Subgroups — #3460×C₁₉₇ #38740394

Order 25216.

1140 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#544×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#542×C₁₉₇	C₂	1	4	yes	maximal, complemented
3	#540×C₁₉₇	C₂	1	4	yes	maximal, complemented
4	#538×C₁₉₇	C₂	1	4	yes	maximal, complemented
5	#537×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#535×C₁₉₇	C₂	1	2	yes	maximal, complemented
7	#532×C₁₉₇	C₂	1	4	yes	maximal, complemented
8	#529×C₁₉₇	C₂	1	4	yes	maximal, complemented
9	#525×C₁₉₇	C₂	1	4	yes	maximal, complemented
10	C₄×#41×C₁₉₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×D₄×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×C₁₉₇	C₂²	1	2	yes	—
13	C₂×#41×C₁₉₇	C₂²	1	4	yes	complemented
14	C₂²×D₄×C₁₉₇	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₁₉₇	C₂²	1	2	yes	—
16	C₄⋊Q₈×C₁₉₇	C₂²	1	4	yes	complemented
17	#127×C₁₉₇	C₂²	1	4	yes	—
18	#126×C₁₉₇	C₂²	1	8	yes	complemented
19	#125×C₁₉₇	C₂²	1	4	yes	complemented
20	#124×C₁₉₇	C₂²	1	4	yes	—
21	#124×C₁₉₇	C₂²	1	8	yes	complemented
22	#123×C₁₉₇	C₂²	1	8	yes	complemented
23	#123×C₁₉₇	C₂²	1	8	yes	complemented
24	C₂²⋊Q₈×C₁₉₇	C₂²	1	4	yes	—
25	C₂²⋊Q₈×C₁₉₇	C₂²	1	4	yes	complemented
26	C₂²⋊Q₈×C₁₉₇	C₂²	1	4	yes	complemented
27	#121×C₁₉₇	C₂²	1	4	yes	—
28	#121×C₁₉₇	C₂²	1	4	yes	—
29	#121×C₁₉₇	C₂²	1	4	yes	—
30	#121×C₁₉₇	C₂²	1	4	yes	complemented
31	#121×C₁₉₇	C₂²	1	4	yes	complemented
32	#121×C₁₉₇	C₂²	1	8	yes	complemented
33	#120×C₁₉₇	C₂²	1	8	yes	—
34	C₄×Q₈×C₁₉₇	C₂²	1	2	yes	complemented
35	C₄×Q₈×C₁₉₇	C₂²	1	2	yes	complemented
36	C₄×D₄×C₁₉₇	C₂²	1	4	yes	—
37	C₄×D₄×C₁₉₇	C₂²	1	4	yes	—
38	C₄×D₄×C₁₉₇	C₂²	1	4	yes	—
39	C₄×D₄×C₁₉₇	C₂²	1	4	yes	—
40	C₄×D₄×C₁₉₇	C₂²	1	2	yes	complemented
41	C₄×D₄×C₁₉₇	C₂²	1	2	yes	complemented
42	C₄×D₄×C₁₉₇	C₂²	1	8	yes	complemented
43	#117×C₁₉₇	C₂²	1	2	yes	—
44	#117×C₁₉₇	C₂²	1	4	yes	complemented
45	#117×C₁₉₇	C₂²	1	4	yes	complemented
46	C₂×C₄⋊C₄×C₁₉₇	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×C₁₉₇	C₂²	1	2	yes	—
48	C₂×C₄²×C₁₉₇	C₂²	1	1	yes	characteristic
