Subgroups — #27155873

Order 12416.

1058 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261489	C₂	1	1	yes	maximal, characteristic, complemented
2	#20261486	C₂	1	2	yes	maximal, complemented
3	#20261482	C₂	1	2	yes	maximal, complemented
4	#20261481	C₂	1	2	yes	maximal, complemented
5	#20261479	C₂	1	1	yes	maximal, characteristic, complemented
6	#20261477	C₂	1	1	yes	maximal, characteristic, complemented
7	#20261475	C₂	1	2	yes	maximal, complemented
8	#20261473	C₂	1	2	yes	maximal, complemented
9	#20261473	C₂	1	2	yes	maximal, complemented
10	#20261284	C₂	1	1	yes	maximal, characteristic, complemented
11	#20261280	C₂	1	2	yes	maximal, complemented
12	#20261271	C₂	1	2	yes	maximal, complemented
13	#20261270	C₂	1	1	yes	maximal, characteristic, complemented
14	#20261264	C₂	1	1	yes	maximal, characteristic, complemented
15	#20261262	C₂	1	2	yes	maximal, complemented
16	#20261248	C₂	1	2	yes	maximal, complemented
17	#20261245	C₂	1	2	yes	maximal, complemented
18	#20261243	C₂	1	2	yes	maximal, complemented
19	#562×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13095512	C₂²	1	1	yes	characteristic
21	C₂×#13095510	C₂²	1	2	yes	—
22	C₂×#13095510	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₄×D₉₇	C₂²	1	2	yes	complemented
24	#15690809	C₂²	1	2	yes	complemented
25	#15690808	C₂²	1	1	yes	characteristic, complemented
26	#15690806	C₂²	1	1	yes	characteristic
27	#15690806	C₂²	1	2	yes	—
28	#15690805	C₂²	1	2	yes	complemented
29	#15690805	C₂²	1	2	yes	complemented
30	#15690805	C₂²	1	2	yes	complemented
31	#15690805	C₂²	1	2	yes	complemented
32	#15690803	C₂²	1	2	yes	complemented
33	#15690803	C₂²	1	2	yes	complemented
34	#15690802	C₂²	1	1	yes	characteristic, complemented
35	#15690801	C₂²	1	2	yes	complemented
36	#15690800	C₂²	1	2	yes	complemented
37	#15690799	C₂²	1	2	yes	—
38	#15690798	C₂²	1	1	yes	characteristic
39	#15690798	C₂²	1	1	yes	characteristic
40	#15690796	C₂²	1	2	yes	—
41	#15690796	C₂²	1	2	yes	—
42	#15690796	C₂²	1	2	yes	complemented
43	#15690795	C₂²	1	2	yes	—
44	#15690795	C₂²	1	2	yes	complemented
45	#15690795	C₂²	1	2	yes	complemented
46	#15690794	C₂²	1	2	yes	complemented
47	#15690794	C₂²	1	2	yes	complemented
48	#15690793	C₂²	1	2	yes	—
49	#15690793	C₂²	1	2	yes	complemented
50	#15690792	C₂²	1	2	yes	—
51	#15690792	C₂²	1	2	yes	complemented
52	#15690792	C₂²	1	2	yes	complemented
53	#15690790	C₂²	1	2	yes	complemented
54	#15690790	C₂²	1	1	yes	characteristic, complemented
