Subgroups — #38756122

Order 25216.

1160 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161704	C₂	1	1	yes	maximal, characteristic, complemented
2	#27161677	C₂	1	2	yes	maximal, complemented
3	#27161673	C₂	1	2	yes	maximal, complemented
4	#27161670	C₂	1	2	yes	maximal, complemented
5	#27161669	C₂	1	1	yes	maximal, characteristic, complemented
6	#27161668	C₂	1	2	yes	maximal, complemented
7	#27161666	C₂	1	1	yes	maximal, characteristic, complemented
8	#27161663	C₂	1	2	yes	maximal, complemented
9	#27161640	C₂	1	2	yes	maximal, complemented
10	#27161637	C₂	1	1	yes	maximal, characteristic, complemented
11	#27161616	C₂	1	2	yes	maximal, complemented
12	#27161613	C₂	1	1	yes	maximal, characteristic, complemented
13	#27161607	C₂	1	2	yes	maximal, complemented
14	#27161591	C₂	1	2	yes	maximal, complemented
15	#27161588	C₂	1	2	yes	maximal, complemented
16	#27161588	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₇₈₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₁₉₇	C₂	1	2	yes	maximal, complemented
19	#529×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#15691358	C₂²	1	2	yes	complemented
21	C₂²×D₇₈₈	C₂²	1	1	yes	characteristic
22	C₂×D₄×D₁₉₇	C₂²	1	2	yes	—
23	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₉₇	C₂²	1	2	yes	complemented
25	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic, complemented
26	#20263321	C₂²	1	2	yes	complemented
27	#20263321	C₂²	1	2	yes	complemented
28	#20263321	C₂²	1	2	yes	complemented
29	#20263320	C₂²	1	2	yes	complemented
30	#20263319	C₂²	1	2	yes	complemented
31	#20263318	C₂²	1	1	yes	characteristic, complemented
32	#20263317	C₂²	1	2	yes	complemented
33	#20263316	C₂²	1	2	yes	complemented
34	#20263315	C₂²	1	2	yes	complemented
35	#20263314	C₂²	1	1	yes	characteristic, complemented
36	#20263312	C₂²	1	2	yes	complemented
37	#20263311	C₂²	1	2	yes	complemented
38	#20263311	C₂²	1	2	yes	complemented
39	#20263311	C₂²	1	2	yes	complemented
40	#20263311	C₂²	1	2	yes	complemented
41	#20263311	C₂²	1	2	yes	complemented
42	#20263310	C₂²	1	2	yes	complemented
43	#20263310	C₂²	1	2	yes	complemented
44	#20263309	C₂²	1	2	yes	complemented
45	#20263308	C₂²	1	2	yes	complemented
46	#20263308	C₂²	1	2	yes	complemented
47	#20263308	C₂²	1	2	yes	complemented
48	#20263306	C₂²	1	2	yes	complemented
49	#20263306	C₂²	1	2	yes	complemented
50	#20263305	C₂²	1	1	yes	characteristic, complemented
51	#20263304	C₂²	1	2	yes	complemented
52	#20263304	C₂²	1	2	yes	complemented
53	#20263304	C₂²	1	2	yes	complemented
54	#20263303	C₂²	1	2	yes	complemented
55	#20263303	C₂²	1	2	yes	complemented
56	#20263302	C₂²	1	2	yes	complemented
57	#20263301	C₂²	1	2	yes	—
58	#20263301	C₂²	1	2	yes	—
59	#20263301	C₂²	1	2	yes	complemented
