Subgroups — #38756006

Order 25216.

1212 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161635	C₂	1	1	yes	maximal, characteristic, complemented
2	#27161633	C₂	1	1	yes	maximal, characteristic, complemented
3	#27161631	C₂	1	1	yes	maximal, characteristic, complemented
4	#27161628	C₂	1	1	yes	maximal, characteristic, complemented
5	#27161626	C₂	1	1	yes	maximal, characteristic, complemented
6	#27161624	C₂	1	1	yes	maximal, characteristic, complemented
7	#27161614	C₂	1	1	yes	maximal, characteristic, complemented
8	#27161613	C₂	1	1	yes	maximal, characteristic, complemented
9	#27161612	C₂	1	2	yes	maximal, complemented
10	#27161612	C₂	1	2	yes	maximal, complemented
11	#27161608	C₂	1	1	yes	maximal, characteristic, complemented
12	#27161607	C₂	1	2	yes	maximal, complemented
13	#27161606	C₂	1	2	yes	maximal, complemented
14	#27161592	C₂	1	1	yes	maximal, characteristic, complemented
15	#27161589	C₂	1	1	yes	maximal, characteristic, complemented
16	#27161588	C₂	1	2	yes	maximal, complemented
17	#27161587	C₂	1	2	yes	maximal, complemented
18	C₄×#15691359	C₂	1	1	yes	maximal, characteristic, complemented
19	#27161547	C₂	1	2	yes	maximal, complemented
20	C₄×#15691357	C₂	1	2	yes	maximal, complemented
21	C₄×#15691357	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄²×D₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15691359	C₂²	1	1	yes	characteristic
25	C₂×#15691358	C₂²	1	2	yes	—
26	C₂×#15691357	C₂²	1	2	yes	—
27	C₂×#15691357	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic
31	#20263325	C₂²	1	1	yes	characteristic, complemented
32	#20263325	C₂²	1	1	yes	characteristic, complemented
33	#20263324	C₂²	1	1	yes	characteristic, complemented
34	#20263322	C₂²	1	1	yes	characteristic, complemented
35	#20263321	C₂²	1	2	yes	complemented
36	#20263320	C₂²	1	2	yes	complemented
37	#20263319	C₂²	1	2	yes	complemented
38	#20263318	C₂²	1	1	yes	characteristic, complemented
39	#20263316	C₂²	1	2	yes	complemented
40	#20263316	C₂²	1	2	yes	complemented
41	#20263314	C₂²	1	1	yes	characteristic, complemented
42	#20263312	C₂²	1	2	yes	complemented
43	#20263312	C₂²	1	2	yes	complemented
44	#20263311	C₂²	1	2	yes	—
45	#20263311	C₂²	1	2	yes	—
46	#20263309	C₂²	1	2	yes	—
47	#20263308	C₂²	1	2	yes	—
48	#20263308	C₂²	1	2	yes	—
49	#20263306	C₂²	1	1	yes	characteristic
50	#20263305	C₂²	1	1	yes	characteristic
51	#20263304	C₂²	1	2	yes	—
52	#20263304	C₂²	1	2	yes	—
53	#20263304	C₂²	1	2	yes	—
54	#20263303	C₂²	1	2	yes	—
55	#20263302	C₂²	1	1	yes	characteristic
56	#20263301	C₂²	1	1	yes	characteristic
57	#20263300	C₂²	1	1	yes	characteristic
58	#20263299	C₂²	1	2	yes	—
59	#20263299	C₂²	1	2	yes	—
60	#20263299	C₂²	1	2	yes	—
61	#20263298	C₂²	1	2	yes	—
