Subgroups — #27155769

Order 12416.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261451	C₂	1	1	yes	maximal, characteristic, complemented
2	#20261438	C₂	1	2	yes	maximal, complemented
3	#20261433	C₂	1	2	yes	maximal, complemented
4	#20261407	C₂	1	1	yes	maximal, characteristic, complemented
5	#20261376	C₂	1	4	yes	maximal, complemented
6	#20261376	C₂	1	2	yes	maximal, complemented
7	D₄×D₃₈₈	C₂	1	2	yes	maximal, complemented
8	D₄×D₃₈₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#20261341	C₂	1	2	yes	maximal, complemented
10	#20261325	C₂	1	4	yes	maximal, complemented
11	#20261286	C₂	1	1	yes	maximal, characteristic, complemented
12	#20261272	C₂	1	1	yes	maximal, characteristic, complemented
13	#20261248	C₂	1	2	yes	maximal, complemented
14	C₂×#15690785	C₂	1	2	yes	maximal, complemented
15	#20261207	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₉₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#554×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13095512	C₂²	1	2	yes	complemented
19	C₂×#13095512	C₂²	1	2	yes	complemented
20	C₂²×D₃₈₈	C₂²	1	2	yes	complemented
21	C₂²×D₃₈₈	C₂²	1	4	yes	complemented
22	C₂×D₄×D₉₇	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₉₇	C₂²	1	2	yes	—
24	C₂²×C₄×D₉₇	C₂²	1	2	yes	complemented
25	#15690807	C₂²	1	1	yes	characteristic, complemented
26	#15690807	C₂²	1	2	yes	complemented
27	#15690805	C₂²	1	4	yes	complemented
28	#15690805	C₂²	1	2	yes	complemented
29	#15690801	C₂²	1	1	yes	characteristic, complemented
30	#15690799	C₂²	1	1	yes	characteristic, complemented
31	#15690799	C₂²	1	4	yes	complemented
32	#15690799	C₂²	1	2	yes	complemented
33	#15690795	C₂²	1	2	yes	complemented
34	#15690795	C₂²	1	4	yes	complemented
35	#15690795	C₂²	1	4	yes	complemented
36	#15690795	C₂²	1	4	yes	complemented
37	#15690786	C₂²	1	1	yes	characteristic, complemented
38	#15690785	C₂²	1	1	yes	characteristic
39	#15690785	C₂²	1	4	yes	complemented
40	#15690785	C₂²	1	4	yes	complemented
41	#15690785	C₂²	1	4	yes	complemented
42	#15690785	C₂²	1	2	yes	complemented
43	#15690785	C₂²	1	2	yes	complemented
44	#15690785	C₂²	1	2	yes	complemented
45	#15690785	C₂²	1	2	yes	complemented
46	#15690785	C₂²	1	2	yes	complemented
47	#15690785	C₂²	1	2	yes	complemented
48	#15690785	C₂²	1	4	yes	complemented
49	#15690784	C₂²	1	2	yes	complemented
50	#15690784	C₂²	1	4	yes	complemented
51	#15690780	C₂²	1	4	yes	complemented
52	#15690780	C₂²	1	4	yes	complemented
53	#15690780	C₂²	1	4	yes	complemented
54	C₄×D₃₈₈	C₂²	1	2	yes	complemented