60	#20263300	C₂²	1	1	yes	characteristic
61	#20263299	C₂²	1	2	yes	—
62	#20263299	C₂²	1	2	yes	—
63	#20263299	C₂²	1	2	yes	complemented
64	#20263298	C₂²	1	2	yes	—
65	#20263298	C₂²	1	2	yes	complemented
66	#20263296	C₂²	1	2	yes	complemented
67	#20263296	C₂²	1	2	yes	complemented
68	#20263296	C₂²	1	2	yes	complemented
69	#20263296	C₂²	1	2	yes	complemented
70	#20263294	C₂²	1	2	yes	complemented
71	#20263294	C₂²	1	2	yes	complemented
72	C₄×Dic₃₉₄	C₂²	1	1	yes	characteristic, complemented
73	C₄×D₇₈₈	C₂²	1	2	yes	complemented
74	C₄×D₇₈₈	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₇₈₈	C₂²	1	2	yes	complemented
76	C₄×D₇₈₈	C₂²	1	2	yes	complemented
77	C₄×D₇₈₈	C₂²	1	2	yes	complemented
78	C₄×D₇₈₈	C₂²	1	2	yes	complemented
79	C₄×D₇₈₈	C₂²	1	2	yes	complemented
80	D₄×Dic₁₉₇	C₂²	1	2	yes	complemented
81	#20263288	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₁₉₇	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊D₁₉₇	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₁₉₇	C₂²	1	2	yes	complemented
85	#20263286	C₂²	1	2	yes	complemented
86	#20263286	C₂²	1	2	yes	complemented
87	#20263283	C₂²	1	2	yes	complemented
88	#20263283	C₂²	1	2	yes	complemented
89	C₂×C₄⋊Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×D₁₉₇	C₂²	1	2	yes	complemented
91	C₂×#15691335	C₂²	1	1	yes	characteristic
92	C₂×#15691335	C₂²	1	1	yes	characteristic, complemented
93	C₂²⋊C₄×D₁₉₇	C₂²	1	2	yes	—
94	C₂²⋊C₄×D₁₉₇	C₂²	1	2	yes	complemented
95	C₄²×D₁₉₇	C₂²	1	2	yes	complemented
96	#126×C₁₉₇	C₂²	1	2	yes	complemented
97	#125×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
98	#124×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
99	#123×C₁₉₇	C₂²	1	2	yes	complemented
100	C₂²⋊Q₈×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
101	#121×C₁₉₇	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₄×C₁₉₇	C₂²	1	2	yes	complemented
104	C₄×D₄×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
105	#117×C₁₉₇	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₉₇	C₂³	1	2	yes	—
108	C₂³×D₁₉₇	C₂³	1	1	yes	characteristic
109	C₂³×D₁₉₇	C₂³	1	1	yes	characteristic
110	#15691358	—	4	4	no	—
111	C₂×Dic₃₉₄	C₂³	1	1	yes	characteristic
112	C₂×Dic₃₉₄	C₂³	1	2	yes	—
113	C₂×D₇₈₈	—	2	4	no	—
114	C₂×D₇₈₈	C₂³	1	2	yes	—
115	C₂×D₇₈₈	C₂³	1	2	yes	—
116	C₂×D₇₈₈	C₂³	1	2	yes	—
117	C₂×D₇₈₈	C₂³	1	2	yes	—
118	C₂×D₇₈₈	C₂³	1	1	yes	characteristic
119	C₂×D₇₈₈	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
125	D₄×D₁₉₇	—	2	8	no	—
126	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
127	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
128	C₂²×Dic₁₉₇	C₂³	1	2	yes	—
129	C₂×C₄×D₁₉₇	—	4	2	no	—
130	C₂×C₄×D₁₉₇	—	4	2	no	—
131	C₂×C₄×D₁₉₇	—	4	4	no	—
132	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
