Subgroups — #30825178

Order 17152.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569341	C₂	1	1	yes	maximal, characteristic
2	#22569334	C₂	1	1	yes	maximal, characteristic
3	#22558998	C₂	1	1	yes	maximal, characteristic, complemented
4	#22558998	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558989	C₂	1	2	yes	maximal, complemented
6	#22558980	C₂	1	2	yes	maximal, complemented
7	#22558976	C₂	1	2	yes	maximal, complemented
8	#22558965	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558961	C₂	1	2	yes	maximal, complemented
10	#22558957	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2965	C₂	1	1	yes	maximal, characteristic
12	#16863527	—	2	1	no	—
13	Q₈×C₆₇⋊C₈	—	2	1	no	—
14	#16863474	—	2	1	no	—
15	#16863474	—	2	2	no	—
16	#16863468	—	2	2	no	—
17	D₄×C₆₇⋊C₈	—	2	1	no	—
18	#16863453	C₂²	1	2	yes	—
19	#16863449	C₂²	1	2	yes	—
20	#16863449	C₂²	1	1	yes	characteristic
21	#16863449	C₂²	1	1	yes	characteristic
22	#16863420	C₂²	1	2	yes	—
23	#16863420	C₂²	1	1	yes	characteristic
24	#16863420	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
26	#16863149	C₂²	1	1	yes	characteristic
27	#16863149	C₂²	1	2	yes	—
28	#16863149	C₂²	1	2	yes	—
29	#16863149	C₂²	1	1	yes	characteristic
30	#16863147	C₂²	1	2	yes	—
31	#16863147	C₂²	1	2	yes	—
32	#16863147	C₂²	1	1	yes	characteristic
33	#16863147	C₂²	1	2	yes	—
34	#16863147	C₂²	1	2	yes	—
35	#16863147	C₂²	1	1	yes	characteristic
36	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
37	#446×C₆₇	C₄	1	1	yes	characteristic
38	#446×C₆₇	C₄	1	1	yes	characteristic
39	#436×C₆₇	C₄	1	1	yes	characteristic
40	#436×C₆₇	C₄	1	1	yes	characteristic
41	#435×C₆₇	C₄	1	2	yes	—
42	#435×C₆₇	C₄	1	2	yes	—
43	#431×C₆₇	C₂²	1	2	yes	—
44	#431×C₆₇	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761612	—	2	1	no	—
48	C₂×#11761612	—	2	2	no	—
49	C₂×#11761612	—	2	1	no	—
50	C₂²×C₆₇⋊C₈	—	2	2	no	—
51	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
53	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
54	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
56	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
57	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
58	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
59	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
60	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
61	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
62	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
65	#14523954	—	2	2	no	—
66	C₄×C₆₇⋊C₈	—	2	1	no	—
67	C₄×C₆₇⋊C₈	—	2	2	no	—
68	C₄×C₆₇⋊C₈	—	2	1	no	—
69	C₂×#41×C₆₇	Q₈	1	1	yes	characteristic
70	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
75	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
76	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
77	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
78	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
79	C₄×D₄×C₆₇	D₄	1	2	yes	—
80	#117×C₆₇	Q₈	1	1	yes	characteristic
81	#117×C₆₇	Q₈	1	2	yes	—
82	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
85	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
86	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
87	C₄⋊C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
90	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
91	#97×C₆₇	C₂×C₄	1	2	yes	—
92	#97×C₆₇	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₆₇	C₂³	1	2	yes	—
98	#11761612	—	8	1	no	—
99	#11761612	—	8	2	no	—
100	#11761612	—	8	1	no	—
101	C₂×C₆₇⋊C₈	—	2	1	no	—
102	C₂×C₆₇⋊C₈	—	2	1	no	—
103	C₂×C₆₇⋊C₈	—	2	1	no	—
104	C₂×C₆₇⋊C₈	—	2	1	no	—
105	C₂×C₆₇⋊C₈	—	2	2	no	—
106	C₂×C₆₇⋊C₈	—	2	2	no	—
107	C₂×C₆₇⋊C₈	—	8	2	no	—
108	#41×C₆₇	—	4	2	no	—
109	C₂×Q₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
110	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
111	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
112	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
118	M₁₆×C₆₇	—	2	4	no	—
119	M₁₆×C₆₇	—	4	2	no	—
120	C₂×C₈×C₆₇	—	2	2	no	—
121	C₂×C₈×C₆₇	—	4	1	no	—
122	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
129	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
130	C₄⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
131	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
