Subgroups — #72266128

Order 4096.

At least 12447 conjugacy classes of subgroups; only the 1511 normal subgroups are shown.

The subgroup lattice has 410 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266122	C₂	1	2	yes	maximal, complemented
2	#72266117	C₂	1	2	yes	maximal, complemented
3	#72266116	C₂	1	4	yes	maximal, complemented
4	#72266106	C₂	1	2	yes	maximal, complemented
5	#72266096	C₂	1	4	yes	maximal, complemented
6	#72266095	C₂²	1	4	yes	complemented
7	#72266092	C₂	1	4	yes	maximal, complemented
8	#72266085	C₂	1	1	yes	maximal, characteristic, complemented
9	#72266082	C₂²	1	4	yes	complemented
10	#72266081	C₂²	1	2	yes	complemented
11	#72266079	C₂²	1	4	yes	complemented
12	#72266079	C₂²	1	2	yes	complemented
13	#72266077	C₂²	1	4	yes	complemented
14	#72266074	C₂²	1	2	yes	complemented
15	#72266073	C₂²	1	4	yes	complemented
16	#72266046	C₂	1	2	yes	maximal, complemented
17	#72266035	C₂²	1	4	yes	complemented
18	#72266030	C₂²	1	2	yes	complemented
19	#72266030	C₂²	1	2	yes	complemented
20	#72266017	C₂	1	4	yes	maximal, complemented
21	#72266011	C₂²	1	4	yes	complemented
22	#72266011	C₂²	1	4	yes	complemented
23	#72262702	C₂	1	1	yes	maximal, characteristic, complemented
24	#72262701	C₂²	1	1	yes	characteristic, complemented
25	#72262637	C₂²	1	1	yes	characteristic, complemented
26	#72261893	C₂²	1	4	yes	complemented
27	#72259008	C₂²	1	4	yes	complemented
28	#72259008	C₂²	1	2	yes	complemented
29	#72258662	C₂	1	2	yes	maximal, complemented
30	#72258649	C₂²	1	2	yes	complemented
31	#72258626	C₂²	1	4	yes	complemented
32	#72258613	C₂²	1	4	yes	complemented
33	#72258613	C₂²	1	2	yes	complemented
34	C₂²×#10336	C₂²	1	2	yes	complemented
35	C₂²×#10336	C₂²	1	4	yes	complemented
36	#72241125	C₂²	1	2	yes	complemented
37	#72240619	C₂²	1	2	yes	complemented
38	#72238531	C₂²	1	4	yes	complemented
39	C₂×#72233348	C₂	1	1	yes	maximal, characteristic, complemented
40	C₂×#233541	C₂²	1	2	yes	—
41	C₂×#233541	C₂²	1	2	yes	—
42	C₂×#233541	C₂²	1	4	yes	complemented
43	C₂×#233541	C₂²	1	4	yes	complemented
44	C₂×#233541	C₂²	1	4	yes	complemented
45	C₂×#233541	C₂²	1	2	yes	complemented
46	C₂×#201664	C₂²	1	4	yes	complemented
47	#72234749	C₂	1	2	yes	maximal, complemented
48	#72234689	C₂²	1	4	yes	complemented
49	#72234675	C₂²	1	1	yes	characteristic
50	#72234668	C₂²	1	4	yes	complemented
51	#72234668	C₂²	1	1	yes	characteristic, complemented
52	#72234629	C₂²	1	4	yes	—
