Subgroups — #72338918

Order 2048.

At least 10272 conjugacy classes of subgroups; only the 1010 normal subgroups are shown.

The subgroup lattice has 409 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338886	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#449492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#133308	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338721	C₂	1	2	yes	maximal, complemented
5	#72266169	C₂	1	1	yes	maximal, characteristic, complemented
6	#72266070	C₂	1	1	yes	maximal, characteristic, complemented
7	#72262289	C₂	1	2	yes	maximal, complemented
8	#72262266	C₂	1	8	yes	maximal, complemented
9	#72256800	C₂	1	4	yes	maximal, complemented
10	#72236108	C₂	1	1	yes	maximal, characteristic, complemented
11	#72235270	C₂	1	4	yes	maximal, complemented
12	C₂×#245233	C₂	1	1	yes	maximal, characteristic, complemented
13	#72213244	C₂	1	2	yes	maximal, complemented
14	#72210498	C₂	1	2	yes	maximal, complemented
15	C₂²×#3019	C₂²	1	2	yes	complemented
16	#8968143	C₂²	1	4	yes	complemented
17	#8934620	C₂²	1	1	yes	characteristic, complemented
18	#8934366	C₂²	1	1	yes	characteristic, complemented
19	#8933771	C₂²	1	1	yes	characteristic, complemented
20	#8933771	C₂²	1	1	yes	characteristic, complemented
21	#7772009	C₂²	1	4	yes	—
22	#7643002	C₂²	1	1	yes	characteristic
23	C₂×#35527	C₂²	1	1	yes	characteristic
24	C₂×#35527	C₂²	1	1	yes	characteristic
25	C₂×#35527	C₂²	1	1	yes	characteristic, complemented
26	#6628892	C₂²	1	2	yes	complemented
27	C₂×#32898	C₂²	1	2	yes	complemented
28	#499839	C₂²	1	8	yes	complemented
29	#499838	C₂²	1	8	yes	complemented
30	#499835	C₂²	1	8	yes	complemented
31	#499832	C₂²	1	8	yes	complemented
32	#494677	C₂²	1	4	yes	complemented
33	C₂×#13082	C₂²	1	4	yes	complemented
34	#493370	C₂²	1	4	yes	complemented
35	#449492	C₂²	1	2	yes	complemented
36	#449492	C₂²	1	2	yes	complemented
37	#449492	C₂²	1	4	yes	complemented
38	C₂×#10989	C₂²	1	2	yes	complemented
39	C₂×#10981	C₂²	1	1	yes	characteristic, complemented
40	#245255	C₂²	1	4	yes	complemented
41	#245234	C₂²	1	2	yes	complemented
42	#245233	C₂²	1	2	yes	complemented
43	#245233	C₂²	1	2	yes	complemented
44	#245233	C₂²	1	2	yes	complemented
45	#245233	C₂²	1	4	yes	complemented
46	#201690	C₂²	1	2	yes	complemented
47	C₂×#9497	C₂²	1	2	yes	complemented
48	C₂×#8546	C₂²	1	1	yes	characteristic, complemented
49	C₂×#8546	C₂²	1	1	yes	characteristic, complemented
50	#133835	C₂²	1	2	yes	complemented
51	#133835	C₂²	1	2	yes	complemented
52	#133835	C₂²	1	4	yes	complemented
53	#133360	C₂²	1	8	yes	complemented
54	#133359	C₂²	1	8	yes	complemented
55	#133358	C₂²	1	8	yes	complemented
56	#133356	C₂²	1	8	yes	complemented
57	#133311	C₂²	1	4	yes	complemented
58	#133309	C₂²	1	2	yes	complemented
59	#133308	C₂²	1	2	yes	complemented
60	#133308	C₂²	1	2	yes	complemented
61	#133308	C₂²	1	2	yes	complemented
