Subgroups — C₂×#27161589 #38755953

Order 25216.

1880 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15691357	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄×D₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#27161589	C₂	1	16	yes	maximal, direct product factor
4	C₂×#20263308	C₂	1	2	yes	maximal, complemented
5	C₂×#20263306	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#20263305	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#20263297	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#20263294	C₂	1	2	yes	maximal, complemented
9	C₂×D₄×Dic₁₉₇	C₂	1	2	yes	maximal, complemented
10	C₂×#20263286	C₂	1	2	yes	maximal, complemented
11	C₂×#20263284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₁₉₇	C₂²	1	1	yes	characteristic
14	C₂×#15691357	—	2	8	no	—
15	C₂×#15691357	C₂²	1	8	yes	complemented
16	C₂²×Dic₃₉₄	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₉₇	C₂²	1	2	yes	—
18	C₂²×C₂²⋊D₁₉₇	C₂²	1	2	yes	—
19	C₂³×Dic₁₉₇	C₂²	1	1	yes	characteristic
20	C₂³×Dic₁₉₇	C₂²	1	2	yes	complemented
21	C₂²×C₄×D₁₉₇	—	2	8	no	—
22	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₉₇	C₂²	1	8	yes	complemented
27	#20263308	C₂²	1	16	yes	complemented
28	#20263306	C₂²	1	8	yes	complemented
29	#20263305	C₂²	1	8	yes	complemented
30	#20263297	C₂²	1	8	yes	complemented
31	#20263294	C₂²	1	16	yes	complemented
32	D₄×Dic₁₉₇	C₂²	1	16	yes	complemented
33	#20263286	C₂²	1	16	yes	complemented
34	#20263284	C₂²	1	8	yes	complemented
35	C₂×C₄⋊Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄⋊Dic₁₉₇	C₂²	1	2	yes	complemented
37	C₂×#15691337	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Dic₁₉₇	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₁₉₇	C₂²	1	2	yes	complemented
40	C₂×#15691335	C₂²	1	2	yes	—
41	C₂×#15691335	C₂²	1	2	yes	—
42	C₂×C₄×Dic₁₉₇	C₂²	1	2	yes	complemented
43	C₂²×D₄×C₁₉₇	C₂²	1	2	yes	—
44	C₂²×D₄×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
45	C₂³×C₄×C₁₉₇	C₂²	1	1	yes	characteristic
46	#121×C₁₉₇	C₂²	1	8	yes	complemented
47	C₂×C₄⋊C₄×C₁₉₇	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊C₄×C₁₉₇	C₂²	1	2	yes	complemented
49	C₂³×D₁₉₇	—	2	4	no	—
50	C₂³×D₁₉₇	—	2	4	no	—
51	C₂³×D₁₉₇	—	2	4	no	—
52	C₂³×D₁₉₇	C₂³	1	4	yes	—
53	C₂³×D₁₉₇	C₂³	1	1	yes	characteristic
