Subgroups — #8097802

Order 512.

7178 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#53116	C₂	1	6	yes	maximal, complemented
2	#52986	C₂	1	3	yes	maximal, complemented
3	#52967	C₂	1	3	yes	maximal, complemented
4	#52530	C₂	1	6	yes	maximal, complemented
5	#52410	C₂	1	12	yes	maximal, complemented
6	#52310	C₂	1	6	yes	maximal, complemented
7	#45509	C₂	1	2	yes	maximal, complemented
8	#45479	C₂	1	1	yes	maximal, characteristic, complemented
9	#45458	C₂	1	2	yes	maximal, complemented
10	#45439	C₂	1	4	yes	maximal, complemented
11	#36675	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#2812	C₂	1	2	yes	maximal, complemented
13	#36152	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×#120	C₂	1	2	yes	maximal, complemented
15	#35903	C₂	1	6	yes	maximal, complemented
16	#35847	C₂	1	3	yes	maximal, complemented
17	#35680	C₂	1	3	yes	maximal, complemented
18	C₂²×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
19	C₂⁴×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂×H(3,𝔽₄)	C₂²	1	2	yes	complemented
21	C₂×#554	C₂²	1	3	yes	complemented
22	C₂×#546	C₂²	1	3	yes	—
23	C₂×D₄²	C₂²	1	6	yes	—
24	C₂²×#120	C₂²	1	4	yes	complemented
25	#2848	C₂²	1	1	yes	characteristic, complemented
26	#2847	C₂²	1	2	yes	complemented
27	#2846	C₂²	1	2	yes	complemented
28	#2846	C₂²	1	4	yes	complemented
29	#2840	C₂²	1	1	yes	characteristic, complemented
30	#2835	C₂²	1	3	yes	complemented
31	#2832	C₂²	1	6	yes	complemented
32	#2828	C₂²	1	12	yes	complemented
33	#2828	C₂²	1	12	yes	complemented
34	#2828	C₂²	1	12	yes	complemented
35	#2824	C₂²	1	3	yes	complemented
36	#2824	C₂²	1	6	yes	complemented
37	#2824	C₂²	1	12	yes	complemented
38	#2819	C₂²	1	12	yes	complemented
39	#2812	C₂²	1	1	yes	characteristic, complemented
40	#2812	C₂²	1	4	yes	complemented
41	#2812	C₂²	1	2	yes	complemented
42	#2812	C₂²	1	2	yes	complemented
43	#2812	C₂²	1	6	yes	complemented
44	#2812	C₂²	1	6	yes	complemented
45	#2812	C₂²	1	12	yes	complemented
46	#2812	C₂²	1	6	yes	complemented
47	#2782	C₂²	1	12	yes	complemented
48	#2753	C₂²	1	12	yes	complemented
49	#2753	C₂²	1	12	yes	complemented
50	#2736	C₂²	1	6	yes	complemented
51	#2733	C₂²	1	6	yes	complemented
52	#2712	C₂²	1	6	yes	complemented
53	#2684	C₂²	1	12	yes	complemented
54	#2684	C₂²	1	6	yes	complemented
55	#2684	C₂²	1	12	yes	complemented
56	#2679	C₂²	1	12	yes	complemented
57	#2670	C₂²	1	12	yes	complemented
58	#2670	C₂²	1	12	yes	complemented
59	#2670	C₂²	1	6	yes	complemented
60	#2670	C₂²	1	6	yes	complemented
61	#2641	C₂²	1	6	yes	complemented
62	#2640	C₂²	1	3	yes	complemented
63	#2639	C₂²	1	6	yes	complemented
64	#2639	C₂²	1	12	yes	complemented
65	#2615	C₂²	1	3	yes	complemented
66	#2613	C₂²	1	6	yes	complemented
67	#2592	C₂²	1	3	yes	complemented
68	#2591	C₂²	1	12	yes	complemented
69	#2562	C₂²	1	6	yes	complemented
70	#2561	C₂²	1	6	yes	complemented
71	#2548	C₂²	1	6	yes	complemented
72	#2547	C₂²	1	3	yes	complemented
73	#2504	C₂²	1	6	yes	complemented
74	#2491	C₂²	1	6	yes	complemented
75	#2491	C₂²	1	6	yes	complemented
76	#2490	C₂²	1	6	yes	complemented
77	#2490	C₂²	1	6	yes	complemented
78	#2490	C₂²	1	6	yes	complemented
79	#2489	C₂²	1	6	yes	complemented
80	#2488	C₂²	1	12	yes	complemented
81	#2472	C₂²	1	12	yes	complemented
82	#2472	C₂²	1	12	yes	complemented
83	#2472	C₂²	1	12	yes	complemented
84	#2472	C₂²	1	12	yes	complemented
85	#2472	C₂²	1	12	yes	complemented
86	#2435	C₂²	1	3	yes	complemented
87	#2435	C₂²	1	12	yes	complemented
88	#2433	C₂²	1	6	yes	complemented
89	#2433	C₂²	1	3	yes	complemented
90	#2431	C₂²	1	6	yes	complemented
