Subgroups — C₆₇×#10058 #30689309

Order 17152.

602 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#487×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#476×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2547	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#332×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂×#124×C₆₇	—	2	1	no	—
11	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
12	#487×C₆₇	—	2	2	no	—
13	#487×C₆₇	—	2	2	no	—
14	#476×C₆₇	—	2	2	no	—
15	#476×C₆₇	—	2	2	no	—
16	C₂×#106×C₆₇	—	2	1	no	—
17	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#103×C₆₇	—	2	2	no	—
20	C₂×#102×C₆₇	—	2	1	no	—
21	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
22	#397×C₆₇	—	2	2	no	—
23	#391×C₆₇	—	2	1	no	—
24	#380×C₆₇	—	2	2	no	—
25	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
26	#340×C₆₇	—	2	2	no	—
27	#332×C₆₇	—	2	2	no	—
28	D₄⋊C₈×C₆₇	—	2	2	no	—
29	C₂²×Q₈×C₆₇	—	2	1	no	—
30	C₂²×Q₈×C₆₇	—	2	1	no	—
31	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₆₇	—	2	1	no	—
33	C₂²×C₈×C₆₇	—	2	1	no	—
34	C₂²×C₈×C₆₇	—	2	1	no	—
35	C₂²×C₈×C₆₇	—	2	1	no	—
36	C₄⋊Q₈×C₆₇	—	2	1	no	—
37	C₄⋊Q₈×C₆₇	—	2	1	no	—
38	C₄⋊Q₈×C₆₇	—	2	1	no	—
39	C₄⋊Q₈×C₆₇	—	2	1	no	—
40	C₄⋊Q₈×C₆₇	—	2	1	no	—
41	C₄⋊Q₈×C₆₇	—	2	1	no	—
42	C₄⋊Q₈×C₆₇	—	2	1	no	—
43	C₄⋊Q₈×C₆₇	D₄	1	2	yes	—
44	#124×C₆₇	—	4	2	no	—
45	#124×C₆₇	—	4	2	no	—
46	C₄×D₄×C₆₇	—	2	1	no	—
47	C₄×D₄×C₆₇	—	2	1	no	—
48	C₄×D₄×C₆₇	—	2	1	no	—
49	C₄×D₄×C₆₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
58	C₂×C₄²×C₆₇	—	2	1	no	—
59	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
60	#106×C₆₇	—	2	4	no	—
61	C₄⋊C₈×C₆₇	—	2	1	no	—
62	C₄⋊C₈×C₆₇	—	2	1	no	—
63	C₄⋊C₈×C₆₇	—	2	1	no	—
64	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
65	#103×C₆₇	—	2	8	no	—
66	#102×C₆₇	—	2	4	no	—
67	C₄×C₈×C₆₇	—	2	1	no	—
68	C₄×C₈×C₆₇	D₄	1	2	yes	—
69	#95×C₆₇	—	2	4	no	—
70	#95×C₆₇	—	2	1	no	—
71	C₂⁴×C₆₇	—	2	1	no	—
72	C₂×Q₈×C₆₇	—	2	2	no	—
73	C₂×Q₈×C₆₇	—	4	4	no	—
74	C₂×Q₈×C₆₇	—	4	1	no	—
75	C₂×Q₈×C₆₇	—	4	1	no	—
76	C₂×Q₈×C₆₇	—	4	1	no	—
77	C₂×Q₈×C₆₇	—	4	1	no	—
78	C₂×Q₈×C₆₇	—	4	1	no	—
79	C₂×Q₈×C₆₇	—	4	1	no	—
80	C₂×Q₈×C₆₇	—	4	1	no	—
81	C₂×D₄×C₆₇	—	2	1	no	—
82	C₂×D₄×C₆₇	—	2	1	no	—
83	C₂×D₄×C₆₇	—	2	1	no	—
84	C₂×D₄×C₆₇	—	2	1	no	—
85	C₂×D₄×C₆₇	—	2	1	no	—
86	C₂×D₄×C₆₇	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₆₇	—	2	2	no	—
88	C₂²×C₄×C₆₇	—	2	2	no	—
89	C₂²×C₄×C₆₇	—	2	1	no	—
90	C₂²×C₄×C₆₇	—	4	1	no	—
91	C₂²×C₄×C₆₇	—	4	1	no	—
92	C₂²×C₄×C₆₇	—	4	1	no	—
93	C₂²×C₄×C₆₇	—	4	2	no	—
94	C₂²×C₄×C₆₇	—	4	2	no	—
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₆₇	—	2	2	no	—
99	C₂×C₈×C₆₇	—	2	2	no	—
100	C₂×C₈×C₆₇	—	4	2	no	—
101	C₂×C₈×C₆₇	—	4	1	no	—
102	C₂×C₈×C₆₇	—	4	1	no	—
103	C₂×C₈×C₆₇	—	4	1	no	—
104	C₂×C₈×C₆₇	—	4	2	no	—
105	C₄⋊C₄×C₆₇	—	2	2	no	—
106	C₄⋊C₄×C₆₇	—	2	2	no	—
107	C₄⋊C₄×C₆₇	—	2	1	no	—
108	C₄⋊C₄×C₆₇	—	2	2	no	—
109	C₄⋊C₄×C₆₇	—	2	1	no	—
110	C₄⋊C₄×C₆₇	—	2	2	no	—
111	C₄⋊C₄×C₆₇	—	2	2	no	—
112	C₄⋊C₄×C₆₇	—	2	2	no	—
113	C₄⋊C₄×C₆₇	—	4	1	no	—
114	C₄⋊C₄×C₆₇	—	4	1	no	—
115	C₄⋊C₄×C₆₇	—	4	1	no	—
116	C₄⋊C₄×C₆₇	—	4	1	no	—
117	C₂²⋊C₄×C₆₇	—	4	8	no	—
118	C₂²⋊C₄×C₆₇	—	4	1	no	—
119	C₂²⋊C₄×C₆₇	—	4	1	no	—
120	C₄²×C₆₇	—	4	1	no	—
121	C₄²×C₆₇	—	4	1	no	—
122	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₆₇	#41	1	1	yes	characteristic
126	C₂³×C₆₇	—	2	2	no	—