133	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
134	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
135	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
136	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
137	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
138	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
139	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
140	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
141	C₄⋊Dic₁₉₇	C₂³	1	2	yes	—
142	C₄⋊Dic₁₉₇	C₂³	1	2	yes	—
143	C₄⋊Dic₁₉₇	C₂³	1	2	yes	—
144	C₄⋊Dic₁₉₇	C₂³	1	2	yes	—
145	C₄⋊Dic₁₉₇	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₉₇	C₂³	1	1	yes	characteristic
147	#15691337	C₂³	1	2	yes	—
148	#15691337	C₂³	1	2	yes	—
149	#15691337	C₂³	1	2	yes	—
150	#15691337	C₂³	1	2	yes	—
151	#15691337	C₂³	1	2	yes	—
152	#15691337	C₂³	1	2	yes	—
153	#15691337	C₂³	1	2	yes	—
154	#15691337	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₉₇	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₉₇	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₉₇	C₂³	1	2	yes	—
158	#15691335	C₂³	1	2	yes	—
159	#15691335	C₂³	1	2	yes	—
160	#15691335	C₂³	1	2	yes	—
161	#15691335	C₂³	1	2	yes	—
162	#15691335	C₂³	1	2	yes	—
163	#15691335	C₂³	1	2	yes	—
164	#15691335	C₂³	1	2	yes	—
165	#15691335	C₂³	1	2	yes	—
166	#15691335	C₂³	1	2	yes	—
167	#15691335	C₂³	1	2	yes	—
168	#15691335	C₂³	1	2	yes	—
169	#15691335	C₂³	1	2	yes	—
170	#15691335	C₂³	1	2	yes	—
171	#15691335	C₂³	1	2	yes	—
172	#15691335	C₂³	1	2	yes	—
173	#15691335	C₂³	1	2	yes	—
174	C₄×Dic₁₉₇	C₂³	1	2	yes	—
175	C₄×Dic₁₉₇	C₂³	1	2	yes	—
176	C₄×Dic₁₉₇	C₂³	1	2	yes	—
177	C₂×Q₈×C₁₉₇	C₂³	1	1	yes	characteristic
178	C₂×D₄×C₁₉₇	C₂³	1	2	yes	—
179	C₂×D₄×C₁₉₇	C₂³	1	1	yes	characteristic
180	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
181	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
182	C₂²×C₄×C₁₉₇	C₂³	1	2	yes	—
183	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
185	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
186	C₄⋊C₄×C₁₉₇	C₂³	1	1	yes	characteristic
187	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
188	C₄⋊C₄×C₁₉₇	C₂³	1	1	yes	characteristic
189	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
195	C₄²×C₁₉₇	C₂³	1	1	yes	characteristic
196	C₄²×C₁₉₇	C₂³	1	1	yes	characteristic
197	C₄²×C₁₉₇	C₂³	1	1	yes	characteristic
198	C₄²×C₁₉₇	C₂³	1	1	yes	characteristic
199	C₄²×C₁₉₇	C₂³	1	2	yes	—
200	C₂²×D₁₉₇	—	2	2	no	—
201	C₂²×D₁₉₇	—	2	4	no	—
202	C₂²×D₁₉₇	—	4	1	no	—
203	C₂²×D₁₉₇	—	4	2	no	—
204	C₂²×D₁₉₇	—	4	1	no	—
205	C₂²×D₁₉₇	—	4	1	no	—
206	C₂²×D₁₉₇	—	4	2	no	—
207	C₂²×D₁₉₇	—	4	1	no	—
208	C₂²×D₁₉₇	#41	1	4	yes	complemented
209	C₂²×D₁₉₇	C₂⁴	1	2	yes	—
210	C₂²×D₁₉₇	C₂⁴	1	2	yes	—