91	#2430	C₂²	1	6	yes	complemented
92	#2410	C₂²	1	12	yes	complemented
93	#2410	C₂²	1	6	yes	complemented
94	#2410	C₂²	1	12	yes	complemented
95	#2408	C₂²	1	3	yes	complemented
96	#2408	C₂²	1	6	yes	complemented
97	#2408	C₂²	1	3	yes	complemented
98	#2407	C₂²	1	6	yes	complemented
99	#2405	C₂²	1	6	yes	complemented
100	#2404	C₂²	1	6	yes	complemented
101	#2403	C₂²	1	12	yes	complemented
102	#2403	C₂²	1	12	yes	complemented
103	#2398	C₂²	1	3	yes	complemented
104	#2398	C₂²	1	6	yes	complemented
105	C₂×#397	C₂²	1	6	yes	complemented
106	#2388	C₂²	1	3	yes	complemented
107	C₂×#394	C₂²	1	12	yes	complemented
108	C₂×#392	C₂²	1	6	yes	complemented
109	#2375	C₂²	1	4	yes	complemented
110	#2339	C₂²	1	3	yes	complemented
111	D₄×C₂²⋊C₄	C₂²	1	6	yes	complemented
112	D₄×C₂²⋊C₄	C₂²	1	3	yes	complemented
113	D₄×C₂²⋊C₄	C₂²	1	6	yes	complemented
114	C₄×#120	C₂²	1	1	yes	characteristic, complemented
115	C₄×#120	C₂²	1	2	yes	complemented
116	C₂×#379	C₂²	1	2	yes	complemented
117	#2275	C₂²	1	3	yes	complemented
118	C₂⁶	C₂³	1	2	yes	—
119	C₂×H(5,𝔽₂)	—	4	12	no	—
120	C₂²×#41	C₂³	1	1	yes	characteristic
121	C₂²×#41	C₂³	1	1	yes	characteristic, complemented
122	C₂²×#41	C₂³	1	2	yes	complemented
123	C₂²×#41	C₂³	1	2	yes	complemented
124	C₂³×D₄	—	4	12	no	—
125	C₂³×D₄	C₂³	1	3	yes	—
126	C₂³×D₄	C₂³	1	2	yes	—
127	C₂³×D₄	C₂³	1	6	yes	—
128	C₂³×D₄	C₂³	1	3	yes	—
129	C₂³×D₄	C₂³	1	12	yes	—
130	C₂³×D₄	C₂³	1	2	yes	complemented
131	C₂³×D₄	C₂³	1	4	yes	complemented
132	C₂³×D₄	C₂³	1	1	yes	characteristic, complemented
133	C₂⁴×C₄	C₂³	1	1	yes	characteristic
134	H(3,𝔽₄)	—	4	8	no	—
135	#554	—	4	12	no	—
136	#546	—	4	12	no	—
137	D₄²	—	4	24	no	—
138	C₂×C₄⋊Q₈	C₂³	1	3	yes	complemented
139	C₂×#127	C₂³	1	6	yes	—
140	C₂×#125	C₂³	1	6	yes	complemented
141	C₂×#124	C₂³	1	3	yes	—
142	C₂×#124	C₂³	1	6	yes	—
143	C₂×#124	C₂³	1	12	yes	—
144	C₂×#124	C₂³	1	12	yes	complemented
145	C₂×#124	C₂³	1	12	yes	complemented
146	C₂×#123	C₂³	1	6	yes	—
147	C₂×C₂²⋊Q₈	C₂³	1	3	yes	—
148	C₂×C₂²⋊Q₈	C₂³	1	6	yes	complemented
149	C₂×C₂²⋊Q₈	C₂³	1	12	yes	complemented
150	C₂×#121	C₂³	1	12	yes	—
151	C₂×#121	C₂³	1	6	yes	—
152	C₂×#121	C₂³	1	6	yes	—
153	C₂×#121	C₂³	1	3	yes	—
154	C₂×#121	C₂³	1	6	yes	—
155	C₂×#120	—	4	16	no	—
156	C₂×#120	C₂³	1	1	yes	characteristic
157	C₂×#120	C₂³	1	4	yes	—
158	C₂×#120	C₂³	1	2	yes	—
159	C₂×#120	C₂³	1	6	yes	—
160	C₂×#120	C₂³	1	12	yes	—
161	C₂×#120	C₂³	1	12	yes	—
162	C₂×#120	C₂³	1	6	yes	—
163	C₂×#120	C₂³	1	12	yes	—
164	C₂×#120	C₂³	1	12	yes	—
165	C₂×#120	C₂³	1	12	yes	—
166	C₂×#120	C₂³	1	6	yes	—
167	C₂×#120	C₂³	1	12	yes	complemented
168	C₂×C₄×Q₈	C₂³	1	3	yes	complemented
169	C₂×C₄×D₄	C₂³	1	3	yes	—
170	C₂×C₄×D₄	C₂³	1	6	yes	—
171	C₂×C₄×D₄	C₂³	1	6	yes	—
172	C₂×C₄×D₄	C₂³	1	3	yes	—
173	C₂²×C₄⋊C₄	C₂³	1	6	yes	complemented
174	C₂²×C₂²⋊C₄	C₂³	1	6	yes	—
175	C₂²×C₂²⋊C₄	C₂³	1	12	yes	—
176	C₂²×C₂²⋊C₄	C₂³	1	6	yes	—
177	C₂²×C₂²⋊C₄	C₂³	1	12	yes	complemented
178	#400	C₂³	1	12	yes	complemented
179	#400	C₂³	1	6	yes	complemented
180	#400	C₂³	1	6	yes	complemented
181	#400	C₂³	1	12	yes	complemented
182	#400	C₂³	1	6	yes	complemented
183	#397	C₂³	1	6	yes	—
184	#397	C₂³	1	3	yes	—
185	#397	C₂³	1	6	yes	—
186	#397	C₂³	1	12	yes	—
187	#397	C₂³	1	6	yes	complemented
188	#397	C₂³	1	6	yes	complemented
189	#397	C₂³	1	6	yes	complemented
190	#397	C₂³	1	3	yes	complemented
191	#397	C₂³	1	12	yes	complemented
192	#397	C₂³	1	6	yes	complemented
193	#397	C₂³	1	12	yes	complemented
194	#397	C₂³	1	12	yes	complemented
195	#397	C₂³	1	6	yes	complemented
196	#395	C₂³	1	3	yes	complemented
197	#394	C₂³	1	12	yes	—