62	#133308	C₂²	1	4	yes	complemented
63	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
64	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
65	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
66	C₂×#3484	D₄	1	1	yes	characteristic, complemented
67	C₂×#3532	D₄	1	4	yes	complemented
68	C₂²×#535	C₂³	1	2	yes	—
69	C₂³×#127	C₂³	1	1	yes	characteristic
70	C₂×#3019	C₂³	1	4	yes	complemented
71	C₂×#3019	C₂³	1	4	yes	complemented
72	C₂³×#100	C₂³	1	2	yes	complemented
73	#59162	D₄	1	4	yes	complemented
74	#59126	D₄	1	4	yes	complemented
75	#52012	C₂³	1	4	yes	—
76	#52004	C₂³	1	4	yes	—
77	#51902	C₂³	1	4	yes	—
78	#51895	C₂³	1	4	yes	—
79	#46324	D₄	1	4	yes	complemented
80	#45977	D₄	1	4	yes	complemented
81	#37232	D₄	1	2	yes	complemented
82	#37232	C₂³	1	2	yes	—
83	#36737	D₄	1	4	yes	complemented
84	#36702	D₄	1	4	yes	complemented
85	#35554	D₄	1	1	yes	characteristic, complemented
86	#35554	C₂³	1	1	yes	characteristic
87	#35527	D₄	1	2	yes	complemented
88	#35527	D₄	1	1	yes	characteristic, complemented
89	#35527	D₄	1	1	yes	characteristic, complemented
90	#35527	D₄	1	2	yes	complemented
91	#35527	D₄	1	1	yes	characteristic, complemented
92	#35527	D₄	1	1	yes	characteristic, complemented
93	#35527	D₄	1	1	yes	characteristic, complemented
94	#35527	C₂³	1	1	yes	characteristic
95	#35527	C₂³	1	1	yes	characteristic
96	#35527	C₂³	1	2	yes	—
97	#35527	C₂³	1	1	yes	characteristic
98	#35527	C₂³	1	1	yes	characteristic
99	#35527	C₂³	1	2	yes	—
100	#35527	C₂³	1	1	yes	characteristic
101	#35527	C₂³	1	2	yes	—
102	#35527	C₂³	1	2	yes	complemented
103	#34980	D₄	1	2	yes	complemented
104	#34980	C₂³	1	2	yes	—
105	C₂×#2403	D₄	1	2	yes	complemented
106	C₂×#2403	C₂³	1	2	yes	—
107	#34406	D₄	1	4	yes	complemented
108	#34171	D₄	1	1	yes	characteristic, complemented
109	C₂×#2309	D₄	1	1	yes	characteristic, complemented
110	C₂×#2309	D₄	1	1	yes	characteristic, complemented
111	C₂×#2309	C₂³	1	1	yes	characteristic, complemented
112	C₂×#2297	D₄	1	2	yes	complemented
113	#32900	C₂³	1	4	yes	complemented
114	#32898	C₂³	1	4	yes	complemented
115	#32898	C₂³	1	4	yes	complemented
116	#32898	C₂³	1	4	yes	complemented
117	C₂×#1781	C₂³	1	2	yes	complemented
118	C₂×#1781	C₂³	1	2	yes	complemented
119	#13082	C₂³	1	8	yes	complemented
120	#13082	C₂³	1	8	yes	complemented
121	#13082	C₂³	1	8	yes	complemented
122	#13080	C₂³	1	8	yes	complemented
123	#12696	C₂³	1	8	yes	complemented
124	#12696	C₂³	1	8	yes	complemented
125	#10989	C₂³	1	4	yes	complemented
126	#10989	C₂³	1	4	yes	complemented
127	#10981	C₂³	1	2	yes	—
128	#10981	C₂³	1	2	yes	complemented
129	#9501	C₂³	1	4	yes	complemented
130	#9497	C₂³	1	4	yes	complemented
131	#9497	C₂³	1	4	yes	complemented
132	#9497	C₂³	1	4	yes	complemented
133	#8546	C₂³	1	2	yes	—
134	#8546	C₂³	1	2	yes	—
135	#8546	C₂³	1	2	yes	complemented
136	#8546	C₂³	1	2	yes	complemented
