	1	yes	characteristic
438	C₄×D₄	C₂³	1	1	yes	characteristic
439	C₄×D₄	C₂³	1	2	yes	—
440	C₄×D₄	C₂³	1	2	yes	—
441	C₄×D₄	C₂³	1	4	yes	—
442	C₄×D₄	C₂³	1	4	yes	—
443	C₄×D₄	C₂³	1	2	yes	—
444	C₄×D₄	C₂³	1	2	yes	—
445	C₄×D₄	C₂³	1	4	yes	—
446	C₄×D₄	C₂³	1	4	yes	—
447	C₄×D₄	C₂³	1	2	yes	—
448	C₄×D₄	C₂³	1	2	yes	—
449	C₄×D₄	C₂³	1	2	yes	—
450	C₄×D₄	C₂³	1	2	yes	—
451	C₄×D₄	C₂³	1	1	yes	characteristic
452	C₄×D₄	C₂³	1	2	yes	—
453	C₄×D₄	C₂³	1	2	yes	—
454	C₄×D₄	C₂³	1	2	yes	—
455	C₄×D₄	C₂³	1	4	yes	—
456	C₄×D₄	C₂³	1	1	yes	characteristic
457	C₄×D₄	C₂³	1	2	yes	—
458	C₄×D₄	C₂³	1	2	yes	—
459	C₄×D₄	C₂³	1	4	yes	—
460	C₄×D₄	C₂³	1	8	yes	—
461	C₄×D₄	C₂³	1	8	yes	—
462	C₄×D₄	C₂³	1	4	yes	—
463	C₄×D₄	C₂³	1	4	yes	—
464	C₄×D₄	C₂³	1	8	yes	—
465	C₄×D₄	C₂³	1	4	yes	—
466	C₄×D₄	C₂³	1	8	yes	—
467	C₄×D₄	C₂³	1	8	yes	—
468	C₄×D₄	C₂³	1	8	yes	—
469	C₄×D₄	C₂³	1	8	yes	—
470	C₄×D₄	C₂³	1	8	yes	—
471	C₄×D₄	C₂³	1	4	yes	—
472	#117	C₂³	1	2	yes	—
473	#117	C₂³	1	1	yes	characteristic
474	#117	C₂³	1	1	yes	characteristic
475	#117	C₂³	1	4	yes	—
476	#117	C₂³	1	2	yes	—
477	#117	C₂³	1	2	yes	—
478	#117	C₂³	1	1	yes	characteristic
479	#117	C₂³	1	2	yes	—
480	#117	C₂³	1	4	yes	—
481	#117	C₂³	1	4	yes	—
482	#117	C₂³	1	2	yes	—
483	#117	C₂³	1	4	yes	—
484	#117	C₂³	1	4	yes	—
485	#117	C₂³	1	4	yes	—
486	#117	C₂³	1	8	yes	—
487	#117	C₂³	1	4	yes	—
488	#117	C₂³	1	8	yes	—
489	C₂×C₄⋊C₄	C₂³	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³	1	8	yes	—
494	C₂×C₄⋊C₄	C₂³	1	8	yes	—
495	C₂×C₄⋊C₄	C₂³	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³	1	8	yes	—
498	C₂×C₄⋊C₄	C₂³	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³	1	8	yes	—
506	C₂×C₄⋊C₄	C₂³	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³	1	8	yes	—
508	C₂×C₄⋊C₄	C₂³	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
511	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
515	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
516	C₂×C₄²	C₂³	1	4	yes	—
517	C₂×C₄²	C₂³	1	2	yes	—
518	C₂×C₄²	C₂³	1	2	yes	—
519	C₂×C₄²	C₂³	1	2	yes	—
520	C₂×C₄²	C₂³	1	1	yes	characteristic
521	C₂⁴	C₂⁴	1	4	yes	—
522	C₂⁴	C₂⁴	1	4	yes	—
523	#41	—	2	8	no	—
524	#41	—	2	16	no	—
525	#41	—	2	4	no	—
