Subgroups — #72312604

Order 2048.

At least 10493 conjugacy classes of subgroups; only the 790 normal subgroups are shown.

The subgroup lattice has 396 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312583	C₂	1	4	yes	maximal, complemented
2	#72266835	C₂	1	1	yes	maximal, characteristic, complemented
3	#72263490	C₂	1	1	yes	maximal, characteristic, complemented
4	#72259136	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#139739	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#139742	C₂	1	1	yes	maximal, characteristic, complemented
7	#72255764	C₂	1	1	yes	maximal, characteristic, complemented
8	#72251567	C₂	1	4	yes	maximal, complemented
9	#72251527	C₂	1	1	yes	maximal, characteristic, complemented
10	#72251420	C₂	1	1	yes	maximal, characteristic, complemented
11	#72240474	C₂	1	4	yes	maximal, complemented
12	#72238342	C₂	1	1	yes	maximal, characteristic, complemented
13	#72236674	C₂	1	1	yes	maximal, characteristic, complemented
14	#72236521	C₂	1	1	yes	maximal, characteristic, complemented
15	#72235130	C₂	1	1	yes	maximal, characteristic, complemented
16	#72234693	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#144364	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#133839	C₂	1	1	yes	maximal, characteristic, complemented
19	#72210342	C₂	1	4	yes	maximal, complemented
20	#10586422	C₂²	1	1	yes	characteristic, complemented
21	#10586404	C₂²	1	1	yes	characteristic, complemented
22	C₂×#60399	C₂²	1	1	yes	characteristic
23	#6499875	C₂²	1	4	yes	complemented
24	#6499874	C₂²	1	4	yes	complemented
25	#6499856	C₂²	1	4	yes	complemented
26	#6499855	C₂²	1	4	yes	complemented
27	C₂×#23895	C₂²	1	1	yes	characteristic
28	C₂×#23895	C₂²	1	1	yes	characteristic, complemented
29	C₂×#23895	C₂²	1	1	yes	characteristic, complemented
30	#6437621	C₂²	1	1	yes	characteristic
31	#6437621	C₂²	1	1	yes	characteristic, complemented
32	#6437621	C₂²	1	1	yes	characteristic, complemented
33	C₂×#23897	C₂²	1	1	yes	characteristic
34	C₂×#23897	C₂²	1	1	yes	characteristic, complemented
35	#6437445	C₂²	1	1	yes	characteristic
36	#6437445	C₂²	1	1	yes	characteristic, complemented
37	#6437445	C₂²	1	1	yes	characteristic, complemented
38	C₂×#21778	C₂²	1	1	yes	characteristic, complemented
39	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
40	#763333	C₂²	1	1	yes	characteristic, complemented
41	#511812	C₂²	1	4	yes	complemented
42	#511811	C₂²	1	4	yes	complemented
43	#511791	C₂²	1	4	yes	complemented
44	#511790	C₂²	1	4	yes	complemented
45	C₂×#12707	C₂²	1	1	yes	characteristic, complemented
46	C₂×#12705	C₂²	1	1	yes	characteristic, complemented
47	C₂×#12705	C₂²	1	1	yes	characteristic, complemented
48	C₂×#12705	C₂²	1	1	yes	characteristic, complemented
49	C₂×#12705	C₂²	1	1	yes	characteristic, complemented
50	#493370	C₂²	1	1	yes	characteristic, complemented
51	#493357	C₂²	1	1	yes	characteristic, complemented
52	#347057	C₂²	1	2	yes	complemented
53	#347056	C₂²	1	2	yes	complemented
54	#347047	C₂²	1	2	yes	complemented