53	#72234629	C₂²	1	4	yes	—
54	#72234629	C₂²	1	4	yes	complemented
55	#72234625	C₂²	1	1	yes	characteristic, complemented
56	#72234625	C₂²	1	4	yes	complemented
57	C₂×#6628892	C₂²	1	4	yes	complemented
58	#72233780	C₂²	1	2	yes	complemented
59	#72225801	C₂²	1	4	yes	complemented
60	#72225796	C₂²	1	4	yes	complemented
61	#72225783	C₂²	1	2	yes	complemented
62	C₂×#188035	C₂²	1	1	yes	characteristic
63	#72225665	C₂²	1	1	yes	characteristic
64	#72219307	C₂²	1	2	yes	—
65	C₂×#7631286	C₂²	1	2	yes	—
66	C₂²×#32898	C₂²	1	4	yes	complemented
67	C₂⁴×H(5,𝔽₂)	C₂³	1	2	yes	—
68	C₂×#62817	C₂³	1	1	yes	characteristic
69	C₂³×D₄²	C₂³	1	1	yes	characteristic
70	C₂×#34980	C₂³	1	4	yes	—
71	C₂×#34980	C₂³	1	1	yes	characteristic
72	C₂×#34980	C₂³	1	4	yes	—
73	C₂×#34980	C₂³	1	2	yes	—
74	C₂×#34980	C₂³	1	4	yes	—
75	C₂×#34980	C₂³	1	4	yes	—
76	C₂²×#2403	C₂³	1	4	yes	—
77	C₂²×#2403	C₂³	1	2	yes	—
78	C₂²×#2403	C₂³	1	2	yes	—
79	C₂²×#2403	C₂³	1	4	yes	—
80	C₂²×#2403	C₂³	1	2	yes	—
81	#7626202	C₂³	1	1	yes	characteristic
82	C₂×#34171	C₂³	1	2	yes	—
83	C₂×#21746	C₂³	1	2	yes	—
84	C₂×#21746	C₂³	1	4	yes	—
85	C₂×#21746	C₂³	1	4	yes	—
86	C₂×#21746	C₂³	1	4	yes	—
87	C₂×#21746	C₂³	1	1	yes	characteristic
88	C₂×#21746	C₂³	1	1	yes	characteristic
89	C₂×#21746	C₂³	1	4	yes	—
90	C₂²×#1781	C₂³	1	4	yes	—
91	C₂²×#1781	C₂³	1	4	yes	—
92	C₂²×#1781	C₂³	1	2	yes	—
93	C₂²×#1781	C₂³	1	4	yes	—
94	C₂²×#1781	C₂³	1	4	yes	—
95	C₂²×#1781	C₂³	1	4	yes	—
96	C₂²×#1781	C₂³	1	4	yes	—
97	C₂²×#1781	C₂³	1	4	yes	—
98	C₂²×#1781	C₂³	1	4	yes	—
99	C₂²×#1781	C₂³	1	4	yes	—
100	#556752	C₂³	1	1	yes	characteristic
101	#517411	C₂³	1	4	yes	—
102	#517411	C₂³	1	2	yes	—
103	#517411	C₂³	1	2	yes	—
104	#517411	C₂³	1	2	yes	—
105	#513778	C₂³	1	2	yes	—
106	#405104	D₄	1	16	yes	complemented
107	#393929	D₄	1	16	yes	complemented
108	#392245	D₄	1	4	yes	complemented
109	#392109	D₄	1	4	yes	complemented
110	#382422	D₄	1	4	yes	complemented
111	#382390	D₄	1	4	yes	complemented
112	#355913	C₂³	1	4	yes	—
113	#355913	C₂³	1	4	yes	—
114	#355913	C₂³	1	2	yes	—
115	#355913	C₂³	1	4	yes	—
116	#355913	C₂³	1	2	yes	—
117	#355913	C₂³	1	4	yes	—
118	#233541	D₄	1	16	yes	complemented
119	C₂×#8546	D₄	1	2	yes	complemented
120	C₂×#8542	D₄	1	4	yes	complemented
121	C₂×#8541	D₄	1	2	yes	complemented
122	C₂×#8101	C₂³	1	2	yes	—
123	C₂×#8101	C₂³	1	4	yes	—
124	C₂×#8101	C₂³	1	4	yes	—
125	C₂×#8101	C₂³	1	4	yes	—
126	C₂×#8101	C₂³	1	2	yes	—
127	C₂×#8101	C₂³	1	2	yes	—
128	C₂²×#1304	C₂³	1	2	yes	—