526	#41	—	2	4	no	—
527	#41	—	4	4	no	—
528	#41	—	4	4	no	—
529	#41	—	4	16	no	—
530	#41	—	4	16	no	—
531	#41	—	4	16	no	—
532	#41	—	4	8	no	—
533	#41	—	4	8	no	—
534	#41	—	4	8	no	—
535	#41	—	4	8	no	—
536	#41	—	4	2	no	—
537	C₂×Q₈	—	4	8	no	—
538	C₂×Q₈	—	4	4	no	—
539	C₂×Q₈	—	4	8	no	—
540	C₂×Q₈	—	4	8	no	—
541	C₂×Q₈	—	4	4	no	—
542	C₂×Q₈	C₂⁴	1	1	yes	characteristic
543	C₂×Q₈	C₂⁴	1	1	yes	characteristic
544	C₂×Q₈	C₂⁴	1	2	yes	—
545	C₂×Q₈	C₂⁴	1	1	yes	characteristic
546	C₂×Q₈	C₂⁴	1	4	yes	—
547	C₂×Q₈	C₂⁴	1	2	yes	—
548	C₂×Q₈	C₂⁴	1	2	yes	—
549	C₂×Q₈	C₂⁴	1	4	yes	—
550	C₂×Q₈	C₂⁴	1	2	yes	—
551	C₂×Q₈	C₂⁴	1	8	yes	—
552	C₂×Q₈	C₂⁴	1	8	yes	—
553	C₂×Q₈	C₂⁴	1	4	yes	—
554	C₂×D₄	—	2	8	no	—
555	C₂×D₄	—	2	8	no	—
556	C₂×D₄	—	2	8	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	16	no	—
559	C₂×D₄	C₂⁴	1	2	yes	—
560	C₂×D₄	C₂⁴	1	4	yes	—
561	C₂×D₄	C₂⁴	1	4	yes	—
562	C₂×D₄	C₂⁴	1	2	yes	—
563	C₂×D₄	C₂⁴	1	2	yes	—
564	C₂×D₄	C₂⁴	1	1	yes	characteristic
565	C₂×D₄	C₂⁴	1	2	yes	—
566	C₂×D₄	C₂⁴	1	2	yes	—
567	C₂×D₄	C₂⁴	1	4	yes	—
568	C₂×D₄	C₂⁴	1	8	yes	—
569	C₂×D₄	C₂⁴	1	4	yes	—
570	C₂×D₄	C₂⁴	1	2	yes	—
571	C₂×D₄	C₂⁴	1	2	yes	—
572	C₂×D₄	C₂⁴	1	2	yes	—
573	C₂×D₄	C₂⁴	1	8	yes	—
574	C₂×D₄	C₂⁴	1	4	yes	—
575	C₂×D₄	C₂⁴	1	4	yes	—
576	C₂×D₄	C₂⁴	1	2	yes	—
577	C₂×D₄	C₂⁴	1	4	yes	—
578	C₂×D₄	C₂⁴	1	8	yes	—
579	C₂×D₄	C₂⁴	1	8	yes	—
580	C₂×D₄	C₂⁴	1	1	yes	characteristic
581	C₂×D₄	C₂⁴	1	1	yes	characteristic
582	C₂²×C₄	—	4	8	no	—
583	C₂²×C₄	—	4	8	no	—
584	C₂²×C₄	—	4	16	no	—
585	C₂²×C₄	C₂⁴	1	2	yes	—
586	C₂²×C₄	C₂⁴	1	2	yes	—
587	C₂²×C₄	C₂⁴	1	2	yes	—
588	C₂²×C₄	C₂⁴	1	4	yes	—
589	C₂²×C₄	C₂⁴	1	2	yes	—
590	C₂²×C₄	C₂⁴	1	2	yes	—
591	C₂²×C₄	C₂⁴	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴	1	2	yes	—
594	C₂²×C₄	C₂⁴	1	2	yes	—
595	C₂²×C₄	C₂⁴	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴	1	2	yes	—
597	C₂²×C₄	C₂⁴	1	8	yes	—
598	C₂²×C₄	C₂⁴	1	4	yes	—
599	C₂²×C₄	C₂⁴	1	4	yes	—
600	C₂²×C₄	C₂⁴	1	4	yes	—
601	C₂²×C₄	C₂⁴	1	2	yes	—
602	C₂²×C₄	C₂⁴	1	4	yes	—
603	C₂²×C₄	C₂⁴	1	4	yes	—
604	C₂²×C₄	C₂⁴	1	4	yes	—
605	C₂²×C₄	C₂⁴	1	8	yes	—
606	C₂²×C₄	C₂⁴	1	8	yes	—
607	C₂²×C₄	C₂⁴	1	8	yes	—
608	C₂²×C₄	C₂⁴	1	4	yes	—
609	C₂²×C₄	C₂⁴	1	8	yes	—
