Subgroups — #72331045

Order 2048.

At least 8352 conjugacy classes of subgroups; only the 964 normal subgroups are shown.

The subgroup lattice has 424 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72309373	C₂	1	2	yes	maximal, complemented
2	#72309370	C₂	1	2	yes	maximal, complemented
3	#72266073	C₂	1	1	yes	maximal, characteristic, complemented
4	#72266028	C₂	1	1	yes	maximal, characteristic, complemented
5	#72237400	C₂	1	1	yes	maximal, characteristic, complemented
6	#72237398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#359428	C₂	1	1	yes	maximal, characteristic, complemented
8	#72218451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#23900	C₂	1	1	yes	maximal, characteristic
10	#72217666	C₂	1	2	yes	maximal, complemented
11	C₂×#115690	C₂	1	2	yes	maximal, complemented
12	C₂²×#3484	C₂²	1	1	yes	characteristic
13	C₂⁴×#120	C₂²	1	1	yes	characteristic
14	C₂³×B(4,𝔽₂)	C₄	1	2	yes	complemented
15	C₂²×#2846	C₂²	1	2	yes	—
16	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#2021	C₄	1	4	yes	complemented
18	C₂×#21746	C₂²	1	2	yes	—
19	C₂×#21746	C₂²	1	2	yes	—
20	C₂×#21746	C₂²	1	2	yes	—
21	C₂×#21746	C₂²	1	2	yes	—
22	C₂²×#1898	C₂²	1	2	yes	—
23	C₂²×#1889	C₄	1	2	yes	complemented
24	C₂²×#1781	C₂²	1	1	yes	characteristic
25	C₂²×#1781	C₂²	1	1	yes	characteristic
26	C₂²×#1781	C₂²	1	1	yes	characteristic
27	C₂²×#1781	C₂²	1	1	yes	characteristic
28	C₂×#14679	C₂²	1	1	yes	characteristic, complemented
29	C₂×#14679	C₂²	1	2	yes	complemented
30	#517411	C₂²	1	1	yes	characteristic
31	#355913	C₂²	1	2	yes	complemented
32	#355913	C₂²	1	2	yes	complemented
33	C₂×#10735	C₂²	1	2	yes	complemented
34	C₂×#10725	C₂²	1	1	yes	characteristic, complemented
35	C₂×#10725	C₂²	1	1	yes	characteristic, complemented
36	C₂×#8101	C₂²	1	2	yes	complemented
37	C₂×#8101	C₂²	1	2	yes	complemented
38	C₂⁸	C₂³	1	1	yes	characteristic
39	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂⁵×D₄	C₂³	1	1	yes	characteristic
41	C₂²×#534	C₂×C₄	1	2	yes	complemented
42	C₂³×#120	C₂×C₄	1	2	yes	—
43	C₂³×#120	C₂×C₄	1	2	yes	—
44	C₂³×#120	C₂×C₄	1	4	yes	—
45	C₂³×#120	D₄	1	2	yes	—
46	C₂³×#120	D₄	1	4	yes	—
47	C₂³×#120	D₄	1	2	yes	—
48	C₂³×#120	C₂³	1	2	yes	—
49	C₂²×#518	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
51	C₂³×#99	C₂×C₄	1	4	yes	complemented
52	C₂³×#99	C₂×C₄	1	2	yes	complemented
53	C₂³×#99	C₂×C₄	1	2	yes	complemented
54	C₂×#2846	D₄	1	4	yes	—
55	C₂×#2846	D₄	1	4	yes	—
56	C₂×#2846	D₄	1	8	yes	—
57	C₂²×#379	C₂×C₄	1	4	yes	—
58	C₂²×#379	C₂³	1	1	yes	characteristic
59	C₂²×#379	C₂³	1	1	yes	characteristic
60	C₂²×#379	C₂³	1	2	yes	—