55	#15690789	C₂²	1	2	yes	complemented
56	#15690788	C₂²	1	2	yes	complemented
57	#15690788	C₂²	1	2	yes	complemented
58	#15690787	C₂²	1	2	yes	complemented
59	#15690786	C₂²	1	2	yes	complemented
60	#15690786	C₂²	1	1	yes	characteristic, complemented
61	#15690785	C₂²	1	1	yes	characteristic
62	#15690785	C₂²	1	2	yes	—
63	#15690784	C₂²	1	2	yes	—
64	#15690784	C₂²	1	2	yes	—
65	#15690784	C₂²	1	2	yes	complemented
66	#15690783	C₂²	1	2	yes	—
67	#15690783	C₂²	1	2	yes	—
68	#15690783	C₂²	1	2	yes	complemented
69	#15690783	C₂²	1	2	yes	complemented
70	#15690782	C₂²	1	2	yes	—
71	#15690782	C₂²	1	2	yes	complemented
72	#15690782	C₂²	1	2	yes	complemented
73	#15690781	C₂²	1	1	yes	characteristic
74	#15690781	C₂²	1	2	yes	—
75	#15690780	C₂²	1	2	yes	—
76	#15690780	C₂²	1	2	yes	—
77	#15690780	C₂²	1	2	yes	complemented
78	#15690778	C₂²	1	2	yes	—
79	#15690778	C₂²	1	2	yes	complemented
80	#15690778	C₂²	1	2	yes	complemented
81	Q₈×Dic₉₇	C₂²	1	1	yes	characteristic, complemented
82	#15690775	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₉₇	C₂²	1	1	yes	characteristic
84	D₄×Dic₉₇	C₂²	1	2	yes	complemented
85	#15690772	C₂²	1	1	yes	characteristic
86	#15690772	C₂²	1	2	yes	—
87	#15690772	C₂²	1	2	yes	complemented
88	#15690770	C₂²	1	2	yes	—
89	#15690770	C₂²	1	2	yes	complemented
90	#15690770	C₂²	1	2	yes	complemented
91	#15690770	C₂²	1	2	yes	complemented
92	#15690770	C₂²	1	2	yes	complemented
93	#15690768	C₂²	1	2	yes	complemented
94	#15690768	C₂²	1	2	yes	complemented
95	#15690766	C₂²	1	2	yes	complemented
96	C₂×C₄×Dic₉₇	C₂²	1	2	yes	complemented
97	C₄²×D₉₇	C₂²	1	1	yes	characteristic, complemented
98	#125×C₉₇	C₂²	1	1	yes	characteristic, complemented
99	#124×C₉₇	C₂²	1	1	yes	characteristic
100	#124×C₉₇	C₂²	1	1	yes	characteristic, complemented
101	#123×C₉₇	C₂²	1	2	yes	complemented
102	#123×C₉₇	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₉₇	C₂²	1	2	yes	complemented
104	C₂²⋊Q₈×C₉₇	C₂²	1	2	yes	complemented
105	#121×C₉₇	C₂²	1	2	yes	—
106	#121×C₉₇	C₂²	1	2	yes	complemented
107	C₂³×D₉₇	C₂³	1	2	yes	—
108	#13095512	—	4	2	no	—
109	#13095510	—	4	4	no	—
110	#13095510	—	4	2	no	—
111	C₂×Dic₁₉₄	C₂³	1	1	yes	characteristic
112	C₂×Dic₁₉₄	C₂³	1	2	yes	—
113	C₂×Dic₁₉₄	C₂³	1	1	yes	characteristic
114	C₂×D₃₈₈	C₂³	1	1	yes	characteristic
115	C₂×D₃₈₈	C₂³	1	2	yes	—
116	C₂×D₃₈₈	C₂³	1	2	yes	—
117	C₂×D₃₈₈	C₂³	1	1	yes	characteristic
118	C₂×D₃₈₈	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
127	C₂²×Dic₉₇	C₂³	1	2	yes	—
128	C₂²×Dic₉₇	C₂³	1	2	yes	—