198	#394	C₂³	1	12	yes	—
199	#394	C₂³	1	12	yes	—
200	#394	C₂³	1	6	yes	—
201	#394	C₂³	1	6	yes	—
202	#394	C₂³	1	6	yes	—
203	#394	C₂³	1	6	yes	—
204	#394	C₂³	1	12	yes	—
205	#394	C₂³	1	12	yes	—
206	#394	C₂³	1	12	yes	complemented
207	#394	C₂³	1	12	yes	complemented
208	#394	C₂³	1	12	yes	complemented
209	#394	C₂³	1	6	yes	complemented
210	#394	C₂³	1	3	yes	complemented
211	#394	C₂³	1	12	yes	complemented
212	#394	C₂³	1	12	yes	complemented
213	#394	C₂³	1	6	yes	complemented
214	#394	C₂³	1	12	yes	complemented
215	#394	C₂³	1	12	yes	complemented
216	#394	C₂³	1	12	yes	complemented
217	#394	C₂³	1	12	yes	complemented
218	#394	C₂³	1	12	yes	complemented
219	#393	C₂³	1	3	yes	—
220	#393	C₂³	1	6	yes	—
221	#393	C₂³	1	3	yes	—
222	#393	C₂³	1	6	yes	complemented
223	#393	C₂³	1	6	yes	complemented
224	#393	C₂³	1	12	yes	complemented
225	#393	C₂³	1	12	yes	complemented
226	#393	C₂³	1	3	yes	complemented
227	#393	C₂³	1	12	yes	complemented
228	#393	C₂³	1	6	yes	complemented
229	#392	C₂³	1	12	yes	—
230	#392	C₂³	1	12	yes	—
231	#392	C₂³	1	12	yes	—
232	#392	C₂³	1	3	yes	—
233	#392	C₂³	1	6	yes	—
234	#392	C₂³	1	6	yes	—
235	#392	C₂³	1	12	yes	—
236	#392	C₂³	1	6	yes	—
237	#392	C₂³	1	12	yes	complemented
238	#392	C₂³	1	12	yes	complemented
239	#392	C₂³	1	6	yes	complemented
240	#392	C₂³	1	12	yes	complemented
241	#392	C₂³	1	6	yes	complemented
242	#392	C₂³	1	6	yes	complemented
243	#391	C₂³	1	6	yes	complemented
244	#391	C₂³	1	6	yes	complemented
245	#390	C₂³	1	6	yes	—
246	#390	C₂³	1	6	yes	—
247	#390	C₂³	1	6	yes	—
248	#390	C₂³	1	12	yes	—
249	#390	C₂³	1	12	yes	complemented
250	#390	C₂³	1	12	yes	complemented
251	#390	C₂³	1	12	yes	complemented
252	#390	C₂³	1	6	yes	complemented
253	#390	C₂³	1	6	yes	complemented
254	#388	C₂³	1	12	yes	—
255	#388	C₂³	1	12	yes	—
256	#388	C₂³	1	12	yes	complemented
257	#388	C₂³	1	12	yes	complemented
258	#388	C₂³	1	12	yes	complemented
259	#388	C₂³	1	12	yes	complemented
260	#388	C₂³	1	12	yes	complemented
261	#388	C₂³	1	12	yes	complemented
262	#388	C₂³	1	12	yes	complemented
263	#386	C₂³	1	6	yes	—
264	#386	C₂³	1	3	yes	—
265	#386	C₂³	1	12	yes	—
266	#386	C₂³	1	12	yes	—
267	#386	C₂³	1	12	yes	—
268	#386	C₂³	1	12	yes	—
269	#386	C₂³	1	12	yes	—
270	#386	C₂³	1	12	yes	complemented
271	#386	C₂³	1	12	yes	complemented
272	#386	C₂³	1	12	yes	complemented
273	#386	C₂³	1	12	yes	complemented
274	#386	C₂³	1	12	yes	complemented
275	#385	C₂³	1	3	yes	—
276	#385	C₂³	1	6	yes	—
277	#385	C₂³	1	6	yes	—
278	#385	C₂³	1	12	yes	complemented
279	#382	C₂³	1	12	yes	complemented
280	#381	C₂³	1	6	yes	complemented
281	#380	C₂³	1	3	yes	—
282	#380	C₂³	1	6	yes	—
283	#380	C₂³	1	6	yes	complemented
284	#380	C₂³	1	3	yes	complemented
285	#379	C₂³	1	12	yes	—
286	#379	C₂³	1	2	yes	—
287	#379	C₂³	1	1	yes	characteristic
288	#379	C₂³	1	2	yes	—
289	#379	C₂³	1	6	yes	—
290	#379	C₂³	1	6	yes	—
291	#379	C₂³	1	12	yes	—
292	#379	C₂³	1	6	yes	—
293	#379	C₂³	1	6	yes	—
294	#379	C₂³	1	12	yes	complemented
295	#379	C₂³	1	6	yes	complemented
296	C₄×C₄⋊C₄	C₂³	1	6	yes	complemented
297	C₄×C₄⋊C₄	C₂³	1	3	yes	complemented
298	C₄×C₂²⋊C₄	C₂³	1	6	yes	—
299	C₄×C₂²⋊C₄	C₂³	1	3	yes	—
300	C₄×C₂²⋊C₄	C₂³	1	6	yes	complemented
301	C₄×C₂²⋊C₄	C₂³	1	12	yes	complemented
302	C₄×C₂²⋊C₄	C₂³	1	6	yes	complemented
303	C₄×C₂²⋊C₄	C₂³	1	3	yes	complemented
304	#376	C₂³	1	3	yes	complemented
305	C₂×#95	C₂³	1	6	yes	complemented
306	C₂×#95	C₂³	1	6	yes	complemented
307	C₂⁵	—	2	8	no	—
308	C₂⁵	—	4	12	no	—
309	C₂⁵	—	8	6	no	—
310	C₂⁵	C₂⁴	1	6	yes	—
311	C₂⁵	C₂⁴	1	4	yes	—
312	C₂⁵	C₂⁴	1	6	yes	—
313	C₂⁵	C₂⁴	1	2	yes	—
