Subgroups — #30825106

Order 17152.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569176	C₂	1	1	yes	maximal, characteristic
2	#22568777	C₂	1	1	yes	maximal, characteristic
3	#22558997	C₂	1	2	yes	maximal, complemented
4	#22558995	C₂	1	2	yes	maximal, complemented
5	#22558983	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558981	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558977	C₂	1	2	yes	maximal, complemented
8	#22558964	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558962	C₂	1	2	yes	maximal, complemented
10	C₂×#16863148	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	—	2	1	no	—
13	#16863527	C₄	1	1	yes	characteristic
14	#16863527	C₄	1	1	yes	characteristic
15	#16863474	C₄	1	1	yes	characteristic
16	#16863474	C₄	1	1	yes	characteristic
17	#16863468	C₄	1	2	yes	—
18	#16863468	C₄	1	2	yes	—
19	#16863449	C₂²	1	1	yes	characteristic
20	#16863449	C₂²	1	2	yes	—
21	#16863423	—	2	1	no	—
22	#16863423	—	2	2	no	—
23	#16863420	C₂²	1	2	yes	—
24	#16863420	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
27	C₄×#11761612	C₂²	1	2	yes	—
28	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
29	#16863148	C₂²	1	1	yes	characteristic
30	#16863148	C₂²	1	2	yes	—
31	#16863148	C₂²	1	2	yes	—
32	#16863148	C₂²	1	1	yes	characteristic
33	#16863148	C₂²	1	1	yes	characteristic
34	#16863148	C₂²	1	1	yes	characteristic
35	#16863146	C₂²	1	2	yes	—
36	#16863146	C₂²	1	2	yes	—
37	#16863146	C₂²	1	2	yes	—
38	#16863146	C₂²	1	2	yes	—
39	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
40	#433×C₆₇	—	2	2	no	—
41	#432×C₆₇	C₂²	1	2	yes	—
42	#431×C₆₇	C₂²	1	2	yes	—
43	#423×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
45	#408×C₆₇	—	2	1	no	—
46	#405×C₆₇	—	2	1	no	—
47	#14524050	—	4	4	no	—
48	C₂×#11761612	—	2	2	no	—
49	C₂×#11761612	—	2	1	no	—
50	C₂×#11761612	C₂×C₄	1	2	yes	—
51	C₂×#11761612	C₂×C₄	1	2	yes	—
52	C₂²×C₆₇⋊C₈	—	2	2	no	—
53	C₂²×C₆₇⋊C₈	—	2	1	no	—
54	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
57	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
58	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
59	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
61	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
62	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
63	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
64	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
67	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
68	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
69	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
70	#14523954	C₂×C₄	1	2	yes	—
71	#14523954	C₂×C₄	1	2	yes	—
72	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
77	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
78	C₂×M₁₆×C₆₇	—	2	1	no	—
79	C₂²×C₈×C₆₇	—	2	1	no	—
80	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
81	C₄×Q₈×C₆₇	Q₈	1	1	yes	characteristic
82	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
83	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
84	C₄×D₄×C₆₇	Q₈	1	2	yes	—
85	C₄×D₄×C₆₇	Q₈	1	1	yes	characteristic
86	#117×C₆₇	D₄	1	1	yes	characteristic
87	#117×C₆₇	D₄	1	2	yes	—
88	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
