Subgroups — #27155347

Order 12416.

1242 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261470	C₂	1	1	yes	maximal, characteristic, complemented
2	#20261446	C₂	1	1	yes	maximal, characteristic, complemented
3	#20261438	C₂	1	2	yes	maximal, complemented
4	#20261433	C₂	1	2	yes	maximal, complemented
5	#20261412	C₂	1	4	yes	maximal, complemented
6	#20261380	C₂	1	2	yes	maximal, complemented
7	#20261376	C₂	1	2	yes	maximal, complemented
8	D₄×D₃₈₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#20261286	C₂	1	1	yes	maximal, characteristic, complemented
10	#20261271	C₂	1	2	yes	maximal, complemented
11	#20261270	C₂	1	2	yes	maximal, complemented
12	#20261248	C₂	1	4	yes	maximal, complemented
13	C₄×#13095512	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#13095510	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15690772	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₉₇	C₂	1	2	yes	maximal, complemented
17	#554×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13095512	C₂²	1	1	yes	characteristic
19	C₂×#13095512	C₂²	1	2	yes	complemented
20	C₂×#13095510	C₂²	1	1	yes	characteristic
21	C₂²×D₃₈₈	C₂²	1	2	yes	—
22	C₂×D₄×D₉₇	C₂²	1	2	yes	—
23	C₂²×C₄×D₉₇	C₂²	1	4	yes	complemented
24	#15690807	C₂²	1	1	yes	characteristic
25	#15690805	C₂²	1	4	yes	complemented
26	#15690805	C₂²	1	4	yes	complemented
27	#15690801	C₂²	1	2	yes	complemented
28	#15690799	C₂²	1	2	yes	complemented
29	#15690799	C₂²	1	2	yes	complemented
30	#15690798	C₂²	1	2	yes	complemented
31	#15690795	C₂²	1	4	yes	complemented
32	#15690795	C₂²	1	4	yes	complemented
33	#15690795	C₂²	1	4	yes	complemented
34	#15690794	C₂²	1	4	yes	complemented
35	#15690790	C₂²	1	2	yes	complemented
36	#15690786	C₂²	1	4	yes	complemented
37	#15690785	C₂²	1	2	yes	—
38	#15690785	C₂²	1	2	yes	complemented
39	#15690785	C₂²	1	4	yes	complemented
40	#15690785	C₂²	1	2	yes	complemented
41	#15690784	C₂²	1	2	yes	—
42	#15690784	C₂²	1	4	yes	complemented
43	#15690780	C₂²	1	4	yes	—
44	#15690780	C₂²	1	4	yes	complemented
45	Q₈×Dic₉₇	C₂²	1	1	yes	characteristic, complemented
46	C₄×Dic₁₉₄	C₂²	1	1	yes	characteristic, complemented
47	#15690775	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₃₈₈	C₂²	1	1	yes	characteristic
49	C₄×D₃₈₈	C₂²	1	2	yes	complemented
50	C₄×D₃₈₈	C₂²	1	2	yes	complemented
51	D₄×Dic₉₇	C₂²	1	1	yes	characteristic