314	C₂⁵	C₂⁴	1	1	yes	characteristic
315	H(5,𝔽₂)	—	4	64	no	—
316	C₂×#41	—	2	12	no	—
317	C₂×#41	—	4	6	no	—
318	C₂×#41	—	4	12	no	—
319	C₂×#41	—	4	12	no	—
320	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
321	C₂²×Q₈	C₂⁴	1	3	yes	—
322	C₂²×Q₈	C₂⁴	1	6	yes	—
323	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
324	C₂²×D₄	—	2	24	no	—
325	C₂²×D₄	—	2	24	no	—
326	C₂²×D₄	—	2	12	no	—
327	C₂²×D₄	—	4	12	no	—
328	C₂²×D₄	—	4	6	no	—
329	C₂²×D₄	—	4	6	no	—
330	C₂²×D₄	—	4	12	no	—
331	C₂²×D₄	—	4	24	no	—
332	C₂²×D₄	—	4	12	no	—
333	C₂²×D₄	—	4	24	no	—
334	C₂²×D₄	—	4	24	no	—
335	C₂²×D₄	—	4	24	no	—
336	C₂²×D₄	—	4	64	no	—
337	C₂²×D₄	—	8	12	no	—
338	C₂²×D₄	C₂⁴	1	4	yes	—
339	C₂²×D₄	C₂⁴	1	2	yes	—
340	C₂²×D₄	C₂⁴	1	6	yes	—
341	C₂²×D₄	C₂⁴	1	3	yes	—
342	C₂²×D₄	C₂⁴	1	2	yes	—
343	C₂²×D₄	C₂⁴	1	3	yes	—
344	C₂²×D₄	C₂⁴	1	6	yes	—
345	C₂²×D₄	C₂⁴	1	12	yes	—
346	C₂²×D₄	C₂⁴	1	12	yes	—
347	C₂²×D₄	C₂⁴	1	6	yes	—
348	C₂²×D₄	C₂⁴	1	12	yes	—
349	C₂²×D₄	C₂⁴	1	12	yes	—
350	C₂²×D₄	C₂⁴	1	6	yes	—
351	C₂²×D₄	C₂⁴	1	1	yes	characteristic
352	C₂²×D₄	C₂⁴	1	4	yes	—
353	C₂²×D₄	C₂⁴	1	2	yes	—
354	C₂²×D₄	C₂⁴	1	2	yes	—
355	C₂²×D₄	C₂⁴	1	1	yes	characteristic
356	C₂³×C₄	—	4	6	no	—
357	C₂³×C₄	C₂⁴	1	2	yes	—
358	C₂³×C₄	C₂⁴	1	2	yes	—
359	C₂³×C₄	C₂⁴	1	1	yes	characteristic
360	C₂³×C₄	C₂⁴	1	3	yes	—
361	C₂³×C₄	C₂⁴	1	6	yes	—
362	C₂³×C₄	C₂⁴	1	12	yes	—
363	C₂³×C₄	C₂⁴	1	3	yes	—
364	C₂³×C₄	C₂⁴	1	4	yes	—
365	C₄⋊Q₈	—	4	6	no	—
366	#127	—	4	12	no	—
367	#125	—	4	12	no	—
368	#124	—	4	6	no	—
369	#124	—	4	12	no	—
370	#124	—	4	24	no	—
371	#124	—	8	12	no	—
372	#124	—	8	12	no	—
373	#123	—	4	12	no	—
374	C₂²⋊Q₈	—	4	12	no	—
375	C₂²⋊Q₈	—	4	24	no	—
376	C₂²⋊Q₈	—	4	6	no	—
377	#121	—	4	12	no	—
378	#121	—	4	12	no	—
379	#121	—	4	6	no	—
380	#121	—	4	24	no	—
381	#121	—	4	12	no	—
382	#120	—	2	8	no	—
383	#120	—	2	16	no	—
384	#120	—	2	4	no	—
385	#120	—	4	24	no	—
386	#120	—	4	24	no	—
387	#120	—	4	24	no	—
388	#120	—	4	24	no	—
389	#120	—	4	12	no	—
390	#120	—	4	12	no	—
391	#120	—	8	6	no	—
392	#120	—	8	12	no	—
393	#120	—	8	12	no	—
394	C₄×Q₈	—	4	6	no	—
395	C₄×D₄	—	2	24	no	—
396	C₄×D₄	—	2	12	no	—
397	C₄×D₄	—	4	12	no	—
398	C₄×D₄	—	4	6	no	—
399	C₂×C₄⋊C₄	—	4	12	no	—
400	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
401	C₂×C₄⋊C₄	C₂⁴	1	3	yes	—
402	C₂×C₄⋊C₄	C₂⁴	1	3	yes	—
403	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
404	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
405	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
406	C₂×C₄⋊C₄	C₂⁴	1	3	yes	—
407	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
408	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
409	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
410	C₂×C₂²⋊C₄	—	4	24	no	—
411	C₂×C₂²⋊C₄	—	4	12	no	—
412	C₂×C₂²⋊C₄	—	8	6	no	—
413	C₂×C₂²⋊C₄	—	8	12	no	—
414	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
415	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
416	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
417	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
418	C₂×C₂²⋊C₄	C₂⁴	1	3	yes	—
419	C₂×C₂²⋊C₄	C₂⁴	1	3	yes	—
420	C₂×C₂²⋊C₄	C₂⁴	1	3	yes	—
421	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
422	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
423	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
424	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
425	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
426	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
427	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
428	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