55	#347045	C₂²	1	2	yes	complemented
56	#346457	C₂²	1	2	yes	complemented
57	#346456	C₂²	1	2	yes	complemented
58	#346447	C₂²	1	2	yes	complemented
59	#346446	C₂²	1	2	yes	complemented
60	#188109	C₂²	1	1	yes	characteristic, complemented
61	#188050	C₂²	1	1	yes	characteristic, complemented
62	C₂×#8534	C₂²	1	1	yes	characteristic, complemented
63	C₂×#8534	C₂²	1	1	yes	characteristic, complemented
64	C₂×#8534	C₂²	1	1	yes	characteristic, complemented
65	C₂×#8453	C₂²	1	1	yes	characteristic, complemented
66	C₂×#8453	C₂²	1	1	yes	characteristic, complemented
67	#144389	C₂²	1	2	yes	complemented
68	#144388	C₂²	1	2	yes	complemented
69	#144387	C₂²	1	2	yes	complemented
70	#144386	C₂²	1	2	yes	complemented
71	#144383	C₂²	1	4	yes	complemented
72	#144382	C₂²	1	4	yes	complemented
73	#144381	C₂²	1	4	yes	complemented
74	#144380	C₂²	1	4	yes	complemented
75	#144364	C₂²	1	4	yes	complemented
76	#144364	C₂²	1	4	yes	complemented
77	#139760	C₂²	1	4	yes	complemented
78	#139759	C₂²	1	4	yes	complemented
79	#139748	C₂²	1	4	yes	complemented
80	#139747	C₂²	1	4	yes	complemented
81	#139742	C₂²	1	4	yes	complemented
82	#139742	C₂²	1	4	yes	complemented
83	#139739	C₂²	1	4	yes	complemented
84	#139739	C₂²	1	4	yes	complemented
85	#133839	C₂²	1	4	yes	complemented
86	#133839	C₂²	1	4	yes	complemented
87	C₂×#7304	C₂²	1	1	yes	characteristic, complemented
88	C₂×#7316	C₂²	1	1	yes	characteristic, complemented
89	C₂×#7314	C₂²	1	1	yes	characteristic, complemented
90	C₂×#7311	C₂²	1	1	yes	characteristic, complemented
91	C₂×H(7,𝔽₂)	D₄	1	1	yes	characteristic, complemented
92	#62832	C₂³	1	2	yes	—
93	#62824	C₂³	1	2	yes	—
94	#62820	C₂³	1	2	yes	—
95	#62817	C₂³	1	2	yes	—
96	C₂×#3484	C₂³	1	1	yes	characteristic
97	C₂×#3484	C₂³	1	1	yes	characteristic
98	C₂×#3484	C₂³	1	1	yes	characteristic
99	C₂×#3484	C₂³	1	1	yes	characteristic
100	C₂×#3484	C₂³	1	1	yes	characteristic
101	C₂²×#535	C₂³	1	1	yes	characteristic
102	C₂²×#534	C₂³	1	1	yes	characteristic
103	#60399	D₄	1	4	yes	complemented
104	#60399	C₂³	1	4	yes	—
105	C₂×#3026	D₄	1	2	yes	complemented
106	C₂×#3019	D₄	1	2	yes	complemented
107	#60359	D₄	1	2	yes	complemented
108	C₂×#2883	D₄	1	1	yes	characteristic, complemented
109	C₂×#2883	D₄	1	1	yes	characteristic, complemented
110	C₂×#2883	D₄	1	1	yes	characteristic, complemented
111	#34980	D₄	1	2	yes	complemented
112	#23907	D₄	1	2	yes	complemented
113	#23907	C₂³	1	2	yes	—
114	#23907	C₂³	1	2	yes	—
115	#23907	C₂³	1	2	yes	complemented
116	#23906	D₄	1	2	yes	complemented
117	#23906	C₂³	1	2	yes	—
118	#23906	C₂³	1	2	yes	—
119	#23906	C₂³	1	2	yes	complemented
120	#23901	D₄	1	2	yes	complemented
121	#23901	C₂³	1	2	yes	—
122	#23901	C₂³	1	2	yes	—
123	#23901	C₂³	1	2	yes	complemented
124	#23900	D₄	1	2	yes	complemented
125	#23900	C₂³	1	2	yes	—
126	#23900	C₂³	1	2	yes	—
127	#23900	C₂³	1	2	yes	complemented
128	#23897	D₄	1	4	yes	complemented
129	#23897	C₂³	1	4	yes	—
130	#23897	C₂³	1	4	yes	—
131	#23895	D₄	1	4	yes	complemented
132	#23895	C₂³	1	4	yes	—
133	#23895	C₂³	1	4	yes	—
134	#23895	C₂³	1	4	yes	complemented