610	C₂²×C₄	C₂⁴	1	4	yes	—
611	C₂²×C₄	C₂⁴	1	4	yes	—
612	C₂²×C₄	C₂⁴	1	4	yes	—
613	C₂²×C₄	C₂⁴	1	8	yes	—
614	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
615	C₄⋊C₄	C₂⁴	1	2	yes	—
616	C₄⋊C₄	C₂⁴	1	4	yes	—
617	C₄⋊C₄	C₂⁴	1	2	yes	—
618	C₄⋊C₄	C₂⁴	1	4	yes	—
619	C₄⋊C₄	C₂⁴	1	4	yes	—
620	C₄⋊C₄	C₂⁴	1	8	yes	—
621	C₄⋊C₄	C₂⁴	1	2	yes	—
622	C₄⋊C₄	C₂⁴	1	2	yes	—
623	C₄⋊C₄	C₂⁴	1	4	yes	—
624	C₄⋊C₄	C₂⁴	1	8	yes	—
625	C₄⋊C₄	C₂⁴	1	8	yes	—
626	C₄⋊C₄	C₂⁴	1	8	yes	—
627	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
628	C₄⋊C₄	C₂⁴	1	4	yes	—
629	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
630	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
631	C₄⋊C₄	C₂⁴	1	2	yes	—
632	C₄⋊C₄	C₂⁴	1	2	yes	—
633	C₄⋊C₄	C₂⁴	1	4	yes	—
634	C₄⋊C₄	C₂⁴	1	8	yes	—
635	C₄⋊C₄	C₂⁴	1	4	yes	—
636	C₄⋊C₄	C₂⁴	1	4	yes	—
637	C₄⋊C₄	C₂⁴	1	2	yes	—
638	C₄⋊C₄	C₂⁴	1	2	yes	—
639	C₄⋊C₄	C₂⁴	1	4	yes	—
640	C₄⋊C₄	C₂⁴	1	8	yes	—
641	C₄⋊C₄	C₂⁴	1	4	yes	—
642	C₄⋊C₄	C₂⁴	1	4	yes	—
643	C₄⋊C₄	C₂⁴	1	8	yes	—
644	C₄⋊C₄	C₂⁴	1	8	yes	—
645	C₄⋊C₄	C₂⁴	1	8	yes	—
646	C₄⋊C₄	C₂⁴	1	4	yes	—
647	C₄⋊C₄	C₂⁴	1	8	yes	—
648	C₄⋊C₄	C₂⁴	1	4	yes	—
649	C₄⋊C₄	C₂⁴	1	4	yes	—
650	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
651	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
652	C₄⋊C₄	C₂⁴	1	4	yes	—
653	C₄⋊C₄	C₂⁴	1	4	yes	—
654	C₄⋊C₄	C₂⁴	1	2	yes	—
655	C₄⋊C₄	C₂⁴	1	4	yes	—
656	C₄⋊C₄	C₂⁴	1	4	yes	—
657	C₄⋊C₄	C₂⁴	1	4	yes	—
658	C₄⋊C₄	C₂⁴	1	4	yes	—
659	C₄⋊C₄	C₂⁴	1	2	yes	—
660	C₄⋊C₄	C₂⁴	1	2	yes	—
661	C₄⋊C₄	C₂⁴	1	2	yes	—
662	C₄⋊C₄	C₂⁴	1	2	yes	—
663	C₄⋊C₄	C₂⁴	1	2	yes	—
664	C₂²⋊C₄	C₂⁴	1	4	yes	—
665	C₂²⋊C₄	C₂⁴	1	4	yes	—
666	C₂²⋊C₄	C₂⁴	1	8	yes	—
667	C₂²⋊C₄	C₂⁴	1	2	yes	—
668	C₂²⋊C₄	C₂⁴	1	2	yes	—
669	C₂²⋊C₄	C₂⁴	1	2	yes	—
670	C₂²⋊C₄	C₂⁴	1	2	yes	—
671	C₂²⋊C₄	C₂⁴	1	4	yes	—
672	C₂²⋊C₄	C₂⁴	1	8	yes	—
673	C₂²⋊C₄	C₂⁴	1	4	yes	—
674	C₂²⋊C₄	C₂⁴	1	4	yes	—
675	C₂²⋊C₄	C₂⁴	1	4	yes	—
676	C₂²⋊C₄	C₂⁴	1	4	yes	—
677	C₂²⋊C₄	C₂⁴	1	8	yes	—
678	C₂²⋊C₄	C₂⁴	1	8	yes	—
679	C₂²⋊C₄	C₂⁴	1	4	yes	—
680	C₂²⋊C₄	C₂⁴	1	4	yes	—
681	C₂²⋊C₄	C₂⁴	1	8	yes	—
682	C₂²⋊C₄	C₂⁴	1	4	yes	—
683	C₂²⋊C₄	C₂⁴	1	4	yes	—
684	C₂²⋊C₄	C₂⁴	1	8	yes	—
685	C₂²⋊C₄	C₂⁴	1	4	yes	—
686	C₂²⋊C₄	C₂⁴	1	4	yes	—