55	C₄×D₃₈₈	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₃₈₈	C₂²	1	2	yes	complemented
57	C₄×D₃₈₈	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₉₇	C₂²	1	1	yes	characteristic
59	#15690772	C₂²	1	2	yes	complemented
60	#15690772	C₂²	1	4	yes	complemented
61	#15690772	C₂²	1	1	yes	characteristic, complemented
62	#15690772	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₉₇	C₂²	1	4	yes	complemented
65	#15690770	C₂²	1	2	yes	complemented
66	#15690770	C₂²	1	4	yes	complemented
67	#15690768	C₂²	1	2	yes	complemented
68	#15690768	C₂²	1	2	yes	complemented
69	#15690767	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₉₇	C₂²	1	1	yes	characteristic, complemented
71	C₂×#13095488	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₉₇	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₉₇	C₂²	1	4	yes	complemented
74	C₄²×D₉₇	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₉₇	C₂²	1	1	yes	characteristic, complemented
76	#125×C₉₇	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₉₇	C₂²	1	2	yes	complemented
78	C₂²⋊Q₈×C₉₇	C₂²	1	4	yes	complemented
79	C₄×Q₈×C₉₇	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₉₇	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₉₇	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×C₉₇	C₂²	1	2	yes	complemented
83	C₂³×D₉₇	C₂³	1	2	yes	—
84	C₂³×D₉₇	C₂³	1	4	yes	—
85	#13095512	—	4	4	no	—
86	#13095512	—	4	4	no	—
87	C₂×D₃₈₈	—	4	4	no	—
88	C₂×D₃₈₈	—	4	8	no	—
89	C₂×D₃₈₈	C₂³	1	1	yes	characteristic
90	C₂×D₃₈₈	C₂³	1	2	yes	—
91	C₂×D₃₈₈	C₂³	1	4	yes	—
92	C₂×D₃₈₈	C₂³	1	2	yes	—
93	C₂×D₃₈₈	C₂³	1	2	yes	—
94	C₂×D₃₈₈	C₂³	1	1	yes	characteristic
95	C₂×D₃₈₈	C₂³	1	4	yes	—
96	C₂×D₃₈₈	C₂³	1	2	yes	—
97	C₂×D₃₈₈	C₂³	1	4	yes	—
98	C₂×D₃₈₈	C₂³	1	4	yes	—
99	C₂×D₃₈₈	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
101	C₂×C₂²⋊D₉₇	C₂³	1	4	yes	—
102	D₄×D₉₇	—	2	4	no	—
103	D₄×D₉₇	—	2	8	no	—
104	C₂²×Dic₉₇	C₂³	1	2	yes	—
105	C₂×C₄×D₉₇	—	4	4	no	—
106	C₂×C₄×D₉₇	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₉₇	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₉₇	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₉₇	C₂³	1	2	yes	—
110	C₂×C₄×D₉₇	C₂³	1	2	yes	—
111	C₂×C₄×D₉₇	C₂³	1	2	yes	—
112	C₂×C₄×D₉₇	C₂³	1	4	yes	—
113	C₂×C₄×D₉₇	C₂³	1	4	yes	—
114	C₂×C₄×D₉₇	C₂³	1	2	yes	—
115	C₄⋊Dic₉₇	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₉₇	C₂³	1	1	yes	characteristic
117	C₄⋊Dic₉₇	C₂³	1	2	yes	—
118	#13095490	C₂³	1	2	yes	—
119	#13095490	C₂³	1	2	yes	—
120	#13095490	C₂³	1	2	yes	—