61	C₂²×#379	C₂³	1	1	yes	characteristic
62	C₂²×#379	C₂³	1	1	yes	characteristic
63	C₂²×#379	C₂³	1	2	yes	—
64	C₂²×#379	C₂³	1	2	yes	—
65	C₂×#1898	D₄	1	8	yes	complemented
66	C₂×#1819	D₄	1	4	yes	complemented
67	C₂×#1781	D₄	1	4	yes	complemented
68	C₂×#1781	D₄	1	2	yes	complemented
69	C₂×#1781	D₄	1	2	yes	complemented
70	C₂×#1781	D₄	1	4	yes	complemented
71	C₂²×#342	C₂×C₄	1	4	yes	complemented
72	C₂⁷	C₂²×C₄	1	2	yes	—
73	C₂⁷	C₂×D₄	1	1	yes	characteristic
74	C₂⁷	C₂×D₄	1	2	yes	—
75	C₂⁷	C₂×D₄	1	2	yes	—
76	C₂⁷	C₂×D₄	1	1	yes	characteristic
77	C₂⁷	C₂×D₄	1	4	yes	—
78	C₂⁷	C₂×D₄	1	2	yes	—
79	C₂⁷	#41	1	1	yes	characteristic
80	C₂⁷	C₂⁴	1	1	yes	characteristic
81	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
82	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
83	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
84	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
85	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
86	C₂⁴×D₄	C₂×D₄	1	2	yes	—
87	C₂⁴×D₄	C₂×D₄	1	2	yes	—
88	C₂⁴×D₄	C₂×D₄	1	2	yes	—
89	C₂⁴×D₄	C₂×D₄	1	2	yes	—
90	C₂⁴×D₄	#41	1	2	yes	—
91	C₂⁴×D₄	#41	1	2	yes	—
92	C₂⁵×C₄	#41	1	1	yes	characteristic
93	C₂²×#120	C₂²⋊C₄	1	4	yes	—
94	C₂²×#120	C₂²⋊C₄	1	4	yes	—
95	C₂²×#120	C₂²⋊C₄	1	4	yes	—
96	C₂²×#120	C₂²⋊C₄	1	4	yes	—
97	C₂²×#120	C₂²⋊C₄	1	8	yes	complemented
98	C₂²×#120	C₂²⋊C₄	1	8	yes	complemented
99	C₂²×#120	C₂×D₄	1	4	yes	—
100	C₂²×#120	C₂×D₄	1	4	yes	—
101	C₂²×#120	C₂×D₄	1	4	yes	—
102	C₂²×#120	#41	1	4	yes	—
103	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
104	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
105	C₂³×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
106	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
107	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
108	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
109	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
110	C₂³×C₂²⋊C₄	#41	1	2	yes	—
111	C₂×#379	C₂²⋊C₄	1	8	yes	complemented
112	C₂×#379	C₂²⋊C₄	1	8	yes	complemented
113	C₂×#379	C₂×D₄	1	4	yes	—
114	C₂×#379	C₂×D₄	1	2	yes	—
115	C₂×#379	C₂×D₄	1	2	yes	—
116	C₂×#379	C₂×D₄	1	4	yes	—
117	C₂×#379	C₂×D₄	1	4	yes	—
118	C₂×#379	C₂×D₄	1	2	yes	—
119	C₂×#379	C₂×D₄	1	2	yes	—
120	C₂×#379	C₂×D₄	1	4	yes	—
121	C₂×#379	C₂×D₄	1	4	yes	—
122	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
123	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
124	C₂⁶	C₂×C₂²⋊C₄	1	4	yes	—
125	C₂⁶	C₂×C₂²⋊C₄	1	4	yes	—
126	C₂⁶	C₄×D₄	1	1	yes	characteristic
127	C₂⁶	C₄×D₄	1	2	yes	—
128	C₂⁶	C₄×D₄	1	1	yes	characteristic
129	C₂⁶	#120	1	1	yes	characteristic