52	#15690772	C₂²	1	2	yes	—
53	#15690772	C₂²	1	1	yes	characteristic
54	#15690772	C₂²	1	4	yes	complemented
55	#15690772	C₂²	1	2	yes	complemented
56	#15690772	C₂²	1	2	yes	complemented
57	#15690772	C₂²	1	4	yes	complemented
58	#15690772	C₂²	1	2	yes	complemented
59	#15690772	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₉₇	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₉₇	C₂²	1	4	yes	complemented
62	#15690770	C₂²	1	4	yes	complemented
63	#15690770	C₂²	1	2	yes	complemented
64	#15690768	C₂²	1	2	yes	complemented
65	#15690768	C₂²	1	1	yes	characteristic, complemented
66	#15690768	C₂²	1	1	yes	characteristic, complemented
67	#15690768	C₂²	1	4	yes	complemented
68	#15690766	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₉₇	C₂²	1	2	yes	complemented
70	C₂×#13095488	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₉₇	C₂²	1	4	yes	complemented
72	C₂×C₄×Dic₉₇	C₂²	1	2	yes	complemented
73	C₄²×D₉₇	C₂²	1	2	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	2	yes	—
81	C₄×D₄×C₉₇	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₉₇	C₂²	1	2	yes	complemented
83	C₂³×D₉₇	C₂³	1	4	yes	—
84	#13095512	—	2	4	no	—
85	#13095512	—	4	4	no	—
86	#13095510	—	2	4	no	—
87	C₂×Dic₁₉₄	C₂³	1	1	yes	characteristic
88	C₂×D₃₈₈	—	2	8	no	—
89	C₂×D₃₈₈	C₂³	1	4	yes	—
90	C₂×D₃₈₈	C₂³	1	2	yes	—
91	C₂×D₃₈₈	C₂³	1	2	yes	—
92	C₂×D₃₈₈	C₂³	1	2	yes	—
93	C₂×D₃₈₈	C₂³	1	2	yes	—
94	C₂×D₃₈₈	C₂³	1	4	yes	—
95	C₂×D₃₈₈	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₉₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₉₇	C₂³	1	2	yes	—
98	D₄×D₉₇	—	2	8	no	—
99	C₂²×Dic₉₇	C₂³	1	2	yes	—
100	C₂²×Dic₉₇	C₂³	1	2	yes	—
101	C₂×C₄×D₉₇	—	4	8	no	—
102	C₂×C₄×D₉₇	C₂³	1	2	yes	—
103	C₂×C₄×D₉₇	C₂³	1	2	yes	—
104	C₂×C₄×D₉₇	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₉₇	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₉₇	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₉₇	C₂³	1	2	yes	—
108	C₂×C₄×D₉₇	C₂³	1	4	yes	—
109	C₂×C₄×D₉₇	C₂³	1	4	yes	—
110	C₂×C₄×D₉₇	C₂³	1	4	yes	—
111	C₄⋊Dic₉₇	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₉₇	C₂³	1	1	yes	characteristic
113	C₄⋊Dic₉₇	C₂³	1	2	yes	—
114	C₄⋊Dic₉₇	C₂³	1	4	yes	—
115	#13095490	C₂³	1	4	yes	—
116	#13095490	C₂³	1	2	yes	—
117	#13095490	C₂³	1	2	yes	—
118	C₂²⋊Dic₉₇	C₂³	1	2	yes	—
119	#13095488	C₂³	1	4	yes	—
120	#13095488	C₂³	1	4	yes	—
121	#13095488	C₂³	1	2	yes	—