121	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
122	#13095488	C₂³	1	2	yes	—
123	#13095488	C₂³	1	4	yes	—
124	#13095488	C₂³	1	2	yes	—
125	#13095488	C₂³	1	2	yes	—
126	#13095488	C₂³	1	2	yes	—
127	#13095488	C₂³	1	4	yes	—
128	#13095488	C₂³	1	4	yes	—
129	#13095488	C₂³	1	4	yes	—
130	#13095488	C₂³	1	2	yes	—
131	#13095488	C₂³	1	4	yes	—
132	#13095488	C₂³	1	4	yes	—
133	#13095488	C₂³	1	2	yes	—
134	#13095488	C₂³	1	2	yes	—
135	C₄×Dic₉₇	C₂³	1	1	yes	characteristic
136	C₄×Dic₉₇	C₂³	1	1	yes	characteristic
137	C₄×Dic₉₇	C₂³	1	1	yes	characteristic
138	C₄×Dic₉₇	C₂³	1	4	yes	—
139	C₂×Q₈×C₉₇	C₂³	1	1	yes	characteristic
140	C₂×Q₈×C₉₇	C₂³	1	2	yes	—
141	C₂×D₄×C₉₇	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₉₇	C₂³	1	2	yes	—
143	C₂²×C₄×C₉₇	C₂³	1	4	yes	—
144	C₄⋊C₄×C₉₇	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
146	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
147	C₄⋊C₄×C₉₇	C₂³	1	4	yes	—
148	C₄⋊C₄×C₉₇	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₉₇	C₂³	1	4	yes	—
150	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₉₇	C₂³	1	4	yes	—
152	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
153	C₄²×C₉₇	C₂³	1	1	yes	characteristic
154	C₄²×C₉₇	C₂³	1	2	yes	—
155	C₂³×C₉₇	C₂⁴	1	2	yes	—
156	C₂²×D₉₇	—	2	4	no	—
157	C₂²×D₉₇	—	2	8	no	—
158	C₂²×D₉₇	—	2	4	no	—
159	C₂²×D₉₇	—	4	2	no	—
160	C₂²×D₉₇	—	4	4	no	—
161	C₂²×D₉₇	—	4	4	no	—
162	C₂²×D₉₇	C₂⁴	1	2	yes	—
163	C₂²×D₉₇	C₂⁴	1	2	yes	—
164	C₂²×D₉₇	C₂⁴	1	4	yes	—
165	C₂²×D₉₇	C₂⁴	1	1	yes	characteristic
166	Q₈×C₉₇	—	2	2	no	—
167	Q₈×C₉₇	—	4	2	no	—
168	D₄×C₉₇	#41	1	4	yes	complemented
169	C₂×C₄×C₉₇	—	2	4	no	—
170	C₂×C₄×C₉₇	—	4	4	no	—
171	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
172	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
174	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
175	C₂×C₄×C₉₇	C₂⁴	1	4	yes	—
176	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₉₇	—	2	4	no	—
179	C₂²⋊D₉₇	—	2	8	no	—
180	C₂×Dic₉₇	—	4	2	no	—
181	C₂×Dic₉₇	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₉₇	C₂⁴	1	2	yes	—
183	C₂×Dic₉₇	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₉₇	C₂⁴	1	2	yes	—
185	C₂×Dic₉₇	C₂⁴	1	1	yes	characteristic
186	D₃₈₈	—	2	4	no	—
187	D₃₈₈	—	2	8	no	—
188	D₃₈₈	—	2	2	no	—
189	D₃₈₈	—	2	4	no	—
190	D₃₈₈	—	2	2	no	—
191	D₃₈₈	—	2	4	no	—
192	D₃₈₈	—	4	4	no	—
193	D₃₈₈	—	4	4	no	—
194	D₃₈₈	—	4	4	no	—
195	D₃₈₈	—	4	2	no	—
196	D₃₈₈	—	4	4	no	—
197	C₄×D₉₇	—	2	2	no	—
198	C₄×D₉₇	—	2	2	no	—
199	C₄×D₉₇	—	2	4	no	—
200	C₄×D₉₇	—	2	2	no	—
201	C₄×D₉₇	—	2	4	no	—
202	C₄×D₉₇	—	4	2	no	—