62	#20263297	C₂²	1	1	yes	characteristic
63	#20263296	C₂²	1	2	yes	—
64	#20263294	C₂²	1	2	yes	—
65	Q₈×Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
66	C₄×Dic₃₉₄	C₂²	1	2	yes	complemented
67	C₄×Dic₃₉₄	C₂²	1	1	yes	characteristic, complemented
68	#20263291	C₂²	1	2	yes	complemented
69	#20263291	C₂²	1	2	yes	complemented
70	#20263291	C₂²	1	2	yes	complemented
71	#20263291	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₇₈₈	C₂²	1	2	yes	—
73	C₄×D₇₈₈	C₂²	1	1	yes	characteristic, complemented
74	D₄×Dic₁₉₇	C₂²	1	2	yes	—
75	D₄×Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
76	#20263288	C₂²	1	2	yes	—
77	#20263288	C₂²	1	2	yes	—
78	#20263288	C₂²	1	2	yes	—
79	#20263288	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₂²⋊D₁₉₇	C₂²	1	2	yes	—
81	C₄×C₂²⋊D₁₉₇	C₂²	1	2	yes	—
82	C₄×C₂²⋊D₁₉₇	C₂²	1	2	yes	complemented
83	#20263286	C₂²	1	2	yes	—
84	#20263286	C₂²	1	2	yes	—
85	#20263286	C₂²	1	2	yes	—
86	#20263286	C₂²	1	2	yes	—
87	#20263286	C₂²	1	2	yes	complemented
88	#20263286	C₂²	1	2	yes	complemented
89	#20263286	C₂²	1	2	yes	complemented
90	#20263284	C₂²	1	1	yes	characteristic
91	#20263284	C₂²	1	1	yes	characteristic
92	#20263284	C₂²	1	2	yes	complemented
93	#20263284	C₂²	1	2	yes	complemented
94	#20263283	C₂²	1	2	yes	—
95	#20263283	C₂²	1	2	yes	complemented
96	#20263282	C₂²	1	2	yes	—
97	#20263282	C₂²	1	2	yes	complemented
98	#20263282	C₂²	1	2	yes	complemented
99	C₂×C₄×Dic₁₉₇	C₂²	1	1	yes	characteristic
100	C₂×C₄×Dic₁₉₇	C₂²	1	1	yes	characteristic
101	C₂×C₄×Dic₁₉₇	C₂²	1	1	yes	characteristic
102	C₂×C₄×Dic₁₉₇	C₂²	1	2	yes	complemented
103	C₄²×D₁₉₇	C₂²	1	1	yes	characteristic
104	C₄²×D₁₉₇	C₂²	1	1	yes	characteristic
105	C₄²×D₁₉₇	C₂²	1	1	yes	characteristic
106	C₄²×D₁₉₇	C₂²	1	1	yes	characteristic
107	C₄²×D₁₉₇	C₂²	1	1	yes	characteristic
108	C₄²×D₁₉₇	C₂²	1	1	yes	characteristic
109	C₄²×D₁₉₇	C₂²	1	1	yes	characteristic
110	C₄²×D₁₉₇	C₂²	1	1	yes	characteristic
111	C₄²×D₁₉₇	C₂²	1	2	yes	complemented
112	#126×C₁₉₇	C₂²	1	2	yes	complemented
113	#125×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
114	#124×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
115	#123×C₁₉₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₉₇	C₂²	1	1	yes	characteristic
117	#121×C₁₉₇	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₉₇	C₂²	1	2	yes	—
120	C₄×D₄×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
121	#117×C₁₉₇	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₉₇	C₂²	1	1	yes	characteristic
123	C₂³×D₁₉₇	C₂³	1	1	yes	characteristic
124	#15691359	—	2	4	no	—
125	#15691358	—	2	8	no	—
126	#15691357	—	2	8	no	—
127	#15691357	—	2	4	no	—
128	C₂×Dic₃₉₄	C₂³	1	2	yes	—
129	C₂×Dic₃₉₄	C₂³	1	2	yes	—
130	C₂×Dic₃₉₄	C₂³	1	1	yes	characteristic