49	C₂×C₄²×C₁₉₇	C₂²	1	4	yes	complemented
50	C₂⁴×C₁₉₇	C₂³	1	2	yes	—
51	#41×C₁₉₇	—	2	8	no	—
52	#41×C₁₉₇	—	4	8	no	—
53	C₂×Q₈×C₁₉₇	C₂³	1	2	yes	—
54	C₂×Q₈×C₁₉₇	C₂³	1	4	yes	—
55	C₂×D₄×C₁₉₇	—	2	4	no	—
56	C₂×D₄×C₁₉₇	C₂³	1	4	yes	—
57	C₂×D₄×C₁₉₇	C₂³	1	4	yes	—
58	C₂×D₄×C₁₉₇	C₂³	1	2	yes	—
59	C₂×D₄×C₁₉₇	C₂³	1	8	yes	—
60	C₂×D₄×C₁₉₇	C₂³	1	8	yes	—
61	C₂×D₄×C₁₉₇	C₂³	1	4	yes	—
62	C₂²×C₄×C₁₉₇	—	4	4	no	—
63	C₂²×C₄×C₁₉₇	C₂³	1	4	yes	—
64	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₉₇	C₂³	1	4	yes	—
66	C₂²×C₄×C₁₉₇	C₂³	1	4	yes	—
67	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₉₇	C₂³	1	4	yes	—
69	C₂²×C₄×C₁₉₇	C₂³	1	2	yes	—
70	C₂²×C₄×C₁₉₇	C₂³	1	4	yes	—
71	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
72	C₄⋊C₄×C₁₉₇	C₂³	1	4	yes	—
73	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
74	C₄⋊C₄×C₁₉₇	C₂³	1	2	yes	—
75	C₄⋊C₄×C₁₉₇	C₂³	1	4	yes	—
76	C₄⋊C₄×C₁₉₇	C₂³	1	4	yes	—
77	C₄⋊C₄×C₁₉₇	C₂³	1	4	yes	—
78	C₄⋊C₄×C₁₉₇	C₂³	1	4	yes	—
79	C₄⋊C₄×C₁₉₇	C₂³	1	8	yes	—
80	C₂²⋊C₄×C₁₉₇	C₂³	1	8	yes	—
81	C₂²⋊C₄×C₁₉₇	C₂³	1	4	yes	—
82	C₂²⋊C₄×C₁₉₇	C₂³	1	4	yes	—
83	C₂²⋊C₄×C₁₉₇	C₂³	1	4	yes	—
84	C₂²⋊C₄×C₁₉₇	C₂³	1	8	yes	—
85	C₂²⋊C₄×C₁₉₇	C₂³	1	8	yes	—
86	C₂²⋊C₄×C₁₉₇	C₂³	1	8	yes	—
87	C₄²×C₁₉₇	C₂³	1	2	yes	—
88	C₄²×C₁₉₇	C₂³	1	4	yes	—
89	C₄²×C₁₉₇	C₂³	1	4	yes	—
90	C₄²×C₁₉₇	C₂³	1	2	yes	—
91	C₄²×C₁₉₇	C₂³	1	4	yes	—
92	C₂³×C₁₉₇	—	2	4	no	—
93	C₂³×C₁₉₇	—	4	2	no	—
94	C₂³×C₁₉₇	—	4	2	no	—
95	C₂³×C₁₉₇	C₂⁴	1	4	yes	—
96	C₂³×C₁₉₇	C₂⁴	1	4	yes	—
97	C₂³×C₁₉₇	C₂⁴	1	1	yes	characteristic
98	Q₈×C₁₉₇	—	2	4	no	—
99	Q₈×C₁₉₇	—	4	4	no	—
100	D₄×C₁₉₇	—	2	8	no	—
101	D₄×C₁₉₇	—	2	8	no	—
102	D₄×C₁₉₇	—	2	4	no	—
103	D₄×C₁₉₇	—	4	8	no	—
104	D₄×C₁₉₇	—	4	4	no	—
105	D₄×C₁₉₇	—	4	8	no	—
106	C₂×C₄×C₁₉₇	—	2	8	no	—
107	C₂×C₄×C₁₉₇	—	2	2	no	—
108	C₂×C₄×C₁₉₇	—	2	8	no	—
109	C₂×C₄×C₁₉₇	—	2	8	no	—
110	C₂×C₄×C₁₉₇	—	4	4	no	—
111	C₂×C₄×C₁₉₇	—	4	2	no	—
112	C₂×C₄×C₁₉₇	—	4	1	no	—
113	C₂×C₄×C₁₉₇	—	4	4	no	—
114	C₂×C₄×C₁₉₇	#41	1	4	yes	complemented
115	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
116	C₂×C₄×C₁₉₇	C₂⁴	1	4	yes	—