129	C₂²×Dic₉₇	C₂³	1	2	yes	—
130	C₂×C₄×D₉₇	—	4	4	no	—
131	C₂×C₄×D₉₇	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₉₇	C₂³	1	2	yes	—
133	C₂×C₄×D₉₇	C₂³	1	2	yes	—
134	C₂×C₄×D₉₇	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₉₇	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₉₇	C₂³	1	2	yes	—
137	C₂×C₄×D₉₇	C₂³	1	2	yes	—
138	C₄⋊Dic₉₇	C₂³	1	2	yes	—
139	C₄⋊Dic₉₇	C₂³	1	2	yes	—
140	C₄⋊Dic₉₇	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₉₇	C₂³	1	2	yes	—
142	C₄⋊Dic₉₇	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₉₇	C₂³	1	2	yes	—
144	#13095490	C₂³	1	2	yes	—
145	#13095490	C₂³	1	2	yes	—
146	#13095490	C₂³	1	2	yes	—
147	#13095490	C₂³	1	2	yes	—
148	#13095490	C₂³	1	2	yes	—
149	#13095490	C₂³	1	2	yes	—
150	#13095490	C₂³	1	2	yes	—
151	#13095490	C₂³	1	2	yes	—
152	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
153	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
154	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
155	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
156	#13095488	C₂³	1	2	yes	—
157	#13095488	C₂³	1	2	yes	—
158	#13095488	C₂³	1	2	yes	—
159	#13095488	C₂³	1	2	yes	—
160	#13095488	C₂³	1	2	yes	—
161	#13095488	C₂³	1	2	yes	—
162	#13095488	C₂³	1	2	yes	—
163	#13095488	C₂³	1	2	yes	—
164	#13095488	C₂³	1	2	yes	—
165	#13095488	C₂³	1	2	yes	—
166	#13095488	C₂³	1	2	yes	—
167	#13095488	C₂³	1	2	yes	—
168	#13095488	C₂³	1	2	yes	—
169	#13095488	C₂³	1	2	yes	—
170	C₄×Dic₉₇	C₂³	1	1	yes	characteristic
171	C₄×Dic₉₇	C₂³	1	1	yes	characteristic
172	C₄×Dic₉₇	C₂³	1	1	yes	characteristic
173	C₄×Dic₉₇	C₂³	1	2	yes	—
174	C₄×Dic₉₇	C₂³	1	2	yes	—
175	C₄×Dic₉₇	C₂³	1	2	yes	—
176	C₄×Dic₉₇	C₂³	1	2	yes	—
177	C₂×Q₈×C₉₇	C₂³	1	1	yes	characteristic
178	C₂×Q₈×C₉₇	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₉₇	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₉₇	C₂³	1	2	yes	—
181	C₂×D₄×C₉₇	C₂³	1	2	yes	—
182	C₂×D₄×C₉₇	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₉₇	C₂³	1	2	yes	—
184	C₂²×C₄×C₉₇	C₂³	1	2	yes	—
185	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
186	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
187	C₄⋊C₄×C₉₇	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
189	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
190	C₄⋊C₄×C₉₇	C₂³	1	1	yes	characteristic
191	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
197	C₄²×C₉₇	C₂³	1	1	yes	characteristic
198	C₂³×C₉₇	C₂⁴	1	2	yes	—
199	C₂³×C₉₇	C₂⁴	1	2	yes	—