687	C₂²⋊C₄	C₂⁴	1	4	yes	—
688	C₂²⋊C₄	C₂⁴	1	2	yes	—
689	C₂²⋊C₄	C₂⁴	1	4	yes	—
690	C₂²⋊C₄	C₂⁴	1	2	yes	—
691	C₂²⋊C₄	C₂⁴	1	2	yes	—
692	C₂²⋊C₄	C₂⁴	1	4	yes	—
693	C₂²⋊C₄	C₂⁴	1	4	yes	—
694	C₂²⋊C₄	C₂⁴	1	8	yes	—
695	C₂²⋊C₄	C₂⁴	1	8	yes	—
696	C₂²⋊C₄	C₂⁴	1	4	yes	—
697	C₂²⋊C₄	C₂⁴	1	4	yes	—
698	C₂²⋊C₄	C₂⁴	1	4	yes	—
699	C₂²⋊C₄	C₂⁴	1	4	yes	—
700	C₂²⋊C₄	C₂⁴	1	2	yes	—
701	C₂²⋊C₄	C₂⁴	1	2	yes	—
702	C₄²	C₂⁴	1	1	yes	characteristic
703	C₄²	C₂⁴	1	2	yes	—
704	C₄²	C₂⁴	1	1	yes	characteristic
705	C₄²	C₂⁴	1	1	yes	characteristic
706	C₄²	C₂⁴	1	1	yes	characteristic
707	C₄²	C₂⁴	1	4	yes	—
708	C₄²	C₂⁴	1	2	yes	—
709	C₄²	C₂⁴	1	2	yes	—
710	C₄²	C₂⁴	1	2	yes	—
711	C₄²	C₂⁴	1	2	yes	—
712	C₄²	C₂⁴	1	2	yes	—
713	C₄²	C₂⁴	1	2	yes	—
714	C₄²	C₂⁴	1	4	yes	—
715	C₄²	C₂⁴	1	2	yes	—
716	C₄²	C₂⁴	1	2	yes	—
717	C₄²	C₂⁴	1	4	yes	—
718	C₄²	C₂⁴	1	8	yes	—
719	C₄²	C₂⁴	1	8	yes	—
720	C₂³	—	2	8	no	—
721	C₂³	—	2	8	no	—
722	C₂³	—	2	8	no	—
723	C₂³	—	4	4	no	—
724	C₂³	—	4	4	no	—
725	C₂³	—	4	4	no	—
726	C₂³	C₂⁵	1	2	yes	—
727	C₂³	C₂⁵	1	4	yes	—
728	C₂³	C₂⁵	1	4	yes	—
729	C₂³	C₂⁵	1	1	yes	characteristic
730	C₂³	C₂⁵	1	2	yes	—
731	C₂³	C₂⁵	1	2	yes	—
732	Q₈	—	2	2	no	—
733	Q₈	—	2	8	no	—
734	Q₈	—	2	4	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	2	no	—
737	Q₈	—	2	4	no	—
738	Q₈	—	4	2	no	—
739	Q₈	—	4	8	no	—
740	Q₈	—	4	4	no	—
741	Q₈	—	4	4	no	—
742	Q₈	—	4	8	no	—
743	Q₈	—	4	2	no	—
744	D₄	—	2	8	no	—
745	D₄	—	2	8	no	—
746	D₄	—	2	16	no	—
747	D₄	—	2	4	no	—
748	D₄	—	2	8	no	—
749	D₄	—	2	8	no	—
750	D₄	—	2	4	no	—
751	D₄	—	2	4	no	—
752	D₄	—	2	4	no	—
753	D₄	—	2	4	no	—
754	D₄	—	2	2	no	—
755	D₄	—	2	4	no	—
756	D₄	—	4	4	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	8	no	—
759	D₄	—	4	4	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	2	no	—
765	D₄	H(5,𝔽₂)	1	4	yes	—
766	D₄	2₋¹⁺⁴	1	4	yes	complemented
767	C₂×C₄	—	2	8	no	—
768	C₂×C₄	—	2	16	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	8	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	8	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	8	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	8	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	8	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	8	no	—