129	C₂²×#1304	C₂³	1	4	yes	—
130	C₂⁵×D₄	C₂×D₄	1	2	yes	—
131	C₂⁵×D₄	C₂⁴	1	2	yes	—
132	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
133	C₂⁵×D₄	C₂⁴	1	4	yes	—
134	C₂²×#534	C₂×D₄	1	8	yes	complemented
135	C₂³×#127	C₂×D₄	1	1	yes	characteristic
136	C₂³×#121	C₂×D₄	1	2	yes	—
137	C₂³×#121	C₂×D₄	1	2	yes	—
138	C₂³×#120	C₂×D₄	1	2	yes	—
139	C₂³×#120	C₂×D₄	1	1	yes	characteristic
140	C₂³×#120	C₂⁴	1	1	yes	characteristic
141	C₂³×#120	C₂⁴	1	2	yes	—
142	C₂³×C₄×D₄	C₂×D₄	1	2	yes	—
143	#34980	C₂×D₄	1	16	yes	—
144	C₂×#2405	C₂×D₄	1	8	yes	—
145	C₂×#2403	C₂×D₄	1	16	yes	—
146	C₂×#2403	C₂×D₄	1	8	yes	—
147	C₂×#2403	C₂×D₄	1	8	yes	complemented
148	C₂×#2308	C₂×D₄	1	8	yes	complemented
149	C₂²×#379	C₂⁴	1	2	yes	—
150	C₂²×#379	C₂⁴	1	4	yes	—
151	C₂²×#379	C₂⁴	1	1	yes	characteristic
152	C₂²×#379	C₂⁴	1	2	yes	—
153	C₂²×#379	C₂⁴	1	4	yes	—
154	C₂²×#379	C₂⁴	1	2	yes	—
155	C₂²×#379	C₂⁴	1	4	yes	—
156	C₂²×#379	C₂⁴	1	2	yes	—
157	#21746	C₂×D₄	1	8	yes	—
158	C₂×#1819	C₂×D₄	1	8	yes	—
159	C₂×#1819	C₂×D₄	1	2	yes	—
160	C₂×#1819	C₂×D₄	1	2	yes	—
161	C₂×#1819	C₂×D₄	1	8	yes	complemented
162	C₂×#1781	C₂×D₄	1	8	yes	—
163	C₂×#1781	C₂×D₄	1	8	yes	—
164	C₂×#1781	C₂×D₄	1	8	yes	—
165	C₂×#1781	C₂×D₄	1	8	yes	—
166	C₂×#1781	C₂×D₄	1	8	yes	—
167	C₂×#1781	C₂×D₄	1	2	yes	—
168	C₂×#1781	C₂×D₄	1	2	yes	—
169	C₂×#1781	C₂×D₄	1	8	yes	complemented
170	C₂×#1781	C₂×D₄	1	16	yes	complemented
171	C₂×#1781	C₂×D₄	1	16	yes	complemented
172	#14681	C₂×D₄	1	4	yes	—
173	#14681	C₂×D₄	1	4	yes	—
174	#14679	C₂×D₄	1	4	yes	—
175	#14679	C₂×D₄	1	4	yes	—
176	#13867	C₂×D₄	1	16	yes	—
177	#10725	C₂×D₄	1	16	yes	complemented
178	#8101	C₂×D₄	1	8	yes	complemented
179	C₂⁷	#127	1	1	yes	characteristic, complemented
180	C₂⁷	C₂²×D₄	1	2	yes	—
181	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂⁷	H(5,𝔽₂)	1	4	yes	—
183	C₂⁷	C₂⁵	1	1	yes	characteristic
184	C₂⁴×D₄	#127	1	2	yes	complemented
185	C₂⁴×D₄	#127	1	2	yes	complemented
186	C₂⁴×D₄	#127	1	1	yes	characteristic, complemented
187	C₂⁴×D₄	C₂²×D₄	1	8	yes	—
188	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
189	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
190	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
191	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
192	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
193	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
194	C₂⁴×D₄	C₂²×D₄	1	8	yes	—
195	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