131	C₂×D₇₈₈	C₂³	1	2	yes	—
132	C₂×D₇₈₈	C₂³	1	2	yes	—
133	C₂×D₇₈₈	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₉₇	C₂³	1	2	yes	—
139	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₉₇	C₂³	1	2	yes	—
142	C₂²×Dic₁₉₇	C₂³	1	2	yes	—
143	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₉₇	—	2	4	no	—
145	C₂×C₄×D₁₉₇	—	2	4	no	—
146	C₂×C₄×D₁₉₇	—	2	4	no	—
147	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
158	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
159	C₂×C₄×D₁₉₇	C₂³	1	2	yes	—
160	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₉₇	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₉₇	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₉₇	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₁₉₇	C₂³	1	2	yes	—
165	C₄⋊Dic₁₉₇	C₂³	1	2	yes	—
166	#15691337	C₂³	1	2	yes	—
167	#15691337	C₂³	1	2	yes	—
168	#15691337	C₂³	1	2	yes	—
169	#15691337	C₂³	1	2	yes	—
170	#15691337	C₂³	1	2	yes	—
171	#15691337	C₂³	1	2	yes	—
172	#15691337	C₂³	1	2	yes	—
173	#15691337	C₂³	1	2	yes	—
174	#15691337	C₂³	1	2	yes	—
175	#15691337	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₉₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₉₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₉₇	C₂³	1	2	yes	—
179	#15691335	C₂³	1	2	yes	—
180	#15691335	C₂³	1	2	yes	—
181	#15691335	C₂³	1	2	yes	—
182	#15691335	C₂³	1	2	yes	—
183	#15691335	C₂³	1	2	yes	—
184	#15691335	C₂³	1	2	yes	—
185	#15691335	C₂³	1	2	yes	—
186	#15691335	C₂³	1	2	yes	—
187	#15691335	C₂³	1	2	yes	—
188	#15691335	C₂³	1	2	yes	—
189	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
190	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₉₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₉₇	C₂³	1	2	yes	—
202	C₄×Dic₁₉₇	C₂³	1	2	yes	—
203	C₄×Dic₁₉₇	C₂³	1	2	yes	—
204	C₄×Dic₁₉₇	C₂³	1	2	yes	—
205	C₄×Dic₁₉₇	C₂³	1	2	yes	—
206	C₂×Q₈×C₁₉₇	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₉₇	C₂³	1	2	yes	—
208	C₂×D₄×C₁₉₇	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₉₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₉₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₉₇	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₉₇	C₂³	1	2	yes	—
224	C₄²×C₁₉₇	C₂³	1	1	yes	characteristic
225	C₄²×C₁₉₇	C₂³	1	1	yes	characteristic
226	C₄²×C₁₉₇	C₂³	1	1	yes	characteristic
227	C₄²×C₁₉₇	C₂³	1	1	yes	characteristic
228	C₄²×C₁₉₇	C₂³	1	2	yes	—
229	C₂²×D₁₉₇	—	2	2	no	—
230	C₂²×D₁₉₇	—	2	2	no	—
231	C₂²×D₁₉₇	—	2	2	no	—
232	C₂²×D₁₉₇	C₂⁴	1	2	yes	—
233	C₂²×D₁₉₇	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₉₇	C₂⁴	1	1	yes	characteristic
235	Dic₃₉₄	—	2	2	no	—
236	Dic₃₉₄	—	2	4	no	—
237	Dic₃₉₄	—	2	4	no	—
238	D₇₈₈	—	2	4	no	—
239	D₇₈₈	—	2	4	no	—