117	C₂×C₄×C₁₉₇	C₂⁴	1	4	yes	—
118	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
119	C₂×C₄×C₁₉₇	C₂⁴	1	4	yes	—
120	C₂×C₄×C₁₉₇	C₂⁴	1	4	yes	—
121	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
122	C₂×C₄×C₁₉₇	C₂⁴	1	1	yes	characteristic
123	C₂²×C₁₉₇	—	2	1	no	—
124	C₂²×C₁₉₇	—	2	1	no	—
125	C₂²×C₁₉₇	—	2	4	no	—
126	C₂²×C₁₉₇	—	2	4	no	—
127	C₂²×C₁₉₇	—	2	4	no	—
128	C₂²×C₁₉₇	—	2	4	no	—
129	C₂²×C₁₉₇	—	2	4	no	—
130	C₂²×C₁₉₇	—	2	4	no	—
131	C₂²×C₁₉₇	—	4	8	no	—
132	C₂²×C₁₉₇	C₂×#41	1	2	yes	—
133	C₂²×C₁₉₇	C₂⁵	1	1	yes	characteristic
134	C₄×C₁₉₇	—	2	4	no	—
135	C₄×C₁₉₇	—	2	1	no	—
136	C₄×C₁₉₇	—	2	4	no	—
137	C₄×C₁₉₇	—	2	4	no	—
138	C₄×C₁₉₇	—	2	2	no	—
139	C₄×C₁₉₇	—	2	4	no	—
140	C₄×C₁₉₇	C₂×#41	1	4	yes	—
141	C₄×C₁₉₇	H(5,𝔽₂)	1	2	yes	—
142	C₂×C₁₉₇	—	2	2	no	—
143	C₂×C₁₉₇	—	4	4	no	—
144	C₂×C₁₉₇	—	4	4	no	—
145	C₂×C₁₉₇	C₂²×#41	1	1	yes	characteristic
146	C₂×C₁₉₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
147	C₂×C₁₉₇	#585	1	1	yes	characteristic
148	C₁₉₇	#3460	1	1	yes	characteristic, direct product factor, Sylow
149	#3460	C₁₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	#544	C₂×C₁₉₇	1	1	yes	characteristic, complemented
151	#542	C₂×C₁₉₇	1	4	yes	complemented
152	#540	C₂×C₁₉₇	1	4	yes	complemented
153	#538	C₂×C₁₉₇	1	4	yes	complemented
154	#537	C₂×C₁₉₇	1	1	yes	characteristic, complemented
155	#535	C₂×C₁₉₇	1	2	yes	complemented
156	#532	C₂×C₁₉₇	1	4	yes	complemented
157	#529	C₂×C₁₉₇	1	4	yes	complemented
158	#525	C₂×C₁₉₇	1	4	yes	complemented
159	C₄×#41	C₂×C₁₉₇	1	2	yes	complemented
160	C₂×C₄×D₄	C₂×C₁₉₇	1	1	yes	characteristic, complemented
161	C₂×#41	C₂²×C₁₉₇	1	2	yes	—
162	C₂×#41	C₂²×C₁₉₇	1	4	yes	complemented
163	C₂²×D₄	C₂²×C₁₉₇	1	1	yes	characteristic
164	C₂³×C₄	C₂²×C₁₉₇	1	2	yes	—
165	C₄⋊Q₈	C₂²×C₁₉₇	1	4	yes	complemented
166	#127	C₂²×C₁₉₇	1	4	yes	—
167	#126	C₂²×C₁₉₇	1	8	yes	complemented
168	#125	C₂²×C₁₉₇	1	4	yes	complemented
169	#124	C₂²×C₁₉₇	1	4	yes	—
170	#124	C₂²×C₁₉₇	1	8	yes	complemented
171	#123	C₂²×C₁₉₇	1	8	yes	complemented
172	#123	C₂²×C₁₉₇	1	8	yes	complemented