196	C₂⁴×D₄	C₂²×D₄	1	8	yes	—
197	C₂⁴×D₄	H(5,𝔽₂)	1	8	yes	—
198	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
199	C₂⁵×C₄	#127	1	2	yes	complemented
200	C₂⁵×C₄	C₂²×D₄	1	2	yes	—
201	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂⁵×C₄	H(5,𝔽₂)	1	4	yes	—
203	C₂²×#120	C₂²×D₄	1	4	yes	—
204	C₂²×#120	H(5,𝔽₂)	1	4	yes	—
205	C₂³×C₄⋊C₄	#127	1	2	yes	complemented
206	C₂³×C₂²⋊C₄	#127	1	2	yes	complemented
207	C₂³×C₂²⋊C₄	#127	1	2	yes	complemented
208	C₂³×C₂²⋊C₄	#127	1	1	yes	characteristic, complemented
209	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
210	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
211	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
212	C₂³×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
213	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
214	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
215	C₂³×C₄²	#127	1	1	yes	characteristic, complemented
216	C₂×#379	#120	1	16	yes	complemented
217	C₂×#379	C₂²×D₄	1	4	yes	—
218	C₂×#379	C₂²×D₄	1	8	yes	—
219	C₂×#379	C₂²×D₄	1	4	yes	—
220	C₂×#379	C₂²×D₄	1	4	yes	—
221	C₂×#379	C₂²×D₄	1	4	yes	—
222	C₂×#379	C₂²×D₄	1	8	yes	—
223	C₂×#379	C₂²×D₄	1	8	yes	—
224	C₂×#379	C₂²×D₄	1	8	yes	—
225	C₂×#379	C₂²×D₄	1	8	yes	—
226	C₂×#379	C₂²×D₄	1	8	yes	—
227	C₂×#379	H(5,𝔽₂)	1	2	yes	—
228	C₂×#379	H(5,𝔽₂)	1	8	yes	—
229	C₂×#379	H(5,𝔽₂)	1	4	yes	—
230	#1819	#120	1	8	yes	complemented
231	#1781	#120	1	8	yes	complemented
232	C₂²⋊#95	#120	1	16	yes	complemented
233	C₂⁶	C₂×#120	1	4	yes	—
234	C₂⁶	C₂×#127	1	2	yes	—
235	C₂⁶	C₂×#127	1	2	yes	—
236	C₂⁶	C₂×#127	1	1	yes	characteristic
237	C₂⁶	#535	1	4	yes	—
238	C₂⁶	D₄²	1	8	yes	—
239	C₂⁶	D₄²	1	2	yes	—
240	C₂⁶	C₂³×D₄	1	2	yes	—
241	C₂⁶	C₂³×D₄	1	4	yes	—
242	C₂⁶	C₂³×D₄	1	1	yes	characteristic
243	C₂⁶	C₂³×D₄	1	2	yes	—
244	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
245	C₂⁶	C₂×H(5,𝔽₂)	1	4	yes	—
246	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
247	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
248	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
249	C₂⁶	C₂×H(5,𝔽₂)	1	4	yes	—
250	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
251	C₂⁶	C₂×H(5,𝔽₂)	1	4	yes	—
252	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
253	C₂³×D₄	C₂×#120	1	2	yes	—
254	C₂³×D₄	#535	1	2	yes	—
255	C₂³×D₄	D₄²	1	8	yes	—
256	C₂³×D₄	D₄²	1	8	yes	—
257	C₂³×D₄	D₄²	1	8	yes	—
258	C₂³×D₄	D₄²	1	8	yes	—
259	C₂³×D₄	D₄²	1	8	yes	—