429	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
430	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
431	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
432	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
433	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
434	C₂×C₂²⋊C₄	C₂⁴	1	3	yes	—
435	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
436	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
437	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
438	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
439	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
440	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
441	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
442	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
443	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
444	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
445	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
446	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
447	C₂×C₄²	C₂⁴	1	3	yes	—
448	C₂×C₄²	C₂⁴	1	6	yes	—
449	C₂×C₄²	C₂⁴	1	6	yes	—
450	C₂×C₄²	C₂⁴	1	12	yes	—
451	#95	C₂⁴	1	3	yes	—
452	#95	C₂⁴	1	3	yes	—
453	#95	C₂⁴	1	6	yes	—
454	#95	C₂⁴	1	12	yes	—
455	#95	C₂⁴	1	6	yes	—
456	#95	C₂⁴	1	12	yes	—
457	#95	C₂⁴	1	3	yes	—
458	#95	C₂⁴	1	6	yes	—
459	#95	C₂⁴	1	6	yes	—
460	#95	C₂⁴	1	6	yes	—
461	#95	C₂⁴	1	6	yes	—
462	#95	C₂⁴	1	3	yes	—
463	#95	C₂⁴	1	6	yes	—
464	#95	C₂⁴	1	6	yes	—
465	#95	C₂⁴	1	12	yes	—
466	#95	C₂⁴	1	6	yes	—
467	#95	C₂⁴	1	12	yes	—
468	#95	C₂⁴	1	12	yes	—
469	C₂⁴	—	2	12	no	—
470	C₂⁴	—	2	12	no	—
471	C₂⁴	—	2	24	no	—
472	C₂⁴	—	2	24	no	—
473	C₂⁴	—	2	12	no	—
474	C₂⁴	—	4	3	no	—
475	C₂⁴	—	4	3	no	—
476	C₂⁴	—	4	6	no	—
477	C₂⁴	—	4	6	no	—
478	C₂⁴	—	4	12	no	—
479	C₂⁴	—	4	12	no	—
480	C₂⁴	—	4	6	no	—
481	C₂⁴	—	4	12	no	—
482	C₂⁴	—	4	6	no	—
483	C₂⁴	—	4	12	no	—
484	C₂⁴	—	4	4	no	—
485	C₂⁴	—	4	2	no	—
486	C₂⁴	—	4	6	no	—
487	C₂⁴	—	4	32	no	—
488	C₂⁴	—	8	48	no	—
489	C₂⁴	—	8	48	no	—
490	C₂⁴	H(5,𝔽₂)	1	4	yes	complemented
491	C₂⁴	C₂⁵	1	6	yes	—
492	C₂⁴	C₂⁵	1	1	yes	characteristic
493	C₂⁴	C₂⁵	1	4	yes	—
494	C₂⁴	C₂⁵	1	2	yes	—
495	C₂⁴	C₂⁵	1	3	yes	—
496	C₂⁴	C₂⁵	1	2	yes	—
497	#41	—	4	32	no	—
498	#41	—	4	32	no	—
499	#41	—	4	16	no	—
500	#41	—	4	16	no	—
501	C₂×Q₈	—	2	6	no	—
502	C₂×Q₈	—	4	3	no	—
503	C₂×Q₈	—	4	3	no	—
504	C₂×Q₈	—	4	6	no	—
505	C₂×Q₈	—	4	6	no	—
506	C₂×Q₈	—	4	6	no	—
507	C₂×Q₈	—	4	6	no	—
508	C₂×D₄	—	2	12	no	—
509	C₂×D₄	—	2	24	no	—
510	C₂×D₄	—	2	24	no	—
511	C₂×D₄	—	2	12	no	—
512	C₂×D₄	—	2	12	no	—
513	C₂×D₄	—	2	6	no	—
514	C₂×D₄	—	2	24	no	—
515	C₂×D₄	—	2	6	no	—
516	C₂×D₄	—	2	12	no	—
517	C₂×D₄	—	2	12	no	—
518	C₂×D₄	—	4	6	no	—
519	C₂×D₄	—	4	12	no	—
520	C₂×D₄	—	4	6	no	—
521	C₂×D₄	—	4	3	no	—
522	C₂×D₄	—	4	6	no	—
523	C₂×D₄	—	4	6	no	—
524	C₂×D₄	—	4	12	no	—
525	C₂×D₄	—	4	6	no	—
526	C₂×D₄	—	4	3	no	—
527	C₂×D₄	—	4	12	no	—
528	C₂×D₄	—	4	12	no	—
529	C₂×D₄	—	4	12	no	—
530	C₂×D₄	—	4	12	no	—
531	C₂×D₄	—	4	3	no	—
532	C₂×D₄	—	4	12	no	—
533	C₂×D₄	—	4	12	no	—
534	C₂×D₄	—	4	12	no	—
535	C₂×D₄	—	4	12	no	—
536	C₂×D₄	—	4	12	no	—
537	C₂×D₄	—	4	6	no	—
538	C₂×D₄	—	4	12	no	—
539	C₂×D₄	—	4	12	no	—
540	C₂×D₄	—	4	12	no	—
541	C₂×D₄	—	4	96	no	—
542	C₂×D₄	—	4	48	no	—
543	C₂×D₄	—	4	64	no	—
544	C₂×D₄	—	4	32	no	—
545	C₂×D₄	—	4	16	no	—
546	C₂×D₄	—	4	48	no	—
547	C₂×D₄	—	4	32	no	—
548	C₂×D₄	—	8	96	no	—
549	C₂×D₄	H(5,𝔽₂)	1	12	yes	—
550	C₂²×C₄	—	2	12	no	—
551	C₂²×C₄	—	2	12	no	—
552	C₂²×C₄	—	2	24	no	—
553	C₂²×C₄	—	2	12	no	—
554	C₂²×C₄	—	2	12	no	—
555	C₂²×C₄	—	2	6	no	—
556	C₂²×C₄	—	2	6	no	—