127	C₂³×C₆₇	—	4	1	no	—
128	C₂³×C₆₇	—	4	2	no	—
129	C₂³×C₆₇	—	4	1	no	—
130	C₂³×C₆₇	—	4	2	no	—
131	C₂³×C₆₇	#120	1	1	yes	characteristic
132	Q₈×C₆₇	—	4	4	no	—
133	Q₈×C₆₇	—	8	2	no	—
134	Q₈×C₆₇	—	8	1	no	—
135	Q₈×C₆₇	—	8	1	no	—
136	Q₈×C₆₇	—	8	1	no	—
137	Q₈×C₆₇	—	8	1	no	—
138	D₄×C₆₇	—	2	2	no	—
139	D₄×C₆₇	—	2	2	no	—
140	D₄×C₆₇	—	4	1	no	—
141	D₄×C₆₇	—	4	1	no	—
142	C₂×C₄×C₆₇	—	2	2	no	—
143	C₂×C₄×C₆₇	—	4	1	no	—
144	C₂×C₄×C₆₇	—	4	2	no	—
145	C₂×C₄×C₆₇	—	4	2	no	—
146	C₂×C₄×C₆₇	—	4	2	no	—
147	C₂×C₄×C₆₇	—	4	2	no	—
148	C₂×C₄×C₆₇	—	4	2	no	—
149	C₂×C₄×C₆₇	—	4	2	no	—
150	C₂×C₄×C₆₇	—	4	2	no	—
151	C₂×C₄×C₆₇	—	4	2	no	—
152	C₂×C₄×C₆₇	—	8	2	no	—
153	C₂×C₄×C₆₇	—	8	2	no	—
154	C₂×C₄×C₆₇	—	8	1	no	—
155	C₂×C₄×C₆₇	—	8	1	no	—
156	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
157	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
158	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
164	C₂×C₄×C₆₇	#135	1	2	yes	—
165	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₆₇	#137	1	1	yes	characteristic
167	C₂×C₄×C₆₇	#137	1	2	yes	—
168	C₈×C₆₇	—	4	2	no	—
169	C₈×C₆₇	—	4	2	no	—
170	C₈×C₆₇	—	8	1	no	—
171	C₂²×C₆₇	—	4	4	no	—
172	C₂²×C₆₇	—	4	2	no	—
173	C₂²×C₆₇	—	8	2	no	—
174	C₂²×C₆₇	—	8	1	no	—
175	C₂²×C₆₇	—	8	1	no	—
176	C₂²×C₆₇	#392	1	1	yes	characteristic
177	C₂²×C₆₇	#450	1	1	yes	characteristic
178	C₂²×C₆₇	#452	1	2	yes	—
179	C₂²×C₆₇	#452	1	1	yes	characteristic
180	C₂²×C₆₇	#454	1	2	yes	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	8	2	no	—
184	C₄×C₆₇	—	8	2	no	—
185	C₄×C₆₇	—	8	2	no	—
186	C₄×C₆₇	—	8	1	no	—
187	C₄×C₆₇	#448	1	1	yes	characteristic
188	C₄×C₆₇	#449	1	1	yes	characteristic
189	C₄×C₆₇	#464	1	2	yes	—
190	C₄×C₆₇	#465	1	1	yes	characteristic
191	C₄×C₆₇	#468	1	1	yes	characteristic
192	C₄×C₆₇	#495	1	1	yes	characteristic
193	C₄×C₆₇	#497	1	1	yes	characteristic
194	#10058	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂×C₆₇	—	8	2	no	—
196	C₂×C₆₇	#1635	1	2	yes	—
197	C₂×C₆₇	#1638	1	2	yes	—
198	C₂×C₆₇	#2000	1	1	yes	characteristic
199	C₂×C₆₇	#2003	1	1	yes	characteristic
200	C₂×C₆₇	#2015	1	1	yes	characteristic
201	C₂×#487	C₂×C₆₇	1	1	yes	characteristic, complemented
202	C₂×#476	C₂×C₆₇	1	1	yes	characteristic
203	#2547	C₂×C₆₇	1	1	yes	characteristic
204	#1987	C₂×C₆₇	1	1	yes	characteristic, complemented
205	C₂×#332	C₂×C₆₇	1	1	yes	characteristic, complemented
206	C₂×D₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic
207	#1279	C₂×C₆₇	1	1	yes	characteristic, complemented
208	C₆₇	#10058	1	1	yes	characteristic, direct product factor, Sylow
209	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
211	C₂×#124	—	2	1	no	—
212	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
213	#487	—	2	2	no	—
214	#487	—	2	2	no	—
215	#476	—	2	2	no	—
216	#476	—	2	2	no	—
217	C₂×#106	—	2	1	no	—
218	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
220	C₂×#103	—	2	2	no	—
221	C₂×#102	—	2	1	no	—
222	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
223	#397	—	2	2	no	—
224	#391	—	2	1	no	—
225	#380	—	2	2	no	—
226	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
227	#340	—	2	2	no	—
228	#332	—	2	2	no	—
229	D₄⋊C₈	—	2	2	no	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	D₄×C₆₇	1	2	yes	—
245	#124	—	4	2	no	—
246	#124	—	4	2	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