90	C₄⋊C₈×C₆₇	—	2	1	no	—
91	C₄⋊C₈×C₆₇	—	2	1	no	—
92	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
93	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²⋊C₈×C₆₇	—	2	2	no	—
96	C₂²⋊C₈×C₆₇	—	2	2	no	—
97	#97×C₆₇	—	2	2	no	—
98	C₄×C₈×C₆₇	—	2	2	no	—
99	#11761612	—	2	4	no	—
100	#11761612	—	4	2	no	—
101	#11761612	—	4	4	no	—
102	#11761612	—	4	2	no	—
103	C₂×C₆₇⋊C₈	—	2	2	no	—
104	C₂×C₆₇⋊C₈	—	2	1	no	—
105	C₂×C₆₇⋊C₈	—	2	2	no	—
106	C₂×C₆₇⋊C₈	—	2	1	no	—
107	C₂×C₆₇⋊C₈	—	4	1	no	—
108	C₂×C₆₇⋊C₈	—	4	4	no	—
109	C₂×C₆₇⋊C₈	—	4	2	no	—
110	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
114	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
115	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
116	#41×C₆₇	—	2	2	no	—
117	#41×C₆₇	—	2	2	no	—
118	C₂×Q₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
119	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
120	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
127	M₁₆×C₆₇	—	4	2	no	—
128	C₂×C₈×C₆₇	—	2	1	no	—
129	C₂×C₈×C₆₇	—	2	1	no	—
130	C₂×C₈×C₆₇	—	2	2	no	—
131	C₂×C₈×C₆₇	—	4	2	no	—
132	C₄⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
133	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
134	C₄⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
135	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
136	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
137	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
138	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
139	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
141	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₆₇	C₂×D₄	1	2	yes	—
143	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
144	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
145	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
146	C₂³×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
147	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	Q₈×C₆₇	—	2	2	no	—
149	D₄×C₆₇	—	2	4	no	—
150	D₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	1	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	2	1	no	—
154	C₂×C₄×C₆₇	—	2	2	no	—
155	C₂×C₄×C₆₇	—	2	2	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	4	1	no	—
158	C₂×C₄×C₆₇	—	4	2	no	—
159	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
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	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₆₇	#137	1	2	yes	—
167	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
170	C₈×C₆₇	—	4	1	no	—
171	C₈×C₆₇	—	4	1	no	—
172	C₈×C₆₇	—	4	2	no	—
173	C₆₇⋊C₈	—	2	1	no	—
174	C₆₇⋊C₈	—	2	2	no	—
175	C₆₇⋊C₈	—	2	1	no	—
176	C₆₇⋊C₈	—	2	1	no	—
177	C₆₇⋊C₈	—	2	2	no	—
178	C₆₇⋊C₈	—	4	1	no	—
179	C₆₇⋊C₈	—	4	2	no	—
180	C₆₇⋊C₈	—	4	1	no	—
181	C₆₇⋊C₈	#131	1	2	yes	complemented
182	C₂²×C₆₇	—	2	1	no	—
183	C₂²×C₆₇	—	2	1	no	—
184	C₂²×C₆₇	—	2	2	no	—
185	C₂²×C₆₇	—	2	2	no	—
186	C₂²×C₆₇	—	2	2	no	—
187	C₂²×C₆₇	#428	1	2	yes	—
188	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₄×C₆₇	—	2	1	no	—
190	C₄×C₆₇	—	2	2	no	—
191	C₄×C₆₇	—	2	2	no	—
192	C₄×C₆₇	—	2	1	no	—
193	C₄×C₆₇	—	2	1	no	—
194	C₄×C₆₇	—	2	2	no	—
195	C₄×C₆₇	#428	1	2	yes	—
196	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