137	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
138	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
139	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
140	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
141	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
142	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
143	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
144	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
145	C₂³×#41	C₂×D₄	1	2	yes	—
146	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
147	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×D₄	C₂×D₄	1	2	yes	—
150	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
153	C₂×H(3,𝔽₄)	C₂×D₄	1	4	yes	complemented
154	C₂×#560	C₂×D₄	1	4	yes	complemented
155	C₂×#551	C₂×D₄	1	4	yes	complemented
156	C₂×D₄²	C₂×D₄	1	4	yes	complemented
157	C₂×#535	C₂×D₄	1	4	yes	—
158	C₂×#535	C₂×D₄	1	4	yes	—
159	C₂×#535	C₂×D₄	1	2	yes	—
160	C₂×#535	C₂×D₄	1	2	yes	—
161	C₂×#535	C₂⁴	1	2	yes	—
162	C₂×#535	C₂⁴	1	2	yes	—
163	C₂×#534	C₂×D₄	1	4	yes	—
164	C₂×#534	C₂×D₄	1	2	yes	complemented
165	C₂²×#127	C₂×D₄	1	1	yes	characteristic
166	C₂²×#127	C₂×D₄	1	1	yes	characteristic
167	C₂²×#127	C₂×D₄	1	1	yes	characteristic
168	C₂²×#127	C₂×D₄	1	1	yes	characteristic
169	C₂²×#127	C₂×D₄	1	1	yes	characteristic
170	C₂²×#127	C₂×D₄	1	1	yes	characteristic
171	C₂²×#127	C₂×D₄	1	4	yes	—
172	C₂²×#127	C₂⁴	1	1	yes	characteristic
173	C₂²×#127	C₂⁴	1	1	yes	characteristic
174	C₂²×#124	C₂×D₄	1	4	yes	—
175	C₂²×#120	C₂×D₄	1	4	yes	—
176	C₂²×#120	C₂×D₄	1	2	yes	—
177	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
178	C₂²×#117	C₂×D₄	1	2	yes	—
179	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
180	C₂²×#100	C₂⁴	1	4	yes	—
181	#2717	C₂×D₄	1	4	yes	complemented
182	#2709	C₂×D₄	1	4	yes	complemented
183	#2684	C₂×D₄	1	4	yes	complemented
184	#2684	C₂×D₄	1	4	yes	complemented
185	#2684	C₂×D₄	1	4	yes	complemented
186	#2669	C₂×D₄	1	4	yes	complemented
187	#2669	C₂×D₄	1	4	yes	complemented
188	#2669	C₂×D₄	1	4	yes	complemented
189	#2405	C₂×D₄	1	4	yes	—
190	#2405	C₂×D₄	1	2	yes	—
191	#2405	C₂×D₄	1	2	yes	complemented
192	#2405	C₂×D₄	1	2	yes	complemented
193	#2405	C₂⁴	1	2	yes	—
194	#2403	C₂×D₄	1	2	yes	—
195	#2403	C₂×D₄	1	2	yes	—
196	#2403	C₂×D₄	1	2	yes	—
197	#2403	C₂×D₄	1	2	yes	—
198	#2403	C₂×D₄	1	2	yes	—
199	#2403	C₂×D₄	1	2	yes	—
200	#2403	C₂×D₄	1	2	yes	—
201	#2403	C₂×D₄	1	4	yes	—
202	#2403	C₂×D₄	1	4	yes	—
203	#2403	C₂×D₄	1	4	yes	—
204	#2403	C₂×D₄	1	2	yes	complemented
205	#2403	C₂×D₄	1	2	yes	complemented
206	#2403	C₂⁴	1	2	yes	—
207	#2403	C₂⁴	1	2	yes	—
208	#2403	C₂⁴	1	2	yes	—
209	#2380	C₂×D₄	1	4	yes	complemented
210	#2379	C₂×D₄	1	4	yes	complemented
211	#2372	C₂×D₄	1	4	yes	complemented
212	#2366	C₂×D₄	1	4	yes	complemented
213	#2309	C₂×D₄	1	1	yes	characteristic
214	#2309	C₂×D₄	1	1	yes	characteristic
215	#2309	C₂×D₄	1	2	yes	—