557	C₂²×C₄	—	4	3	no	—
558	C₂²×C₄	—	4	6	no	—
559	C₂²×C₄	—	4	12	no	—
560	C₂²×C₄	—	4	12	no	—
561	C₂²×C₄	—	4	12	no	—
562	C₂²×C₄	—	4	12	no	—
563	C₂²×C₄	—	4	16	no	—
564	C₂²×C₄	C₂⁵	1	1	yes	characteristic
565	C₂²×C₄	C₂⁵	1	2	yes	—
566	C₂²×C₄	C₂⁵	1	2	yes	—
567	C₂²×C₄	C₂⁵	1	3	yes	—
568	C₂²×C₄	C₂⁵	1	6	yes	—
569	C₂²×C₄	C₂⁵	1	6	yes	—
570	C₂²×C₄	C₂⁵	1	12	yes	—
571	C₂²×C₄	C₂⁵	1	3	yes	—
572	C₂²×C₄	C₂⁵	1	3	yes	—
573	C₂²×C₄	C₂⁵	1	6	yes	—
574	C₂²×C₄	C₂⁵	1	1	yes	characteristic
575	C₄⋊C₄	—	2	12	no	—
576	C₄⋊C₄	—	2	6	no	—
577	C₄⋊C₄	—	4	3	no	—
578	C₄⋊C₄	—	4	12	no	—
579	C₄⋊C₄	—	4	6	no	—
580	C₄⋊C₄	—	4	6	no	—
581	C₄⋊C₄	—	4	3	no	—
582	C₄⋊C₄	—	4	6	no	—
583	C₄⋊C₄	—	4	6	no	—
584	C₄⋊C₄	—	4	12	no	—
585	C₂²⋊C₄	—	2	12	no	—
586	C₂²⋊C₄	—	2	24	no	—
587	C₂²⋊C₄	—	2	24	no	—
588	C₂²⋊C₄	—	2	12	no	—
589	C₂²⋊C₄	—	2	6	no	—
590	C₂²⋊C₄	—	4	3	no	—
591	C₂²⋊C₄	—	4	12	no	—
592	C₂²⋊C₄	—	4	12	no	—
593	C₂²⋊C₄	—	4	6	no	—
594	C₂²⋊C₄	—	4	6	no	—
595	C₂²⋊C₄	—	4	6	no	—
596	C₂²⋊C₄	—	4	3	no	—
597	C₂²⋊C₄	—	4	6	no	—
598	C₂²⋊C₄	—	4	6	no	—
599	C₂²⋊C₄	—	4	12	no	—
600	C₂²⋊C₄	—	4	12	no	—
601	C₂²⋊C₄	—	4	12	no	—
602	C₂²⋊C₄	—	4	12	no	—
603	C₂²⋊C₄	—	4	6	no	—
604	C₂²⋊C₄	—	4	6	no	—
605	C₂²⋊C₄	—	4	3	no	—
606	C₂²⋊C₄	—	4	12	no	—
607	C₂²⋊C₄	—	4	12	no	—
608	C₂²⋊C₄	—	4	6	no	—
609	C₂²⋊C₄	—	4	12	no	—
610	C₂²⋊C₄	—	4	6	no	—
611	C₂²⋊C₄	—	4	6	no	—
612	C₂²⋊C₄	—	4	6	no	—
613	C₂²⋊C₄	—	4	12	no	—
614	C₂²⋊C₄	—	4	12	no	—
615	C₂²⋊C₄	—	4	12	no	—
616	C₂²⋊C₄	—	4	12	no	—
617	C₂²⋊C₄	—	4	6	no	—
618	C₄²	—	2	6	no	—
619	C₄²	—	2	12	no	—
620	C₄²	—	4	6	no	—
621	C₄²	—	4	12	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	6	no	—
624	C₂³	—	2	3	no	—
625	C₂³	—	2	6	no	—
626	C₂³	—	2	3	no	—
627	C₂³	—	2	6	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	6	no	—
630	C₂³	—	2	4	no	—
631	C₂³	—	2	6	no	—
632	C₂³	—	2	3	no	—
633	C₂³	—	2	6	no	—
634	C₂³	—	2	12	no	—
635	C₂³	—	2	12	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	6	no	—
638	C₂³	—	2	6	no	—
639	C₂³	—	2	12	no	—
640	C₂³	—	2	3	no	—
641	C₂³	—	2	12	no	—
642	C₂³	—	4	12	no	—
643	C₂³	—	4	48	no	—
644	C₂³	—	4	24	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	12	no	—
647	C₂³	—	4	24	no	—
648	C₂³	—	4	8	no	—
649	C₂³	—	4	24	no	—
650	C₂³	—	4	16	no	—
651	C₂³	—	8	12	no	—
652	C₂³	—	8	24	no	—
653	C₂³	—	8	24	no	—
654	C₂³	—	8	12	no	—
655	C₂³	—	8	24	no	—
656	C₂³	—	8	24	no	—
657	C₂³	—	8	12	no	—
658	C₂³	—	8	24	no	—
659	C₂³	—	8	128	no	—
660	C₂³	—	16	6	no	—
661	C₂³	—	16	6	no	—
662	C₂³	C₂×H(5,𝔽₂)	1	6	yes	—
663	C₂³	C₂×H(5,𝔽₂)	1	12	yes	—
664	C₂³	C₂⁶	1	1	yes	characteristic
665	Q₈	—	4	4	no	—
666	Q₈	—	4	4	no	—
667	Q₈	—	8	6	no	—
668	Q₈	—	16	6	no	—
669	D₄	—	4	24	no	—
670	D₄	—	4	24	no	—
671	D₄	—	4	8	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	8	no	—
674	D₄	—	4	16	no	—
675	D₄	—	4	24	no	—
676	D₄	—	4	16	no	—
677	D₄	—	4	8	no	—
678	D₄	—	4	12	no	—
679	D₄	—	4	8	no	—
680	D₄	—	8	6	no	—
681	D₄	—	8	24	no	—
682	D₄	—	8	24	no	—
683	D₄	—	8	24	no	—
684	D₄	—	16	6	no	—
685	D₄	—	16	12	no	—
686	D₄	H(3,𝔽₄)	1	16	yes	complemented
687	C₂×C₄	—	2	6	no	—
688	C₂×C₄	—	2	3	no	—
689	C₂×C₄	—	2	3	no	—
690	C₂×C₄	—	2	6	no	—
691	C₂×C₄	—	2	3	no	—
692	C₂×C₄	—	2	12	no	—
693	C₂×C₄	—	2	6	no	—
694	C₂×C₄	—	2	6	no	—
695	C₂×C₄	—	2	12	no	—
696	C₂×C₄	—	2	3	no	—
697	C₂×C₄	—	2	6	no	—
698	C₂×C₄	—	2	6	no	—
699	C₂×C₄	—	2	6	no	—
700	C₂×C₄	—	2	3	no	—
701	C₂×C₄	—	2	6	no	—
702	C₂×C₄	—	2	12	no	—
703	C₂×C₄	—	2	12	no	—
704	C₂×C₄	—	2	6	no	—
705	C₂×C₄	—	2	6	no	—
706	C₂×C₄	—	2	3	no	—
707	C₂×C₄	—	2	6	no	—
708	C₂×C₄	—	4	12	no	—
709	C₂×C₄	—	4	16	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	12	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	8	12	no	—