794	C₂×C₄	—	4	8	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	C₂⁵	1	2	yes	—
797	C₂×C₄	C₂⁵	1	2	yes	—
798	C₂×C₄	C₂⁵	1	2	yes	—
799	C₂×C₄	C₂⁵	1	1	yes	characteristic
800	C₂×C₄	C₂⁵	1	2	yes	—
801	C₂×C₄	C₂⁵	1	1	yes	characteristic
802	C₂×C₄	C₂⁵	1	4	yes	—
803	C₂×C₄	C₂⁵	1	1	yes	characteristic
804	C₂×C₄	C₂⁵	1	2	yes	—
805	C₂×C₄	C₂⁵	1	2	yes	—
806	C₂×C₄	C₂⁵	1	4	yes	—
807	C₂×C₄	C₂⁵	1	2	yes	—
808	C₂×C₄	C₂⁵	1	2	yes	—
809	C₂×C₄	C₂⁵	1	2	yes	—
810	C₂×C₄	C₂⁵	1	8	yes	—
811	C₂×C₄	C₂⁵	1	4	yes	—
812	C₂×C₄	C₂⁵	1	4	yes	—
813	C₂×C₄	C₂⁵	1	1	yes	characteristic
814	C₂×C₄	C₂⁵	1	1	yes	characteristic
815	C₂×C₄	C₂⁵	1	1	yes	characteristic
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	4	16	no	—
833	C₂²	—	8	8	no	—
834	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
835	C₂²	C₂×2₋¹⁺⁴	1	4	yes	—
836	C₂²	C₂⁶	1	1	yes	characteristic
837	C₄	—	2	2	no	—
838	C₄	—	2	4	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	4	no	—
842	C₄	—	2	8	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	4	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	2	no	—
854	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
855	C₄	C₂×2₋¹⁺⁴	1	2	yes	—
856	C₄	#585	1	2	yes	—
857	C₂	—	2	4	no	—
858	C₂	—	2	4	no	—
859	C₂	—	4	1	no	—
860	C₂	—	4	4	no	—
861	C₂	—	4	4	no	—
862	C₂	—	4	2	no	—
863	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
864	C₂	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
865	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. #3559	C₂	semidirect
2. #3554	C₂	semidirect
3. #3552	C₂	semidirect
4. #3548	C₂	semidirect
5. #3544	C₂	semidirect
6. #3541	C₂	semidirect
7. #3536	C₂	semidirect
8. #3535	C₂	semidirect
9. #3522	C₂	semidirect
10. #3520	C₂	semidirect
11. #3520	C₂	semidirect
12. #3519	C₂	semidirect
13. #3515	C₂	semidirect
14. #3513	C₂	semidirect
15. #3511	C₂	semidirect
16. #3503	C₂	semidirect
17. #3501	C₂	semidirect
18. #3499	C₂	semidirect
19. #3492	C₂	semidirect
20. #3489	C₂	semidirect
21. #3482	C₂	semidirect
22. #3481	C₂	semidirect
23. #3481	C₂	semidirect
24. C₂×#554	C₂	semidirect
25. D₄×#41	C₂	semidirect