200	C₂²×D₉₇	—	4	2	no	—
201	C₂²×D₉₇	—	4	2	no	—
202	C₂²×D₉₇	—	4	2	no	—
203	C₂²×D₉₇	C₂⁴	1	2	yes	—
204	C₂²×D₉₇	C₂⁴	1	2	yes	—
205	C₂²×D₉₇	C₂⁴	1	1	yes	characteristic
206	Q₈×C₉₇	—	4	1	no	—
207	Q₈×C₉₇	—	4	1	no	—
208	D₄×C₉₇	—	4	1	no	—
209	D₄×C₉₇	—	4	2	no	—
210	D₄×C₉₇	—	4	2	no	—
211	D₄×C₉₇	—	4	1	no	—
212	C₂×C₄×C₉₇	—	4	2	no	—
213	C₂×C₄×C₉₇	—	4	2	no	—
214	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
218	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
219	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
220	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
221	C₂²⋊D₉₇	—	4	2	no	—
222	C₂²⋊D₉₇	—	4	2	no	—
223	C₂²⋊D₉₇	—	4	2	no	—
224	C₂²⋊D₉₇	—	4	2	no	—
225	C₂²⋊D₉₇	—	4	2	no	—
226	C₂²⋊D₉₇	—	4	2	no	—
227	C₂²⋊D₉₇	—	4	2	no	—
228	C₂²⋊D₉₇	—	4	2	no	—
229	C₂×Dic₉₇	—	2	4	no	—
230	C₂×Dic₉₇	—	2	4	no	—
231	C₂×Dic₉₇	—	4	2	no	—
232	C₂×Dic₉₇	C₂⁴	1	2	yes	—
233	C₂×Dic₉₇	C₂⁴	1	2	yes	—
234	C₂×Dic₉₇	C₂⁴	1	2	yes	—
235	C₂×Dic₉₇	C₂⁴	1	1	yes	characteristic
236	C₂×Dic₉₇	C₂⁴	1	1	yes	characteristic
237	C₂×Dic₉₇	C₂⁴	1	2	yes	—
238	C₂×Dic₉₇	C₂⁴	1	1	yes	characteristic
239	D₃₈₈	—	4	1	no	—
240	D₃₈₈	—	4	2	no	—
241	D₃₈₈	—	4	2	no	—
242	D₃₈₈	—	4	1	no	—
243	D₃₈₈	—	4	2	no	—
244	C₄×D₉₇	—	2	4	no	—
245	C₄×D₉₇	—	2	4	no	—
246	C₄×D₉₇	—	2	2	no	—
247	C₄×D₉₇	—	4	2	no	—
248	C₄×D₉₇	—	4	2	no	—
249	C₄×D₉₇	—	4	1	no	—
250	C₄×D₉₇	—	4	1	no	—
251	Dic₁₉₄	—	4	1	no	—
252	Dic₁₉₄	—	4	1	no	—
253	Dic₁₉₄	—	4	2	no	—
254	C₂²×C₉₇	—	2	2	no	—
255	C₂²×C₉₇	—	2	2	no	—
256	C₂²×C₉₇	—	2	2	no	—
257	C₂²×C₉₇	—	2	2	no	—
258	C₂²×C₉₇	—	2	2	no	—
259	C₂²×C₉₇	—	2	2	no	—
260	C₂²×C₉₇	C₂⁵	1	1	yes	characteristic
261	C₂×D₉₇	—	2	2	no	—
262	C₂×D₉₇	—	2	2	no	—
263	C₂×D₉₇	—	2	1	no	—
264	C₂×D₉₇	—	2	1	no	—
265	C₂×D₉₇	—	2	1	no	—
266	C₂×D₉₇	—	2	2	no	—
267	C₂×D₉₇	—	2	2	no	—
268	C₂×D₉₇	—	2	2	no	—
269	C₂×D₉₇	—	2	2	no	—
270	C₂×D₉₇	—	4	8	no	—
271	C₄×C₉₇	—	2	2	no	—
272	C₄×C₉₇	—	2	1	no	—
273	C₄×C₉₇	—	2	2	no	—
274	C₄×C₉₇	—	2	1	no	—
275	C₄×C₉₇	—	2	1	no	—
276	C₄×C₉₇	—	2	2	no	—
277	C₄×C₉₇	—	2	2	no	—
278	Dic₉₇	—	2	2	no	—
279	Dic₉₇	—	2	2	no	—
280	Dic₉₇	—	2	2	no	—
281	Dic₉₇	—	2	1	no	—
282	Dic₉₇	—	2	1	no	—
283	Dic₉₇	—	2	2	no	—
284	Dic₉₇	H(5,𝔽₂)	1	2	yes	—
285	C₂×C₉₇	—	4	2	no	—
286	C₂×C₉₇	—	4	2	no	—
287	C₂×C₉₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₉₇	#585	1	1	yes	characteristic
289	C₂×C₉₇	#585	1	1	yes	characteristic
290	D₉₇	—	4	1	no	—
291	D₉₇	—	4	2	no	—
292	D₉₇	—	4	2	no	—
293	#3529	—	97	1	no	maximal, Sylow
294	C₉₇	#3529	1	1	yes	characteristic, complemented, Sylow