240	D₇₈₈	—	2	2	no	—
241	C₂²⋊D₁₉₇	—	2	4	no	—
242	C₂²⋊D₁₉₇	—	2	4	no	—
243	C₂²⋊D₁₉₇	—	2	4	no	—
244	C₂²⋊D₁₉₇	—	2	4	no	—
245	C₂²⋊D₁₉₇	—	2	4	no	—
246	C₂×Dic₁₉₇	—	2	2	no	—
247	C₂×Dic₁₉₇	—	2	2	no	—
248	C₂×Dic₁₉₇	—	2	4	no	—
249	C₂×Dic₁₉₇	—	2	4	no	—
250	C₂×Dic₁₉₇	#41	1	4	yes	complemented
251	C₂×Dic₁₉₇	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₉₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
254	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
255	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
256	C₂×Dic₁₉₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₉₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₉₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₉₇	C₂⁴	1	1	yes	characteristic
260	C₄×D₁₉₇	—	2	2	no	—
261	C₄×D₁₉₇	—	2	2	no	—
262	C₄×D₁₉₇	—	2	2	no	—
263	C₄×D₁₉₇	—	2	2	no	—
264	C₄×D₁₉₇	—	2	4	no	—
265	C₄×D₁₉₇	—	2	2	no	—
266	C₄×D₁₉₇	—	2	2	no	—
267	C₄×D₁₉₇	—	2	2	no	—
268	C₄×D₁₉₇	—	2	2	no	—
269	C₄×D₁₉₇	—	2	2	no	—
270	C₄×D₁₉₇	—	2	2	no	—
271	C₄×D₁₉₇	—	2	4	no	—
272	C₄×D₁₉₇	—	2	4	no	—
273	C₄×D₁₉₇	#41	1	4	yes	complemented
274	C₄×D₁₉₇	#41	1	4	yes	complemented
275	C₂³×C₁₉₇	C₂⁴	1	2	yes	—
276	C₂³×C₁₉₇	C₂⁴	1	1	yes	characteristic
277	Q₈×C₁₉₇	—	2	2	no	—
278	D₄×C₁₉₇	—	2	4	no	—
279	D₄×C₁₉₇	—	2	2	no	—
280	C₂×C₄×C₁₉₇	—	2	2	no	—
281	C₂×C₄×C₁₉₇	—	2	2	no	—
282	C₂×C₄×C₁₉₇	—	2	2	no	—
283	C₂×C₄×C₁₉₇	—	2	4	no	—
284	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
289	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
290	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
291	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₁₉₇	—	2	1	no	—
294	C₂²×C₁₉₇	—	2	1	no	—
295	C₂²×C₁₉₇	—	2	2	no	—
296	C₂²×C₁₉₇	—	2	2	no	—
297	C₂²×C₁₉₇	—	2	2	no	—
298	C₂²×C₁₉₇	C₂×#41	1	2	yes	—
299	C₂²×C₁₉₇	C₂⁵	1	1	yes	characteristic
300	C₂×D₁₉₇	—	2	8	no	—
301	C₂×D₁₉₇	—	2	1	no	—
302	C₂×D₁₉₇	—	2	1	no	—
303	C₂×D₁₉₇	—	2	1	no	—
304	C₂×D₁₉₇	—	2	1	no	—
305	C₂×D₁₉₇	—	2	2	no	—
306	C₂×D₁₉₇	—	2	2	no	—
307	C₂×D₁₉₇	—	2	2	no	—
308	C₂×D₁₉₇	C₂×#41	1	2	yes	—
309	C₂×D₁₉₇	C₂×#41	1	2	yes	—
310	C₄×C₁₉₇	—	2	1	no	—
311	C₄×C₁₉₇	—	2	1	no	—
312	C₄×C₁₉₇	—	2	1	no	—
313	C₄×C₁₉₇	—	2	1	no	—
314	C₄×C₁₉₇	—	2	2	no	—
315	C₄×C₁₉₇	—	2	2	no	—
316	C₄×C₁₉₇	—	2	2	no	—
317	C₄×C₁₉₇	C₂×#41	1	2	yes	—
318	C₄×C₁₉₇	C₂×#41	1	2	yes	—
319	Dic₁₉₇	—	2	1	no	—
320	Dic₁₉₇	—	2	1	no	—
321	Dic₁₉₇	—	2	2	no	—
322	Dic₁₉₇	—	2	2	no	—
323	Dic₁₉₇	—	2	2	no	—
324	Dic₁₉₇	C₂×#41	1	2	yes	—
325	Dic₁₉₇	C₂×#41	1	2	yes	—
326	Dic₁₉₇	C₂×#41	1	2	yes	—
327	Dic₁₉₇	C₂×#41	1	2	yes	—
328	C₂×C₁₉₇	—	2	2	no	—
329	C₂×C₁₉₇	—	4	2	no	—
330	C₂×C₁₉₇	C₂²×#41	1	1	yes	characteristic
331	C₂×C₁₉₇	C₂²×#41	1	1	yes	characteristic
332	C₂×C₁₉₇	C₂²×#41	1	1	yes	characteristic
333	D₁₉₇	—	2	2	no	—
334	D₁₉₇	—	2	2	no	—