255	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
256	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
261	#106	—	2	4	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	D₄×C₆₇	1	2	yes	—
266	#103	—	2	8	no	—
267	#102	—	2	4	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	D₄×C₆₇	1	2	yes	—
270	#95	—	2	4	no	—
271	#95	—	2	1	no	—
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	4	4	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	SD₁₆×C₆₇	1	2	yes	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	8	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₄²	—	4	1	no	—
322	C₄²	—	4	1	no	—
323	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
324	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
326	C₄²	#41×C₆₇	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	#120×C₆₇	1	1	yes	characteristic
333	Q₈	—	4	4	no	—
334	Q₈	—	8	2	no	—
335	Q₈	—	8	1	no	—
336	Q₈	—	8	1	no	—
337	Q₈	—	8	1	no	—
338	Q₈	—	8	1	no	—
339	D₄	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	1	no	—
342	D₄	—	4	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	—	8	1	no	—
356	C₂×C₄	—	8	1	no	—
357	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
358	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
359	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
360	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
361	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
362	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
363	C₂×C₄	C₂×SD₁₆×C₆₇	1	1	yes	characteristic
364	C₂×C₄	#135×C₆₇	1	1	yes	characteristic
365	C₂×C₄	#135×C₆₇	1	2	yes	—
366	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
367	C₂×C₄	#137×C₆₇	1	1	yes	characteristic
368	C₂×C₄	#137×C₆₇	1	2	yes	—
369	C₈	—	4	2	no	—
370	C₈	—	4	2	no	—
371	C₈	—	8	1	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	4	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	1	no	—
376	C₂²	—	8	2	no	—
377	C₂²	#392×C₆₇	1	1	yes	characteristic
378	C₂²	#450×C₆₇	1	1	yes	characteristic
379	C₂²	#452×C₆₇	1	1	yes	characteristic
380	C₂²	#452×C₆₇	1	2	yes	—
381	C₂²	#454×C₆₇	1	2	yes	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	2	no	—
388	C₄	#448×C₆₇	1	1	yes	characteristic
389	C₄	#449×C₆₇	1	1	yes	characteristic
390	C₄	#464×C₆₇	1	2	yes	—
391	C₄	#465×C₆₇	1	1	yes	characteristic
392	C₄	#468×C₆₇	1	1	yes	characteristic
393	C₄	#495×C₆₇	1	1	yes	characteristic
394	C₄	#497×C₆₇	1	1	yes	characteristic
395	C₂	—	8	2	no	—
396	C₂	C₆₇×#1635	1	2	yes	—
397	C₂	C₆₇×#1638	1	2	yes	—
398	C₂	C₆₇×#2000	1	1	yes	characteristic
399	C₂	C₆₇×#2003	1	1	yes	characteristic
400	C₂	C₆₇×#2015	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₆₇
prime radical	C₂²×D₄×C₆₇	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#487×C₆₇	C₂	semidirect
4. C₆₇×#1987	C₂	semidirect
5. C₂×#332×C₆₇	C₂	semidirect
7. C₆₇×#1279	C₂	semidirect
194. #10058	C₆₇	direct (N × H)
201. C₂×#487	C₂×C₆₇	semidirect
204. #1987	C₂×C₆₇	semidirect
205. C₂×#332	C₂×C₆₇	semidirect
207. #1279	C₂×C₆₇	semidirect
208. C₆₇	#10058	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#487×C₆₇	2
C₂×#476×C₆₇	2
C₆₇×#2547	2
C₆₇×#1987	2
C₂×#332×C₆₇	2
C₂×D₄⋊C₈×C₆₇	2
C₆₇×#1279	2
#10058	67

Subgroups — C67×#10058 #30689309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#10058 #30689309