295	#563	—	97	1	no	—
296	#563	—	97	2	no	—
297	#562	—	97	1	no	—
298	#562	—	97	2	no	—
299	#562	—	97	2	no	—
300	#562	D₉₇	1	1	yes	characteristic, complemented
301	H(3,𝔽₄)	—	97	1	no	—
302	#560	—	97	2	no	—
303	#560	—	97	2	no	—
304	#560	—	97	2	no	—
305	#532	—	97	1	no	—
306	#532	—	97	2	no	—
307	#529	—	97	1	no	—
308	#529	—	97	1	no	—
309	#529	—	97	2	no	—
310	#529	—	97	2	no	—
311	#525	—	97	2	no	—
312	#525	—	97	2	no	—
313	#525	—	97	2	no	—
314	C₂×#41	—	97	1	no	—
315	C₂×#41	—	97	2	no	—
316	C₂×#41	—	97	1	no	—
317	C₂³×C₄	—	97	2	no	—
318	C₄⋊Q₈	—	97	1	no	—
319	C₄⋊Q₈	—	97	2	no	—
320	#127	—	97	1	no	—
321	#127	—	97	2	no	—
322	#126	—	97	2	no	—
323	#126	—	97	2	no	—
324	#126	—	97	2	no	—
325	#126	—	97	2	no	—
326	#126	—	97	2	no	—
327	#126	—	97	2	no	—
328	#125	—	97	2	no	—
329	#125	—	97	2	no	—
330	#125	—	97	1	no	—
331	#125	C₂×D₉₇	1	1	yes	characteristic, complemented
332	#124	—	97	2	no	—
333	#124	—	97	2	no	—
334	#124	—	97	2	no	—
335	#124	—	97	2	no	—
336	#124	—	97	1	no	—
337	#124	—	97	1	no	—
338	#124	C₂×D₉₇	1	1	yes	characteristic
339	#124	C₂×D₉₇	1	1	yes	characteristic, complemented
340	#123	—	97	2	no	—
341	#123	—	97	2	no	—
342	#123	—	97	2	no	—
343	#123	—	97	2	no	—
344	#123	—	97	2	no	—
345	#123	—	97	2	no	—
346	#123	—	97	2	no	—
347	#123	—	97	2	no	—
348	#123	—	97	2	no	—
349	#123	—	97	2	no	—
350	#123	C₂×D₉₇	1	2	yes	complemented
351	#123	C₂×D₉₇	1	2	yes	complemented
352	C₂²⋊Q₈	—	97	2	no	—
353	C₂²⋊Q₈	—	97	1	no	—
354	C₂²⋊Q₈	—	97	2	no	—
355	C₂²⋊Q₈	—	97	2	no	—
356	C₂²⋊Q₈	—	97	2	no	—
357	C₂²⋊Q₈	—	97	2	no	—
358	C₂²⋊Q₈	—	97	1	no	—
359	C₂²⋊Q₈	—	97	2	no	—
360	C₂²⋊Q₈	C₂×D₉₇	1	2	yes	complemented
361	C₂²⋊Q₈	C₂×D₉₇	1	2	yes	complemented
362	#121	—	97	2	no	—
363	#121	—	97	1	no	—
364	#121	—	97	2	no	—
365	#121	—	97	2	no	—
366	#121	—	97	2	no	—
367	#121	—	97	2	no	—
368	#121	—	97	2	no	—
369	#121	—	97	2	no	—
370	#121	—	97	2	no	—
371	#121	—	97	1	no	—
372	#121	—	97	2	no	—
373	#121	—	97	2	no	—
374	#121	—	97	2	no	—
375	#121	—	97	2	no	—
376	#121	C₂×D₉₇	1	2	yes	—
377	#121	C₂×D₉₇	1	2	yes	complemented
378	#120	—	97	2	no	—
379	#120	—	97	2	no	—
380	#120	—	97	2	no	—
381	#120	—	97	2	no	—
382	#120	—	97	2	no	—
383	#120	—	97	2	no	—
384	C₄×Q₈	—	97	1	no	—
385	C₄×Q₈	—	97	1	no	—
386	C₄×D₄	—	97	1	no	—
387	C₄×D₄	—	97	2	no	—
388	C₄×D₄	—	97	1	no	—
389	C₄×D₄	—	97	2	no	—
390	C₄×D₄	—	97	2	no	—
391	C₄×D₄	—	97	2	no	—
392	C₄×D₄	—	97	2	no	—
393	C₄×D₄	—	97	2	no	—
394	C₄×D₄	—	97	2	no	—
395	C₄×D₄	—	97	2	no	—
396	#117	—	97	2	no	—
397	#117	—	97	2	no	—