54	C₂³×D₁₉₇	C₂³	1	1	yes	characteristic
55	#15691357	—	2	32	no	—
56	C₂×Dic₃₉₄	—	2	4	no	—
57	C₂×Dic₃₉₄	C₂³	1	4	yes	complemented
58	C₂×C₂²⋊D₁₉₇	—	2	8	no	—
59	C₂×C₂²⋊D₁₉₇	—	2	8	no	—
60	C₂×C₂²⋊D₁₉₇	C₂³	1	8	yes	—
61	C₂×C₂²⋊D₁₉₇	C₂³	1	8	yes	—
62	C₂²×Dic₁₉₇	—	2	4	no	—
63	C₂²×Dic₁₉₇	—	2	8	no	—
64	C₂²×Dic₁₉₇	C₂³	1	2	yes	—
65	C₂²×Dic₁₉₇	C₂³	1	2	yes	—
66	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
67	C₂²×Dic₁₉₇	C₂³	1	4	yes	—
68	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
69	C₂²×Dic₁₉₇	C₂³	1	8	yes	complemented
70	C₂×C₄×D₁₉₇	—	2	4	no	—
71	C₂×C₄×D₁₉₇	—	2	4	no	—
72	C₂×C₄×D₁₉₇	—	2	32	no	—
73	C₂×C₄×D₁₉₇	—	2	4	no	—
74	C₂×C₄×D₁₉₇	D₄	1	8	yes	complemented
75	C₂×C₄×D₁₉₇	C₂³	1	4	yes	—
76	C₂×C₄×D₁₉₇	C₂³	1	4	yes	—
77	C₂×C₄×D₁₉₇	C₂³	1	4	yes	—
78	C₂×C₄×D₁₉₇	C₂³	1	4	yes	—
79	C₄⋊Dic₁₉₇	C₂³	1	4	yes	complemented
80	C₄⋊Dic₁₉₇	C₂³	1	8	yes	complemented
81	#15691337	C₂³	1	8	yes	complemented
82	C₂²⋊Dic₁₉₇	C₂³	1	8	yes	—
83	C₂²⋊Dic₁₉₇	C₂³	1	8	yes	complemented
84	#15691335	C₂³	1	8	yes	—
85	#15691335	C₂³	1	8	yes	—
86	C₄×Dic₁₉₇	C₂³	1	8	yes	complemented
87	C₂⁴×C₁₉₇	C₂³	1	2	yes	—
88	C₂⁴×C₁₉₇	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₁₉₇	—	2	8	no	—
90	C₂×D₄×C₁₉₇	—	2	4	no	—
91	C₂×D₄×C₁₉₇	C₂³	1	8	yes	—
92	C₂×D₄×C₁₉₇	C₂³	1	4	yes	complemented
93	C₂²×C₄×C₁₉₇	—	2	4	no	—
94	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₉₇	C₂³	1	2	yes	—
96	C₂²×C₄×C₁₉₇	C₂³	1	4	yes	—
97	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₄×C₁₉₇	C₂³	1	4	yes	complemented
99	C₂²⋊C₄×C₁₉₇	C₂³	1	8	yes	complemented
100	C₂²×D₁₉₇	—	2	32	no	—
101	C₂²×D₁₉₇	—	2	2	no	—
102	C₂²×D₁₉₇	—	2	2	no	—
103	C₂²×D₁₉₇	—	2	2	no	—
104	C₂²×D₁₉₇	—	2	2	no	—
105	C₂²×D₁₉₇	—	2	8	no	—
106	C₂²×D₁₉₇	—	2	8	no	—
107	C₂²×D₁₉₇	—	2	8	no	—
108	C₂²×D₁₉₇	C₂×D₄	1	4	yes	—
109	C₂²×D₁₉₇	#41	1	4	yes	complemented
110	C₂²×D₁₉₇	C₂⁴	1	2	yes	—
111	C₂²×D₁₉₇	C₂⁴	1	2	yes	—
112	Dic₃₉₄	—	2	8	no	—
113	C₂²⋊D₁₉₇	—	2	16	no	—
114	C₂²⋊D₁₉₇	—	2	16	no	—
115	C₂×Dic₁₉₇	—	2	2	no	—
116	C₂×Dic₁₉₇	—	2	4	no	—
117	C₂×Dic₁₉₇	—	2	4	no	—
118	C₂×Dic₁₉₇	—	2	8	no	—
119	C₂×Dic₁₉₇	—	2	16	no	—
120	C₂×Dic₁₉₇	C₂×D₄	1	4	yes	—
121	C₂×Dic₁₉₇	C₂⁴	1	4	yes	—
122	C₂×Dic₁₉₇	C₂⁴	1	4	yes	—
123	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
124	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