173	C₂²⋊Q₈	C₂²×C₁₉₇	1	4	yes	—
174	C₂²⋊Q₈	C₂²×C₁₉₇	1	4	yes	complemented
175	C₂²⋊Q₈	C₂²×C₁₉₇	1	4	yes	complemented
176	#121	C₂²×C₁₉₇	1	4	yes	—
177	#121	C₂²×C₁₉₇	1	4	yes	—
178	#121	C₂²×C₁₉₇	1	4	yes	—
179	#121	C₂²×C₁₉₇	1	4	yes	complemented
180	#121	C₂²×C₁₉₇	1	4	yes	complemented
181	#121	C₂²×C₁₉₇	1	8	yes	complemented
182	#120	C₂²×C₁₉₇	1	8	yes	—
183	C₄×Q₈	C₂²×C₁₉₇	1	2	yes	complemented
184	C₄×Q₈	C₂²×C₁₉₇	1	2	yes	complemented
185	C₄×D₄	C₂²×C₁₉₇	1	4	yes	—
186	C₄×D₄	C₂²×C₁₉₇	1	4	yes	—
187	C₄×D₄	C₂²×C₁₉₇	1	4	yes	—
188	C₄×D₄	C₂²×C₁₉₇	1	4	yes	—
189	C₄×D₄	C₂²×C₁₉₇	1	2	yes	complemented
190	C₄×D₄	C₂²×C₁₉₇	1	2	yes	complemented
191	C₄×D₄	C₂²×C₁₉₇	1	8	yes	complemented
192	#117	C₂²×C₁₉₇	1	2	yes	—
193	#117	C₂²×C₁₉₇	1	4	yes	complemented
194	#117	C₂²×C₁₉₇	1	4	yes	complemented
195	C₂×C₄⋊C₄	C₂²×C₁₉₇	1	1	yes	characteristic
196	C₂×C₂²⋊C₄	C₂²×C₁₉₇	1	2	yes	—
197	C₂×C₄²	C₂²×C₁₉₇	1	1	yes	characteristic
198	C₂×C₄²	C₂²×C₁₉₇	1	4	yes	complemented
199	C₂⁴	C₂³×C₁₉₇	1	2	yes	—
200	#41	—	2	8	no	—
201	#41	—	4	8	no	—
202	C₂×Q₈	C₂³×C₁₉₇	1	2	yes	—
203	C₂×Q₈	C₂³×C₁₉₇	1	4	yes	—
204	C₂×D₄	—	2	4	no	—
205	C₂×D₄	C₂³×C₁₉₇	1	4	yes	—
206	C₂×D₄	C₂³×C₁₉₇	1	4	yes	—
207	C₂×D₄	C₂³×C₁₉₇	1	2	yes	—
208	C₂×D₄	C₂³×C₁₉₇	1	8	yes	—
209	C₂×D₄	C₂³×C₁₉₇	1	8	yes	—
210	C₂×D₄	C₂³×C₁₉₇	1	4	yes	—
211	C₂²×C₄	—	4	4	no	—
212	C₂²×C₄	C₂³×C₁₉₇	1	1	yes	characteristic
213	C₂²×C₄	C₂³×C₁₉₇	1	4	yes	—
214	C₂²×C₄	C₂³×C₁₉₇	1	4	yes	—
215	C₂²×C₄	C₂³×C₁₉₇	1	4	yes	—
216	C₂²×C₄	C₂³×C₁₉₇	1	1	yes	characteristic
217	C₂²×C₄	C₂³×C₁₉₇	1	4	yes	—
218	C₂²×C₄	C₂³×C₁₉₇	1	2	yes	—
219	C₂²×C₄	C₂³×C₁₉₇	1	4	yes	—
220	C₂²×C₄	C₂³×C₁₉₇	1	1	yes	characteristic
221	C₄⋊C₄	C₂³×C₁₉₇	1	4	yes	—
222	C₄⋊C₄	C₂³×C₁₉₇	1	2	yes	—
223	C₄⋊C₄	C₂³×C₁₉₇	1	2	yes	—
224	C₄⋊C₄	C₂³×C₁₉₇	1	4	yes	—
225	C₄⋊C₄	C₂³×C₁₉₇	1	4	yes	—
226	C₄⋊C₄	C₂³×C₁₉₇	1	4	yes	—
227	C₄⋊C₄	C₂³×C₁₉₇	1	4	yes	—
228	C₄⋊C₄	C₂³×C₁₉₇	1	8	yes	—
229	C₂²⋊C₄	C₂³×C₁₉₇	1	8	yes	—
230	C₂²⋊C₄	C₂³×C₁₉₇	1	4	yes	—
231	C₂²⋊C₄	C₂³×C₁₉₇	1	4	yes	—
232	C₂²⋊C₄	C₂³×C₁₉₇	1	4	yes	—
233	C₂²⋊C₄	C₂³×C₁₉₇	1	8	yes	—