135	#21778	C₂³	1	4	yes	—
136	#21776	C₂³	1	4	yes	—
137	C₂×#1913	D₄	1	2	yes	complemented
138	C₂×#1911	D₄	1	2	yes	complemented
139	C₂×#1898	D₄	1	2	yes	complemented
140	#20979	D₄	1	2	yes	complemented
141	C₂×#1783	C₂³	1	1	yes	characteristic
142	C₂×#1783	C₂³	1	1	yes	characteristic
143	C₂×#1783	C₂³	1	1	yes	characteristic
144	C₂×#1781	C₂³	1	1	yes	characteristic
145	C₂×#1781	C₂³	1	1	yes	characteristic
146	C₂×#1781	C₂³	1	1	yes	characteristic
147	C₂×#1781	C₂³	1	1	yes	characteristic
148	#15262	C₂³	1	1	yes	characteristic, complemented
149	#15261	C₂³	1	1	yes	characteristic, complemented
150	#15259	C₂³	1	1	yes	characteristic, complemented
151	#15258	C₂³	1	1	yes	characteristic, complemented
152	C₂×#1438	C₂³	1	1	yes	characteristic
153	#12707	C₂³	1	4	yes	—
154	#12705	C₂³	1	4	yes	—
155	#12705	C₂³	1	4	yes	—
156	#12705	C₂³	1	4	yes	complemented
157	#12705	C₂³	1	4	yes	complemented
158	#12694	C₂³	1	2	yes	complemented
159	#12693	C₂³	1	2	yes	complemented
160	#12688	C₂³	1	2	yes	complemented
161	#12687	C₂³	1	2	yes	complemented
162	#8548	C₂³	1	2	yes	complemented
163	#8547	C₂³	1	2	yes	complemented
164	#8546	C₂³	1	2	yes	complemented
165	#8544	C₂³	1	2	yes	complemented
166	#8534	C₂³	1	2	yes	—
167	#8534	C₂³	1	2	yes	—
168	#8534	C₂³	1	2	yes	—
169	#8534	C₂³	1	2	yes	—
170	#8534	C₂³	1	2	yes	complemented
171	#8534	C₂³	1	2	yes	complemented
172	#8453	C₂³	1	2	yes	—
173	#8453	C₂³	1	2	yes	—
174	#8453	C₂³	1	2	yes	complemented
175	#8453	C₂³	1	2	yes	complemented
176	#7316	C₂³	1	4	yes	complemented
177	#7314	C₂³	1	4	yes	complemented
178	#7311	C₂³	1	4	yes	complemented
179	#7304	C₂³	1	2	yes	complemented
180	#7304	C₂³	1	2	yes	complemented
181	H(7,𝔽₂)	C₂×D₄	1	4	yes	complemented
182	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
183	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
184	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
185	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
186	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
187	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
188	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
190	#3484	C₂×D₄	1	2	yes	—
191	#3484	C₂×D₄	1	2	yes	—
192	#3484	C₂×D₄	1	2	yes	—
193	#3484	C₂×D₄	1	2	yes	—
194	#3484	C₂×D₄	1	2	yes	—
195	#3484	C₂×D₄	1	2	yes	—
196	#3484	C₂×D₄	1	2	yes	—
197	#3484	C₂×D₄	1	2	yes	—
198	#3484	C₂×D₄	1	2	yes	complemented
199	#3484	C₂⁴	1	2	yes	—
200	#3484	C₂⁴	1	2	yes	—
201	#3484	C₂⁴	1	2	yes	—
202	#3484	C₂⁴	1	2	yes	—
203	#3484	C₂⁴	1	2	yes	—
204	C₂×#535	C₂×D₄	1	2	yes	—
205	C₂×#534	C₂×D₄	1	2	yes	—
206	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
207	C₂²×#127	C₂⁴	1	1	yes	characteristic
208	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
209	C₂²×#124	C₂⁴	1	1	yes	characteristic
210	C₂×#525	C₂×D₄	1	2	yes	—
211	C₂²×#123	C₂×D₄	1	1	yes	characteristic
212	C₂²×#123	C₂⁴	1	1	yes	characteristic
213	C₂²×#120	C₂×D₄	1	2	yes	—
214	C₂²×#120	C₂×D₄	1	1	yes	characteristic
215	C₂²×#120	C₂⁴	1	1	yes	characteristic
216	C₂×#518	C₂×D₄	1	1	yes	characteristic