125	C₄×D₁₉₇	—	2	8	no	—
126	C₄×D₁₉₇	—	2	8	no	—
127	C₄×D₁₉₇	—	2	8	no	—
128	C₄×D₁₉₇	C₂×D₄	1	16	yes	complemented
129	C₂³×C₁₉₇	—	2	2	no	—
130	C₂³×C₁₉₇	—	2	2	no	—
131	C₂³×C₁₉₇	—	2	4	no	—
132	C₂³×C₁₉₇	—	2	4	no	—
133	C₂³×C₁₉₇	—	2	4	no	—
134	C₂³×C₁₉₇	#41	1	4	yes	complemented
135	C₂³×C₁₉₇	C₂⁴	1	4	yes	—
136	C₂³×C₁₉₇	C₂⁴	1	2	yes	—
137	C₂³×C₁₉₇	C₂⁴	1	1	yes	characteristic
138	D₄×C₁₉₇	—	2	16	no	—
139	D₄×C₁₉₇	—	2	8	no	—
140	C₂×C₄×C₁₉₇	—	2	2	no	—
141	C₂×C₄×C₁₉₇	—	2	4	no	—
142	C₂×C₄×C₁₉₇	—	2	8	no	—
143	C₂×C₄×C₁₉₇	C₂×D₄	1	4	yes	—
144	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
145	C₂×C₄×C₁₉₇	C₂⁴	1	4	yes	—
146	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
147	C₂²×C₁₉₇	—	2	8	no	—
148	C₂²×C₁₉₇	—	2	2	no	—
149	C₂²×C₁₉₇	—	2	2	no	—
150	C₂²×C₁₉₇	—	2	4	no	—
151	C₂²×C₁₉₇	—	2	4	no	—
152	C₂²×C₁₉₇	—	2	4	no	—
153	C₂²×C₁₉₇	—	4	8	no	—
154	C₂²×C₁₉₇	C₂²×D₄	1	2	yes	—
155	C₂²×C₁₉₇	C₂×#41	1	2	yes	—
156	C₂²×C₁₉₇	C₂×#41	1	2	yes	—
157	C₂²×C₁₉₇	C₂×#41	1	4	yes	complemented
158	C₂²×C₁₉₇	C₂⁵	1	1	yes	characteristic
159	C₂×D₁₉₇	—	2	32	no	—
160	C₂×D₁₉₇	—	2	8	no	—
161	C₂×D₁₉₇	—	2	8	no	—
162	C₂×D₁₉₇	—	2	2	no	—
163	C₂×D₁₉₇	—	2	2	no	—
164	C₂×D₁₉₇	—	2	2	no	—
165	C₂×D₁₉₇	—	2	2	no	—
166	C₂×D₁₉₇	C₂²×D₄	1	4	yes	—
167	C₂×D₁₉₇	C₂×#41	1	4	yes	complemented
168	C₄×C₁₉₇	—	2	2	no	—
169	C₄×C₁₉₇	—	2	4	no	—
170	C₄×C₁₉₇	C₂²×D₄	1	4	yes	—
171	Dic₁₉₇	—	2	2	no	—
172	Dic₁₉₇	—	2	4	no	—
173	Dic₁₉₇	—	2	4	no	—
174	Dic₁₉₇	C₂²×D₄	1	4	yes	—
175	C₂×C₁₉₇	—	2	4	no	—
176	C₂×C₁₉₇	—	4	4	no	—
177	C₂×C₁₉₇	#525	1	4	yes	complemented
178	C₂×C₁₉₇	C₂³×D₄	1	1	yes	characteristic
179	C₂×C₁₉₇	C₂²×#41	1	1	yes	characteristic
180	C₂×C₁₉₇	C₂²×#41	1	1	yes	characteristic
181	D₁₉₇	—	2	4	no	—
182	D₁₉₇	—	2	4	no	—
183	C₁₉₇	C₂×#525	1	1	yes	characteristic, complemented, Sylow
184	C₂×#525	—	197	1	no	maximal, Sylow
185	C₂²×#41	—	197	1	no	—
186	C₂⁴×C₄	—	197	1	no	—
187	#525	—	197	16	no	—
188	C₂×#123	—	197	2	no	—
189	C₂×C₂²⋊Q₈	—	197	1	no	—
190	C₂×C₂²⋊Q₈	—	197	1	no	—
191	C₂×#121	—	197	1	no	—
192	C₂×#121	D₁₉₇	1	1	yes	characteristic, complemented
193	C₂×#120	—	197	2	no	—
194	C₂×C₄×D₄	—	197	2	no	—
195	C₂×C₄×D₄	—	197	2	no	—
196	C₂×#117	—	197	1	no	—
197	C₂⁵	—	197	1	no	—
198	C₂×#41	—	394	8	no	—
199	C₂×#41	—	197	8	no	—
200	C₂²×Q₈	—	197	1	no	—