203	C₄×D₉₇	—	4	2	no	—
204	C₄×D₉₇	—	4	4	no	—
205	C₄×D₉₇	—	4	4	no	—
206	C₂²×C₉₇	—	2	2	no	—
207	C₂²×C₉₇	—	2	2	no	—
208	C₂²×C₉₇	C₂×#41	1	4	yes	—
209	C₂²×C₉₇	C₂⁵	1	1	yes	characteristic
210	C₂×D₉₇	—	2	1	no	—
211	C₂×D₉₇	—	2	1	no	—
212	C₂×D₉₇	—	2	2	no	—
213	C₂×D₉₇	—	2	2	no	—
214	C₂×D₉₇	—	2	4	no	—
215	C₂×D₉₇	—	2	2	no	—
216	C₂×D₉₇	—	2	4	no	—
217	C₂×D₉₇	—	2	4	no	—
218	C₂×D₉₇	—	2	2	no	—
219	C₂×D₉₇	—	2	2	no	—
220	C₂×D₉₇	—	2	2	no	—
221	C₂×D₉₇	—	4	8	no	—
222	C₂×D₉₇	—	8	8	no	—
223	C₂×D₉₇	H(5,𝔽₂)	1	2	yes	—
224	C₄×C₉₇	—	2	1	no	—
225	C₄×C₉₇	—	2	2	no	—
226	C₄×C₉₇	—	2	2	no	—
227	C₄×C₉₇	—	2	4	no	—
228	C₄×C₉₇	—	2	2	no	—
229	C₄×C₉₇	C₂×#41	1	2	yes	—
230	C₄×C₉₇	H(5,𝔽₂)	1	2	yes	—
231	Dic₉₇	—	2	1	no	—
232	Dic₉₇	—	2	2	no	—
233	Dic₉₇	—	2	1	no	—
234	Dic₉₇	—	2	2	no	—
235	Dic₉₇	—	2	1	no	—
236	C₂×C₉₇	—	2	4	no	—
237	C₂×C₉₇	C₂²×#41	1	1	yes	characteristic
238	C₂×C₉₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₉₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	D₉₇	—	2	2	no	—
241	D₉₇	—	4	2	no	—
242	D₉₇	—	4	4	no	—
243	D₉₇	—	4	2	no	—
244	#3519	—	97	1	no	maximal, Sylow
245	C₉₇	#3519	1	1	yes	characteristic, complemented, Sylow
246	#555	—	97	1	no	—
247	#554	D₉₇	1	1	yes	characteristic, complemented
248	#553	—	97	2	no	—
249	#553	—	97	2	no	—
250	#550	—	97	1	no	—
251	#546	—	97	4	no	—
252	#546	—	97	2	no	—
253	D₄²	—	97	2	no	—
254	D₄²	—	97	1	no	—
255	#540	—	97	2	no	—
256	#538	—	97	4	no	—
257	#532	—	97	1	no	—
258	#529	—	97	1	no	—
259	#525	—	97	2	no	—
260	C₂×#121	—	97	2	no	—
261	#518	—	97	2	no	—
262	C₂×C₄×D₄	—	97	1	no	—
263	C₂×#41	—	97	2	no	—
264	C₂×#41	—	97	2	no	—
265	C₂²×D₄	—	97	1	no	—
266	C₂²×D₄	—	97	2	no	—
267	C₂²×D₄	—	97	2	no	—
268	C₂²×D₄	—	97	4	no	—
269	C₂³×C₄	—	97	2	no	—
270	C₄⋊Q₈	C₂×D₉₇	1	1	yes	characteristic, complemented
271	#127	—	97	1	no	—
272	#127	—	97	2	no	—
273	#126	—	97	2	no	—
274	#126	—	97	4	no	—
275	#125	—	97	1	no	—
276	#125	C₂×D₉₇	1	2	yes	complemented
277	#124	—	97	1	no	—
278	#124	—	97	2	no	—
279	#124	—	97	4	no	—
280	#123	—	97	4	no	—
281	#123	—	97	2	no	—
282	#123	—	97	4	no	—
283	#123	—	97	4	no	—
284	C₂²⋊Q₈	—	97	1	no	—
285	C₂²⋊Q₈	C₂×D₉₇	1	2	yes	complemented
286	C₂²⋊Q₈	C₂×D₉₇	1	4	yes	complemented
287	#121	—	97	2	no	—
288	#121	—	97	4	no	—
289	#121	—	97	1	no	—
290	#121	—	97	2	no	—
291	#121	—	97	4	no	—
292	#121	—	97	4	no	—
293	#121	—	97	2	no	—
294	#121	—	97	2	no	—
295	#121	—	97	2	no	—
296	#121	—	97	4	no	—
297	#121	—	97	2	no	—
298	#121	—	97	2	no	—
299	#121	—	97	4	no	—
300	#120	—	97	4	no	—
301	#120	—	97	4	no	—
302	#120	—	97	4	no	—