398	#117	—	97	2	no	—
399	C₂×C₄²	—	97	2	no	—
400	C₂×C₄²	—	97	1	no	—
401	C₂⁴	—	97	2	no	—
402	#41	—	388	4	no	—
403	#41	—	388	2	no	—
404	#41	—	388	2	no	—
405	C₂×Q₈	—	97	1	no	—
406	C₂×Q₈	—	97	2	no	—
407	C₂×Q₈	—	97	1	no	—
408	C₂×Q₈	C₂²×D₉₇	1	1	yes	characteristic
409	C₂×Q₈	C₂²×D₉₇	1	1	yes	characteristic
410	C₂×D₄	—	97	2	no	—
411	C₂×D₄	—	97	2	no	—
412	C₂×D₄	—	97	2	no	—
413	C₂×D₄	—	97	2	no	—
414	C₂×D₄	—	97	2	no	—
415	C₂×D₄	—	97	2	no	—
416	C₂×D₄	—	97	2	no	—
417	C₂×D₄	—	97	2	no	—
418	C₂×D₄	—	97	2	no	—
419	C₂×D₄	—	97	1	no	—
420	C₂×D₄	—	97	2	no	—
421	C₂×D₄	—	97	1	no	—
422	C₂×D₄	—	97	2	no	—
423	C₂×D₄	C₂²×D₉₇	1	1	yes	characteristic
424	C₂×D₄	C₂²×D₉₇	1	2	yes	—
425	C₂×D₄	C₂²×D₉₇	1	2	yes	—
426	C₂×D₄	C₂²×D₉₇	1	1	yes	characteristic
427	C₂²×C₄	—	97	2	no	—
428	C₂²×C₄	—	97	2	no	—
429	C₂²×C₄	—	97	2	no	—
430	C₂²×C₄	—	97	1	no	—
431	C₂²×C₄	—	97	1	no	—
432	C₂²×C₄	—	97	2	no	—
433	C₂²×C₄	—	97	2	no	—
434	C₂²×C₄	—	97	1	no	—
435	C₂²×C₄	—	97	2	no	—
436	C₂²×C₄	—	97	2	no	—
437	C₂²×C₄	—	388	4	no	—
438	C₂²×C₄	C₂²×D₉₇	1	2	yes	—
439	C₂²×C₄	C₂²×D₉₇	1	2	yes	—
440	C₄⋊C₄	—	97	2	no	—
441	C₄⋊C₄	—	97	2	no	—
442	C₄⋊C₄	—	97	2	no	—
443	C₄⋊C₄	—	97	2	no	—
444	C₄⋊C₄	—	97	2	no	—
445	C₄⋊C₄	—	97	2	no	—
446	C₄⋊C₄	—	97	2	no	—
447	C₄⋊C₄	—	97	2	no	—
448	C₄⋊C₄	—	97	2	no	—
449	C₄⋊C₄	—	97	2	no	—
450	C₄⋊C₄	—	97	2	no	—
451	C₄⋊C₄	—	97	1	no	—
452	C₄⋊C₄	—	97	2	no	—
453	C₄⋊C₄	—	97	1	no	—
454	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
455	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
456	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
457	C₄⋊C₄	C₂²×D₉₇	1	1	yes	characteristic
458	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
459	C₄⋊C₄	C₂²×D₉₇	1	1	yes	characteristic
460	C₂²⋊C₄	—	97	2	no	—
461	C₂²⋊C₄	—	97	2	no	—
462	C₂²⋊C₄	—	97	2	no	—
463	C₂²⋊C₄	—	97	2	no	—
464	C₂²⋊C₄	—	97	2	no	—
465	C₂²⋊C₄	—	97	2	no	—
466	C₂²⋊C₄	—	97	2	no	—
467	C₂²⋊C₄	—	97	2	no	—
468	C₂²⋊C₄	—	97	2	no	—
469	C₂²⋊C₄	—	97	2	no	—
470	C₂²⋊C₄	—	97	2	no	—
471	C₂²⋊C₄	—	97	2	no	—
472	C₂²⋊C₄	—	97	2	no	—
473	C₂²⋊C₄	—	97	2	no	—
474	C₂²⋊C₄	—	97	2	no	—
475	C₂²⋊C₄	—	97	2	no	—
476	C₂²⋊C₄	—	97	2	no	—
477	C₂²⋊C₄	—	97	2	no	—
478	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
479	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
480	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
484	C₄²	—	97	2	no	—
485	C₄²	—	97	2	no	—
486	C₄²	—	97	1	no	—
487	C₄²	—	97	1	no	—
488	C₄²	—	97	2	no	—
489	C₄²	—	97	1	no	—
490	C₄²	—	97	2	no	—