130	C₂⁶	#120	1	1	yes	characteristic
131	C₂⁶	#120	1	2	yes	—
132	C₂⁶	#120	1	4	yes	—
133	C₂⁶	#120	1	4	yes	—
134	C₂⁶	#120	1	2	yes	—
135	C₂⁶	#120	1	2	yes	—
136	C₂⁶	#121	1	2	yes	—
137	C₂⁶	#123	1	2	yes	—
138	C₂⁶	C₂³×C₄	1	1	yes	characteristic
139	C₂⁶	C₂²×D₄	1	1	yes	characteristic
140	C₂⁶	C₂²×D₄	1	1	yes	characteristic
141	C₂⁶	C₂²×D₄	1	2	yes	—
142	C₂⁶	C₂²×D₄	1	2	yes	—
143	C₂⁶	C₂²×D₄	1	2	yes	—
144	C₂⁶	C₂²×D₄	1	2	yes	—
145	C₂⁶	C₂²×D₄	1	1	yes	characteristic
146	C₂⁶	C₂²×D₄	1	1	yes	characteristic
147	C₂⁶	C₂×#41	1	1	yes	characteristic
148	C₂⁶	C₂×#41	1	2	yes	—
149	C₂⁶	C₂×#41	1	2	yes	—
150	C₂⁶	C₂×#41	1	1	yes	characteristic
151	C₂⁶	H(5,𝔽₂)	1	2	yes	—
152	C₂⁶	H(5,𝔽₂)	1	2	yes	—
153	C₂⁶	H(5,𝔽₂)	1	2	yes	—
154	C₂⁶	H(5,𝔽₂)	1	2	yes	—
155	C₂⁶	H(5,𝔽₂)	1	2	yes	—
156	C₂⁶	H(5,𝔽₂)	1	2	yes	—
157	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂³×D₄	C₄×D₄	1	2	yes	—
161	C₂³×D₄	C₄×D₄	1	2	yes	—
162	C₂³×D₄	C₄×D₄	1	4	yes	—
163	C₂³×D₄	#120	1	2	yes	—
164	C₂³×D₄	#120	1	2	yes	—
165	C₂³×D₄	#120	1	4	yes	—
166	C₂³×D₄	#121	1	2	yes	—
167	C₂³×D₄	#121	1	2	yes	—
168	C₂³×D₄	#121	1	4	yes	—
169	C₂³×D₄	#121	1	4	yes	—
170	C₂³×D₄	#123	1	4	yes	—
171	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
172	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
173	C₂⁴×C₄	C₄×D₄	1	2	yes	—
174	C₂⁴×C₄	C₄×D₄	1	2	yes	—
175	C₂⁴×C₄	C₄×D₄	1	2	yes	—
176	C₂⁴×C₄	#121	1	2	yes	—
177	C₂⁴×C₄	#123	1	2	yes	—
178	C₂×#120	#99	1	16	yes	complemented
179	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
180	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
181	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
182	C₂²×C₂²⋊C₄	C₄×D₄	1	4	yes	—
183	C₂²×C₂²⋊C₄	#120	1	4	yes	—
184	C₂²×C₂²⋊C₄	#121	1	4	yes	—
185	C₂²×C₂²⋊C₄	#121	1	4	yes	—
186	C₂²×C₂²⋊C₄	#123	1	4	yes	—
187	#379	#120	1	4	yes	—
188	#379	#120	1	4	yes	—
189	C₂⁵	#379	1	4	yes	—
190	C₂⁵	#379	1	2	yes	—
191	C₂⁵	#379	1	2	yes	—
192	C₂⁵	#386	1	2	yes	—
193	C₂⁵	#386	1	2	yes	—
194	C₂⁵	#386	1	4	yes	—
195	C₂⁵	C₂×#99	1	8	yes	—
196	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
197	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
198	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂⁵	C₂×C₄×D₄	1	2	yes	—
200	C₂⁵	C₂×C₄×D₄	1	2	yes	—
201	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂⁵	#518	1	2	yes	—
203	C₂⁵	#518	1	2	yes	—
204	C₂⁵	#518	1	2	yes	—
205	C₂⁵	C₂×#120	1	1	yes	characteristic
206	C₂⁵	C₂×#120	1	2	yes	—
207	C₂⁵	C₂×#120	1	2	yes	—
208	C₂⁵	C₂×#120	1	1	yes	characteristic
209	C₂⁵	C₂×#120	1	1	yes	characteristic
210	C₂⁵	C₂×#120	1	1	yes	characteristic
211	C₂⁵	C₂×#120	1	1	yes	characteristic