122	#13095488	C₂³	1	4	yes	—
123	#13095488	C₂³	1	4	yes	—
124	#13095488	C₂³	1	4	yes	—
125	#13095488	C₂³	1	2	yes	—
126	#13095488	C₂³	1	2	yes	—
127	#13095488	C₂³	1	2	yes	—
128	#13095488	C₂³	1	4	yes	—
129	#13095488	C₂³	1	4	yes	—
130	C₄×Dic₉₇	C₂³	1	1	yes	characteristic
131	C₄×Dic₉₇	C₂³	1	1	yes	characteristic
132	C₄×Dic₉₇	C₂³	1	1	yes	characteristic
133	C₄×Dic₉₇	C₂³	1	2	yes	—
134	C₄×Dic₉₇	C₂³	1	2	yes	—
135	C₄×Dic₉₇	C₂³	1	2	yes	—
136	C₄×Dic₉₇	C₂³	1	2	yes	—
137	C₄×Dic₉₇	C₂³	1	2	yes	—
138	C₂×Q₈×C₉₇	C₂³	1	1	yes	characteristic
139	C₂×Q₈×C₉₇	C₂³	1	2	yes	—
140	C₂×D₄×C₉₇	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₉₇	C₂³	1	2	yes	—
142	C₂²×C₄×C₉₇	C₂³	1	4	yes	—
143	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
144	C₄⋊C₄×C₉₇	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
146	C₄⋊C₄×C₉₇	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₉₇	C₂³	1	4	yes	—
148	C₄⋊C₄×C₉₇	C₂³	1	2	yes	—
149	C₄⋊C₄×C₉₇	C₂³	1	4	yes	—
150	C₂²⋊C₄×C₉₇	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₉₇	C₂³	1	2	yes	—
152	C₄²×C₉₇	C₂³	1	1	yes	characteristic
153	C₄²×C₉₇	C₂³	1	2	yes	—
154	C₂³×C₉₇	C₂⁴	1	2	yes	—
155	C₂²×D₉₇	—	2	8	no	—
156	C₂²×D₉₇	—	2	8	no	—
157	C₂²×D₉₇	—	4	4	no	—
158	C₂²×D₉₇	C₂⁴	1	4	yes	—
159	C₂²×D₉₇	C₂⁴	1	1	yes	characteristic
160	C₂²×D₉₇	C₂⁴	1	2	yes	—
161	Q₈×C₉₇	—	2	2	no	—
162	Q₈×C₉₇	—	4	2	no	—
163	D₄×C₉₇	#41	1	4	yes	complemented
164	C₂×C₄×C₉₇	—	2	4	no	—
165	C₂×C₄×C₉₇	—	4	4	no	—
166	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
167	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
169	C₂×C₄×C₉₇	C₂⁴	1	2	yes	—
170	C₂×C₄×C₉₇	C₂⁴	1	4	yes	—
171	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₉₇	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₉₇	—	2	8	no	—
174	C₂²⋊D₉₇	—	2	4	no	—
175	C₂×Dic₉₇	—	2	4	no	—
176	C₂×Dic₉₇	—	2	4	no	—
177	C₂×Dic₉₇	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₉₇	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₉₇	C₂⁴	1	2	yes	—
180	C₂×Dic₉₇	C₂⁴	1	2	yes	—
181	C₂×Dic₉₇	C₂⁴	1	2	yes	—
182	C₂×Dic₉₇	C₂⁴	1	1	yes	characteristic
183	D₃₈₈	—	2	8	no	—
184	D₃₈₈	—	2	4	no	—
185	D₃₈₈	—	2	4	no	—
186	D₃₈₈	—	2	4	no	—
187	D₃₈₈	—	4	4	no	—
188	D₃₈₈	—	4	2	no	—
189	D₃₈₈	#41	1	4	yes	complemented
190	C₄×D₉₇	—	2	4	no	—
191	C₄×D₉₇	—	2	4	no	—
192	C₄×D₉₇	—	2	2	no	—
193	C₄×D₉₇	—	2	2	no	—
194	C₄×D₉₇	—	2	4	no	—