216	#2309	C₂×D₄	1	1	yes	characteristic, complemented
217	#2309	C₂×D₄	1	1	yes	characteristic, complemented
218	#2309	C₂×D₄	1	1	yes	characteristic, complemented
219	#2309	C₂×D₄	1	1	yes	characteristic, complemented
220	#2309	C₂×D₄	1	2	yes	complemented
221	#2309	C₂⁴	1	2	yes	—
222	#2308	C₂×D₄	1	4	yes	—
223	#2308	C₂×D₄	1	2	yes	complemented
224	#2297	C₂×D₄	1	2	yes	complemented
225	#2297	C₂×D₄	1	2	yes	complemented
226	#2297	C₂×D₄	1	2	yes	complemented
227	#2297	C₂×D₄	1	2	yes	complemented
228	C₂×#386	C₂×D₄	1	4	yes	—
229	C₂×#379	C₂×D₄	1	2	yes	—
230	C₂×#379	C₂×D₄	1	2	yes	—
231	#1781	C₂⁴	1	4	yes	—
232	#1781	C₂⁴	1	4	yes	—
233	C₂⁶	#120	1	1	yes	characteristic
234	C₂⁶	#120	1	1	yes	characteristic
235	C₂⁶	#120	1	2	yes	—
236	C₂⁶	C₂²×D₄	1	1	yes	characteristic
237	C₂⁶	C₂²×D₄	1	1	yes	characteristic
238	C₂²×#41	#120	1	2	yes	—
239	C₂²×#41	#120	1	2	yes	—
240	C₂²×#41	C₂²×D₄	1	2	yes	—
241	C₂²×#41	C₂²×D₄	1	2	yes	—
242	C₂³×Q₈	#120	1	2	yes	—
243	C₂³×D₄	#120	1	1	yes	characteristic
244	C₂³×D₄	#120	1	1	yes	characteristic
245	C₂³×D₄	#120	1	1	yes	characteristic
246	C₂³×D₄	#120	1	1	yes	characteristic
247	C₂³×D₄	#120	1	1	yes	characteristic
248	C₂³×D₄	#120	1	1	yes	characteristic
249	C₂³×D₄	#120	1	2	yes	—
250	C₂³×D₄	#120	1	2	yes	—
251	C₂³×D₄	#120	1	2	yes	—
252	C₂³×D₄	#120	1	1	yes	characteristic
253	C₂³×D₄	#120	1	2	yes	—
254	C₂³×D₄	#120	1	1	yes	characteristic
255	C₂³×D₄	#120	1	1	yes	characteristic
256	C₂³×D₄	#120	1	2	yes	—
257	C₂³×D₄	#120	1	1	yes	characteristic
258	C₂³×D₄	C₂²×D₄	1	4	yes	—
259	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
260	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
261	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
262	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
263	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
264	C₂³×D₄	C₂²×D₄	1	2	yes	—
265	C₂³×D₄	C₂²×D₄	1	2	yes	—
266	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
267	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
268	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
269	C₂³×D₄	C₂²×D₄	1	2	yes	—
270	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
271	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
272	C₂³×D₄	C₂²×D₄	1	4	yes	—
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	C₂⁵	1	1	yes	characteristic
277	C₂⁴×C₄	#120	1	1	yes	characteristic
278	C₂⁴×C₄	#120	1	1	yes	characteristic
279	C₂⁴×C₄	#120	1	2	yes	—
280	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
281	C₂×#127	#120	1	4	yes	—
282	C₂×#127	#120	1	4	yes	—
283	C₂×#127	C₂²×D₄	1	4	yes	—
284	C₂×#127	C₂²×D₄	1	4	yes	—
285	C₂×#124	#120	1	4	yes	—
286	C₂×#124	#120	1	4	yes	—
287	C₂×#124	C₂²×D₄	1	4	yes	—
288	C₂×#124	C₂²×D₄	1	4	yes	—
289	C₂×#123	#120	1	4	yes	—
290	C₂×#123	C₂²×D₄	1	4	yes	—
291	C₂×#120	#120	1	4	yes	—
292	C₂×#120	#120	1	4	yes	—
293	C₂×#120	#120	1	4	yes	—
294	C₂×#120	C₂²×D₄	1	4	yes	—