335	D₁₉₇	—	4	2	no	—
336	C₁₉₇	#3444	1	1	yes	characteristic, complemented, Sylow
337	#3444	—	197	1	no	maximal, Sylow
338	#533	—	197	1	no	—
339	#533	—	197	1	no	—
340	#533	—	197	1	no	—
341	#532	—	197	1	no	—
342	#532	—	197	1	no	—
343	#532	—	197	1	no	—
344	#529	—	197	2	no	—
345	#529	—	197	2	no	—
346	#529	—	197	1	no	—
347	#529	—	197	1	no	—
348	#529	—	197	2	no	—
349	#529	—	197	2	no	—
350	#529	—	197	1	no	—
351	#529	D₁₉₇	1	1	yes	characteristic, complemented
352	#525	—	197	2	no	—
353	#525	—	197	1	no	—
354	#525	—	197	1	no	—
355	#525	—	197	2	no	—
356	C₄×#41	—	197	1	no	—
357	C₄×#41	—	197	2	no	—
358	C₄×#41	—	197	1	no	—
359	C₄×#41	—	197	2	no	—
360	C₂²×C₄²	—	197	1	no	—
361	C₂×#41	—	197	1	no	—
362	C₂×#41	—	197	1	no	—
363	C₂×#41	—	197	2	no	—
364	C₂×#41	—	197	2	no	—
365	C₂³×C₄	—	197	1	no	—
366	C₂³×C₄	—	197	1	no	—
367	C₂³×C₄	—	197	1	no	—
368	C₄⋊Q₈	—	197	1	no	—
369	C₄⋊Q₈	—	197	1	no	—
370	C₄⋊Q₈	—	197	1	no	—
371	#127	—	197	1	no	—
372	#126	—	197	2	no	—
373	#126	—	197	2	no	—
374	#126	—	197	2	no	—
375	#126	C₂×D₁₉₇	1	2	yes	complemented
376	#125	—	197	2	no	—
377	#125	—	197	2	no	—
378	#125	—	197	1	no	—
379	#125	C₂×D₁₉₇	1	1	yes	characteristic, complemented
380	#124	—	197	2	no	—
381	#124	—	197	2	no	—
382	#124	—	197	1	no	—
383	#124	C₂×D₁₉₇	1	1	yes	characteristic, complemented
384	#123	—	197	2	no	—
385	#123	—	197	2	no	—
386	#123	—	197	2	no	—
387	#123	—	197	2	no	—
388	#123	—	197	2	no	—
389	#123	C₂×D₁₉₇	1	2	yes	—
390	C₂²⋊Q₈	—	197	1	no	—
391	C₂²⋊Q₈	—	197	1	no	—
392	C₂²⋊Q₈	—	197	2	no	—
393	C₂²⋊Q₈	—	197	2	no	—
394	C₂²⋊Q₈	—	197	2	no	—
395	C₂²⋊Q₈	—	197	1	no	—
396	C₂²⋊Q₈	—	197	2	no	—
397	C₂²⋊Q₈	C₂×D₁₉₇	1	1	yes	characteristic
398	#121	—	197	1	no	—
399	#121	—	197	2	no	—
400	#121	—	197	1	no	—
401	#121	—	197	1	no	—
402	#121	—	197	2	no	—
403	#121	—	197	2	no	—
404	#121	—	197	2	no	—
405	#121	C₂×D₁₉₇	1	1	yes	characteristic
406	#120	—	197	2	no	—
407	#120	—	197	2	no	—
408	C₄×Q₈	—	197	1	no	—
409	C₄×Q₈	—	197	2	no	—
410	C₄×Q₈	—	197	2	no	—
411	C₄×Q₈	—	197	2	no	—
412	C₄×Q₈	—	197	1	no	—
413	C₄×Q₈	—	197	2	no	—
414	C₄×Q₈	—	197	1	no	—
415	C₄×Q₈	C₂×D₁₉₇	1	1	yes	characteristic, complemented
416	C₄×D₄	—	197	2	no	—
417	C₄×D₄	—	197	1	no	—
418	C₄×D₄	—	197	2	no	—
419	C₄×D₄	—	197	2	no	—
420	C₄×D₄	—	197	2	no	—
421	C₄×D₄	—	197	2	no	—
422	C₄×D₄	—	197	2	no	—
423	C₄×D₄	—	197	2	no	—
424	C₄×D₄	—	197	1	no	—
425	C₄×D₄	—	197	2	no	—
426	C₄×D₄	—	197	2	no	—
427	C₄×D₄	—	197	2	no	—
428	C₄×D₄	—	197	2	no	—
429	C₄×D₄	—	197	2	no	—
430	C₄×D₄	—	197	2	no	—
431	C₄×D₄	—	197	2	no	—
432	C₄×D₄	—	197	2	no	—
433	C₄×D₄	—	197	1	no	—
434	C₄×D₄	C₂×D₁₉₇	1	2	yes	—
435	C₄×D₄	C₂×D₁₉₇	1	1	yes	characteristic, complemented
436	#117	—	197	1	no	—
437	#117	—	197	1	no	—
438	#117	—	197	2	no	—