195	C₄×D₉₇	—	2	8	no	—
196	C₄×D₉₇	—	2	2	no	—
197	C₄×D₉₇	—	4	4	no	—
198	C₄×D₉₇	—	4	4	no	—
199	Dic₁₉₄	—	2	2	no	—
200	C₂²×C₉₇	—	2	2	no	—
201	C₂²×C₉₇	—	2	2	no	—
202	C₂²×C₉₇	C₂×#41	1	4	yes	—
203	C₂²×C₉₇	C₂⁵	1	1	yes	characteristic
204	C₂×D₉₇	—	2	2	no	—
205	C₂×D₉₇	—	2	2	no	—
206	C₂×D₉₇	—	2	1	no	—
207	C₂×D₉₇	—	2	1	no	—
208	C₂×D₉₇	—	2	4	no	—
209	C₂×D₉₇	—	2	4	no	—
210	C₂×D₉₇	—	2	4	no	—
211	C₂×D₉₇	—	2	1	no	—
212	C₂×D₉₇	—	4	16	no	—
213	C₂×D₉₇	C₂×#41	1	4	yes	—
214	C₄×C₉₇	—	2	2	no	—
215	C₄×C₉₇	—	2	2	no	—
216	C₄×C₉₇	—	2	2	no	—
217	C₄×C₉₇	—	2	4	no	—
218	C₄×C₉₇	—	2	1	no	—
219	C₄×C₉₇	C₂×#41	1	2	yes	—
220	C₄×C₉₇	C₂×#41	1	2	yes	—
221	Dic₉₇	—	2	2	no	—
222	Dic₉₇	—	2	1	no	—
223	Dic₉₇	—	2	1	no	—
224	Dic₉₇	—	2	2	no	—
225	Dic₉₇	—	2	2	no	—
226	Dic₉₇	H(5,𝔽₂)	1	2	yes	—
227	C₂×C₉₇	—	2	4	no	—
228	C₂×C₉₇	C₂²×#41	1	1	yes	characteristic
229	C₂×C₉₇	C₂²×#41	1	1	yes	characteristic
230	C₂×C₉₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	D₉₇	—	2	4	no	—
232	D₉₇	—	4	1	no	—
233	D₉₇	—	4	4	no	—
234	#3481	—	97	1	no	maximal, Sylow
235	C₉₇	#3481	1	1	yes	characteristic, complemented, Sylow
236	#559	—	97	1	no	—
237	#554	—	97	1	no	—
238	#554	D₉₇	1	1	yes	characteristic, complemented
239	#553	—	97	2	no	—
240	#553	—	97	2	no	—
241	#551	—	97	4	no	—
242	#546	—	97	2	no	—
243	#546	—	97	2	no	—
244	D₄²	—	97	1	no	—
245	#532	—	97	1	no	—
246	#529	—	97	2	no	—
247	#529	—	97	2	no	—
248	#525	—	97	4	no	—
249	C₄×#41	—	97	1	no	—
250	C₄×#41	—	97	1	no	—
251	C₂×C₄×D₄	—	97	2	no	—
252	C₂×C₄×D₄	—	97	2	no	—
253	C₂×#41	—	97	2	no	—
254	C₂×#41	—	97	1	no	—
255	C₂×#41	—	97	1	no	—
256	C₂²×D₄	—	97	2	no	—
257	C₂²×D₄	—	97	2	no	—
258	C₂³×C₄	—	97	4	no	—
259	C₄⋊Q₈	C₂×D₉₇	1	1	yes	characteristic, complemented
260	#127	—	97	1	no	—
261	#126	—	97	4	no	—
262	#126	—	97	4	no	—
263	#125	—	97	2	no	—
264	#125	C₂×D₉₇	1	2	yes	complemented
265	#124	—	97	2	no	—
266	#124	—	97	2	no	—
267	#124	—	97	2	no	—
268	#123	—	97	4	no	—
269	#123	—	97	4	no	—
270	#123	—	97	4	no	—
271	#123	—	97	4	no	—
272	C₂²⋊Q₈	—	97	4	no	—
273	C₂²⋊Q₈	—	97	2	no	—
274	C₂²⋊Q₈	C₂×D₉₇	1	4	yes	complemented
275	C₂²⋊Q₈	C₂×D₉₇	1	2	yes	complemented
276	#121	—	97	4	no	—
277	#121	—	97	2	no	—
278	#121	—	97	4	no	—
279	#121	—	97	2	no	—
280	#121	—	97	2	no	—
281	#121	—	97	2	no	—
282	#120	—	97	4	no	—
283	#120	—	97	4	no	—
284	C₄×Q₈	—	97	1	no	—
285	C₄×Q₈	—	97	1	no	—
286	C₄×Q₈	—	97	1	no	—