491	C₄²	C₂²×D₉₇	1	1	yes	characteristic
492	C₂³	—	97	2	no	—
493	C₂³	—	97	2	no	—
494	C₂³	—	97	1	no	—
495	C₂³	—	388	2	no	—
496	C₂³	—	388	2	no	—
497	C₂³	—	388	2	no	—
498	C₂³	C₂³×D₉₇	1	2	yes	—
499	C₂³	C₂³×D₉₇	1	2	yes	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	388	2	no	—
503	Q₈	—	388	1	no	—
504	Q₈	—	388	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	1	no	—
509	D₄	—	388	2	no	—
510	D₄	—	388	1	no	—
511	D₄	—	388	2	no	—
512	D₄	—	388	2	no	—
513	D₄	—	388	1	no	—
514	D₄	—	388	2	no	—
515	D₄	—	388	2	no	—
516	D₄	—	388	2	no	—
517	D₄	—	388	2	no	—
518	D₄	—	388	2	no	—
519	D₄	—	388	2	no	—
520	D₄	—	388	2	no	—
521	D₄	—	388	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	97	1	no	—
525	C₂×C₄	—	97	2	no	—
526	C₂×C₄	—	97	1	no	—
527	C₂×C₄	—	97	2	no	—
528	C₂×C₄	—	97	1	no	—
529	C₂×C₄	—	97	2	no	—
530	C₂×C₄	—	97	2	no	—
531	C₂×C₄	—	388	2	no	—
532	C₂×C₄	—	388	2	no	—
533	C₂×C₄	—	388	1	no	—
534	C₂×C₄	—	388	1	no	—
535	C₂×C₄	—	388	2	no	—
536	C₂×C₄	—	194	4	no	—
537	C₂×C₄	—	194	4	no	—
538	C₂×C₄	—	194	2	no	—
539	C₂×C₄	—	194	4	no	—
540	C₂×C₄	—	194	4	no	—
541	C₂×C₄	C₂³×D₉₇	1	2	yes	—
542	C₂×C₄	C₂³×D₉₇	1	2	yes	—
543	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₉₇	1	2	yes	—
547	C₂×C₄	C₂³×D₉₇	1	2	yes	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	388	8	no	—
555	C₂²	—	194	2	no	—
556	C₂²	—	194	2	no	—
557	C₂²	—	194	1	no	—
558	C₂²	—	194	1	no	—
559	C₂²	—	194	2	no	—
560	C₂²	—	194	2	no	—
561	C₂²	—	194	1	no	—
562	C₂²	—	194	2	no	—
563	C₂²	—	194	2	no	—
564	C₂²	C₂⁴×D₉₇	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	97	2	no	—
573	C₄	—	194	2	no	—
574	C₄	—	194	2	no	—
575	C₄	—	194	1	no	—
576	C₄	—	194	1	no	—
577	C₄	—	194	2	no	—
578	C₄	—	194	2	no	—
579	C₂	—	4	2	no	—
580	C₂	—	4	2	no	—
581	C₂	—	388	2	no	—
582	C₂	—	388	2	no	—
583	C₂	—	388	1	no	—
584	C₂	H(5,𝔽₂)×D₉₇	1	1	yes	characteristic
585	C₂	#20261570	1	1	yes	characteristic
586	C₂	#20261572	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₉₇
commutator, socle, cosocle	C₂²×C₉₇	C₂⁵
Fitting	#562×C₉₇	C₂
hypercenter	#562	D₉₇
hypocenter	C₉₇	#3529
LCS	G ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #20261489	C₂	semidirect
2. #20261486	C₂	semidirect
3. #20261482	C₂	semidirect
4. #20261481	C₂	semidirect
5. #20261479	C₂	semidirect
6. #20261477	C₂	semidirect
7. #20261475	C₂	semidirect
8. #20261473	C₂	semidirect
9. #20261473	C₂	semidirect
10. #20261284	C₂	semidirect
11. #20261280	C₂	semidirect
12. #20261271	C₂	semidirect
13. #20261270	C₂	semidirect