217	C₂×#518	C₂×D₄	1	1	yes	characteristic
218	C₂×#518	C₂×D₄	1	1	yes	characteristic
219	C₂×#518	C₂×D₄	1	1	yes	characteristic
220	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
221	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
222	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
223	#3026	C₂×D₄	1	8	yes	—
224	#3019	C₂×D₄	1	8	yes	complemented
225	#3004	C₂×D₄	1	4	yes	complemented
226	#3003	C₂×D₄	1	4	yes	complemented
227	C₂²×#100	C₂×D₄	1	2	yes	complemented
228	#2883	C₂×D₄	1	4	yes	complemented
229	#2883	C₂×D₄	1	4	yes	complemented
230	#2883	C₂×D₄	1	4	yes	complemented
231	C₂²×#99	C₂×D₄	1	2	yes	—
232	C₂×#407	C₂×D₄	1	2	yes	complemented
233	#2849	C₂×D₄	1	4	yes	complemented
234	#2846	C₂×D₄	1	4	yes	complemented
235	C₂×#379	C₂×D₄	1	2	yes	—
236	#1913	C₂×D₄	1	8	yes	—
237	#1911	C₂×D₄	1	8	yes	complemented
238	#1898	C₂×D₄	1	4	yes	complemented
239	#1898	C₂×D₄	1	4	yes	complemented
240	#1896	C₂×D₄	1	4	yes	complemented
241	#1896	C₂×D₄	1	4	yes	complemented
242	#1783	C₂×D₄	1	2	yes	complemented
243	#1783	C₂×D₄	1	2	yes	complemented
244	#1783	C₂⁴	1	2	yes	—
245	#1783	C₂⁴	1	2	yes	—
246	#1783	C₂⁴	1	2	yes	—
247	#1781	C₂×D₄	1	2	yes	—
248	#1781	C₂×D₄	1	2	yes	—
249	#1781	C₂⁴	1	2	yes	—
250	#1781	C₂⁴	1	2	yes	—
251	#1781	C₂⁴	1	2	yes	—
252	#1781	C₂⁴	1	2	yes	—
253	#1438	C₂⁴	1	1	yes	characteristic
254	#1438	C₂⁴	1	1	yes	characteristic
255	C₂⁶	C₂²×D₄	1	1	yes	characteristic
256	C₂⁶	C₂²×D₄	1	1	yes	characteristic
257	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂×H(5,𝔽₂)	#120	1	2	yes	—
259	C₂×H(5,𝔽₂)	#120	1	2	yes	—
260	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
261	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
262	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
263	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
264	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
265	C₂²×#41	#120	1	2	yes	—
266	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
267	C₂³×D₄	#120	1	2	yes	—
268	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
269	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
270	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
271	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
272	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
273	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
274	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
275	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
276	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
277	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
278	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂³×D₄	C₂⁵	1	1	yes	characteristic
281	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
282	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
283	#535	#120	1	4	yes	—
284	#535	C₂²×D₄	1	4	yes	—
285	#534	#120	1	4	yes	—
286	#534	C₂²×D₄	1	4	yes	—
287	#525	#120	1	4	yes	—
288	#525	C₂²×D₄	1	4	yes	—
289	C₂×#120	#120	1	4	yes	—
290	C₂×#120	C₂²×D₄	1	4	yes	—