287	C₄×Q₈	C₂×D₉₇	1	1	yes	characteristic, complemented
288	C₄×D₄	—	97	1	no	—
289	C₄×D₄	—	97	4	no	—
290	C₄×D₄	—	97	2	no	—
291	C₄×D₄	—	97	1	no	—
292	C₄×D₄	—	97	4	no	—
293	C₄×D₄	—	97	2	no	—
294	C₄×D₄	—	97	2	no	—
295	C₄×D₄	—	97	2	no	—
296	C₄×D₄	—	97	4	no	—
297	C₄×D₄	—	97	2	no	—
298	C₄×D₄	—	97	2	no	—
299	C₄×D₄	—	97	4	no	—
300	C₄×D₄	—	97	2	no	—
301	C₄×D₄	—	97	2	no	—
302	C₄×D₄	—	97	1	no	—
303	C₄×D₄	—	97	2	no	—
304	C₄×D₄	C₂×D₉₇	1	2	yes	—
305	C₄×D₄	C₂×D₉₇	1	1	yes	characteristic
306	#117	—	97	2	no	—
307	#117	—	97	1	no	—
308	#117	—	97	1	no	—
309	#117	—	97	4	no	—
310	#117	—	97	2	no	—
311	C₂×C₄⋊C₄	—	97	2	no	—
312	C₂×C₄⋊C₄	C₂×D₉₇	1	2	yes	complemented
313	C₂×C₂²⋊C₄	—	97	4	no	—
314	C₂×C₂²⋊C₄	—	97	4	no	—
315	C₂×C₄²	—	97	2	no	—
316	C₂×C₄²	—	97	2	no	—
317	C₂×C₄²	—	97	1	no	—
318	C₂⁴	—	97	4	no	—
319	#41	—	388	4	no	—
320	#41	—	194	4	no	—
321	#41	—	194	4	no	—
322	C₂×Q₈	—	97	1	no	—
323	C₂×Q₈	C₂²×D₉₇	1	1	yes	characteristic
324	C₂×Q₈	C₂²×D₉₇	1	2	yes	—
325	C₂×D₄	—	97	2	no	—
326	C₂×D₄	—	97	4	no	—
327	C₂×D₄	—	97	1	no	—
328	C₂×D₄	—	97	2	no	—
329	C₂×D₄	—	97	4	no	—
330	C₂×D₄	—	97	2	no	—
331	C₂×D₄	—	97	4	no	—
332	C₂×D₄	—	97	2	no	—
333	C₂×D₄	—	97	2	no	—
334	C₂×D₄	—	194	8	no	—
335	C₂×D₄	—	194	8	no	—
336	C₂×D₄	C₂²×D₉₇	1	1	yes	characteristic
337	C₂²×C₄	—	97	2	no	—
338	C₂²×C₄	—	97	2	no	—
339	C₂²×C₄	—	97	4	no	—
340	C₂²×C₄	—	97	4	no	—
341	C₂²×C₄	—	97	2	no	—
342	C₂²×C₄	—	97	2	no	—
343	C₂²×C₄	—	97	1	no	—
344	C₂²×C₄	—	97	1	no	—
345	C₂²×C₄	—	97	2	no	—
346	C₂²×C₄	—	97	1	no	—
347	C₂²×C₄	—	97	4	no	—
348	C₂²×C₄	—	388	8	no	—
349	C₂²×C₄	C₂²×D₉₇	1	2	yes	—
350	C₂²×C₄	C₂²×D₉₇	1	4	yes	—
351	C₄⋊C₄	—	97	4	no	—
352	C₄⋊C₄	—	97	2	no	—
353	C₄⋊C₄	—	97	2	no	—
354	C₄⋊C₄	—	97	1	no	—
355	C₄⋊C₄	—	97	1	no	—
356	C₄⋊C₄	—	97	2	no	—
357	C₄⋊C₄	—	97	4	no	—
358	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
359	C₄⋊C₄	C₂²×D₉₇	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
361	C₄⋊C₄	C₂²×D₉₇	1	4	yes	—
362	C₄⋊C₄	C₂²×D₉₇	1	2	yes	—
363	C₄⋊C₄	C₂²×D₉₇	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×D₉₇	1	4	yes	—
365	C₂²⋊C₄	—	97	2	no	—
366	C₂²⋊C₄	—	97	2	no	—
367	C₂²⋊C₄	—	97	4	no	—
368	C₂²⋊C₄	—	97	4	no	—
369	C₂²⋊C₄	—	97	4	no	—
370	C₂²⋊C₄	—	97	4	no	—
371	C₂²⋊C₄	—	97	4	no	—
372	C₂²⋊C₄	—	97	2	no	—
373	C₂²⋊C₄	—	97	2	no	—
374	C₂²⋊C₄	—	97	2	no	—
375	C₂²⋊C₄	—	97	4	no	—
376	C₂²⋊C₄	—	97	4	no	—
377	C₂²⋊C₄	C₂²×D₉₇	1	4	yes	—