132	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
133	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
134	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
135	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
137	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₆₇	C₂×D₄	1	2	yes	—
139	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
140	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
141	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
142	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
144	Q₈×C₆₇	—	2	2	no	—
145	D₄×C₆₇	—	2	2	no	—
146	D₄×C₆₇	—	4	2	no	—
147	C₂×C₄×C₆₇	—	2	1	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	1	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	2	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	2	1	no	—
154	C₂×C₄×C₆₇	—	2	1	no	—
155	C₂×C₄×C₆₇	—	2	2	no	—
156	C₂×C₄×C₆₇	—	4	2	no	—
157	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	—	2	2	no	—
168	C₈×C₆₇	—	2	1	no	—
169	C₈×C₆₇	—	2	1	no	—
170	C₈×C₆₇	—	2	2	no	—
171	C₈×C₆₇	#131	1	2	yes	—
172	C₆₇⋊C₈	—	4	1	no	—
173	C₆₇⋊C₈	—	4	1	no	—
174	C₆₇⋊C₈	—	4	1	no	—
175	C₆₇⋊C₈	—	4	2	no	—
176	C₆₇⋊C₈	—	4	1	no	—
177	C₆₇⋊C₈	—	4	2	no	—
178	C₂²×C₆₇	—	2	1	no	—
179	C₂²×C₆₇	—	2	2	no	—
180	C₂²×C₆₇	—	2	2	no	—
181	C₂²×C₆₇	—	2	1	no	—
182	C₂²×C₆₇	—	2	1	no	—
183	C₂²×C₆₇	—	2	2	no	—
184	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₄×C₆₇	—	2	1	no	—
186	C₄×C₆₇	—	2	2	no	—
187	C₄×C₆₇	—	2	2	no	—
188	C₄×C₆₇	—	2	1	no	—
189	C₄×C₆₇	—	2	1	no	—
190	C₄×C₆₇	—	2	2	no	—
191	C₄×C₆₇	#430	1	2	yes	—
192	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
193	C₄×C₆₇	#568	1	1	yes	characteristic
194	C₄×C₆₇	#577	1	1	yes	characteristic
195	C₄×C₆₇	#577	1	1	yes	characteristic
196	#17841	—	67	1	no	maximal, Sylow
197	C₂×C₆₇	—	4	1	no	—
198	C₂×C₆₇	—	4	2	no	—
199	C₂×C₆₇	#2906	1	1	yes	characteristic
200	C₂×C₆₇	#2912	1	1	yes	characteristic
201	C₂×C₆₇	C₂×#430	1	1	yes	characteristic
202	#2991	—	67	1	no	—
203	#2990	—	67	1	no	—
204	#2965	D₆₇	1	1	yes	characteristic
205	#1574	—	67	1	no	—
206	#1574	—	67	1	no	—
207	#1572	—	67	2	no	—
208	#1570	—	67	2	no	—
209	#1569	—	67	2	no	—
210	#1566	—	67	1	no	—
211	#1565	—	67	2	no	—
212	#1564	—	67	1	no	—
213	C₆₇	#17841	1	1	yes	characteristic, complemented, Sylow
214	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
215	#446	—	134	1	no	—
216	#446	Dic₆₇	1	1	yes	characteristic
217	#446	Dic₆₇	1	1	yes	characteristic
218	C₈×Q₈	—	134	1	no	—
219	#436	—	134	1	no	—
220	#436	—	134	2	no	—
221	#436	Dic₆₇	1	1	yes	characteristic
222	#436	Dic₆₇	1	1	yes	characteristic
223	#435	—	134	2	no	—
224	#435	Dic₆₇	1	2	yes	—
225	#435	Dic₆₇	1	2	yes	—
226	C₈×D₄	—	134	1	no	—
227	#432	—	67	2	no	—
228	#431	—	67	1	no	—
229	#431	—	67	1	no	—
230	#431	—	67	2	no	—
231	#431	C₂×D₆₇	1	2	yes	—
232	#431	C₂×D₆₇	1	1	yes	characteristic
233	#423	—	67	1	no	—
234	#423	—	67	1	no	—
235	#423	—	67	2	no	—
236	C₂×C₄⋊C₈	—	67	2	no	—
237	C₄×M₁₆	C₂×D₆₇	1	2	yes	—
238	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
239	#335	—	67	1	no	—
240	#335	—	67	1	no	—
241	#335	—	67	2	no	—
242	#335	—	67	2	no	—
243	#334	—	67	1	no	—
244	#334	—	67	1	no	—
245	#334	—	67	2	no	—
246	#334	—	67	2	no	—
247	#334	—	67	2	no	—
248	#334	—	67	2	no	—
249	C₂×#41	Dic₁₃₄	1	1	yes	characteristic
250	C₂×M₁₆	—	134	1	no	—
251	C₂×M₁₆	—	134	2	no	—
252	C₂×M₁₆	—	134	1	no	—
253	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
254	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
255	C₂²×C₈	—	134	2	no	—
256	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
257	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
258	C₄×Q₈	D₂₆₈	1	1	yes	characteristic
259	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
260	C₄×D₄	D₂₆₈	1	1	yes	characteristic
261	C₄×D₄	D₂₆₈	1	2	yes	—
262	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
263	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
264	#117	Dic₁₃₄	1	1	yes	characteristic
265	#117	Dic₁₃₄	1	2	yes	—
266	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
268	C₄⋊C₈	—	67	1	no	—
269	C₄⋊C₈	—	67	2	no	—
270	C₄⋊C₈	—	67	1	no	—
271	C₄⋊C₈	—	67	2	no	—
272	C₄⋊C₈	—	67	1	no	—
273	C₄⋊C₈	—	67	1	no	—
274	C₄⋊C₈	—	134	2	no	—
275	C₄⋊C₈	—	134	1	no	—
276	C₄⋊C₈	—	134	1	no	—
277	C₄⋊C₈	—	134	2	no	—
278	C₄⋊C₈	C₂×Dic₆₇	1	2	yes	—
279	C₄⋊C₈	C₂×Dic₆₇	1	2	yes	—