211	C₂²×D₁₉₇	C₂⁴	1	2	yes	—
212	Dic₃₉₄	—	4	1	no	—
213	Dic₃₉₄	—	4	2	no	—
214	D₇₈₈	—	2	4	no	—
215	D₇₈₈	—	2	4	no	—
216	D₇₈₈	—	2	4	no	—
217	D₇₈₈	—	4	1	no	—
218	D₇₈₈	—	4	2	no	—
219	D₇₈₈	—	4	2	no	—
220	C₂²⋊D₁₉₇	—	2	4	no	—
221	C₂²⋊D₁₉₇	—	2	4	no	—
222	C₂²⋊D₁₉₇	—	4	2	no	—
223	C₂²⋊D₁₉₇	—	4	2	no	—
224	C₂²⋊D₁₉₇	—	4	2	no	—
225	C₂×Dic₁₉₇	—	4	1	no	—
226	C₂×Dic₁₉₇	—	4	2	no	—
227	C₂×Dic₁₉₇	—	4	1	no	—
228	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
229	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
230	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
231	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
232	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
233	C₄×D₁₉₇	—	2	4	no	—
234	C₄×D₁₉₇	—	2	4	no	—
235	C₄×D₁₉₇	—	2	4	no	—
236	C₄×D₁₉₇	—	2	4	no	—
237	C₄×D₁₉₇	—	4	2	no	—
238	C₄×D₁₉₇	—	4	2	no	—
239	C₄×D₁₉₇	—	4	2	no	—
240	C₄×D₁₉₇	—	4	2	no	—
241	C₄×D₁₉₇	—	4	2	no	—
242	C₂³×C₁₉₇	C₂⁴	1	2	yes	—
243	C₂³×C₁₉₇	C₂⁴	1	1	yes	characteristic
244	Q₈×C₁₉₇	—	4	1	no	—
245	D₄×C₁₉₇	—	2	4	no	—
246	D₄×C₁₉₇	—	4	1	no	—
247	C₂×C₄×C₁₉₇	—	2	2	no	—
248	C₂×C₄×C₁₉₇	—	2	2	no	—
249	C₂×C₄×C₁₉₇	—	2	4	no	—
250	C₂×C₄×C₁₉₇	—	4	1	no	—
251	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₁₉₇	—	2	1	no	—
261	C₂²×C₁₉₇	—	2	1	no	—
262	C₂²×C₁₉₇	—	2	2	no	—
263	C₂²×C₁₉₇	—	2	2	no	—
264	C₂²×C₁₉₇	—	2	2	no	—
265	C₂²×C₁₉₇	C₂×#41	1	2	yes	—
266	C₂²×C₁₉₇	C₂⁵	1	1	yes	characteristic
267	C₂×D₁₉₇	—	2	2	no	—
268	C₂×D₁₉₇	—	2	2	no	—
269	C₂×D₁₉₇	—	2	2	no	—
270	C₂×D₁₉₇	—	2	2	no	—
271	C₂×D₁₉₇	—	2	2	no	—
272	C₂×D₁₉₇	—	2	2	no	—
273	C₂×D₁₉₇	—	2	2	no	—
274	C₂×D₁₉₇	—	2	2	no	—
275	C₂×D₁₉₇	—	4	4	no	—
276	C₂×D₁₉₇	—	4	8	no	—
277	C₂×D₁₉₇	—	4	4	no	—
278	C₂×D₁₉₇	C₂×#41	1	4	yes	—
279	C₄×C₁₉₇	—	2	1	no	—
280	C₄×C₁₉₇	—	2	1	no	—
281	C₄×C₁₉₇	—	2	2	no	—
282	C₄×C₁₉₇	—	2	1	no	—
283	C₄×C₁₉₇	—	2	2	no	—
284	C₄×C₁₉₇	—	2	1	no	—
285	C₄×C₁₉₇	—	2	1	no	—
286	C₄×C₁₉₇	—	2	2	no	—
287	C₄×C₁₉₇	H(5,𝔽₂)	1	2	yes	—
288	Dic₁₉₇	—	2	2	no	—
289	Dic₁₉₇	—	2	2	no	—
290	Dic₁₉₇	—	2	2	no	—
291	Dic₁₉₇	—	2	2	no	—
292	Dic₁₉₇	—	2	2	no	—
293	C₂×C₁₉₇	—	2	2	no	—
294	C₂×C₁₉₇	—	4	2	no	—
295	C₂×C₁₉₇	C₂²×#41	1	1	yes	characteristic
296	C₂×C₁₉₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
297	C₂×C₁₉₇	#585	1	1	yes	characteristic
298	D₁₉₇	—	2	4	no	—
299	D₁₉₇	—	4	2	no	—
300	D₁₉₇	—	4	2	no	—
301	C₁₉₇	#3459	1	1	yes	characteristic, complemented, Sylow
302	#3459	—	197	1	no	maximal, Sylow
303	#543	—	197	1	no	—
304	#539	—	197	2	no	—
305	#539	—	197	2	no	—
306	#539	—	197	2	no	—
307	#538	—	197	2	no	—
308	#538	—	197	2	no	—
309	#538	—	197	1	no	—
310	#538	—	197	1	no	—
311	#534	—	197	2	no	—
312	#534	—	197	1	no	—
313	#529	—	197	2	no	—
314	#529	—	197	2	no	—
315	#529	—	197	1	no	—
316	#529	D₁₉₇	1	1	yes	characteristic, complemented