439	#117	—	197	2	no	—
440	#117	—	197	2	no	—
441	#117	—	197	2	no	—
442	#117	—	197	2	no	—
443	#117	—	197	2	no	—
444	#117	—	197	2	no	—
445	#117	C₂×D₁₉₇	1	2	yes	complemented
446	C₂×C₄²	—	197	2	no	—
447	C₂×C₄²	—	197	1	no	—
448	C₂×C₄²	—	197	1	no	—
449	C₂×C₄²	—	197	1	no	—
450	C₂×C₄²	—	197	2	no	—
451	C₂×C₄²	—	197	1	no	—
452	C₂×C₄²	—	197	1	no	—
453	C₂×C₄²	—	197	1	no	—
454	C₂×C₄²	—	197	1	no	—
455	C₂×C₄²	—	197	1	no	—
456	C₂×C₄²	—	197	1	no	—
457	C₂×C₄²	—	197	1	no	—
458	C₂×C₄²	—	197	1	no	—
459	C₂×C₄²	C₂×D₁₉₇	1	1	yes	characteristic
460	C₂⁴	—	197	1	no	—
461	#41	—	394	8	no	—
462	#41	—	394	8	no	—
463	#41	—	394	4	no	—
464	#41	—	394	4	no	—
465	C₂×Q₈	—	197	1	no	—
466	C₂×Q₈	—	197	2	no	—
467	C₂×Q₈	—	197	2	no	—
468	C₂×Q₈	C₂²×D₁₉₇	1	1	yes	characteristic
469	C₂×D₄	—	197	2	no	—
470	C₂×D₄	—	197	2	no	—
471	C₂×D₄	—	197	2	no	—
472	C₂×D₄	—	197	2	no	—
473	C₂×D₄	—	197	2	no	—
474	C₂×D₄	—	197	2	no	—
475	C₂×D₄	—	197	2	no	—
476	C₂×D₄	—	197	1	no	—
477	C₂×D₄	C₂²×D₁₉₇	1	2	yes	—
478	C₂×D₄	C₂²×D₁₉₇	1	1	yes	characteristic
479	C₂²×C₄	—	394	4	no	—
480	C₂²×C₄	—	394	4	no	—
481	C₂²×C₄	—	394	4	no	—
482	C₂²×C₄	—	197	1	no	—
483	C₂²×C₄	—	197	1	no	—
484	C₂²×C₄	—	197	2	no	—
485	C₂²×C₄	—	197	2	no	—
486	C₂²×C₄	—	197	1	no	—
487	C₂²×C₄	—	197	1	no	—
488	C₂²×C₄	—	197	1	no	—
489	C₂²×C₄	—	197	1	no	—
490	C₂²×C₄	—	197	1	no	—
491	C₂²×C₄	—	197	1	no	—
492	C₂²×C₄	—	197	1	no	—
493	C₂²×C₄	—	197	1	no	—
494	C₂²×C₄	—	197	1	no	—
495	C₂²×C₄	—	197	2	no	—
496	C₂²×C₄	—	197	2	no	—
497	C₂²×C₄	—	197	1	no	—
498	C₂²×C₄	—	197	2	no	—
499	C₂²×C₄	—	197	1	no	—
500	C₂²×C₄	—	197	1	no	—
501	C₂²×C₄	—	197	1	no	—
502	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₉₇	1	2	yes	—
506	C₄⋊C₄	—	197	2	no	—
507	C₄⋊C₄	—	197	2	no	—
508	C₄⋊C₄	—	197	2	no	—
509	C₄⋊C₄	—	197	2	no	—
510	C₄⋊C₄	—	197	2	no	—
511	C₄⋊C₄	—	197	2	no	—
512	C₄⋊C₄	—	197	2	no	—
513	C₄⋊C₄	—	197	2	no	—
514	C₄⋊C₄	—	197	2	no	—
515	C₄⋊C₄	—	197	2	no	—
516	C₄⋊C₄	—	197	1	no	—
517	C₄⋊C₄	—	197	1	no	—
518	C₄⋊C₄	—	197	2	no	—
519	C₄⋊C₄	—	197	2	no	—
520	C₄⋊C₄	C₂²×D₁₉₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₉₇	1	2	yes	—
522	C₄⋊C₄	C₂²×D₁₉₇	1	2	yes	—
523	C₄⋊C₄	C₂²×D₁₉₇	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₉₇	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₉₇	1	2	yes	—
526	C₂²⋊C₄	—	197	2	no	—
527	C₂²⋊C₄	—	197	2	no	—
528	C₂²⋊C₄	—	197	2	no	—
529	C₂²⋊C₄	—	197	2	no	—
530	C₂²⋊C₄	—	197	2	no	—
531	C₂²⋊C₄	—	197	2	no	—
532	C₂²⋊C₄	—	197	2	no	—
533	C₂²⋊C₄	—	197	2	no	—
534	C₂²⋊C₄	—	197	2	no	—
535	C₂²⋊C₄	—	197	2	no	—
536	C₂²⋊C₄	—	197	2	no	—
537	C₂²⋊C₄	—	197	2	no	—
538	C₂²⋊C₄	—	197	2	no	—
539	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₉₇	1	2	yes	—
544	C₄²	—	197	1	no	—
545	C₄²	—	197	1	no	—
546	C₄²	—	197	1	no	—