197	C₄×C₆₇	#568	1	1	yes	characteristic
198	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
200	#17832	—	67	1	no	maximal, Sylow
201	C₂×C₆₇	—	2	2	no	—
202	C₂×C₆₇	—	4	2	no	—
203	C₂×C₆₇	#2906	1	1	yes	characteristic
204	C₂×C₆₇	C₂×#428	1	1	yes	characteristic
205	C₂×C₆₇	#2916	1	1	yes	characteristic
206	#2965	—	67	1	no	—
207	#2925	D₆₇	1	1	yes	characteristic
208	#2906	—	67	1	no	—
209	#1574	—	67	2	no	—
210	#1573	—	67	2	no	—
211	#1571	—	67	1	no	—
212	#1570	—	67	1	no	—
213	#1569	—	67	2	no	—
214	#1566	—	67	1	no	—
215	#1565	—	67	2	no	—
216	C₂×#335	—	67	1	no	—
217	C₆₇	#17832	1	1	yes	characteristic, complemented, Sylow
218	C₂×#131	—	134	1	no	—
219	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
220	#446	—	67	1	no	—
221	#446	—	67	1	no	—
222	#436	—	67	1	no	—
223	#436	—	67	1	no	—
224	#435	—	67	2	no	—
225	#435	—	67	2	no	—
226	#433	—	2	2	no	—
227	#432	C₂×D₆₇	1	2	yes	—
228	#431	—	67	1	no	—
229	#431	—	67	2	no	—
230	#431	C₂×D₆₇	1	2	yes	—
231	#424	—	134	1	no	—
232	#424	—	134	2	no	—
233	#423	—	67	1	no	—
234	#423	—	67	2	no	—
235	#423	C₂×D₆₇	1	1	yes	characteristic
236	C₂×C₄⋊C₈	—	67	1	no	—
237	C₂×C₄⋊C₈	—	67	2	no	—
238	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
239	#408	—	2	1	no	—
240	#405	—	2	1	no	—
241	C₄×M₁₆	—	67	2	no	—
242	C₂×C₄×C₈	—	67	1	no	—
243	#335	—	67	1	no	—
244	#335	—	67	1	no	—
245	#335	—	67	1	no	—
246	#335	—	67	1	no	—
247	#335	—	67	2	no	—
248	#335	—	67	2	no	—
249	#334	—	67	2	no	—
250	#334	—	67	2	no	—
251	#334	—	67	2	no	—
252	#334	—	67	2	no	—
253	C₂×#41	C₂²⋊D₆₇	1	1	yes	characteristic
254	#131	—	268	4	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	67	2	no	—
257	C₂×M₁₆	—	67	2	no	—
258	C₂×M₁₆	—	134	2	no	—
259	C₂×M₁₆	—	134	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	67	1	no	—
262	C₂²×C₈	—	67	1	no	—
263	C₂²×C₈	—	134	2	no	—
264	C₂²×C₈	—	134	1	no	—
265	C₄×Q₈	Dic₁₃₄	1	1	yes	characteristic
266	C₄×Q₈	C₄×D₆₇	1	1	yes	characteristic
267	C₄×D₄	Dic₁₃₄	1	2	yes	—
268	C₄×D₄	Dic₁₃₄	1	1	yes	characteristic
269	C₄×D₄	C₄×D₆₇	1	2	yes	—
270	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
271	#117	C₂²⋊D₆₇	1	1	yes	characteristic
272	#117	C₂²⋊D₆₇	1	2	yes	—
273	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	67	2	no	—
278	C₄⋊C₈	—	67	2	no	—
279	C₄⋊C₈	—	67	1	no	—
280	C₄⋊C₈	—	67	1	no	—
281	C₄⋊C₈	—	67	1	no	—
282	C₄⋊C₈	—	67	2	no	—
283	C₄⋊C₈	—	67	1	no	—
284	C₄⋊C₈	—	134	2	no	—
285	C₄⋊C₈	—	134	1	no	—
286	C₄⋊C₈	—	134	2	no	—
287	C₄⋊C₈	—	134	1	no	—
288	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
289	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
291	C₂²⋊C₈	—	2	2	no	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	—	67	2	no	—
294	C₂²⋊C₈	—	67	2	no	—
295	C₂²⋊C₈	—	67	2	no	—
296	#97	—	2	2	no	—
297	#97	—	67	2	no	—
298	#97	—	67	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	67	1	no	—
301	C₄×C₈	—	67	1	no	—
302	C₄×C₈	—	67	1	no	—
303	C₄×C₈	—	67	1	no	—
304	C₄×C₈	—	67	2	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	C₂×Q₈	Dic₆₇⋊C₄	1	1	yes	characteristic
308	C₂×D₄	Dic₆₇⋊C₄	1	2	yes	—
309	C₂×D₄	Dic₆₇⋊C₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₆₇	1	2	yes	—
312	C₂²×C₄	C₂×C₂²⋊D₆₇	1	2	yes	—