212	C₂⁵	C₂×#121	1	1	yes	characteristic
213	C₂⁵	C₂×#121	1	1	yes	characteristic
214	C₂⁵	C₂×#121	1	2	yes	—
215	C₂⁵	C₂×#121	1	2	yes	—
216	C₂⁵	C₂×#123	1	1	yes	characteristic
217	C₂⁵	C₂×#123	1	2	yes	—
218	C₂⁵	#525	1	2	yes	—
219	C₂⁵	#525	1	1	yes	characteristic
220	C₂⁵	#525	1	2	yes	—
221	C₂⁵	#525	1	1	yes	characteristic
222	C₂⁵	#534	1	1	yes	characteristic
223	C₂⁵	#534	1	2	yes	—
224	C₂⁵	#534	1	1	yes	characteristic
225	C₂⁵	#534	1	2	yes	—
226	C₂⁵	#534	1	2	yes	—
227	C₂⁵	#534	1	2	yes	—
228	C₂⁵	#534	1	2	yes	—
229	C₂⁵	#534	1	2	yes	—
230	C₂⁵	#534	1	2	yes	—
231	C₂⁵	#534	1	1	yes	characteristic
232	C₂⁵	#534	1	1	yes	characteristic
233	C₂⁵	#535	1	2	yes	—
234	C₂⁵	#535	1	2	yes	—
235	C₂⁵	#535	1	1	yes	characteristic
236	C₂⁵	#535	1	1	yes	characteristic
237	C₂⁵	#538	1	2	yes	—
238	C₂⁵	#538	1	2	yes	—
239	C₂⁵	#538	1	2	yes	—
240	C₂⁵	#538	1	2	yes	—
241	C₂⁵	#538	1	2	yes	—
242	C₂⁵	#538	1	2	yes	—
243	C₂⁵	D₄²	1	2	yes	—
244	C₂⁵	D₄²	1	2	yes	—
245	C₂⁵	D₄²	1	2	yes	—
246	C₂⁵	D₄²	1	2	yes	—
247	C₂⁵	D₄²	1	2	yes	—
248	C₂⁵	D₄²	1	2	yes	—
249	C₂⁵	D₄²	1	2	yes	—
250	C₂⁵	D₄²	1	2	yes	—
251	C₂⁵	D₄²	1	2	yes	—
252	C₂⁵	D₄²	1	2	yes	—
253	C₂⁵	D₄²	1	2	yes	—
254	C₂⁵	D₄²	1	2	yes	—
255	C₂⁵	D₄²	1	2	yes	—
256	C₂⁵	D₄²	1	2	yes	—
257	C₂⁵	D₄²	1	2	yes	—
258	C₂⁵	#546	1	2	yes	—
259	C₂⁵	#546	1	2	yes	—
260	C₂⁵	#546	1	2	yes	—
261	C₂⁵	#546	1	2	yes	—
262	C₂⁵	#546	1	2	yes	—
263	C₂⁵	#546	1	2	yes	—
264	C₂⁵	#546	1	2	yes	—
265	C₂⁵	#546	1	2	yes	—
266	C₂⁵	#546	1	2	yes	—
267	C₂⁵	#546	1	2	yes	—
268	C₂⁵	#546	1	2	yes	—
269	C₂⁵	#546	1	2	yes	—
270	C₂⁵	#546	1	2	yes	—
271	C₂⁵	#546	1	2	yes	—
272	C₂⁵	#546	1	2	yes	—
273	C₂⁵	#546	1	2	yes	—
274	C₂⁵	#546	1	2	yes	—
275	C₂⁵	#546	1	2	yes	—
276	C₂⁵	#551	1	2	yes	—
277	C₂⁵	#551	1	2	yes	—
278	C₂⁵	#551	1	2	yes	—
279	C₂⁵	#560	1	2	yes	—
280	C₂⁵	#560	1	2	yes	—
281	C₂⁵	#560	1	2	yes	—
282	C₂⁵	H(3,𝔽₄)	1	2	yes	—
283	C₂²×D₄	C₂×#99	1	8	yes	—
284	C₂³×C₄	#386	1	2	yes	—
285	C₂³×C₄	#386	1	2	yes	—
286	C₂³×C₄	#386	1	4	yes	—
287	C₂³×C₄	#386	1	4	yes	—
288	C₂³×C₄	#386	1	4	yes	—
289	C₂×C₂²⋊C₄	C₂×#99	1	8	yes	—
290	C₂⁴	#1781	1	4	yes	—
291	C₂⁴	#1781	1	4	yes	—
292	C₂⁴	#1898	1	4	yes	complemented
293	C₂⁴	C₂×#379	1	1	yes	characteristic
294	C₂⁴	C₂×#386	1	2	yes	—
295	C₂⁴	C₂×#386	1	1	yes	characteristic
296	C₂⁴	C₄×#120	1	1	yes	characteristic
297	C₂⁴	C₄×#120	1	1	yes	characteristic
298	C₂⁴	#2308	1	2	yes	—
299	C₂⁴	#2308	1	1	yes	characteristic
300	C₂⁴	#2321	1	2	yes	—
301	C₂⁴	#2321	1	2	yes	—
302	C₂⁴	#2321	1	1	yes	characteristic
303	C₂⁴	#2321	1	1	yes	characteristic
304	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
305	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