317	#525	—	197	2	no	—
318	#525	—	197	2	no	—
319	#525	—	197	2	no	—
320	C₂×C₄×D₄	—	197	2	no	—
321	C₂×C₄×D₄	—	197	1	no	—
322	C₂×#41	—	197	2	no	—
323	C₂²×D₄	—	197	2	no	—
324	C₂²×D₄	—	197	1	no	—
325	C₂³×C₄	—	197	1	no	—
326	C₂³×C₄	—	197	1	no	—
327	C₂³×C₄	—	197	2	no	—
328	#126	—	197	2	no	—
329	#126	—	197	2	no	—
330	#126	—	197	2	no	—
331	#126	—	197	2	no	—
332	#126	—	197	2	no	—
333	#126	C₂×D₁₉₇	1	2	yes	complemented
334	#125	—	197	2	no	—
335	#125	—	197	2	no	—
336	#125	—	197	1	no	—
337	#125	C₂×D₁₉₇	1	1	yes	characteristic, complemented
338	#124	—	197	2	no	—
339	#124	—	197	2	no	—
340	#124	—	197	1	no	—
341	#124	C₂×D₁₉₇	1	1	yes	characteristic, complemented
342	#123	—	197	2	no	—
343	#123	—	197	2	no	—
344	#123	—	197	2	no	—
345	#123	—	197	2	no	—
346	#123	—	197	2	no	—
347	#123	—	197	2	no	—
348	#123	—	197	2	no	—
349	#123	—	197	2	no	—
350	#123	—	197	2	no	—
351	#123	—	197	2	no	—
352	#123	—	197	2	no	—
353	#123	C₂×D₁₉₇	1	2	yes	complemented
354	C₂²⋊Q₈	—	197	2	no	—
355	C₂²⋊Q₈	—	197	1	no	—
356	C₂²⋊Q₈	—	197	2	no	—
357	C₂²⋊Q₈	—	197	2	no	—
358	C₂²⋊Q₈	—	197	2	no	—
359	C₂²⋊Q₈	—	197	2	no	—
360	C₂²⋊Q₈	—	197	2	no	—
361	C₂²⋊Q₈	—	197	2	no	—
362	C₂²⋊Q₈	—	197	2	no	—
363	C₂²⋊Q₈	C₂×D₁₉₇	1	1	yes	characteristic, complemented
364	#121	—	197	2	no	—
365	#121	—	197	2	no	—
366	#121	—	197	1	no	—
367	#121	—	197	2	no	—
368	#121	—	197	2	no	—
369	#121	—	197	2	no	—
370	#121	—	197	2	no	—
371	#121	—	197	2	no	—
372	#121	—	197	2	no	—
373	#121	C₂×D₁₉₇	1	1	yes	characteristic
374	#120	—	197	2	no	—
375	#120	—	197	2	no	—
376	#120	—	197	2	no	—
377	#120	—	197	2	no	—
378	#120	—	197	2	no	—
379	#120	—	197	2	no	—
380	C₄×Q₈	—	197	1	no	—
381	C₄×Q₈	C₂×D₁₉₇	1	1	yes	characteristic, complemented
382	C₄×D₄	—	197	2	no	—
383	C₄×D₄	—	197	2	no	—
384	C₄×D₄	—	197	2	no	—
385	C₄×D₄	—	197	2	no	—
386	C₄×D₄	—	197	2	no	—
387	C₄×D₄	—	197	2	no	—
388	C₄×D₄	—	197	2	no	—
389	C₄×D₄	—	197	2	no	—
390	C₄×D₄	—	197	2	no	—
391	C₄×D₄	—	197	2	no	—
392	C₄×D₄	—	197	2	no	—
393	C₄×D₄	—	197	2	no	—
394	C₄×D₄	—	197	2	no	—
395	C₄×D₄	—	197	1	no	—
396	C₄×D₄	C₂×D₁₉₇	1	2	yes	complemented
397	C₄×D₄	C₂×D₁₉₇	1	1	yes	characteristic, complemented
398	#117	—	197	2	no	—
399	#117	—	197	2	no	—
400	#117	C₂×D₁₉₇	1	2	yes	complemented
401	C₂×C₄⋊C₄	—	197	1	no	—
402	C₂×C₄⋊C₄	—	197	2	no	—
403	C₂×C₂²⋊C₄	—	197	1	no	—
404	C₂×C₂²⋊C₄	—	197	1	no	—
405	C₂×C₂²⋊C₄	—	197	2	no	—
406	C₂×C₂²⋊C₄	—	197	2	no	—
407	C₂×C₄²	—	197	2	no	—
408	C₂×C₄²	C₂×D₁₉₇	1	1	yes	characteristic, complemented
409	C₂⁴	—	197	2	no	—
410	C₂⁴	—	197	1	no	—
411	C₂⁴	—	197	1	no	—
412	#41	—	788	4	no	—
413	C₂×Q₈	—	197	1	no	—
414	C₂×Q₈	—	197	2	no	—
415	C₂×Q₈	C₂²×D₁₉₇	1	1	yes	characteristic
416	C₂×D₄	—	394	4	no	—
417	C₂×D₄	—	394	8	no	—
418	C₂×D₄	—	197	2	no	—
419	C₂×D₄	—	197	2	no	—