303	C₄×Q₈	C₂×D₉₇	1	1	yes	characteristic, complemented
304	C₄×D₄	—	97	1	no	—
305	C₄×D₄	—	97	2	no	—
306	C₄×D₄	—	97	4	no	—
307	C₄×D₄	—	97	1	no	—
308	C₄×D₄	—	97	2	no	—
309	C₄×D₄	—	97	4	no	—
310	C₄×D₄	—	97	2	no	—
311	C₄×D₄	—	97	2	no	—
312	C₄×D₄	—	97	4	no	—
313	C₄×D₄	—	97	1	no	—
314	C₄×D₄	—	97	2	no	—
315	C₄×D₄	—	97	2	no	—
316	C₄×D₄	—	97	1	no	—
317	C₄×D₄	C₂×D₉₇	1	1	yes	characteristic
318	C₄×D₄	C₂×D₉₇	1	2	yes	—
319	#117	—	97	2	no	—
320	#117	—	97	2	no	—
321	#117	—	97	2	no	—
322	C₂×C₄⋊C₄	—	97	1	no	—
323	C₂×C₄⋊C₄	C₂×D₉₇	1	2	yes	complemented
324	C₂×C₂²⋊C₄	—	97	4	no	—
325	C₂×C₂²⋊C₄	—	97	2	no	—
326	C₂×C₂²⋊C₄	—	97	4	no	—
327	C₂×C₄²	—	97	1	no	—
328	C₂⁴	—	97	4	no	—
329	C₂⁴	—	97	2	no	—
330	#41	—	388	4	no	—
331	#41	—	388	4	no	—
332	C₂×Q₈	C₂²×D₉₇	1	1	yes	characteristic
333	C₂×Q₈	C₂²×D₉₇	1	2	yes	—
334	C₂×D₄	—	97	2	no	—
335	C₂×D₄	—	97	4	no	—
336	C₂×D₄	—	97	4	no	—
337	C₂×D₄	—	97	2	no	—
338	C₂×D₄	—	97	4	no	—
339	C₂×D₄	—	97	4	no	—
340	C₂×D₄	—	97	4	no	—
341	C₂×D₄	—	97	1	no	—
342	C₂×D₄	—	97	2	no	—
343	C₂×D₄	—	97	4	no	—
344	C₂×D₄	—	97	2	no	—
345	C₂×D₄	—	97	1	no	—
346	C₂×D₄	—	97	2	no	—
347	C₂×D₄	—	388	4	no	—
348	C₂×D₄	—	388	8	no	—
349	C₂×D₄	—	194	8	no	—
350	C₂×D₄	—	194	4	no	—
351	C₂×D₄	C₂²×D₉₇	1	1	yes	characteristic
352	C₂²×C₄	—	97	2	no	—
353	C₂²×C₄	—	97	2	no	—
354	C₂²×C₄	—	97	4	no	—
355	C₂²×C₄	—	97	4	no	—
356	C₂²×C₄	—	97	2	no	—
357	C₂²×C₄	—	97	1	no	—
358	C₂²×C₄	—	97	1	no	—
359	C₂²×C₄	—	97	1	no	—
360	C₂²×C₄	—	97	2	no	—
361	C₂²×C₄	—	97	2	no	—
362	C₂²×C₄	—	388	4	no	—
363	C₂²×C₄	C₂²×D₉₇	1	2	yes	—
364	C₂²×C₄	C₂²×D₉₇	1	4	yes	—
365	C₄⋊C₄	—	97	2	no	—
366	C₄⋊C₄	—	97	2	no	—
367	C₄⋊C₄	—	97	2	no	—
368	C₄⋊C₄	—	97	1	no	—
369	C₄⋊C₄	—	97	1	no	—
370	C₄⋊C₄	—	97	2	no	—
371	C₄⋊C₄	C₂²×D₉₇	1	1	yes	characteristic
372	C₄⋊C₄	C₂²×D₉₇	1	1	yes	characteristic
373	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
374	C₄⋊C₄	C₂²×D₉₇	1	4	yes	—
375	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
376	C₄⋊C₄	C₂²×D₉₇	1	4	yes	—
377	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
378	C₂²⋊C₄	—	97	2	no	—
379	C₂²⋊C₄	—	97	2	no	—
380	C₂²⋊C₄	—	97	4	no	—
381	C₂²⋊C₄	—	97	2	no	—
382	C₂²⋊C₄	—	97	4	no	—
383	C₂²⋊C₄	—	97	2	no	—
384	C₂²⋊C₄	—	97	4	no	—
385	C₂²⋊C₄	—	97	2	no	—
386	C₂²⋊C₄	—	97	4	no	—
387	C₂²⋊C₄	—	97	2	no	—
388	C₂²⋊C₄	—	97	2	no	—
389	C₂²⋊C₄	—	97	2	no	—
390	C₂²⋊C₄	—	97	4	no	—
391	C₂²⋊C₄	—	97	4	no	—
392	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₉₇	1	4	yes	—
394	C₄²	—	97	1	no	—
395	C₄²	—	97	1	no	—
396	C₄²	—	97	1	no	—
397	C₄²	—	97	4	no	—
398	C₄²	C₂²×D₉₇	1	1	yes	characteristic