547	C₄²	—	197	1	no	—
548	C₄²	—	197	1	no	—
549	C₄²	—	197	1	no	—
550	C₄²	—	197	1	no	—
551	C₄²	—	197	1	no	—
552	C₄²	—	197	1	no	—
553	C₄²	—	197	1	no	—
554	C₄²	—	197	2	no	—
555	C₄²	—	197	2	no	—
556	C₄²	—	197	2	no	—
557	C₄²	—	197	2	no	—
558	C₄²	—	197	1	no	—
559	C₄²	—	197	1	no	—
560	C₄²	—	197	2	no	—
561	C₄²	C₂²×D₁₉₇	1	1	yes	characteristic
562	C₄²	C₂²×D₁₉₇	1	1	yes	characteristic
563	C₄²	C₂²×D₁₉₇	1	1	yes	characteristic
564	C₄²	C₂²×D₁₉₇	1	1	yes	characteristic
565	C₄²	C₂²×D₁₉₇	1	2	yes	—
566	C₂³	—	394	2	no	—
567	C₂³	—	394	2	no	—
568	C₂³	—	394	2	no	—
569	C₂³	—	197	2	no	—
570	C₂³	—	197	1	no	—
571	C₂³	—	197	1	no	—
572	C₂³	C₂³×D₁₉₇	1	2	yes	—
573	C₂³	C₂³×D₁₉₇	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	394	4	no	—
576	Q₈	—	394	4	no	—
577	Q₈	—	394	2	no	—
578	D₄	—	2	4	no	—
579	D₄	—	2	2	no	—
580	D₄	—	394	4	no	—
581	D₄	—	394	4	no	—
582	D₄	—	394	4	no	—
583	D₄	—	394	4	no	—
584	D₄	—	394	4	no	—
585	D₄	—	394	4	no	—
586	D₄	—	394	4	no	—
587	D₄	—	394	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	394	2	no	—
593	C₂×C₄	—	394	2	no	—
594	C₂×C₄	—	394	2	no	—
595	C₂×C₄	—	394	2	no	—
596	C₂×C₄	—	394	2	no	—
597	C₂×C₄	—	394	2	no	—
598	C₂×C₄	—	394	2	no	—
599	C₂×C₄	—	394	2	no	—
600	C₂×C₄	—	394	4	no	—
601	C₂×C₄	—	394	4	no	—
602	C₂×C₄	—	394	2	no	—
603	C₂×C₄	—	394	2	no	—
604	C₂×C₄	—	394	4	no	—
605	C₂×C₄	—	394	4	no	—
606	C₂×C₄	—	394	2	no	—
607	C₂×C₄	—	394	2	no	—
608	C₂×C₄	—	394	4	no	—
609	C₂×C₄	—	197	1	no	—
610	C₂×C₄	—	197	1	no	—
611	C₂×C₄	—	197	2	no	—
612	C₂×C₄	—	197	2	no	—
613	C₂×C₄	—	197	2	no	—
614	C₂×C₄	—	197	4	no	—
615	C₂×C₄	—	197	1	no	—
616	C₂×C₄	—	197	1	no	—
617	C₂×C₄	—	197	1	no	—
618	C₂×C₄	—	197	1	no	—
619	C₂×C₄	—	197	4	no	—
620	C₂×C₄	—	197	4	no	—
621	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
626	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
627	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
628	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₉₇	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	394	8	no	—
636	C₂²	—	394	2	no	—
637	C₂²	—	394	2	no	—
638	C₂²	—	394	2	no	—
639	C₂²	—	394	1	no	—
640	C₂²	—	394	1	no	—
641	C₂²	—	394	1	no	—
642	C₂²	—	394	1	no	—
643	C₂²	—	197	2	no	—
644	C₂²	—	197	2	no	—
645	C₂²	#41×D₁₉₇	1	2	yes	—
646	C₂²	C₂⁴×D₁₉₇	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	394	1	no	—
655	C₄	—	394	1	no	—
656	C₄	—	394	2	no	—
657	C₄	—	394	2	no	—
658	C₄	—	394	2	no	—
659	C₄	—	197	2	no	—
660	C₄	—	197	2	no	—
661	C₄	—	197	2	no	—
662	C₄	—	197	2	no	—
663	C₄	#41×D₁₉₇	1	2	yes	—
664	C₄	#41×D₁₉₇	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	788	2	no	—
668	C₂	—	394	2	no	—
669	C₂	—	394	2	no	—
670	C₂	C₂×#41×D₁₉₇	1	1	yes	characteristic
671	C₂	C₂×#41×D₁₉₇	1	1	yes	characteristic