378	C₂²⋊C₄	C₂²×D₉₇	1	2	yes	—
379	C₄²	—	97	1	no	—
380	C₄²	—	97	1	no	—
381	C₄²	—	97	1	no	—
382	C₄²	—	97	2	no	—
383	C₄²	—	97	2	no	—
384	C₄²	—	97	2	no	—
385	C₄²	—	97	2	no	—
386	C₄²	—	97	2	no	—
387	C₄²	C₂²×D₉₇	1	2	yes	—
388	C₄²	C₂²×D₉₇	1	1	yes	characteristic
389	C₂³	—	97	2	no	—
390	C₂³	—	97	4	no	—
391	C₂³	—	97	1	no	—
392	C₂³	—	388	4	no	—
393	C₂³	—	194	8	no	—
394	C₂³	—	194	8	no	—
395	C₂³	C₂³×D₉₇	1	2	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	194	2	no	—
399	D₄	—	97	4	no	—
400	D₄	—	388	4	no	—
401	D₄	—	388	2	no	—
402	D₄	—	194	8	no	—
403	D₄	—	194	4	no	—
404	D₄	—	194	8	no	—
405	D₄	—	194	4	no	—
406	D₄	—	194	4	no	—
407	D₄	—	194	4	no	—
408	D₄	#13095512	1	4	yes	complemented
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	97	1	no	—
412	C₂×C₄	—	97	1	no	—
413	C₂×C₄	—	97	1	no	—
414	C₂×C₄	—	97	2	no	—
415	C₂×C₄	—	97	2	no	—
416	C₂×C₄	—	97	2	no	—
417	C₂×C₄	—	388	4	no	—
418	C₂×C₄	—	388	4	no	—
419	C₂×C₄	—	194	4	no	—
420	C₂×C₄	—	194	8	no	—
421	C₂×C₄	—	194	2	no	—
422	C₂×C₄	—	194	4	no	—
423	C₂×C₄	—	194	4	no	—
424	C₂×C₄	—	194	4	no	—
425	C₂×C₄	—	194	2	no	—
426	C₂×C₄	—	194	4	no	—
427	C₂×C₄	—	194	2	no	—
428	C₂×C₄	C₂³×D₉₇	1	2	yes	—
429	C₂×C₄	C₂³×D₉₇	1	2	yes	—
430	C₂×C₄	C₂³×D₉₇	1	2	yes	—
431	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₉₇	1	4	yes	—
433	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₉₇	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	97	4	no	—
438	C₂²	—	388	16	no	—
439	C₂²	—	194	1	no	—
440	C₂²	—	194	4	no	—
441	C₂²	—	194	1	no	—
442	C₂²	—	194	4	no	—
443	C₂²	—	194	4	no	—
444	C₂²	—	194	1	no	—
445	C₂²	—	194	2	no	—
446	C₂²	—	194	2	no	—
447	C₂²	C₂×#13095512	1	4	yes	—
448	C₂²	C₂⁴×D₉₇	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	2	1	no	—
454	C₄	—	97	2	no	—
455	C₄	—	194	1	no	—
456	C₄	—	194	1	no	—
457	C₄	—	194	2	no	—
458	C₄	—	194	2	no	—
459	C₄	—	194	2	no	—
460	C₄	#41×D₉₇	1	2	yes	—
461	C₄	C₂×#13095512	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	388	4	no	—
464	C₂	—	388	1	no	—
465	C₂	—	194	4	no	—
466	C₂	C₂×#41×D₉₇	1	1	yes	characteristic
467	C₂	C₂²×#13095512	1	1	yes	characteristic
468	C₂	H(5,𝔽₂)×D₉₇	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	#3481
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. #20261470	C₂	semidirect
2. #20261446	C₂	semidirect
3. #20261438	C₂	semidirect
4. #20261433	C₂	semidirect
5. #20261412	C₂	semidirect