313	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
314	C₂²×C₄	C₂×Dic₁₃₄	1	2	yes	—
315	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
316	M₁₆	—	4	2	no	—
317	M₁₆	—	268	4	no	—
318	M₁₆	—	268	2	no	—
319	M₁₆	—	268	2	no	—
320	M₁₆	—	134	4	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	—	268	4	no	—
326	C₂×C₈	—	268	2	no	—
327	C₂×C₈	—	268	1	no	—
328	C₂×C₈	—	67	1	no	—
329	C₂×C₈	—	67	1	no	—
330	C₂×C₈	—	67	1	no	—
331	C₂×C₈	—	67	1	no	—
332	C₂×C₈	—	67	2	no	—
333	C₂×C₈	—	67	2	no	—
334	C₂×C₈	—	134	1	no	—
335	C₂×C₈	—	134	2	no	—
336	C₂×C₈	—	134	1	no	—
337	C₂×C₈	—	134	2	no	—
338	C₄⋊C₄	Dic₆₇⋊C₄	1	2	yes	—
339	C₄⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
340	C₄⋊C₄	Dic₆₇⋊C₄	1	2	yes	—
341	C₄⋊C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
342	C₂²⋊C₄	Dic₆₇⋊C₄	1	2	yes	—
343	C₂²⋊C₄	Dic₆₇⋊C₄	1	2	yes	—
344	C₂²⋊C₄	Dic₆₇⋊C₄	1	2	yes	—
345	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
346	C₄²	C₂×C₄×D₆₇	1	2	yes	—
347	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
348	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
349	C₄²	C₂×Dic₁₃₄	1	2	yes	—
350	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
351	C₄²	C₂³×D₆₇	1	1	yes	characteristic
352	C₂³	C₂×Dic₆₇⋊C₄	1	2	yes	—
353	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₂×Dic₆₇⋊C₄	1	2	yes	—
367	C₂×C₄	C₂×Dic₆₇⋊C₄	1	2	yes	—
368	C₂×C₄	C₂×Dic₆₇⋊C₄	1	2	yes	—
369	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
371	C₂×C₄	#14524068	1	2	yes	—
372	C₂×C₄	#14524073	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
375	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
376	C₈	—	4	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	268	1	no	—
380	C₈	—	268	2	no	—
381	C₈	—	268	1	no	—
382	C₈	—	67	2	no	—
383	C₈	—	134	1	no	—
384	C₈	—	134	2	no	—
385	C₈	—	134	1	no	—
386	C₈	—	134	1	no	—
387	C₈	—	134	2	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	#16863439	1	2	yes	—
394	C₂²	C₂²×Dic₆₇⋊C₄	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	#16863439	1	2	yes	—
402	C₄	#131×D₆₇	1	1	yes	characteristic
403	C₄	#16864161	1	1	yes	characteristic
404	C₄	C₂×#14524068	1	1	yes	characteristic
405	C₄	C₂×#14524073	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	4	2	no	—
408	C₂	#22568775	1	1	yes	characteristic
409	C₂	C₂×#16863439	1	1	yes	characteristic
410	C₂	#22568818	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2925	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₆₇	D₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#2925	D₆₇
hypocenter	C₆₇	#17832
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2925

Complements

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

N	H ≅ G/N	type
3. #22558997	C₂	semidirect
4. #22558995	C₂	semidirect
5. #22558983	C₂	semidirect
6. #22558981	C₂	semidirect
7. #22558977	C₂	semidirect
8. #22558964	C₂	semidirect
9. #22558962	C₂	semidirect
10. C₂×#16863148	C₂	semidirect
181. C₆₇⋊C₈	#131	semidirect
217. C₆₇	#17832	semidirect

Maximal subgroups

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

subgroup	index
#22569176	2
#22568777	2
#22558997	2
#22558995	2
#22558983	2
#22558981	2
#22558977	2
#22558964	2
#22558962	2
C₂×#16863148	2
C₆₇×#2925	2
#17832	67