399	C₄²	C₂²×D₉₇	1	2	yes	—
400	C₂³	—	97	1	no	—
401	C₂³	—	97	2	no	—
402	C₂³	—	97	4	no	—
403	C₂³	—	97	2	no	—
404	C₂³	—	388	4	no	—
405	C₂³	—	388	4	no	—
406	C₂³	—	388	2	no	—
407	C₂³	—	194	4	no	—
408	C₂³	—	194	8	no	—
409	C₂³	—	194	4	no	—
410	C₂³	C₂³×D₉₇	1	2	yes	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	388	4	no	—
414	D₄	—	388	4	no	—
415	D₄	—	388	4	no	—
416	D₄	—	388	2	no	—
417	D₄	—	388	4	no	—
418	D₄	—	194	4	no	—
419	D₄	—	194	8	no	—
420	D₄	—	194	8	no	—
421	D₄	—	194	4	no	—
422	D₄	—	194	4	no	—
423	D₄	—	194	2	no	—
424	D₄	—	194	2	no	—
425	D₄	—	194	4	no	—
426	D₄	#13095512	1	4	yes	complemented
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	97	1	no	—
430	C₂×C₄	—	97	2	no	—
431	C₂×C₄	—	97	1	no	—
432	C₂×C₄	—	97	1	no	—
433	C₂×C₄	—	97	2	no	—
434	C₂×C₄	—	388	2	no	—
435	C₂×C₄	—	388	2	no	—
436	C₂×C₄	—	388	4	no	—
437	C₂×C₄	—	388	4	no	—
438	C₂×C₄	—	388	2	no	—
439	C₂×C₄	—	194	2	no	—
440	C₂×C₄	—	194	4	no	—
441	C₂×C₄	—	194	2	no	—
442	C₂×C₄	—	194	2	no	—
443	C₂×C₄	—	194	4	no	—
444	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₉₇	1	4	yes	—
446	C₂×C₄	C₂³×D₉₇	1	2	yes	—
447	C₂×C₄	C₂³×D₉₇	1	2	yes	—
448	C₂×C₄	C₂³×D₉₇	1	2	yes	—
449	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	776	8	no	—
454	C₂²	—	97	2	no	—
455	C₂²	—	388	8	no	—
456	C₂²	—	194	2	no	—
457	C₂²	—	194	4	no	—
458	C₂²	—	194	2	no	—
459	C₂²	—	194	4	no	—
460	C₂²	—	194	2	no	—
461	C₂²	—	194	2	no	—
462	C₂²	—	194	2	no	—
463	C₂²	—	194	4	no	—
464	C₂²	—	194	2	no	—
465	C₂²	—	194	1	no	—
466	C₂²	—	194	1	no	—
467	C₂²	C₂×#13095512	1	4	yes	—
468	C₂²	C₂⁴×D₉₇	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	194	1	no	—
475	C₄	—	194	2	no	—
476	C₄	—	194	1	no	—
477	C₄	—	194	1	no	—
478	C₄	—	194	2	no	—
479	C₄	C₂×#13095512	1	2	yes	—
480	C₄	#15690856	1	2	yes	—
481	C₂	—	2	4	no	—
482	C₂	—	388	2	no	—
483	C₂	—	388	4	no	—
484	C₂	—	388	2	no	—
485	C₂	—	194	2	no	—
486	C₂	C₂²×#13095512	1	1	yes	characteristic
487	C₂	H(5,𝔽₂)×D₉₇	1	1	yes	characteristic
488	C₂	C₂×#15690856	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₉₇
commutator, socle, cosocle	C₂²×C₉₇	C₂⁵
Fitting	#554×C₉₇	C₂
hypercenter	#554	D₉₇
hypocenter	C₉₇	#3519
LCS	G ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #20261451	C₂	semidirect
2. #20261438	C₂	semidirect
3. #20261433	C₂	semidirect
4. #20261407	C₂	semidirect
5. #20261376	C₂	semidirect
6. #20261376	C₂	semidirect
7. D₄×D₃₈₈	C₂	semidirect
8. D₄×D₃₈₈	C₂	semidirect
9. #20261341	C₂	semidirect
10. #20261325	C₂	semidirect
11. #20261286	C₂	semidirect