260	C₂⁴×C₄	C₂×#120	1	4	yes	—
261	C₂⁴×C₄	C₂×#127	1	2	yes	—
262	C₂⁴×C₄	C₂×#127	1	2	yes	—
263	C₂⁴×C₄	C₂×#127	1	2	yes	—
264	C₂⁴×C₄	C₂×#127	1	1	yes	characteristic
265	C₂⁴×C₄	#535	1	4	yes	—
266	C₂⁴×C₄	D₄²	1	8	yes	—
267	C₂⁴×C₄	D₄²	1	4	yes	—
268	C₂⁴×C₄	D₄²	1	2	yes	—
269	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
270	C₂²×C₂²⋊C₄	C₂×#120	1	16	yes	—
271	C₂²×C₂²⋊C₄	#535	1	2	yes	—
272	C₂²×C₂²⋊C₄	D₄²	1	8	yes	—
273	#379	C₂×#120	1	8	yes	—
274	#379	D₄²	1	16	yes	—
275	#379	D₄²	1	8	yes	—
276	C₂⁵	#2433	1	4	yes	—
277	C₂⁵	#2433	1	4	yes	—
278	C₂⁵	#2433	1	2	yes	—
279	C₂⁵	C₂²×#120	1	2	yes	—
280	C₂⁵	C₂²×#120	1	1	yes	characteristic
281	C₂⁵	C₂²×#127	1	1	yes	characteristic
282	C₂⁵	C₂×#535	1	2	yes	—
283	C₂⁵	C₂×#535	1	1	yes	characteristic
284	C₂⁵	C₂×D₄²	1	4	yes	—
285	C₂⁵	C₂×D₄²	1	2	yes	—
286	C₂⁵	C₂×D₄²	1	2	yes	—
287	C₂⁵	C₂×D₄²	1	4	yes	—
288	C₂⁵	C₂×D₄²	1	4	yes	—
289	C₂⁵	C₂×D₄²	1	4	yes	—
290	C₂⁵	C₂×D₄²	1	4	yes	—
291	C₂⁵	#3484	1	4	yes	—
292	C₂⁵	#3484	1	2	yes	—
293	C₂⁵	#3484	1	2	yes	—
294	C₂⁵	#3484	1	4	yes	—
295	C₂⁵	#3484	1	4	yes	—
296	C₂⁵	#3484	1	4	yes	—
297	C₂⁵	#3484	1	4	yes	—
298	C₂⁵	#3484	1	4	yes	—
299	C₂⁵	#3484	1	2	yes	—
300	C₂⁵	#3484	1	1	yes	characteristic
301	C₂⁵	#3484	1	2	yes	—
302	C₂⁵	#3484	1	2	yes	—
303	C₂⁵	#3484	1	1	yes	characteristic
304	C₂⁵	#3484	1	4	yes	—
305	C₂⁵	#3484	1	4	yes	—
306	C₂⁵	#3484	1	4	yes	—
307	C₂⁵	#3484	1	4	yes	—
308	C₂⁵	#3484	1	1	yes	characteristic
309	C₂⁵	#3484	1	1	yes	characteristic
310	C₂⁵	#3484	1	4	yes	—
311	C₂⁵	#3484	1	2	yes	—
312	C₂⁵	#3498	1	4	yes	—
313	C₂⁵	#3498	1	4	yes	—
314	C₂⁵	#3498	1	4	yes	—
315	C₂⁵	#3532	1	2	yes	—
316	C₂⁵	#3532	1	4	yes	—
317	C₂⁵	#3532	1	2	yes	—
318	C₂⁵	#3532	1	4	yes	—
319	C₂⁵	#3532	1	2	yes	—
320	C₂⁵	#3537	1	2	yes	—
321	C₂⁵	#3537	1	4	yes	—
322	C₂⁵	#3537	1	4	yes	—
323	C₂⁵	#3537	1	2	yes	—
324	C₂⁵	#3537	1	4	yes	—
325	C₂⁵	#3537	1	4	yes	—
326	C₂⁵	#3537	1	4	yes	—
327	C₂⁵	#3537	1	4	yes	—
328	C₂⁵	#3537	1	2	yes	—
329	C₂⁵	#3543	1	4	yes	—
330	C₂⁵	#3543	1	2	yes	—
331	C₂⁵	#3549	1	2	yes	—
332	C₂³×C₄	#2433	1	4	yes	—
333	C₂³×C₄	#2433	1	4	yes	—
334	C₂³×C₄	#2433	1	2	yes	—
335	C₂³×C₄	#2433	1	4	yes	—
336	C₂⁴	C₂×#2433	1	2	yes	—
337	C₂⁴	C₂×#2433	1	1	yes	characteristic
338	C₂⁴	#35346	1	1	yes	characteristic
339	C₂⁴	#35346	1	2	yes	—
340	C₂⁴	#35390	1	1	yes	characteristic
341	C₂⁴	#35390	1	2	yes	—
342	C₂⁴	#35390	1	1	yes	characteristic
343	C₂⁴	#35527	1	2	yes	—
344	C₂⁴	#35527	1	1	yes	characteristic