201	C₂²×D₄	—	197	2	no	—
202	C₂²×D₄	—	197	2	no	—
203	C₂²×D₄	C₂×D₁₉₇	1	2	yes	—
204	C₂²×D₄	C₂×D₁₉₇	1	1	yes	characteristic, complemented
205	C₂³×C₄	—	394	8	no	—
206	C₂³×C₄	—	197	1	no	—
207	C₂³×C₄	—	197	2	no	—
208	C₂³×C₄	—	197	1	no	—
209	C₂³×C₄	—	197	1	no	—
210	C₂³×C₄	—	197	1	no	—
211	C₂³×C₄	—	197	8	no	—
212	C₂³×C₄	—	197	1	no	—
213	C₂³×C₄	C₂×D₁₉₇	1	1	yes	characteristic
214	#123	—	197	16	no	—
215	C₂²⋊Q₈	—	197	8	no	—
216	C₂²⋊Q₈	—	197	8	no	—
217	#121	—	197	8	no	—
218	#121	C₂×D₁₉₇	1	8	yes	complemented
219	#120	—	197	16	no	—
220	C₄×D₄	—	197	16	no	—
221	C₄×D₄	—	197	16	no	—
222	#117	—	197	8	no	—
223	C₂×C₄⋊C₄	—	197	1	no	—
224	C₂×C₄⋊C₄	—	197	2	no	—
225	C₂×C₄⋊C₄	—	197	2	no	—
226	C₂×C₄⋊C₄	C₂×D₁₉₇	1	1	yes	characteristic, complemented
227	C₂×C₂²⋊C₄	—	197	2	no	—
228	C₂×C₂²⋊C₄	—	197	2	no	—
229	C₂×C₂²⋊C₄	—	197	2	no	—
230	C₂×C₂²⋊C₄	—	197	2	no	—
231	C₂×C₂²⋊C₄	C₂×D₁₉₇	1	2	yes	complemented
232	C₂×C₄²	—	197	2	no	—
233	C₂⁴	—	394	4	no	—
234	C₂⁴	—	394	4	no	—
235	C₂⁴	—	394	4	no	—
236	C₂⁴	—	197	4	no	—
237	C₂⁴	—	197	1	no	—
238	C₂⁴	—	197	1	no	—
239	C₂⁴	C₂²×D₁₉₇	1	2	yes	—
240	C₂⁴	C₂²×D₁₉₇	1	1	yes	characteristic
241	#41	—	394	32	no	—
242	C₂×Q₈	—	394	4	no	—
243	C₂×Q₈	—	197	4	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	394	8	no	—
247	C₂×D₄	—	394	8	no	—
248	C₂×D₄	—	197	8	no	—
249	C₂×D₄	—	197	8	no	—
250	C₂×D₄	C₂²×D₁₉₇	1	8	yes	—
251	C₂×D₄	C₂²×D₁₉₇	1	4	yes	complemented
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	394	4	no	—
254	C₂²×C₄	—	394	4	no	—
255	C₂²×C₄	—	394	32	no	—
256	C₂²×C₄	—	394	4	no	—
257	C₂²×C₄	—	394	8	no	—
258	C₂²×C₄	—	394	4	no	—
259	C₂²×C₄	—	197	4	no	—
260	C₂²×C₄	—	197	8	no	—
261	C₂²×C₄	—	197	2	no	—
262	C₂²×C₄	—	197	1	no	—
263	C₂²×C₄	—	197	2	no	—
264	C₂²×C₄	—	197	4	no	—
265	C₂²×C₄	—	197	4	no	—
266	C₂²×C₄	—	197	4	no	—
267	C₂²×C₄	—	197	1	no	—
268	C₂²×C₄	—	197	8	no	—
269	C₂²×C₄	—	197	4	no	—
270	C₂²×C₄	C₂²×D₁₉₇	1	4	yes	—
271	C₂²×C₄	C₂²×D₁₉₇	1	2	yes	—
272	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
274	C₄⋊C₄	—	197	8	no	—
275	C₄⋊C₄	—	197	4	no	—
276	C₄⋊C₄	—	197	8	no	—
277	C₄⋊C₄	C₂²×D₁₉₇	1	4	yes	complemented
278	C₂²⋊C₄	—	197	8	no	—
279	C₂²⋊C₄	—	197	8	no	—
280	C₂²⋊C₄	—	197	8	no	—
281	C₂²⋊C₄	—	197	8	no	—
282	C₂²⋊C₄	C₂²×D₁₉₇	1	8	yes	complemented