295	C₂×#120	C₂²×D₄	1	4	yes	—
296	C₂×#120	C₂²×D₄	1	4	yes	—
297	C₂×#117	#120	1	4	yes	—
298	C₂×#117	C₂²×D₄	1	2	yes	—
299	C₂×#117	C₂²×D₄	1	2	yes	—
300	C₂²×C₂²⋊C₄	#120	1	2	yes	—
301	C₂²×C₂²⋊C₄	#120	1	2	yes	—
302	C₂²×C₂²⋊C₄	#120	1	4	yes	—
303	C₂²×C₂²⋊C₄	#120	1	4	yes	—
304	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
305	C₂²×C₄²	#120	1	1	yes	characteristic
306	C₂²×C₄²	#120	1	1	yes	characteristic
307	C₂²×C₄²	#120	1	4	yes	—
308	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
309	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
310	#386	#120	1	4	yes	—
311	#386	#120	1	4	yes	—
312	#386	#120	1	4	yes	—
313	#386	#120	1	4	yes	—
314	#386	C₂²×D₄	1	4	yes	—
315	#386	C₂²×D₄	1	4	yes	—
316	#386	C₂²×D₄	1	4	yes	—
317	#386	C₂²×D₄	1	4	yes	—
318	#379	#120	1	4	yes	—
319	#379	#120	1	4	yes	—
320	#379	C₂²×D₄	1	2	yes	—
321	#379	C₂²×D₄	1	2	yes	—
322	#379	C₂²×D₄	1	2	yes	—
323	#379	C₂²×D₄	1	2	yes	—
324	C₂⁵	B(4,𝔽₂)	1	2	yes	—
325	C₂⁵	B(4,𝔽₂)	1	2	yes	—
326	C₂⁵	C₂×#120	1	2	yes	—
327	C₂⁵	C₂×#120	1	2	yes	—
328	C₂⁵	C₂×#120	1	1	yes	characteristic
329	C₂⁵	C₂×#120	1	1	yes	characteristic
330	C₂⁵	C₂×#120	1	2	yes	—
331	C₂⁵	C₂×#120	1	2	yes	—
332	C₂⁵	C₂×#120	1	1	yes	characteristic
333	C₂⁵	C₂×#120	1	1	yes	characteristic
334	C₂⁵	C₂×#120	1	1	yes	characteristic
335	C₂⁵	C₂×#120	1	1	yes	characteristic
336	C₂⁵	C₂×#120	1	2	yes	—
337	C₂⁵	C₂×#120	1	2	yes	—
338	C₂⁵	C₂×#120	1	2	yes	—
339	C₂⁵	C₂×#120	1	1	yes	characteristic
340	C₂⁵	C₂³×D₄	1	1	yes	characteristic
341	C₂⁵	C₂³×D₄	1	1	yes	characteristic
342	C₂×#41	B(4,𝔽₂)	1	8	yes	complemented
343	C₂²×Q₈	C₂×#120	1	2	yes	—
344	C₂²×Q₈	C₂×#120	1	2	yes	—
345	C₂²×D₄	C₂×#120	1	4	yes	—
346	C₂²×D₄	C₂×#120	1	4	yes	—
347	C₂²×D₄	C₂×#120	1	2	yes	—
348	C₂²×D₄	C₂×#120	1	4	yes	—
349	C₂²×D₄	C₂×#120	1	2	yes	—
350	C₂²×D₄	C₂³×D₄	1	4	yes	—
351	C₂³×C₄	C₂×#120	1	1	yes	characteristic
352	C₂³×C₄	C₂×#120	1	2	yes	—
353	C₂³×C₄	C₂×#120	1	2	yes	—
354	C₂³×C₄	C₂×#120	1	1	yes	characteristic
355	C₂³×C₄	C₂×#120	1	1	yes	characteristic
356	C₂³×C₄	C₂×#120	1	1	yes	characteristic
357	C₂³×C₄	C₂×#120	1	1	yes	characteristic
358	C₂³×C₄	C₂×#120	1	2	yes	—
359	C₂³×C₄	C₂×#120	1	2	yes	—
360	C₂³×C₄	C₂×#120	1	2	yes	—
361	C₂³×C₄	C₂×#120	1	2	yes	—
362	C₂³×C₄	C₂×#120	1	2	yes	—
363	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
365	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
368	C₂×C₄²	C₂×#120	1	4	yes	—
369	C₂×C₄²	C₂×#120	1	4	yes	—
370	C₂⁴	#2846	1	1	yes	characteristic
371	C₂⁴	#2846	1	2	yes	—
372	C₂⁴	#2846	1	2	yes	—
373	C₂⁴	#2846	1	1	yes	characteristic
374	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
375	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
376	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
377	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
378	C₂⁴	#3026	1	1	yes	characteristic
379	C₂⁴	#3026	1	1	yes	characteristic
380	C₂⁴	C₂²×#120	1	2	yes	—