306	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
307	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
308	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
309	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
310	C₂⁴	#2358	1	2	yes	—
311	C₂⁴	#2358	1	2	yes	—
312	C₂⁴	#2358	1	2	yes	—
313	C₂⁴	#2375	1	2	yes	—
314	C₂⁴	#2403	1	2	yes	—
315	C₂⁴	#2403	1	2	yes	—
316	C₂⁴	#2403	1	1	yes	characteristic
317	C₂⁴	#2403	1	1	yes	characteristic
318	C₂⁴	#2403	1	2	yes	—
319	C₂⁴	#2403	1	2	yes	—
320	C₂⁴	#2403	1	1	yes	characteristic
321	C₂⁴	#2403	1	1	yes	characteristic
322	C₂⁴	#2404	1	2	yes	—
323	C₂⁴	#2404	1	1	yes	characteristic
324	C₂⁴	#2404	1	1	yes	characteristic
325	C₂⁴	#2404	1	2	yes	—
326	C₂⁴	#2405	1	1	yes	characteristic
327	C₂⁴	#2405	1	2	yes	—
328	C₂⁴	#2405	1	2	yes	—
329	C₂⁴	#2405	1	1	yes	characteristic
330	C₂⁴	#2408	1	1	yes	characteristic
331	C₂⁴	#2408	1	2	yes	—
332	C₂⁴	#2408	1	2	yes	—
333	C₂⁴	#2408	1	1	yes	characteristic
334	C₂⁴	#2410	1	2	yes	—
335	C₂⁴	#2410	1	2	yes	—
336	C₂⁴	#2410	1	2	yes	—
337	C₂⁴	#2410	1	2	yes	—
338	C₂⁴	#2410	1	2	yes	—
339	C₂⁴	#2410	1	2	yes	—
340	C₂⁴	#2418	1	2	yes	—
341	C₂⁴	#2418	1	2	yes	—
342	C₂⁴	#2418	1	2	yes	—
343	C₂⁴	#2418	1	2	yes	—
344	C₂⁴	#2418	1	2	yes	—
345	C₂⁴	#2418	1	2	yes	—
346	C₂⁴	#2424	1	2	yes	—
347	C₂⁴	#2424	1	2	yes	—
348	C₂⁴	#2424	1	2	yes	—
349	C₂⁴	#2424	1	2	yes	—
350	C₂⁴	#2424	1	2	yes	—
351	C₂⁴	#2424	1	2	yes	—
352	C₂⁴	#2534	1	2	yes	—
353	C₂⁴	#2534	1	1	yes	characteristic
354	C₂⁴	#2534	1	1	yes	characteristic
355	C₂⁴	#2534	1	2	yes	—
356	C₂⁴	#2668	1	2	yes	—
357	C₂⁴	#2668	1	2	yes	—
358	C₂⁴	#2668	1	2	yes	—
359	C₂⁴	#2668	1	2	yes	—
360	C₂⁴	#2668	1	2	yes	—
361	C₂⁴	#2668	1	2	yes	—
362	C₂⁴	#2669	1	2	yes	—
363	C₂⁴	#2669	1	2	yes	—
364	C₂⁴	#2669	1	2	yes	—
365	C₂⁴	#2678	1	2	yes	—
366	C₂⁴	#2678	1	2	yes	—
367	C₂⁴	#2678	1	2	yes	—
368	C₂⁴	#2678	1	2	yes	—
369	C₂⁴	#2678	1	2	yes	—
370	C₂⁴	#2678	1	2	yes	—
371	C₂⁴	#2679	1	2	yes	—
372	C₂⁴	#2679	1	2	yes	—
373	C₂⁴	#2679	1	2	yes	—
374	C₂⁴	#2684	1	2	yes	—
375	C₂⁴	#2684	1	2	yes	—
376	C₂⁴	#2684	1	2	yes	—
377	C₂⁴	#2697	1	2	yes	—
378	C₂⁴	#2697	1	2	yes	—
379	C₂⁴	#2697	1	2	yes	—
380	C₂⁴	C₂²×#99	1	4	yes	—
381	C₂⁴	#2883	1	4	yes	—
382	C₂²×C₄	#1898	1	4	yes	complemented
383	C₂³	#13867	1	1	yes	characteristic
384	C₂³	#13867	1	2	yes	—
385	C₂³	#13967	1	2	yes	—
386	C₂³	#13967	1	1	yes	characteristic
387	C₂³	#13967	1	1	yes	characteristic
388	C₂³	#13967	1	2	yes	—
389	C₂³	#14357	1	2	yes	—
390	C₂³	#14357	1	2	yes	—
391	C₂³	#14357	1	2	yes	—
392	C₂³	#15257	1	1	yes	characteristic
393	C₂³	#15257	1	1	yes	characteristic