291	#518	#120	1	2	yes	—
292	#518	#120	1	2	yes	—
293	#518	C₂²×D₄	1	2	yes	—
294	#518	C₂²×D₄	1	2	yes	—
295	#518	C₂²×D₄	1	2	yes	—
296	#518	C₂²×D₄	1	2	yes	—
297	#518	C₂²×D₄	1	2	yes	—
298	C₂×#117	#120	1	2	yes	—
299	C₂²×C₂²⋊C₄	#120	1	2	yes	—
300	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
301	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
304	C₂×#100	C₂²×D₄	1	4	yes	—
305	C₂×#99	C₂²×D₄	1	4	yes	—
306	#407	C₂²×D₄	1	4	yes	—
307	#379	C₂²×D₄	1	4	yes	—
308	C₂⁵	B(4,𝔽₂)	1	2	yes	—
309	C₂⁵	C₂×#120	1	1	yes	characteristic
310	C₂⁵	C₂×#120	1	1	yes	characteristic
311	C₂⁵	#534	1	1	yes	characteristic
312	C₂⁵	#534	1	1	yes	characteristic
313	C₂⁵	D₄²	1	1	yes	characteristic
314	C₂⁵	D₄²	1	1	yes	characteristic
315	C₂⁵	D₄²	1	1	yes	characteristic
316	C₂⁵	D₄²	1	1	yes	characteristic
317	C₂⁵	D₄²	1	1	yes	characteristic
318	C₂⁵	D₄²	1	1	yes	characteristic
319	C₂⁵	D₄²	1	1	yes	characteristic
320	C₂⁵	C₂³×D₄	1	1	yes	characteristic
321	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×#41	B(4,𝔽₂)	1	4	yes	complemented
323	C₂×#41	C₂×#120	1	4	yes	—
324	C₂²×Q₈	B(4,𝔽₂)	1	2	yes	complemented
325	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
326	C₂²×D₄	B(4,𝔽₂)	1	2	yes	complemented
327	C₂²×D₄	C₂×#120	1	1	yes	characteristic
328	C₂²×D₄	C₂×#120	1	1	yes	characteristic
329	C₂²×D₄	C₂×#120	1	1	yes	characteristic
330	C₂²×D₄	C₂×#120	1	1	yes	characteristic
331	C₂²×D₄	C₂×#120	1	4	yes	—
332	C₂²×D₄	#534	1	1	yes	characteristic
333	C₂²×D₄	#534	1	1	yes	characteristic
334	C₂²×D₄	D₄²	1	1	yes	characteristic
335	C₂²×D₄	D₄²	1	1	yes	characteristic
336	C₂²×D₄	D₄²	1	1	yes	characteristic
337	C₂²×D₄	D₄²	1	1	yes	characteristic
338	C₂²×D₄	D₄²	1	1	yes	characteristic
339	C₂²×D₄	D₄²	1	1	yes	characteristic
340	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
341	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
342	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
343	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂³×C₄	B(4,𝔽₂)	1	2	yes	—
345	C₂³×C₄	C₂×#120	1	1	yes	characteristic
346	C₂³×C₄	C₂×#120	1	1	yes	characteristic
347	C₂³×C₄	D₄²	1	1	yes	characteristic
348	C₂³×C₄	D₄²	1	1	yes	characteristic
349	C₂³×C₄	D₄²	1	1	yes	characteristic
350	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
351	#117	C₂×#120	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
353	C₂⁴	#2403	1	1	yes	characteristic
354	C₂⁴	#2403	1	1	yes	characteristic
355	C₂⁴	#2403	1	1	yes	characteristic
356	C₂⁴	#2403	1	1	yes	characteristic
357	C₂⁴	#2403	1	1	yes	characteristic
358	C₂⁴	#2403	1	1	yes	characteristic
359	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
360	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
361	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
362	C₂⁴	C₂²×#120	1	1	yes	characteristic
363	C₂⁴	C₂×#534	1	1	yes	characteristic
364	C₂⁴	C₂×D₄²	1	1	yes	characteristic
365	C₂⁴	C₂×D₄²	1	1	yes	characteristic
366	C₂⁴	C₂×D₄²	1	1	yes	characteristic
367	C₂×Q₈	C₂×B(4,𝔽₂)	1	4	yes	—
368	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