234	C₂²⋊C₄	C₂³×C₁₉₇	1	8	yes	—
235	C₂²⋊C₄	C₂³×C₁₉₇	1	8	yes	—
236	C₄²	C₂³×C₁₉₇	1	2	yes	—
237	C₄²	C₂³×C₁₉₇	1	2	yes	—
238	C₄²	C₂³×C₁₉₇	1	4	yes	—
239	C₄²	C₂³×C₁₉₇	1	4	yes	—
240	C₄²	C₂³×C₁₉₇	1	4	yes	—
241	C₂³	—	2	4	no	—
242	C₂³	—	4	2	no	—
243	C₂³	—	4	2	no	—
244	C₂³	C₂⁴×C₁₉₇	1	4	yes	—
245	C₂³	C₂⁴×C₁₉₇	1	4	yes	—
246	C₂³	C₂⁴×C₁₉₇	1	1	yes	characteristic
247	Q₈	—	2	4	no	—
248	Q₈	—	4	4	no	—
249	D₄	—	2	8	no	—
250	D₄	—	2	8	no	—
251	D₄	—	2	4	no	—
252	D₄	—	4	4	no	—
253	D₄	—	4	8	no	—
254	D₄	—	4	8	no	—
255	C₂×C₄	—	2	8	no	—
256	C₂×C₄	—	2	2	no	—
257	C₂×C₄	—	2	8	no	—
258	C₂×C₄	—	2	8	no	—
259	C₂×C₄	—	4	4	no	—
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	4	4	no	—
263	C₂×C₄	#41×C₁₉₇	1	4	yes	complemented
264	C₂×C₄	C₂⁴×C₁₉₇	1	2	yes	—
265	C₂×C₄	C₂⁴×C₁₉₇	1	4	yes	—
266	C₂×C₄	C₂⁴×C₁₉₇	1	4	yes	—
267	C₂×C₄	C₂⁴×C₁₉₇	1	1	yes	characteristic
268	C₂×C₄	C₂⁴×C₁₉₇	1	4	yes	—
269	C₂×C₄	C₂⁴×C₁₉₇	1	4	yes	—
270	C₂×C₄	C₂⁴×C₁₉₇	1	2	yes	—
271	C₂×C₄	C₂⁴×C₁₉₇	1	1	yes	characteristic
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	2	4	no	—
275	C₂²	—	2	4	no	—
276	C₂²	—	2	4	no	—
277	C₂²	—	2	4	no	—
278	C₂²	—	2	4	no	—
279	C₂²	—	2	4	no	—
280	C₂²	—	4	8	no	—
281	C₂²	C₂×#41×C₁₉₇	1	2	yes	—
282	C₂²	C₂⁵×C₁₉₇	1	1	yes	characteristic
283	C₄	—	2	4	no	—
284	C₄	—	2	1	no	—
285	C₄	—	2	4	no	—
286	C₄	—	2	4	no	—
287	C₄	—	2	2	no	—
288	C₄	—	2	4	no	—
289	C₄	C₂×#41×C₁₉₇	1	4	yes	—
290	C₄	H(5,𝔽₂)×C₁₉₇	1	2	yes	—
291	C₂	—	2	2	no	—
292	C₂	—	4	4	no	—
293	C₂	—	4	4	no	—
294	C₂	C₂²×#41×C₁₉₇	1	1	yes	characteristic
295	C₂	C₂×H(5,𝔽₂)×C₁₉₇	1	1	yes	characteristic
296	C₂	#585×C₁₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₉₇
socle	C₂²×C₁₉₇	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #544×C₁₉₇	C₂	semidirect
2. #542×C₁₉₇	C₂	semidirect
3. #540×C₁₉₇	C₂	semidirect
4. #538×C₁₉₇	C₂	semidirect
5. #537×C₁₉₇	C₂	semidirect
6. #535×C₁₉₇	C₂	semidirect
7. #532×C₁₉₇	C₂	semidirect
8. #529×C₁₉₇	C₂	semidirect
9. #525×C₁₉₇	C₂	semidirect
10. C₄×#41×C₁₉₇	C₂	semidirect
11. C₂×C₄×D₄×C₁₉₇	C₂	semidirect
13. C₂×#41×C₁₉₇	C₂²	semidirect