283	C₄²	—	197	8	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	394	32	no	—
290	C₂³	—	394	8	no	—
291	C₂³	—	394	8	no	—
292	C₂³	—	394	2	no	—
293	C₂³	—	394	2	no	—
294	C₂³	—	394	2	no	—
295	C₂³	—	394	2	no	—
296	C₂³	—	394	8	no	—
297	C₂³	—	197	4	no	—
298	C₂³	—	197	4	no	—
299	C₂³	—	197	2	no	—
300	C₂³	—	197	2	no	—
301	C₂³	#15691357	1	4	yes	complemented
302	C₂³	C₂³×D₁₉₇	1	4	yes	—
303	C₂³	C₂³×D₁₉₇	1	2	yes	—
304	C₂³	C₂³×D₁₉₇	1	1	yes	characteristic
305	Q₈	—	394	8	no	—
306	D₄	—	2	16	no	—
307	D₄	—	2	8	no	—
308	D₄	—	394	16	no	—
309	D₄	—	394	16	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	394	8	no	—
314	C₂×C₄	—	394	8	no	—
315	C₂×C₄	—	394	2	no	—
316	C₂×C₄	—	394	4	no	—
317	C₂×C₄	—	394	4	no	—
318	C₂×C₄	—	394	8	no	—
319	C₂×C₄	—	394	16	no	—
320	C₂×C₄	—	394	8	no	—
321	C₂×C₄	—	197	4	no	—
322	C₂×C₄	—	197	2	no	—
323	C₂×C₄	—	197	4	no	—
324	C₂×C₄	—	197	4	no	—
325	C₂×C₄	—	197	2	no	—
326	C₂×C₄	—	197	16	no	—
327	C₂×C₄	D₄×D₁₉₇	1	4	yes	—
328	C₂×C₄	C₂³×D₁₉₇	1	4	yes	—
329	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
330	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	8	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	4	8	no	—
338	C₂²	—	394	32	no	—
339	C₂²	—	394	2	no	—
340	C₂²	—	394	2	no	—
341	C₂²	—	394	2	no	—
342	C₂²	—	394	2	no	—
343	C₂²	—	394	8	no	—
344	C₂²	—	394	8	no	—
345	C₂²	—	197	4	no	—
346	C₂²	—	197	4	no	—
347	C₂²	C₂×D₄×D₁₉₇	1	2	yes	—
348	C₂²	#41×D₁₉₇	1	2	yes	—
349	C₂²	C₂×#15691357	1	2	yes	—
350	C₂²	C₂×#15691357	1	4	yes	complemented
351	C₂²	C₂⁴×D₁₉₇	1	1	yes	characteristic
352	C₄	—	2	2	no	—
353	C₄	—	2	4	no	—
354	C₄	—	394	2	no	—
355	C₄	—	394	4	no	—
356	C₄	—	394	4	no	—
357	C₄	—	197	4	no	—
358	C₄	C₂×D₄×D₁₉₇	1	4	yes	—
359	C₂	—	2	4	no	—
360	C₂	—	4	4	no	—
361	C₂	—	394	4	no	—
362	C₂	—	394	4	no	—
363	C₂	#27161589	1	4	yes	direct product factor
364	C₂	C₂²×D₄×D₁₉₇	1	1	yes	characteristic
365	C₂	C₂×#41×D₁₉₇	1	1	yes	characteristic
366	C₂	C₂²×#15691357	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₉₇
commutator, cosocle	C₂²×C₁₉₇	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉₇
Fitting	C₂×#121×C₁₉₇	C₂
socle	C₂³×C₁₉₇	C₂⁴
hypercenter	C₂×#121	D₁₉₇
hypocenter	C₁₉₇	C₂×#525
LCS	G ▷ C₂²×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×#15691357	C₂	semidirect