369	C₂²×C₄	#2403	1	1	yes	characteristic
370	C₂²×C₄	#2403	1	1	yes	characteristic
371	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
372	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
373	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
374	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
376	C₂³	#23895	1	1	yes	characteristic
377	C₂³	#23895	1	1	yes	characteristic
378	C₂³	#23900	1	2	yes	—
379	C₂³	#23900	1	1	yes	characteristic
380	C₂³	#23900	1	1	yes	characteristic
381	C₂³	#23900	1	1	yes	characteristic
382	C₂³	#23900	1	1	yes	characteristic
383	C₂³	C₂×#2403	1	1	yes	characteristic
384	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
385	C₂×C₄	#23900	1	2	yes	—
386	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
387	C₂²	#245225	1	1	yes	characteristic
388	C₂²	#245225	1	1	yes	characteristic
389	C₂²	#245225	1	1	yes	characteristic
390	C₂²	#245225	1	1	yes	characteristic
391	C₂²	C₂×#23900	1	1	yes	characteristic
392	C₂²	C₂×#23900	1	1	yes	characteristic
393	C₂²	C₂×#23895	1	1	yes	characteristic
394	C₂	C₂×#245225	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#245225
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72312583	C₂	semidirect
2. #72266835	C₂	semidirect
3. #72263490	C₂	semidirect
4. #72259136	C₂	semidirect
5. C₂×#139739	C₂	semidirect
6. C₂×#139742	C₂	semidirect
7. #72255764	C₂	semidirect
8. #72251567	C₂	semidirect
9. #72251527	C₂	semidirect
10. #72251420	C₂	semidirect
11. #72240474	C₂	semidirect
12. #72238342	C₂	semidirect
13. #72236674	C₂	semidirect
14. #72236521	C₂	semidirect
15. #72235130	C₂	semidirect
16. #72234693	C₂	semidirect
17. C₂×#144364	C₂	semidirect
18. C₂×#133839	C₂	semidirect
19. #72210342	C₂	semidirect
20. #10586422	C₂²	semidirect
21. #10586404	C₂²	semidirect
23. #6499875	C₂²	semidirect
24. #6499874	C₂²	semidirect
25. #6499856	C₂²	semidirect
26. #6499855	C₂²	semidirect
28. C₂×#23895	C₂²	semidirect
29. C₂×#23895	C₂²	semidirect
31. #6437621	C₂²	semidirect
32. #6437621	C₂²	semidirect
34. C₂×#23897	C₂²	semidirect
36. #6437445	C₂²	semidirect
37. #6437445	C₂²	semidirect
38. C₂×#21778	C₂²	semidirect
39. C₂×#21776	C₂²	semidirect
40. #763333	C₂²	semidirect
41. #511812	C₂²	semidirect
42. #511811	C₂²	semidirect
43. #511791	C₂²	semidirect
44. #511790	C₂²	semidirect
45. C₂×#12707	C₂²	semidirect
46. C₂×#12705	C₂²	semidirect
47. C₂×#12705	C₂²	semidirect
48. C₂×#12705	C₂²	semidirect
49. C₂×#12705	C₂²	semidirect
50. #493370	C₂²	semidirect
51. #493357	C₂²	semidirect
52. #347057	C₂²	semidirect
53. #347056	C₂²	semidirect
54. #347047	C₂²	semidirect
55. #347045	C₂²	semidirect
56. #346457	C₂²	semidirect
57. #346456	C₂²	semidirect
58. #346447	C₂²	semidirect
59. #346446	C₂²	semidirect
60. #188109	C₂²	semidirect
61. #188050	C₂²	semidirect
62. C₂×#8534	C₂²	semidirect
63. C₂×#8534	C₂²	semidirect
64. C₂×#8534	C₂²	semidirect
65. C₂×#8453	C₂²	semidirect
66. C₂×#8453	C₂²	semidirect
67. #144389	C₂²	semidirect
68. #144388	C₂²	semidirect
69. #144387	C₂²	semidirect