26. C₂×#547	C₂	semidirect
27. C₂×2₋¹⁺⁴	C₂²	semidirect
28. C₂²×#41	C₂²	semidirect
29. #563	C₂²	semidirect
30. #563	C₂²	semidirect
31. #562	C₂²	semidirect
32. #562	C₂²	semidirect
33. #562	C₂²	semidirect
34. #559	C₂²	semidirect
35. #559	C₂²	semidirect
36. #559	C₂²	semidirect
37. Q₈²	C₂²	semidirect
38. #557	C₂²	semidirect
39. #557	C₂²	semidirect
40. #556	C₂²	semidirect
41. #556	C₂²	semidirect
42. #556	C₂²	semidirect
43. #555	C₂²	semidirect
48. #554	C₂²	semidirect
49. #554	C₂²	semidirect
50. #554	C₂²	semidirect
51. #554	C₂²	semidirect
52. #554	C₂²	semidirect
53. #554	C₂²	semidirect
54. #554	C₂²	semidirect
55. #554	C₂²	semidirect
56. #554	C₂²	semidirect
57. #554	C₂²	semidirect
58. #554	C₂²	semidirect
59. #554	C₂²	semidirect
60. #554	C₂²	semidirect
61. #553	C₂²	semidirect
62. #553	C₂²	semidirect
63. #553	C₂²	semidirect
64. #553	C₂²	semidirect
65. #553	C₂²	semidirect
66. #553	C₂²	semidirect
67. #553	C₂²	semidirect
68. #553	C₂²	semidirect
69. #552	C₂²	semidirect
70. #552	C₂²	semidirect
71. #552	C₂²	semidirect
72. #552	C₂²	semidirect
73. #552	C₂²	semidirect
74. #552	C₂²	semidirect
75. #551	C₂²	semidirect
76. #551	C₂²	semidirect
77. #551	C₂²	semidirect
78. #551	C₂²	semidirect
79. #550	C₂²	semidirect
80. #550	C₂²	semidirect
82. D₄×Q₈	C₂²	semidirect
83. D₄×Q₈	C₂²	semidirect
84. D₄×Q₈	C₂²	semidirect
85. D₄×Q₈	C₂²	semidirect
86. D₄×Q₈	C₂²	semidirect
87. #548	C₂²	semidirect
88. #548	C₂²	semidirect
89. #548	C₂²	semidirect
90. #548	C₂²	semidirect
91. #548	C₂²	semidirect
93. #547	C₂²	semidirect
94. #547	C₂²	semidirect
95. #547	C₂²	semidirect
96. #547	C₂²	semidirect
97. #547	C₂²	semidirect
98. #547	C₂²	semidirect
99. #547	C₂²	semidirect
100. #547	C₂²	semidirect
101. #547	C₂²	semidirect
102. #547	C₂²	semidirect
103. #547	C₂²	semidirect
104. #547	C₂²	semidirect
105. #547	C₂²	semidirect
106. #547	C₂²	semidirect
107. #547	C₂²	semidirect
108. #547	C₂²	semidirect
111. #546	C₂²	semidirect
112. #546	C₂²	semidirect
113. #546	C₂²	semidirect
114. #546	C₂²	semidirect
115. #546	C₂²	semidirect
116. #546	C₂²	semidirect
117. #546	C₂²	semidirect
121. #544	C₂²	semidirect
122. #544	C₂²	semidirect