381	C₂⁴	C₂²×#120	1	2	yes	—
382	C₂⁴	C₂²×#120	1	1	yes	characteristic
383	C₂×Q₈	C₂×B(4,𝔽₂)	1	4	yes	complemented
384	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	complemented
385	C₂²×C₄	#2846	1	2	yes	—
386	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
387	C₂²×C₄	#3026	1	4	yes	—
388	C₂²×C₄	C₂²×#120	1	2	yes	—
389	C₂³	#32898	1	1	yes	characteristic
390	C₂³	#32898	1	1	yes	characteristic
391	C₂³	#32898	1	1	yes	characteristic
392	C₂³	#32898	1	1	yes	characteristic
393	C₂³	#32898	1	4	yes	—
394	C₂³	C₂×#2846	1	1	yes	characteristic
395	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
396	C₂³	C₂×#3026	1	1	yes	characteristic
397	C₂×C₄	#32898	1	4	yes	—
398	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
399	C₂×C₄	C₂×#3026	1	2	yes	—
400	C₂²	#347042	1	2	yes	—
401	C₂²	#347042	1	2	yes	—
402	C₂²	#511790	1	2	yes	—
403	C₂²	C₂×#32898	1	2	yes	—
404	C₂²	C₂×#32898	1	1	yes	characteristic
405	C₂	C₂×#511790	1	1	yes	characteristic
406	C₂	C₂×#347042	1	1	yes	characteristic
407	C₂	#72235130	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#127 ◁ 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. #72338886	C₂	semidirect
2. C₂×#449492	C₂	semidirect
3. C₂×#133308	C₂	semidirect
4. #72338721	C₂	semidirect
5. #72266169	C₂	semidirect
6. #72266070	C₂	semidirect
7. #72262289	C₂	semidirect
8. #72262266	C₂	semidirect
9. #72256800	C₂	semidirect
10. #72236108	C₂	semidirect
11. #72235270	C₂	semidirect
12. C₂×#245233	C₂	semidirect
13. #72213244	C₂	semidirect
14. #72210498	C₂	semidirect
15. C₂²×#3019	C₂²	semidirect
16. #8968143	C₂²	semidirect
17. #8934620	C₂²	semidirect
18. #8934366	C₂²	semidirect
19. #8933771	C₂²	semidirect
20. #8933771	C₂²	semidirect
25. C₂×#35527	C₂²	semidirect
26. #6628892	C₂²	semidirect
27. C₂×#32898	C₂²	semidirect
28. #499839	C₂²	semidirect
29. #499838	C₂²	semidirect
30. #499835	C₂²	semidirect
31. #499832	C₂²	semidirect
32. #494677	C₂²	semidirect
33. C₂×#13082	C₂²	semidirect
34. #493370	C₂²	semidirect
35. #449492	C₂²	semidirect
36. #449492	C₂²	semidirect
37. #449492	C₂²	semidirect
38. C₂×#10989	C₂²	semidirect
39. C₂×#10981	C₂²	semidirect
40. #245255	C₂²	semidirect
41. #245234	C₂²	semidirect
42. #245233	C₂²	semidirect
43. #245233	C₂²	semidirect
44. #245233	C₂²	semidirect
45. #245233	C₂²	semidirect
46. #201690	C₂²	semidirect
47. C₂×#9497	C₂²	semidirect
48. C₂×#8546	C₂²	semidirect
49. C₂×#8546	C₂²	semidirect
50. #133835	C₂²	semidirect
51. #133835	C₂²	semidirect
52. #133835	C₂²	semidirect
53. #133360	C₂²	semidirect
54. #133359	C₂²	semidirect
55. #133358	C₂²	semidirect
56. #133356	C₂²	semidirect
57. #133311	C₂²	semidirect
58. #133309	C₂²	semidirect
59. #133308	C₂²	semidirect
60. #133308	C₂²	semidirect
61. #133308	C₂²	semidirect
62. #133308	C₂²	semidirect
63. C₂³×H(5,𝔽₂)	D₄	semidirect
64. C₂³×H(5,𝔽₂)	D₄	semidirect
65. C₂³×H(5,𝔽₂)	C₂³	semidirect