14. #20261264	C₂	semidirect
15. #20261262	C₂	semidirect
16. #20261248	C₂	semidirect
17. #20261245	C₂	semidirect
18. #20261243	C₂	semidirect
19. #562×C₉₇	C₂	semidirect
22. C₂×#13095510	C₂²	semidirect
23. C₂²×C₄×D₉₇	C₂²	semidirect
24. #15690809	C₂²	semidirect
25. #15690808	C₂²	semidirect
28. #15690805	C₂²	semidirect
29. #15690805	C₂²	semidirect
30. #15690805	C₂²	semidirect
31. #15690805	C₂²	semidirect
32. #15690803	C₂²	semidirect
33. #15690803	C₂²	semidirect
34. #15690802	C₂²	semidirect
35. #15690801	C₂²	semidirect
36. #15690800	C₂²	semidirect
42. #15690796	C₂²	semidirect
44. #15690795	C₂²	semidirect
45. #15690795	C₂²	semidirect
46. #15690794	C₂²	semidirect
47. #15690794	C₂²	semidirect
49. #15690793	C₂²	semidirect
51. #15690792	C₂²	semidirect
52. #15690792	C₂²	semidirect
53. #15690790	C₂²	semidirect
54. #15690790	C₂²	semidirect
55. #15690789	C₂²	semidirect
56. #15690788	C₂²	semidirect
57. #15690788	C₂²	semidirect
58. #15690787	C₂²	semidirect
59. #15690786	C₂²	semidirect
60. #15690786	C₂²	semidirect
65. #15690784	C₂²	semidirect
68. #15690783	C₂²	semidirect
69. #15690783	C₂²	semidirect
71. #15690782	C₂²	semidirect
72. #15690782	C₂²	semidirect
77. #15690780	C₂²	semidirect
79. #15690778	C₂²	semidirect
80. #15690778	C₂²	semidirect
81. Q₈×Dic₉₇	C₂²	semidirect
82. #15690775	C₂²	semidirect
84. D₄×Dic₉₇	C₂²	semidirect
87. #15690772	C₂²	semidirect
89. #15690770	C₂²	semidirect
90. #15690770	C₂²	semidirect
91. #15690770	C₂²	semidirect
92. #15690770	C₂²	semidirect
93. #15690768	C₂²	semidirect
94. #15690768	C₂²	semidirect
95. #15690766	C₂²	semidirect
96. C₂×C₄×Dic₉₇	C₂²	semidirect
97. C₄²×D₉₇	C₂²	semidirect
98. #125×C₉₇	C₂²	semidirect
100. #124×C₉₇	C₂²	semidirect
101. #123×C₉₇	C₂²	semidirect
102. #123×C₉₇	C₂²	semidirect
103. C₂²⋊Q₈×C₉₇	C₂²	semidirect
104. C₂²⋊Q₈×C₉₇	C₂²	semidirect
106. #121×C₉₇	C₂²	semidirect
294. C₉₇	#3529	semidirect
300. #562	D₉₇	semidirect
331. #125	C₂×D₉₇	semidirect
339. #124	C₂×D₉₇	semidirect
350. #123	C₂×D₉₇	semidirect
351. #123	C₂×D₉₇	semidirect
360. C₂²⋊Q₈	C₂×D₉₇	semidirect
361. C₂²⋊Q₈	C₂×D₉₇	semidirect
377. #121	C₂×D₉₇	semidirect

Maximal subgroups

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

subgroup	index
#20261489	2
#20261486	2
#20261482	2
#20261481	2
#20261479	2
#20261477	2
#20261475	2
#20261473	2
#20261284	2
#20261280	2
#20261271	2
#20261270	2
#20261264	2
#20261262	2
#20261248	2
#20261245	2
#20261243	2
#562×C₉₇	2
#3529	97