12. #20261272	C₂	semidirect
13. #20261248	C₂	semidirect
14. C₂×#15690785	C₂	semidirect
15. #20261207	C₂	semidirect
16. C₄×D₄×D₉₇	C₂	semidirect
17. #554×C₉₇	C₂	semidirect
18. C₂×#13095512	C₂²	semidirect
19. C₂×#13095512	C₂²	semidirect
20. C₂²×D₃₈₈	C₂²	semidirect
21. C₂²×D₃₈₈	C₂²	semidirect
24. C₂²×C₄×D₉₇	C₂²	semidirect
25. #15690807	C₂²	semidirect
26. #15690807	C₂²	semidirect
27. #15690805	C₂²	semidirect
28. #15690805	C₂²	semidirect
29. #15690801	C₂²	semidirect
30. #15690799	C₂²	semidirect
31. #15690799	C₂²	semidirect
32. #15690799	C₂²	semidirect
33. #15690795	C₂²	semidirect
34. #15690795	C₂²	semidirect
35. #15690795	C₂²	semidirect
36. #15690795	C₂²	semidirect
37. #15690786	C₂²	semidirect
39. #15690785	C₂²	semidirect
40. #15690785	C₂²	semidirect
41. #15690785	C₂²	semidirect
42. #15690785	C₂²	semidirect
43. #15690785	C₂²	semidirect
44. #15690785	C₂²	semidirect
45. #15690785	C₂²	semidirect
46. #15690785	C₂²	semidirect
47. #15690785	C₂²	semidirect
48. #15690785	C₂²	semidirect
49. #15690784	C₂²	semidirect
50. #15690784	C₂²	semidirect
51. #15690780	C₂²	semidirect
52. #15690780	C₂²	semidirect
53. #15690780	C₂²	semidirect
54. C₄×D₃₈₈	C₂²	semidirect
55. C₄×D₃₈₈	C₂²	semidirect
56. C₄×D₃₈₈	C₂²	semidirect
57. C₄×D₃₈₈	C₂²	semidirect
59. #15690772	C₂²	semidirect
60. #15690772	C₂²	semidirect
61. #15690772	C₂²	semidirect
62. #15690772	C₂²	semidirect
63. C₄×C₂²⋊D₉₇	C₂²	semidirect
64. C₄×C₂²⋊D₉₇	C₂²	semidirect
65. #15690770	C₂²	semidirect
66. #15690770	C₂²	semidirect
67. #15690768	C₂²	semidirect
68. #15690768	C₂²	semidirect
69. #15690767	C₂²	semidirect
70. C₄⋊C₄×D₉₇	C₂²	semidirect
71. C₂×#13095488	C₂²	semidirect
72. C₂²⋊C₄×D₉₇	C₂²	semidirect
73. C₂²⋊C₄×D₉₇	C₂²	semidirect
74. C₄²×D₉₇	C₂²	semidirect
75. C₄⋊Q₈×C₉₇	C₂²	semidirect
76. #125×C₉₇	C₂²	semidirect
77. C₂²⋊Q₈×C₉₇	C₂²	semidirect
78. C₂²⋊Q₈×C₉₇	C₂²	semidirect
79. C₄×Q₈×C₉₇	C₂²	semidirect
82. C₂×C₄⋊C₄×C₉₇	C₂²	semidirect
168. D₄×C₉₇	#41	semidirect
245. C₉₇	#3519	semidirect
247. #554	D₉₇	semidirect
270. C₄⋊Q₈	C₂×D₉₇	semidirect
276. #125	C₂×D₉₇	semidirect
285. C₂²⋊Q₈	C₂×D₉₇	semidirect
286. C₂²⋊Q₈	C₂×D₉₇	semidirect
303. C₄×Q₈	C₂×D₉₇	semidirect
323. C₂×C₄⋊C₄	C₂×D₉₇	semidirect
426. D₄	#13095512	semidirect

Maximal subgroups

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

subgroup	index
#20261451	2
#20261438	2
#20261433	2
#20261407	2
#20261376	2
D₄×D₃₈₈	2
#20261341	2
#20261325	2
#20261286	2
#20261272	2
#20261248	2
C₂×#15690785	2
#20261207	2
C₄×D₄×D₉₇	2
#554×C₉₇	2
#3519	97