70. #144386	C₂²	semidirect
71. #144383	C₂²	semidirect
72. #144382	C₂²	semidirect
73. #144381	C₂²	semidirect
74. #144380	C₂²	semidirect
75. #144364	C₂²	semidirect
76. #144364	C₂²	semidirect
77. #139760	C₂²	semidirect
78. #139759	C₂²	semidirect
79. #139748	C₂²	semidirect
80. #139747	C₂²	semidirect
81. #139742	C₂²	semidirect
82. #139742	C₂²	semidirect
83. #139739	C₂²	semidirect
84. #139739	C₂²	semidirect
85. #133839	C₂²	semidirect
86. #133839	C₂²	semidirect
87. C₂×#7304	C₂²	semidirect
88. C₂×#7316	C₂²	semidirect
89. C₂×#7314	C₂²	semidirect
90. C₂×#7311	C₂²	semidirect
91. C₂×H(7,𝔽₂)	D₄	semidirect
103. #60399	D₄	semidirect
105. C₂×#3026	D₄	semidirect
106. C₂×#3019	D₄	semidirect
107. #60359	D₄	semidirect
108. C₂×#2883	D₄	semidirect
109. C₂×#2883	D₄	semidirect
110. C₂×#2883	D₄	semidirect
111. #34980	D₄	semidirect
112. #23907	D₄	semidirect
115. #23907	C₂³	semidirect
116. #23906	D₄	semidirect
119. #23906	C₂³	semidirect
120. #23901	D₄	semidirect
123. #23901	C₂³	semidirect
124. #23900	D₄	semidirect
127. #23900	C₂³	semidirect
128. #23897	D₄	semidirect
131. #23895	D₄	semidirect
134. #23895	C₂³	semidirect
137. C₂×#1913	D₄	semidirect
138. C₂×#1911	D₄	semidirect
139. C₂×#1898	D₄	semidirect
140. #20979	D₄	semidirect
148. #15262	C₂³	semidirect
149. #15261	C₂³	semidirect
150. #15259	C₂³	semidirect
151. #15258	C₂³	semidirect
156. #12705	C₂³	semidirect
157. #12705	C₂³	semidirect
158. #12694	C₂³	semidirect
159. #12693	C₂³	semidirect
160. #12688	C₂³	semidirect
161. #12687	C₂³	semidirect
162. #8548	C₂³	semidirect
163. #8547	C₂³	semidirect
164. #8546	C₂³	semidirect
165. #8544	C₂³	semidirect
170. #8534	C₂³	semidirect
171. #8534	C₂³	semidirect
174. #8453	C₂³	semidirect
175. #8453	C₂³	semidirect
176. #7316	C₂³	semidirect
177. #7314	C₂³	semidirect
178. #7311	C₂³	semidirect
179. #7304	C₂³	semidirect
180. #7304	C₂³	semidirect
181. H(7,𝔽₂)	C₂×D₄	semidirect
186. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
187. C₂³×#41	C₂×D₄	semidirect
198. #3484	C₂×D₄	semidirect
206. C₂²×#127	C₂×D₄	semidirect
208. C₂²×#124	C₂×D₄	semidirect
220. C₂×#518	C₂×D₄	semidirect
221. C₂²×#117	C₂×D₄	semidirect
224. #3019	C₂×D₄	semidirect
225. #3004	C₂×D₄	semidirect
226. #3003	C₂×D₄	semidirect
227. C₂²×#100	C₂×D₄	semidirect
228. #2883	C₂×D₄	semidirect
229. #2883	C₂×D₄	semidirect
230. #2883	C₂×D₄	semidirect
232. C₂×#407	C₂×D₄	semidirect
233. #2849	C₂×D₄	semidirect
234. #2846	C₂×D₄	semidirect
237. #1911	C₂×D₄	semidirect
238. #1898	C₂×D₄	semidirect
239. #1898	C₂×D₄	semidirect
240. #1896	C₂×D₄	semidirect
241. #1896	C₂×D₄	semidirect
242. #1783	C₂×D₄	semidirect
243. #1783	C₂×D₄	semidirect
322. C₂×#41	B(4,𝔽₂)	semidirect
324. C₂²×Q₈	B(4,𝔽₂)	semidirect
326. C₂²×D₄	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72312583	2
#72266835	2
#72263490	2
#72259136	2
C₂×#139739	2
C₂×#139742	2
#72255764	2
#72251567	2
#72251527	2
#72251420	2
#72240474	2
#72238342	2
#72236674	2
#72236521	2
#72235130	2
#72234693	2
C₂×#144364	2
C₂×#133839	2
#72210342	2