6. #20261380	C₂	semidirect
7. #20261376	C₂	semidirect
8. D₄×D₃₈₈	C₂	semidirect
9. #20261286	C₂	semidirect
10. #20261271	C₂	semidirect
11. #20261270	C₂	semidirect
12. #20261248	C₂	semidirect
13. C₄×#13095512	C₂	semidirect
14. C₄×#13095510	C₂	semidirect
15. C₂×#15690772	C₂	semidirect
16. C₄×D₄×D₉₇	C₂	semidirect
17. #554×C₉₇	C₂	semidirect
19. C₂×#13095512	C₂²	semidirect
23. C₂²×C₄×D₉₇	C₂²	semidirect
25. #15690805	C₂²	semidirect
26. #15690805	C₂²	semidirect
27. #15690801	C₂²	semidirect
28. #15690799	C₂²	semidirect
29. #15690799	C₂²	semidirect
30. #15690798	C₂²	semidirect
31. #15690795	C₂²	semidirect
32. #15690795	C₂²	semidirect
33. #15690795	C₂²	semidirect
34. #15690794	C₂²	semidirect
35. #15690790	C₂²	semidirect
36. #15690786	C₂²	semidirect
38. #15690785	C₂²	semidirect
39. #15690785	C₂²	semidirect
40. #15690785	C₂²	semidirect
42. #15690784	C₂²	semidirect
44. #15690780	C₂²	semidirect
45. Q₈×Dic₉₇	C₂²	semidirect
46. C₄×Dic₁₉₄	C₂²	semidirect
47. #15690775	C₂²	semidirect
49. C₄×D₃₈₈	C₂²	semidirect
50. C₄×D₃₈₈	C₂²	semidirect
54. #15690772	C₂²	semidirect
55. #15690772	C₂²	semidirect
56. #15690772	C₂²	semidirect
57. #15690772	C₂²	semidirect
58. #15690772	C₂²	semidirect
59. #15690772	C₂²	semidirect
60. C₄×C₂²⋊D₉₇	C₂²	semidirect
61. C₄×C₂²⋊D₉₇	C₂²	semidirect
62. #15690770	C₂²	semidirect
63. #15690770	C₂²	semidirect
64. #15690768	C₂²	semidirect
65. #15690768	C₂²	semidirect
66. #15690768	C₂²	semidirect
67. #15690768	C₂²	semidirect
68. #15690766	C₂²	semidirect
69. C₄⋊C₄×D₉₇	C₂²	semidirect
70. C₂×#13095488	C₂²	semidirect
71. C₂²⋊C₄×D₉₇	C₂²	semidirect
72. C₂×C₄×Dic₉₇	C₂²	semidirect
73. C₄²×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
163. D₄×C₉₇	#41	semidirect
189. D₃₈₈	#41	semidirect
235. C₉₇	#3481	semidirect
238. #554	D₉₇	semidirect
259. C₄⋊Q₈	C₂×D₉₇	semidirect
264. #125	C₂×D₉₇	semidirect
274. C₂²⋊Q₈	C₂×D₉₇	semidirect
275. C₂²⋊Q₈	C₂×D₉₇	semidirect
287. C₄×Q₈	C₂×D₉₇	semidirect
312. C₂×C₄⋊C₄	C₂×D₉₇	semidirect
408. D₄	#13095512	semidirect

Maximal subgroups

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

subgroup	index
#20261470	2
#20261446	2
#20261438	2
#20261433	2
#20261412	2
#20261380	2
#20261376	2
D₄×D₃₈₈	2
#20261286	2
#20261271	2
#20261270	2
#20261248	2
C₄×#13095512	2
C₄×#13095510	2
C₂×#15690772	2
C₄×D₄×D₉₇	2
#554×C₉₇	2
#3481	97