420	C₂×D₄	—	197	2	no	—
421	C₂×D₄	—	197	2	no	—
422	C₂×D₄	—	197	2	no	—
423	C₂×D₄	—	197	2	no	—
424	C₂×D₄	—	197	1	no	—
425	C₂×D₄	—	197	2	no	—
426	C₂×D₄	—	197	2	no	—
427	C₂×D₄	—	197	2	no	—
428	C₂×D₄	—	197	2	no	—
429	C₂×D₄	C₂²×D₁₉₇	1	2	yes	—
430	C₂×D₄	C₂²×D₁₉₇	1	1	yes	characteristic
431	C₂²×C₄	—	788	2	no	—
432	C₂²×C₄	—	788	2	no	—
433	C₂²×C₄	—	788	4	no	—
434	C₂²×C₄	—	197	1	no	—
435	C₂²×C₄	—	197	1	no	—
436	C₂²×C₄	—	197	2	no	—
437	C₂²×C₄	—	197	2	no	—
438	C₂²×C₄	—	197	2	no	—
439	C₂²×C₄	—	197	2	no	—
440	C₂²×C₄	—	197	2	no	—
441	C₂²×C₄	—	197	2	no	—
442	C₂²×C₄	—	197	2	no	—
443	C₂²×C₄	—	197	2	no	—
444	C₂²×C₄	—	197	2	no	—
445	C₂²×C₄	—	197	2	no	—
446	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
447	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
448	C₂²×C₄	C₂²×D₁₉₇	1	2	yes	—
449	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
450	C₄⋊C₄	—	197	2	no	—
451	C₄⋊C₄	—	197	2	no	—
452	C₄⋊C₄	—	197	2	no	—
453	C₄⋊C₄	—	197	2	no	—
454	C₄⋊C₄	—	197	2	no	—
455	C₄⋊C₄	—	197	2	no	—
456	C₄⋊C₄	—	197	2	no	—
457	C₄⋊C₄	—	197	2	no	—
458	C₄⋊C₄	—	197	2	no	—
459	C₄⋊C₄	—	197	2	no	—
460	C₄⋊C₄	—	197	2	no	—
461	C₄⋊C₄	—	197	2	no	—
462	C₄⋊C₄	—	197	1	no	—
463	C₄⋊C₄	—	197	1	no	—
464	C₄⋊C₄	C₂²×D₁₉₇	1	2	yes	—
465	C₄⋊C₄	C₂²×D₁₉₇	1	2	yes	—
466	C₄⋊C₄	C₂²×D₁₉₇	1	2	yes	—
467	C₄⋊C₄	C₂²×D₁₉₇	1	1	yes	characteristic
468	C₄⋊C₄	C₂²×D₁₉₇	1	2	yes	—
469	C₄⋊C₄	C₂²×D₁₉₇	1	1	yes	characteristic
470	C₂²⋊C₄	—	197	2	no	—
471	C₂²⋊C₄	—	197	2	no	—
472	C₂²⋊C₄	—	197	2	no	—
473	C₂²⋊C₄	—	197	2	no	—
474	C₂²⋊C₄	—	197	2	no	—
475	C₂²⋊C₄	—	197	2	no	—
476	C₂²⋊C₄	—	197	2	no	—
477	C₂²⋊C₄	—	197	2	no	—
478	C₂²⋊C₄	—	197	2	no	—
479	C₂²⋊C₄	—	197	2	no	—
480	C₂²⋊C₄	—	197	2	no	—
481	C₂²⋊C₄	—	197	2	no	—
482	C₂²⋊C₄	—	197	2	no	—
483	C₂²⋊C₄	—	197	2	no	—
484	C₂²⋊C₄	—	197	2	no	—
485	C₂²⋊C₄	—	197	2	no	—
486	C₂²⋊C₄	—	197	2	no	—
487	C₂²⋊C₄	—	197	2	no	—
488	C₂²⋊C₄	—	197	2	no	—
489	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
491	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
494	C₄²	—	197	2	no	—
495	C₄²	—	197	2	no	—
496	C₄²	—	197	2	no	—
497	C₄²	C₂²×D₁₉₇	1	1	yes	characteristic
498	C₄²	C₂²×D₁₉₇	1	1	yes	characteristic
499	C₄²	C₂²×D₁₉₇	1	2	yes	—
500	C₄²	C₂²×D₁₉₇	1	1	yes	characteristic
501	C₄²	C₂²×D₁₉₇	1	1	yes	characteristic
502	C₂³	—	788	1	no	—
503	C₂³	—	788	1	no	—
504	C₂³	—	788	2	no	—
505	C₂³	—	788	1	no	—
506	C₂³	—	788	1	no	—
507	C₂³	—	788	2	no	—
508	C₂³	—	394	4	no	—
509	C₂³	—	394	2	no	—
510	C₂³	—	197	4	no	—
511	C₂³	—	197	2	no	—
512	C₂³	—	197	2	no	—
513	C₂³	—	197	2	no	—
514	C₂³	C₂³×D₁₉₇	1	2	yes	—
515	C₂³	C₂³×D₁₉₇	1	1	yes	characteristic
516	Q₈	—	4	1	no	—
517	Q₈	—	788	2	no	—
518	Q₈	—	788	1	no	—
519	D₄	—	2	4	no	—
520	D₄	—	4	1	no	—
521	D₄	—	788	2	no	—
522	D₄	—	788	1	no	—
523	D₄	—	788	2	no	—