715	C₂×C₄	—	8	24	no	—
716	C₂×C₄	C₂×H(5,𝔽₂)	1	6	yes	—
717	C₂²	—	2	12	no	—
718	C₂²	—	2	12	no	—
719	C₂²	—	2	12	no	—
720	C₂²	—	2	6	no	—
721	C₂²	—	4	16	no	—
722	C₂²	—	4	3	no	—
723	C₂²	—	4	6	no	—
724	C₂²	—	4	3	no	—
725	C₂²	—	4	3	no	—
726	C₂²	—	4	6	no	—
727	C₂²	—	4	12	no	—
728	C₂²	—	4	12	no	—
729	C₂²	—	4	6	no	—
730	C₂²	—	4	6	no	—
731	C₂²	—	4	12	no	—
732	C₂²	—	4	12	no	—
733	C₂²	—	4	3	no	—
734	C₂²	—	4	6	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	6	no	—
739	C₂²	—	8	48	no	—
740	C₂²	—	8	48	no	—
741	C₂²	—	16	16	no	—
742	C₂²	—	16	8	no	—
743	C₂²	C₂×H(3,𝔽₄)	1	8	yes	—
744	C₂²	C₂²×H(5,𝔽₂)	1	3	yes	—
745	C₂²	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
746	C₂²	H(7,𝔽₂)	1	3	yes	—
747	C₄	—	4	3	no	—
748	C₄	—	4	6	no	—
749	C₄	—	4	6	no	—
750	C₄	—	4	6	no	—
751	C₄	—	4	12	no	—
752	C₄	—	4	3	no	—
753	C₄	—	4	3	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	C₂×H(3,𝔽₄)	1	4	yes	—
758	C₂	—	2	8	no	—
759	C₂	—	4	6	no	—
760	C₂	—	8	6	no	—
761	C₂	—	8	1	no	—
762	C₂	—	8	4	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂²×H(3,𝔽₄)	1	1	yes	characteristic
765	C₂	#62892	1	3	yes	—
766	C₂	#63041	1	3	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁶
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #53116	C₂	semidirect
2. #52986	C₂	semidirect
3. #52967	C₂	semidirect
4. #52530	C₂	semidirect
5. #52410	C₂	semidirect
6. #52310	C₂	semidirect
7. #45509	C₂	semidirect
8. #45479	C₂	semidirect
9. #45458	C₂	semidirect
10. #45439	C₂	semidirect
11. #36675	C₂	semidirect
12. C₂×#2812	C₂	semidirect
13. #36152	C₂	semidirect
14. D₄×#120	C₂	semidirect
15. #35903	C₂	semidirect
16. #35847	C₂	semidirect
17. #35680	C₂	semidirect
18. C₂²×H(5,𝔽₂)	C₂²	semidirect
19. C₂⁴×D₄	C₂²	semidirect
20. C₂×H(3,𝔽₄)	C₂²	semidirect
21. C₂×#554	C₂²	semidirect
24. C₂²×#120	C₂²	semidirect
25. #2848	C₂²	semidirect
26. #2847	C₂²	semidirect
27. #2846	C₂²	semidirect
28. #2846	C₂²	semidirect
29. #2840	C₂²	semidirect
30. #2835	C₂²	semidirect
31. #2832	C₂²	semidirect
32. #2828	C₂²	semidirect
33. #2828	C₂²	semidirect
34. #2828	C₂²	semidirect
35. #2824	C₂²	semidirect
36. #2824	C₂²	semidirect
37. #2824	C₂²	semidirect
38. #2819	C₂²	semidirect
39. #2812	C₂²	semidirect
40. #2812	C₂²	semidirect
41. #2812	C₂²	semidirect
42. #2812	C₂²	semidirect
43. #2812	C₂²	semidirect
44. #2812	C₂²	semidirect
45. #2812	C₂²	semidirect
46. #2812	C₂²	semidirect
47. #2782	C₂²	semidirect
48. #2753	C₂²	semidirect
49. #2753	C₂²	semidirect
50. #2736	C₂²	semidirect
51. #2733	C₂²	semidirect
52. #2712	C₂²	semidirect
53. #2684	C₂²	semidirect
54. #2684	C₂²	semidirect
55. #2684	C₂²	semidirect
56. #2679	C₂²	semidirect
57. #2670	C₂²	semidirect
58. #2670	C₂²	semidirect
59. #2670	C₂²	semidirect
60. #2670	C₂²	semidirect
61. #2641	C₂²	semidirect
62. #2640	C₂²	semidirect
63. #2639	C₂²	semidirect
64. #2639	C₂²	semidirect
65. #2615	C₂²	semidirect
66. #2613	C₂²	semidirect
67. #2592	C₂²	semidirect
68. #2591	C₂²	semidirect
69. #2562	C₂²	semidirect
70. #2561	C₂²	semidirect
71. #2548	C₂²	semidirect
72. #2547	C₂²	semidirect
73. #2504	C₂²	semidirect
74. #2491	C₂²	semidirect
75. #2491	C₂²	semidirect
76. #2490	C₂²	semidirect
77. #2490	C₂²	semidirect
78. #2490	C₂²	semidirect
79. #2489	C₂²	semidirect
80. #2488	C₂²	semidirect
81. #2472	C₂²	semidirect
82. #2472	C₂²	semidirect
83. #2472	C₂²	semidirect
84. #2472	C₂²	semidirect
85. #2472	C₂²	semidirect
86. #2435	C₂²	semidirect
87. #2435	C₂²	semidirect
88. #2433	C₂²	semidirect
89. #2433	C₂²	semidirect