280	C₄⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
281	C₄⋊C₈	C₂×Dic₆₇	1	1	yes	characteristic
282	C₂²⋊C₈	—	134	1	no	—
283	C₂²⋊C₈	—	134	2	no	—
284	C₂²⋊C₈	—	134	1	no	—
285	C₂²⋊C₈	—	134	2	no	—
286	C₂²⋊C₈	C₂×Dic₆₇	1	2	yes	—
287	C₂²⋊C₈	C₂×Dic₆₇	1	2	yes	—
288	C₂²⋊C₈	C₂×Dic₆₇	1	2	yes	—
289	#97	—	134	2	no	—
290	#97	C₂×Dic₆₇	1	2	yes	—
291	#97	C₂×Dic₆₇	1	2	yes	—
292	C₄×C₈	—	134	1	no	—
293	C₄×C₈	—	134	1	no	—
294	C₄×C₈	—	134	2	no	—
295	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
296	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₆₇	1	2	yes	—
300	#41	—	4	2	no	—
301	C₂×Q₈	C₄⋊Dic₆₇	1	1	yes	characteristic
302	C₂×D₄	C₄⋊Dic₆₇	1	1	yes	characteristic
303	C₂×D₄	C₄⋊Dic₆₇	1	2	yes	—
304	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
305	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
306	C₂²×C₄	C₂×D₂₆₈	1	2	yes	—
307	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
308	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
309	C₂²×C₄	C₂×Dic₁₃₄	1	2	yes	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	4	2	no	—
312	M₁₆	—	536	1	no	—
313	M₁₆	—	536	2	no	—
314	M₁₆	—	536	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	536	2	no	—
318	C₂×C₈	—	134	1	no	—
319	C₂×C₈	—	134	1	no	—
320	C₂×C₈	—	134	1	no	—
321	C₂×C₈	—	134	1	no	—
322	C₂×C₈	—	134	2	no	—
323	C₂×C₈	—	134	2	no	—
324	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
325	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
327	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
328	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
329	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
330	C₄⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
331	C₄⋊C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
332	C₄⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
333	C₄⋊C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
334	C₂²⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
335	C₂²⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
336	C₂²⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
337	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
338	C₄²	C₂²×Dic₆₇	1	2	yes	—
339	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
340	C₄²	C₂×D₂₆₈	1	2	yes	—
341	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
342	C₄²	C₂×Dic₁₃₄	1	2	yes	—
343	C₄²	C₂³×D₆₇	1	1	yes	characteristic
344	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
345	C₂³	C₂×C₄⋊Dic₆₇	1	2	yes	—
346	Q₈	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
360	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
362	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
364	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
365	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
367	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	2	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	2	no	—
373	C₈	—	268	1	no	—
374	C₈	—	268	2	no	—
375	C₈	—	268	1	no	—
376	C₈	—	268	2	no	—
377	C₈	—	268	1	no	—
378	C₈	—	268	1	no	—
379	C₈	#14524050	1	2	yes	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	#16863445	1	2	yes	—
394	C₄	C₂×#14524050	1	1	yes	characteristic
395	C₄	#16864163	1	1	yes	characteristic
396	C₄	#16864208	1	1	yes	characteristic
397	C₄	#16864208	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	4	2	no	—
400	C₂	#22568777	1	1	yes	characteristic
401	C₂	#22568804	1	1	yes	characteristic
402	C₂	C₂×#16863445	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2965	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₆₇	Q₈
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#2965	D₆₇
hypocenter	C₆₇	#17841
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2965

Complements

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

N	H ≅ G/N	type
3. #22558998	C₂	semidirect
4. #22558998	C₂	semidirect
5. #22558989	C₂	semidirect
6. #22558980	C₂	semidirect
7. #22558976	C₂	semidirect
8. #22558965	C₂	semidirect
9. #22558961	C₂	semidirect
10. #22558957	C₂	semidirect
213. C₆₇	#17841	semidirect

Maximal subgroups

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

subgroup	index
#22569341	2
#22569334	2
#22558998	2
#22558989	2
#22558980	2
#22558976	2
#22558965	2
#22558961	2
#22558957	2
C₆₇×#2965	2
#17841	67