524	D₄	—	788	2	no	—
525	D₄	—	788	2	no	—
526	D₄	—	788	2	no	—
527	D₄	—	394	4	no	—
528	D₄	—	394	4	no	—
529	D₄	—	394	4	no	—
530	D₄	—	394	4	no	—
531	D₄	—	394	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	788	2	no	—
537	C₂×C₄	—	788	2	no	—
538	C₂×C₄	—	788	2	no	—
539	C₂×C₄	—	788	2	no	—
540	C₂×C₄	—	788	2	no	—
541	C₂×C₄	—	788	1	no	—
542	C₂×C₄	—	788	2	no	—
543	C₂×C₄	—	788	1	no	—
544	C₂×C₄	—	394	4	no	—
545	C₂×C₄	—	394	4	no	—
546	C₂×C₄	—	394	4	no	—
547	C₂×C₄	—	394	4	no	—
548	C₂×C₄	—	197	2	no	—
549	C₂×C₄	—	197	2	no	—
550	C₂×C₄	—	197	2	no	—
551	C₂×C₄	—	197	2	no	—
552	C₂×C₄	—	197	2	no	—
553	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
554	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
555	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
556	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
560	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
561	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	788	4	no	—
568	C₂²	—	788	4	no	—
569	C₂²	—	788	8	no	—
570	C₂²	—	394	2	no	—
571	C₂²	—	394	2	no	—
572	C₂²	—	394	2	no	—
573	C₂²	—	394	2	no	—
574	C₂²	—	394	2	no	—
575	C₂²	—	394	2	no	—
576	C₂²	—	394	2	no	—
577	C₂²	—	394	2	no	—
578	C₂²	—	197	4	no	—
579	C₂²	#41×D₁₉₇	1	2	yes	—
580	C₂²	C₂⁴×D₁₉₇	1	1	yes	characteristic
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	2	no	—
589	C₄	—	394	2	no	—
590	C₄	—	394	2	no	—
591	C₄	—	394	2	no	—
592	C₄	—	394	2	no	—
593	C₄	—	394	2	no	—
594	C₄	#20263372	1	2	yes	—
595	C₂	—	2	2	no	—
596	C₂	—	4	2	no	—
597	C₂	—	788	2	no	—
598	C₂	—	788	2	no	—
599	C₂	—	394	4	no	—
600	C₂	C₂×#41×D₁₉₇	1	1	yes	characteristic
601	C₂	C₂×#20263372	1	1	yes	characteristic
602	C₂	#27161915	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₉₇
commutator, socle, cosocle	C₂²×C₁₉₇	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉₇
Fitting	#529×C₁₉₇	C₂
hypercenter	#529	D₁₉₇
hypocenter	C₁₉₇	#3459
LCS	G ▷ C₂²×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #27161704	C₂	semidirect
2. #27161677	C₂	semidirect
3. #27161673	C₂	semidirect
4. #27161670	C₂	semidirect
5. #27161669	C₂	semidirect
6. #27161668	C₂	semidirect
7. #27161666	C₂	semidirect
8. #27161663	C₂	semidirect
9. #27161640	C₂	semidirect
10. #27161637	C₂	semidirect
11. #27161616	C₂	semidirect
12. #27161613	C₂	semidirect
13. #27161607	C₂	semidirect
14. #27161591	C₂	semidirect
15. #27161588	C₂	semidirect
16. #27161588	C₂	semidirect
17. C₂×C₄×D₇₈₈	C₂	semidirect
18. C₄×D₄×D₁₉₇	C₂	semidirect
19. #529×C₁₉₇	C₂	semidirect
20. C₂×#15691358	C₂²	semidirect
24. C₂²×C₄×D₁₉₇	C₂²	semidirect
25. C₂²×C₄×D₁₉₇	C₂²	semidirect
26. #20263321	C₂²	semidirect
27. #20263321	C₂²	semidirect
28. #20263321	C₂²	semidirect
29. #20263320	C₂²	semidirect
30. #20263319	C₂²	semidirect