90. #2431	C₂²	semidirect
91. #2430	C₂²	semidirect
92. #2410	C₂²	semidirect
93. #2410	C₂²	semidirect
94. #2410	C₂²	semidirect
95. #2408	C₂²	semidirect
96. #2408	C₂²	semidirect
97. #2408	C₂²	semidirect
98. #2407	C₂²	semidirect
99. #2405	C₂²	semidirect
100. #2404	C₂²	semidirect
101. #2403	C₂²	semidirect
102. #2403	C₂²	semidirect
103. #2398	C₂²	semidirect
104. #2398	C₂²	semidirect
105. C₂×#397	C₂²	semidirect
106. #2388	C₂²	semidirect
107. C₂×#394	C₂²	semidirect
108. C₂×#392	C₂²	semidirect
109. #2375	C₂²	semidirect
110. #2339	C₂²	semidirect
111. D₄×C₂²⋊C₄	C₂²	semidirect
112. D₄×C₂²⋊C₄	C₂²	semidirect
113. D₄×C₂²⋊C₄	C₂²	semidirect
114. C₄×#120	C₂²	semidirect
115. C₄×#120	C₂²	semidirect
116. C₂×#379	C₂²	semidirect
117. #2275	C₂²	semidirect
121. C₂²×#41	C₂³	semidirect
122. C₂²×#41	C₂³	semidirect
123. C₂²×#41	C₂³	semidirect
130. C₂³×D₄	C₂³	semidirect
131. C₂³×D₄	C₂³	semidirect
132. C₂³×D₄	C₂³	semidirect
138. C₂×C₄⋊Q₈	C₂³	semidirect
140. C₂×#125	C₂³	semidirect
144. C₂×#124	C₂³	semidirect
145. C₂×#124	C₂³	semidirect
148. C₂×C₂²⋊Q₈	C₂³	semidirect
149. C₂×C₂²⋊Q₈	C₂³	semidirect
167. C₂×#120	C₂³	semidirect
168. C₂×C₄×Q₈	C₂³	semidirect
173. C₂²×C₄⋊C₄	C₂³	semidirect
177. C₂²×C₂²⋊C₄	C₂³	semidirect
178. #400	C₂³	semidirect
179. #400	C₂³	semidirect
180. #400	C₂³	semidirect
181. #400	C₂³	semidirect
182. #400	C₂³	semidirect
187. #397	C₂³	semidirect
188. #397	C₂³	semidirect
189. #397	C₂³	semidirect
190. #397	C₂³	semidirect
191. #397	C₂³	semidirect
192. #397	C₂³	semidirect
193. #397	C₂³	semidirect
194. #397	C₂³	semidirect
195. #397	C₂³	semidirect
196. #395	C₂³	semidirect
206. #394	C₂³	semidirect
207. #394	C₂³	semidirect
208. #394	C₂³	semidirect
209. #394	C₂³	semidirect
210. #394	C₂³	semidirect
211. #394	C₂³	semidirect
212. #394	C₂³	semidirect
213. #394	C₂³	semidirect
214. #394	C₂³	semidirect
215. #394	C₂³	semidirect
216. #394	C₂³	semidirect
217. #394	C₂³	semidirect
218. #394	C₂³	semidirect
222. #393	C₂³	semidirect
223. #393	C₂³	semidirect
224. #393	C₂³	semidirect
225. #393	C₂³	semidirect
226. #393	C₂³	semidirect
227. #393	C₂³	semidirect
228. #393	C₂³	semidirect
237. #392	C₂³	semidirect
238. #392	C₂³	semidirect
239. #392	C₂³	semidirect
240. #392	C₂³	semidirect
241. #392	C₂³	semidirect
242. #392	C₂³	semidirect
243. #391	C₂³	semidirect
244. #391	C₂³	semidirect
249. #390	C₂³	semidirect
250. #390	C₂³	semidirect
251. #390	C₂³	semidirect
252. #390	C₂³	semidirect
253. #390	C₂³	semidirect
256. #388	C₂³	semidirect
257. #388	C₂³	semidirect
258. #388	C₂³	semidirect
259. #388	C₂³	semidirect
260. #388	C₂³	semidirect
261. #388	C₂³	semidirect
262. #388	C₂³	semidirect
270. #386	C₂³	semidirect
271. #386	C₂³	semidirect
272. #386	C₂³	semidirect
273. #386	C₂³	semidirect
274. #386	C₂³	semidirect
278. #385	C₂³	semidirect
279. #382	C₂³	semidirect
280. #381	C₂³	semidirect
283. #380	C₂³	semidirect
284. #380	C₂³	semidirect
294. #379	C₂³	semidirect
295. #379	C₂³	semidirect
296. C₄×C₄⋊C₄	C₂³	semidirect
297. C₄×C₄⋊C₄	C₂³	semidirect
300. C₄×C₂²⋊C₄	C₂³	semidirect
301. C₄×C₂²⋊C₄	C₂³	semidirect
302. C₄×C₂²⋊C₄	C₂³	semidirect
303. C₄×C₂²⋊C₄	C₂³	semidirect
304. #376	C₂³	semidirect
305. C₂×#95	C₂³	semidirect
306. C₂×#95	C₂³	semidirect
490. C₂⁴	H(5,𝔽₂)	semidirect
686. D₄	H(3,𝔽₄)	semidirect

Maximal subgroups

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

subgroup	index
#53116	2
#52986	2
#52967	2
#52530	2
#52410	2
#52310	2
#45509	2
#45479	2
#45458	2
#45439	2
#36675	2
C₂×#2812	2
#36152	2
D₄×#120	2
#35903	2
#35847	2
#35680	2