123. #544	C₂²	semidirect
124. #544	C₂²	semidirect
125. #543	C₂²	semidirect
126. #542	C₂²	semidirect
127. #542	C₂²	semidirect
128. #542	C₂²	semidirect
129. #542	C₂²	semidirect
130. #542	C₂²	semidirect
131. #542	C₂²	semidirect
132. #541	C₂²	semidirect
133. #540	C₂²	semidirect
134. #540	C₂²	semidirect
135. #539	C₂²	semidirect
136. #539	C₂²	semidirect
137. #539	C₂²	semidirect
138. #539	C₂²	semidirect
139. #539	C₂²	semidirect
140. #539	C₂²	semidirect
141. #538	C₂²	semidirect
142. #538	C₂²	semidirect
143. #537	C₂²	semidirect
144. #537	C₂²	semidirect
145. #537	C₂²	semidirect
146. #537	C₂²	semidirect
147. #536	C₂²	semidirect
148. #536	C₂²	semidirect
149. #536	C₂²	semidirect
150. #536	C₂²	semidirect
151. #533	C₂²	semidirect
152. #533	C₂²	semidirect
153. #533	C₂²	semidirect
154. #533	C₂²	semidirect
155. #532	C₂²	semidirect
156. #532	C₂²	semidirect
157. #532	C₂²	semidirect
158. #532	C₂²	semidirect
159. #532	C₂²	semidirect
160. C₂×C₄⋊Q₈	C₂²	semidirect
161. C₂×C₄⋊Q₈	C₂²	semidirect
162. C₂×C₄⋊Q₈	C₂²	semidirect
163. #529	C₂²	semidirect
164. #529	C₂²	semidirect
165. #529	C₂²	semidirect
166. #529	C₂²	semidirect
167. #529	C₂²	semidirect
168. #529	C₂²	semidirect
169. #529	C₂²	semidirect
170. C₂×#125	C₂²	semidirect
171. #525	C₂²	semidirect
172. #525	C₂²	semidirect
173. #525	C₂²	semidirect
174. #525	C₂²	semidirect
175. #525	C₂²	semidirect
176. #525	C₂²	semidirect
177. C₂×#123	C₂²	semidirect
178. C₂×C₂²⋊Q₈	C₂²	semidirect
179. C₂×C₂²⋊Q₈	C₂²	semidirect
180. C₂×C₂²⋊Q₈	C₂²	semidirect
181. C₂×C₂²⋊Q₈	C₂²	semidirect
182. C₂×#121	C₂²	semidirect
184. #520	C₂²	semidirect
185. #520	C₂²	semidirect
186. #520	C₂²	semidirect
189. C₄×#41	C₂²	semidirect
190. C₄×#41	C₂²	semidirect
191. C₄×#41	C₂²	semidirect
192. C₂×C₄×Q₈	C₂²	semidirect
196. C₂×C₄×D₄	C₂²	semidirect
197. C₂×C₄×D₄	C₂²	semidirect
198. C₂²×C₄⋊C₄	C₂²	semidirect
766. D₄	2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
#3559	2
#3554	2
#3552	2
#3548	2
#3544	2
#3541	2
#3536	2
#3535	2
#3522	2
#3520	2
#3519	2
#3515	2
#3513	2
#3511	2
#3503	2
#3501	2
#3499	2
#3492	2
#3489	2
#3482	2
#3481	2
C₂×#554	2
D₄×#41	2
C₂×#547	2