345	C₂⁴	D₄×#120	1	4	yes	—
346	C₂⁴	D₄×#120	1	4	yes	—
347	C₂⁴	D₄×#120	1	4	yes	—
348	C₂⁴	#36717	1	2	yes	—
349	C₂⁴	#36717	1	2	yes	—
350	C₂⁴	#36717	1	1	yes	characteristic
351	C₂⁴	#36717	1	1	yes	characteristic
352	C₂⁴	#37645	1	4	yes	—
353	C₂⁴	#37645	1	4	yes	—
354	C₂⁴	#37645	1	4	yes	—
355	C₂⁴	#43001	1	4	yes	—
356	C₂⁴	#43001	1	4	yes	—
357	C₂⁴	#43001	1	4	yes	—
358	C₂⁴	#43001	1	4	yes	—
359	C₂⁴	#43001	1	4	yes	—
360	C₂⁴	#43001	1	4	yes	—
361	C₂⁴	#43001	1	4	yes	—
362	C₂⁴	#43001	1	4	yes	—
363	C₂⁴	#43001	1	4	yes	—
364	C₂⁴	#44870	1	2	yes	—
365	C₂⁴	#44870	1	4	yes	—
366	C₂⁴	#45355	1	2	yes	—
367	C₂⁴	#45355	1	4	yes	—
368	C₂⁴	#47827	1	4	yes	—
369	C₂⁴	#47827	1	4	yes	—
370	C₂⁴	#47827	1	2	yes	—
371	C₂⁴	#47827	1	2	yes	—
372	C₂⁴	#47942	1	4	yes	—
373	C₂⁴	#47942	1	4	yes	—
374	C₂⁴	#47942	1	4	yes	—
375	C₂⁴	#49545	1	4	yes	—
376	C₂⁴	#49545	1	2	yes	—
377	C₂⁴	#52004	1	4	yes	—
378	C₂⁴	#52004	1	2	yes	—
379	C₂⁴	#56346	1	4	yes	—
380	C₂⁴	#56346	1	2	yes	—
381	C₂⁴	#58260	1	2	yes	—
382	C₂⁴	#58990	1	2	yes	—
383	C₂⁴	#58990	1	4	yes	—
384	C₂⁴	#58990	1	4	yes	—
385	C₂⁴	#58990	1	2	yes	—
386	C₂⁴	#58990	1	2	yes	—
387	C₂⁴	#59126	1	4	yes	—
388	C₂⁴	#59126	1	2	yes	—
389	C₂³	#648360	1	2	yes	—
390	C₂³	#648360	1	1	yes	characteristic
391	C₂³	#763814	1	1	yes	characteristic
392	C₂³	#763814	1	2	yes	—
393	C₂³	#1418363	1	2	yes	—
394	C₂³	#1418363	1	4	yes	—
395	C₂³	#1418385	1	2	yes	—
396	C₂³	#1418385	1	4	yes	—
397	C₂³	#2805677	1	4	yes	—
398	C₂³	#2805677	1	2	yes	—
399	C₂³	#2805719	1	4	yes	—
400	C₂³	#2805719	1	2	yes	—
401	C₂³	#5024691	1	1	yes	characteristic
402	C₂³	#6499874	1	8	yes	—
403	C₂²	#72225634	1	8	yes	—
404	C₂²	#72225644	1	4	yes	—
405	C₂²	#72237724	1	2	yes	—
406	C₂²	#72264994	1	1	yes	characteristic
407	C₂	#72265819	1	2	yes	—
408	C₂	#72265890	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72264994
commutator, Frattini, cosocle	C₂⁷	C₂⁵
LCS	G ▷ C₂⁷ ▷ 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. #72266122	C₂	semidirect
2. #72266117	C₂	semidirect
3. #72266116	C₂	semidirect
4. #72266106	C₂	semidirect
5. #72266096	C₂	semidirect
6. #72266095	C₂²	semidirect
7. #72266092	C₂	semidirect
8. #72266085	C₂	semidirect
9. #72266082	C₂²	semidirect
10. #72266081	C₂²	semidirect
11. #72266079	C₂²	semidirect
12. #72266079	C₂²	semidirect
13. #72266077	C₂²	semidirect
14. #72266074	C₂²	semidirect
15. #72266073	C₂²	semidirect
16. #72266046	C₂	semidirect
17. #72266035	C₂²	semidirect