16. C₄⋊Q₈×C₁₉₇	C₂²	semidirect
18. #126×C₁₉₇	C₂²	semidirect
19. #125×C₁₉₇	C₂²	semidirect
21. #124×C₁₉₇	C₂²	semidirect
22. #123×C₁₉₇	C₂²	semidirect
23. #123×C₁₉₇	C₂²	semidirect
25. C₂²⋊Q₈×C₁₉₇	C₂²	semidirect
26. C₂²⋊Q₈×C₁₉₇	C₂²	semidirect
30. #121×C₁₉₇	C₂²	semidirect
31. #121×C₁₉₇	C₂²	semidirect
32. #121×C₁₉₇	C₂²	semidirect
34. C₄×Q₈×C₁₉₇	C₂²	semidirect
35. C₄×Q₈×C₁₉₇	C₂²	semidirect
40. C₄×D₄×C₁₉₇	C₂²	semidirect
41. C₄×D₄×C₁₉₇	C₂²	semidirect
42. C₄×D₄×C₁₉₇	C₂²	semidirect
44. #117×C₁₉₇	C₂²	semidirect
45. #117×C₁₉₇	C₂²	semidirect
49. C₂×C₄²×C₁₉₇	C₂²	semidirect
114. C₂×C₄×C₁₉₇	#41	semidirect
148. C₁₉₇	#3460	direct (N × H)
149. #3460	C₁₉₇	direct (N × H)
150. #544	C₂×C₁₉₇	semidirect
151. #542	C₂×C₁₉₇	semidirect
152. #540	C₂×C₁₉₇	semidirect
153. #538	C₂×C₁₉₇	semidirect
154. #537	C₂×C₁₉₇	semidirect
155. #535	C₂×C₁₉₇	semidirect
156. #532	C₂×C₁₉₇	semidirect
157. #529	C₂×C₁₉₇	semidirect
158. #525	C₂×C₁₉₇	semidirect
159. C₄×#41	C₂×C₁₉₇	semidirect
160. C₂×C₄×D₄	C₂×C₁₉₇	semidirect
162. C₂×#41	C₂²×C₁₉₇	semidirect
165. C₄⋊Q₈	C₂²×C₁₉₇	semidirect
167. #126	C₂²×C₁₉₇	semidirect
168. #125	C₂²×C₁₉₇	semidirect
170. #124	C₂²×C₁₉₇	semidirect
171. #123	C₂²×C₁₉₇	semidirect
172. #123	C₂²×C₁₉₇	semidirect
174. C₂²⋊Q₈	C₂²×C₁₉₇	semidirect
175. C₂²⋊Q₈	C₂²×C₁₉₇	semidirect
179. #121	C₂²×C₁₉₇	semidirect
180. #121	C₂²×C₁₉₇	semidirect
181. #121	C₂²×C₁₉₇	semidirect
183. C₄×Q₈	C₂²×C₁₉₇	semidirect
184. C₄×Q₈	C₂²×C₁₉₇	semidirect
189. C₄×D₄	C₂²×C₁₉₇	semidirect
190. C₄×D₄	C₂²×C₁₉₇	semidirect
191. C₄×D₄	C₂²×C₁₉₇	semidirect
193. #117	C₂²×C₁₉₇	semidirect
194. #117	C₂²×C₁₉₇	semidirect
198. C₂×C₄²	C₂²×C₁₉₇	semidirect
263. C₂×C₄	#41×C₁₉₇	semidirect

Maximal subgroups

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

subgroup	index
#544×C₁₉₇	2
#542×C₁₉₇	2
#540×C₁₉₇	2
#538×C₁₉₇	2
#537×C₁₉₇	2
#535×C₁₉₇	2
#532×C₁₉₇	2
#529×C₁₉₇	2
#525×C₁₉₇	2
C₄×#41×C₁₉₇	2
C₂×C₄×D₄×C₁₉₇	2
#3460	197

Subgroups — #3460×C197 #38740394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3460×C₁₉₇ #38740394