2. C₂³×C₄×D₁₉₇	C₂	semidirect
3. #27161589	C₂	direct (N × H)
4. C₂×#20263308	C₂	semidirect
5. C₂×#20263306	C₂	semidirect
6. C₂×#20263305	C₂	semidirect
7. C₂×#20263297	C₂	semidirect
8. C₂×#20263294	C₂	semidirect
9. C₂×D₄×Dic₁₉₇	C₂	semidirect
10. C₂×#20263286	C₂	semidirect
11. C₂×#20263284	C₂	semidirect
12. C₂×#121×C₁₉₇	C₂	semidirect
15. C₂×#15691357	C₂²	semidirect
16. C₂²×Dic₃₉₄	C₂²	semidirect
20. C₂³×Dic₁₉₇	C₂²	semidirect
26. C₂²×C₄×D₁₉₇	C₂²	semidirect
27. #20263308	C₂²	semidirect
28. #20263306	C₂²	semidirect
29. #20263305	C₂²	semidirect
30. #20263297	C₂²	semidirect
31. #20263294	C₂²	semidirect
32. D₄×Dic₁₉₇	C₂²	semidirect
33. #20263286	C₂²	semidirect
34. #20263284	C₂²	semidirect
35. C₂×C₄⋊Dic₁₉₇	C₂²	semidirect
36. C₂×C₄⋊Dic₁₉₇	C₂²	semidirect
37. C₂×#15691337	C₂²	semidirect
39. C₂×C₂²⋊Dic₁₉₇	C₂²	semidirect
42. C₂×C₄×Dic₁₉₇	C₂²	semidirect
44. C₂²×D₄×C₁₉₇	C₂²	semidirect
46. #121×C₁₉₇	C₂²	semidirect
47. C₂×C₄⋊C₄×C₁₉₇	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₁₉₇	C₂²	semidirect
57. C₂×Dic₃₉₄	C₂³	semidirect
69. C₂²×Dic₁₉₇	C₂³	semidirect
74. C₂×C₄×D₁₉₇	D₄	semidirect
79. C₄⋊Dic₁₉₇	C₂³	semidirect
80. C₄⋊Dic₁₉₇	C₂³	semidirect
81. #15691337	C₂³	semidirect
83. C₂²⋊Dic₁₉₇	C₂³	semidirect
86. C₄×Dic₁₉₇	C₂³	semidirect
92. C₂×D₄×C₁₉₇	C₂³	semidirect
98. C₄⋊C₄×C₁₉₇	C₂³	semidirect
99. C₂²⋊C₄×C₁₉₇	C₂³	semidirect
109. C₂²×D₁₉₇	#41	semidirect
128. C₄×D₁₉₇	C₂×D₄	semidirect
134. C₂³×C₁₉₇	#41	semidirect
157. C₂²×C₁₉₇	C₂×#41	semidirect
167. C₂×D₁₉₇	C₂×#41	semidirect
177. C₂×C₁₉₇	#525	semidirect
183. C₁₉₇	C₂×#525	semidirect
192. C₂×#121	D₁₉₇	semidirect
204. C₂²×D₄	C₂×D₁₉₇	semidirect
218. #121	C₂×D₁₉₇	semidirect
226. C₂×C₄⋊C₄	C₂×D₁₉₇	semidirect
231. C₂×C₂²⋊C₄	C₂×D₁₉₇	semidirect
251. C₂×D₄	C₂²×D₁₉₇	semidirect
277. C₄⋊C₄	C₂²×D₁₉₇	semidirect
282. C₂²⋊C₄	C₂²×D₁₉₇	semidirect
301. C₂³	#15691357	semidirect
350. C₂²	C₂×#15691357	semidirect
363. C₂	#27161589	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#15691357	2
C₂³×C₄×D₁₉₇	2
#27161589	2
C₂×#20263308	2
C₂×#20263306	2
C₂×#20263305	2
C₂×#20263297	2
C₂×#20263294	2
C₂×D₄×Dic₁₉₇	2
C₂×#20263286	2
C₂×#20263284	2
C₂×#121×C₁₉₇	2
C₂×#525	197

Subgroups — C2×#27161589 #38755953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27161589 #38755953