18. #72266030	C₂²	semidirect
19. #72266030	C₂²	semidirect
20. #72266017	C₂	semidirect
21. #72266011	C₂²	semidirect
22. #72266011	C₂²	semidirect
23. #72262702	C₂	semidirect
24. #72262701	C₂²	semidirect
25. #72262637	C₂²	semidirect
26. #72261893	C₂²	semidirect
27. #72259008	C₂²	semidirect
28. #72259008	C₂²	semidirect
29. #72258662	C₂	semidirect
30. #72258649	C₂²	semidirect
31. #72258626	C₂²	semidirect
32. #72258613	C₂²	semidirect
33. #72258613	C₂²	semidirect
34. C₂²×#10336	C₂²	semidirect
35. C₂²×#10336	C₂²	semidirect
36. #72241125	C₂²	semidirect
37. #72240619	C₂²	semidirect
38. #72238531	C₂²	semidirect
39. C₂×#72233348	C₂	semidirect
42. C₂×#233541	C₂²	semidirect
43. C₂×#233541	C₂²	semidirect
44. C₂×#233541	C₂²	semidirect
45. C₂×#233541	C₂²	semidirect
46. C₂×#201664	C₂²	semidirect
47. #72234749	C₂	semidirect
48. #72234689	C₂²	semidirect
50. #72234668	C₂²	semidirect
51. #72234668	C₂²	semidirect
54. #72234629	C₂²	semidirect
55. #72234625	C₂²	semidirect
56. #72234625	C₂²	semidirect
57. C₂×#6628892	C₂²	semidirect
58. #72233780	C₂²	semidirect
59. #72225801	C₂²	semidirect
60. #72225796	C₂²	semidirect
61. #72225783	C₂²	semidirect
66. C₂²×#32898	C₂²	semidirect
106. #405104	D₄	semidirect
107. #393929	D₄	semidirect
108. #392245	D₄	semidirect
109. #392109	D₄	semidirect
110. #382422	D₄	semidirect
111. #382390	D₄	semidirect
118. #233541	D₄	semidirect
119. C₂×#8546	D₄	semidirect
120. C₂×#8542	D₄	semidirect
121. C₂×#8541	D₄	semidirect
134. C₂²×#534	C₂×D₄	semidirect
147. C₂×#2403	C₂×D₄	semidirect
148. C₂×#2308	C₂×D₄	semidirect
161. C₂×#1819	C₂×D₄	semidirect
169. C₂×#1781	C₂×D₄	semidirect
170. C₂×#1781	C₂×D₄	semidirect
171. C₂×#1781	C₂×D₄	semidirect
177. #10725	C₂×D₄	semidirect
178. #8101	C₂×D₄	semidirect
179. C₂⁷	#127	semidirect
184. C₂⁴×D₄	#127	semidirect
185. C₂⁴×D₄	#127	semidirect
186. C₂⁴×D₄	#127	semidirect
199. C₂⁵×C₄	#127	semidirect
205. C₂³×C₄⋊C₄	#127	semidirect
206. C₂³×C₂²⋊C₄	#127	semidirect
207. C₂³×C₂²⋊C₄	#127	semidirect
208. C₂³×C₂²⋊C₄	#127	semidirect
215. C₂³×C₄²	#127	semidirect
216. C₂×#379	#120	semidirect
230. #1819	#120	semidirect
231. #1781	#120	semidirect
232. C₂²⋊#95	#120	semidirect

Maximal subgroups

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

subgroup	index
#72266122	2
#72266117	2
#72266116	2
#72266106	2
#72266096	2
#72266092	2
#72266085	2
#72266046	2
#72266017	2
#72262702	2
#72258662	2
C₂×#72233348	2
#72234749	2