66. C₂×#3484	D₄	semidirect
67. C₂×#3532	D₄	semidirect
70. C₂×#3019	C₂³	semidirect
71. C₂×#3019	C₂³	semidirect
72. C₂³×#100	C₂³	semidirect
73. #59162	D₄	semidirect
74. #59126	D₄	semidirect
79. #46324	D₄	semidirect
80. #45977	D₄	semidirect
81. #37232	D₄	semidirect
83. #36737	D₄	semidirect
84. #36702	D₄	semidirect
85. #35554	D₄	semidirect
87. #35527	D₄	semidirect
88. #35527	D₄	semidirect
89. #35527	D₄	semidirect
90. #35527	D₄	semidirect
91. #35527	D₄	semidirect
92. #35527	D₄	semidirect
93. #35527	D₄	semidirect
102. #35527	C₂³	semidirect
103. #34980	D₄	semidirect
105. C₂×#2403	D₄	semidirect
107. #34406	D₄	semidirect
108. #34171	D₄	semidirect
109. C₂×#2309	D₄	semidirect
110. C₂×#2309	D₄	semidirect
111. C₂×#2309	C₂³	semidirect
112. C₂×#2297	D₄	semidirect
113. #32900	C₂³	semidirect
114. #32898	C₂³	semidirect
115. #32898	C₂³	semidirect
116. #32898	C₂³	semidirect
117. C₂×#1781	C₂³	semidirect
118. C₂×#1781	C₂³	semidirect
119. #13082	C₂³	semidirect
120. #13082	C₂³	semidirect
121. #13082	C₂³	semidirect
122. #13080	C₂³	semidirect
123. #12696	C₂³	semidirect
124. #12696	C₂³	semidirect
125. #10989	C₂³	semidirect
126. #10989	C₂³	semidirect
128. #10981	C₂³	semidirect
129. #9501	C₂³	semidirect
130. #9497	C₂³	semidirect
131. #9497	C₂³	semidirect
132. #9497	C₂³	semidirect
135. #8546	C₂³	semidirect
136. #8546	C₂³	semidirect
140. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
141. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
142. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
143. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
153. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
154. C₂×#560	C₂×D₄	semidirect
155. C₂×#551	C₂×D₄	semidirect
156. C₂×D₄²	C₂×D₄	semidirect
164. C₂×#534	C₂×D₄	semidirect
177. C₂×#518	C₂×D₄	semidirect
181. #2717	C₂×D₄	semidirect
182. #2709	C₂×D₄	semidirect
183. #2684	C₂×D₄	semidirect
184. #2684	C₂×D₄	semidirect
185. #2684	C₂×D₄	semidirect
186. #2669	C₂×D₄	semidirect
187. #2669	C₂×D₄	semidirect
188. #2669	C₂×D₄	semidirect
191. #2405	C₂×D₄	semidirect
192. #2405	C₂×D₄	semidirect
204. #2403	C₂×D₄	semidirect
205. #2403	C₂×D₄	semidirect
209. #2380	C₂×D₄	semidirect
210. #2379	C₂×D₄	semidirect
211. #2372	C₂×D₄	semidirect
212. #2366	C₂×D₄	semidirect
216. #2309	C₂×D₄	semidirect
217. #2309	C₂×D₄	semidirect
218. #2309	C₂×D₄	semidirect
219. #2309	C₂×D₄	semidirect
220. #2309	C₂×D₄	semidirect
223. #2308	C₂×D₄	semidirect
224. #2297	C₂×D₄	semidirect
225. #2297	C₂×D₄	semidirect
226. #2297	C₂×D₄	semidirect
227. #2297	C₂×D₄	semidirect
342. C₂×#41	B(4,𝔽₂)	semidirect
383. C₂×Q₈	C₂×B(4,𝔽₂)	semidirect
384. C₂×D₄	C₂×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
#72338886	2
C₂×#449492	2
C₂×#133308	2
#72338721	2
#72266169	2
#72266070	2
#72262289	2
#72262266	2
#72256800	2
#72236108	2
#72235270	2
C₂×#245233	2
#72213244	2
#72210498	2