31. #20263318	C₂²	semidirect
32. #20263317	C₂²	semidirect
33. #20263316	C₂²	semidirect
34. #20263315	C₂²	semidirect
35. #20263314	C₂²	semidirect
36. #20263312	C₂²	semidirect
37. #20263311	C₂²	semidirect
38. #20263311	C₂²	semidirect
39. #20263311	C₂²	semidirect
40. #20263311	C₂²	semidirect
41. #20263311	C₂²	semidirect
42. #20263310	C₂²	semidirect
43. #20263310	C₂²	semidirect
44. #20263309	C₂²	semidirect
45. #20263308	C₂²	semidirect
46. #20263308	C₂²	semidirect
47. #20263308	C₂²	semidirect
48. #20263306	C₂²	semidirect
49. #20263306	C₂²	semidirect
50. #20263305	C₂²	semidirect
51. #20263304	C₂²	semidirect
52. #20263304	C₂²	semidirect
53. #20263304	C₂²	semidirect
54. #20263303	C₂²	semidirect
55. #20263303	C₂²	semidirect
56. #20263302	C₂²	semidirect
59. #20263301	C₂²	semidirect
63. #20263299	C₂²	semidirect
65. #20263298	C₂²	semidirect
66. #20263296	C₂²	semidirect
67. #20263296	C₂²	semidirect
68. #20263296	C₂²	semidirect
69. #20263296	C₂²	semidirect
70. #20263294	C₂²	semidirect
71. #20263294	C₂²	semidirect
72. C₄×Dic₃₉₄	C₂²	semidirect
73. C₄×D₇₈₈	C₂²	semidirect
74. C₄×D₇₈₈	C₂²	semidirect
75. C₄×D₇₈₈	C₂²	semidirect
76. C₄×D₇₈₈	C₂²	semidirect
77. C₄×D₇₈₈	C₂²	semidirect
78. C₄×D₇₈₈	C₂²	semidirect
79. C₄×D₇₈₈	C₂²	semidirect
80. D₄×Dic₁₉₇	C₂²	semidirect
81. #20263288	C₂²	semidirect
82. C₄×C₂²⋊D₁₉₇	C₂²	semidirect
83. C₄×C₂²⋊D₁₉₇	C₂²	semidirect
84. C₄×C₂²⋊D₁₉₇	C₂²	semidirect
85. #20263286	C₂²	semidirect
86. #20263286	C₂²	semidirect
87. #20263283	C₂²	semidirect
88. #20263283	C₂²	semidirect
89. C₂×C₄⋊Dic₁₉₇	C₂²	semidirect
90. C₄⋊C₄×D₁₉₇	C₂²	semidirect
92. C₂×#15691335	C₂²	semidirect
94. C₂²⋊C₄×D₁₉₇	C₂²	semidirect
95. C₄²×D₁₉₇	C₂²	semidirect
96. #126×C₁₉₇	C₂²	semidirect
97. #125×C₁₉₇	C₂²	semidirect
98. #124×C₁₉₇	C₂²	semidirect
99. #123×C₁₉₇	C₂²	semidirect
100. C₂²⋊Q₈×C₁₉₇	C₂²	semidirect
102. C₄×Q₈×C₁₉₇	C₂²	semidirect
103. C₄×D₄×C₁₉₇	C₂²	semidirect
104. C₄×D₄×C₁₉₇	C₂²	semidirect
105. #117×C₁₉₇	C₂²	semidirect
106. C₂×C₄²×C₁₉₇	C₂²	semidirect
208. C₂²×D₁₉₇	#41	semidirect
301. C₁₉₇	#3459	semidirect
316. #529	D₁₉₇	semidirect
333. #126	C₂×D₁₉₇	semidirect
337. #125	C₂×D₁₉₇	semidirect
341. #124	C₂×D₁₉₇	semidirect
353. #123	C₂×D₁₉₇	semidirect
363. C₂²⋊Q₈	C₂×D₁₉₇	semidirect
381. C₄×Q₈	C₂×D₁₉₇	semidirect
396. C₄×D₄	C₂×D₁₉₇	semidirect
397. C₄×D₄	C₂×D₁₉₇	semidirect
400. #117	C₂×D₁₉₇	semidirect
408. C₂×C₄²	C₂×D₁₉₇	semidirect

Maximal subgroups

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

subgroup	index
#27161704	2
#27161677	2
#27161673	2
#27161670	2
#27161669	2
#27161668	2
#27161666	2
#27161663	2
#27161640	2
#27161637	2
#27161616	2
#27161613	2
#27161607	2
#27161591	2
#27161588	2
C₂×C₄×D₇₈₈	2
C₄×D₄×D₁₉₇	2
#529×C₁₉₇	2
#3459	197