394	C₂³	#15257	1	2	yes	—
395	C₂³	#15257	1	2	yes	—
396	C₂³	#15266	1	2	yes	—
397	C₂³	#15266	1	2	yes	—
398	C₂³	#15266	1	2	yes	—
399	C₂³	#15947	1	1	yes	characteristic
400	C₂³	#15948	1	1	yes	characteristic
401	C₂³	#15948	1	2	yes	—
402	C₂³	C₂×#1781	1	2	yes	—
403	C₂³	#20585	1	2	yes	—
404	C₂³	C₂×#1898	1	2	yes	—
405	C₂³	#20984	1	2	yes	—
406	C₂³	#21746	1	2	yes	—
407	C₂³	#21749	1	2	yes	—
408	C₂³	D₄×#99	1	8	yes	—
409	C₂³	D₄×#99	1	8	yes	—
410	C₂³	#23996	1	8	yes	—
411	C₂²	#154670	1	1	yes	characteristic
412	C₂²	#359428	1	1	yes	characteristic
413	C₂²	#359434	1	1	yes	characteristic
414	C₂²	#359579	1	4	yes	—
415	C₂²	#364471	1	2	yes	—
416	C₂²	#364471	1	2	yes	—
417	C₂²	#364532	1	4	yes	—
418	C₂²	#383069	1	4	yes	—
419	C₂²	#417538	1	4	yes	—
420	C₂²	#449578	1	4	yes	—
421	C₂	#72225649	1	1	yes	characteristic
422	C₂	#72240550	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#154670
commutator	C₂⁶	C₂³×C₄
Frattini, cosocle	C₂⁷	C₂⁴
prime radical	C₂²×#23900	C₂
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁷ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72309373	C₂	semidirect
2. #72309370	C₂	semidirect
3. #72266073	C₂	semidirect
4. #72266028	C₂	semidirect
5. #72237400	C₂	semidirect
6. #72237398	C₂	semidirect
7. C₂×#359428	C₂	semidirect
8. #72218451	C₂	semidirect
10. #72217666	C₂	semidirect
11. C₂×#115690	C₂	semidirect
14. C₂³×B(4,𝔽₂)	C₄	semidirect
16. C₂³×#379	C₂²	semidirect
17. C₂²×#2021	C₄	semidirect
23. C₂²×#1889	C₄	semidirect
28. C₂×#14679	C₂²	semidirect
29. C₂×#14679	C₂²	semidirect
31. #355913	C₂²	semidirect
32. #355913	C₂²	semidirect
33. C₂×#10735	C₂²	semidirect
34. C₂×#10725	C₂²	semidirect
35. C₂×#10725	C₂²	semidirect
36. C₂×#8101	C₂²	semidirect
37. C₂×#8101	C₂²	semidirect
39. C₂³×H(5,𝔽₂)	C₂×C₄	semidirect
41. C₂²×#534	C₂×C₄	semidirect
49. C₂²×#518	C₂×C₄	semidirect
51. C₂³×#99	C₂×C₄	semidirect
52. C₂³×#99	C₂×C₄	semidirect
53. C₂³×#99	C₂×C₄	semidirect
65. C₂×#1898	D₄	semidirect
66. C₂×#1819	D₄	semidirect
67. C₂×#1781	D₄	semidirect
68. C₂×#1781	D₄	semidirect
69. C₂×#1781	D₄	semidirect
70. C₂×#1781	D₄	semidirect
71. C₂²×#342	C₂×C₄	semidirect
97. C₂²×#120	C₂²⋊C₄	semidirect
98. C₂²×#120	C₂²⋊C₄	semidirect
111. C₂×#379	C₂²⋊C₄	semidirect
112. C₂×#379	C₂²⋊C₄	semidirect
178. C₂×#120	#99	semidirect
292. C₂⁴	#1898	semidirect
382. C₂²×C₄	#1898	semidirect

Maximal subgroups

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

subgroup	index
#72309373	2
#72309370	2
#72266073	2
#72266028	2
#72237400	2
#72237398	2
C₂×#359428	2
#72218451	2
C₂²×#23900	2
#72217666	2
C₂×#115690	2