672	C₂	C₂×#41×D₁₉₇	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	#3444
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. #27161635	C₂	semidirect
2. #27161633	C₂	semidirect
3. #27161631	C₂	semidirect
4. #27161628	C₂	semidirect
5. #27161626	C₂	semidirect
6. #27161624	C₂	semidirect
7. #27161614	C₂	semidirect
8. #27161613	C₂	semidirect
9. #27161612	C₂	semidirect
10. #27161612	C₂	semidirect
11. #27161608	C₂	semidirect
12. #27161607	C₂	semidirect
13. #27161606	C₂	semidirect
14. #27161592	C₂	semidirect
15. #27161589	C₂	semidirect
16. #27161588	C₂	semidirect
17. #27161587	C₂	semidirect
18. C₄×#15691359	C₂	semidirect
19. #27161547	C₂	semidirect
20. C₄×#15691357	C₂	semidirect
21. C₄×#15691357	C₂	semidirect
22. C₂×C₄²×D₁₉₇	C₂	semidirect
23. #529×C₁₉₇	C₂	semidirect
31. #20263325	C₂²	semidirect
32. #20263325	C₂²	semidirect
33. #20263324	C₂²	semidirect
34. #20263322	C₂²	semidirect
35. #20263321	C₂²	semidirect
36. #20263320	C₂²	semidirect
37. #20263319	C₂²	semidirect
38. #20263318	C₂²	semidirect
39. #20263316	C₂²	semidirect
40. #20263316	C₂²	semidirect
41. #20263314	C₂²	semidirect
42. #20263312	C₂²	semidirect
43. #20263312	C₂²	semidirect
65. Q₈×Dic₁₉₇	C₂²	semidirect
66. C₄×Dic₃₉₄	C₂²	semidirect
67. C₄×Dic₃₉₄	C₂²	semidirect
68. #20263291	C₂²	semidirect
69. #20263291	C₂²	semidirect
70. #20263291	C₂²	semidirect
71. #20263291	C₂²	semidirect
73. C₄×D₇₈₈	C₂²	semidirect
75. D₄×Dic₁₉₇	C₂²	semidirect
79. #20263288	C₂²	semidirect
82. C₄×C₂²⋊D₁₉₇	C₂²	semidirect
87. #20263286	C₂²	semidirect
88. #20263286	C₂²	semidirect
89. #20263286	C₂²	semidirect
92. #20263284	C₂²	semidirect
93. #20263284	C₂²	semidirect
95. #20263283	C₂²	semidirect
97. #20263282	C₂²	semidirect
98. #20263282	C₂²	semidirect
102. C₂×C₄×Dic₁₉₇	C₂²	semidirect
111. C₄²×D₁₉₇	C₂²	semidirect
112. #126×C₁₉₇	C₂²	semidirect
113. #125×C₁₉₇	C₂²	semidirect
114. #124×C₁₉₇	C₂²	semidirect
118. C₄×Q₈×C₁₉₇	C₂²	semidirect
120. C₄×D₄×C₁₉₇	C₂²	semidirect
121. #117×C₁₉₇	C₂²	semidirect
250. C₂×Dic₁₉₇	#41	semidirect
273. C₄×D₁₉₇	#41	semidirect
274. C₄×D₁₉₇	#41	semidirect
336. C₁₉₇	#3444	semidirect
351. #529	D₁₉₇	semidirect
375. #126	C₂×D₁₉₇	semidirect
379. #125	C₂×D₁₉₇	semidirect
383. #124	C₂×D₁₉₇	semidirect
415. C₄×Q₈	C₂×D₁₉₇	semidirect
435. C₄×D₄	C₂×D₁₉₇	semidirect
445. #117	C₂×D₁₉₇	semidirect

Maximal subgroups

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

subgroup	index
#27161635	2
#27161633	2
#27161631	2
#27161628	2
#27161626	2
#27161624	2
#27161614	2
#27161613	2
#27161612	2
#27161608	2
#27161607	2
#27161606	2
#27161592	2
#27161589	2
#27161588	2
#27161587	2
C₄×#15691359	2
#27161547	2
C₄×#15691357	2
C₂×C₄²×D₁₉₇	2
#529×C₁₉₇	2
#3444	197