Subgroups — C₆₇×#22441 #30701692

Order 17152.

1438 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#441×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2341	C₂	1	2	yes	maximal, complemented
4	C₆₇×#1972	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1880	C₂	1	4	yes	maximal, complemented
6	C₆₇×#1807	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1788	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₆₇	C₂²	1	2	yes	—
10	C₂×#135×C₆₇	—	2	8	no	—
11	C₂×#135×C₆₇	C₄	1	8	yes	complemented
12	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
14	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	—
17	#441×C₆₇	—	2	8	no	—
18	C₂×#106×C₆₇	C₂²	1	2	yes	—
19	C₂×#103×C₆₇	C₂²	1	4	yes	—
20	C₂×#102×C₆₇	C₂²	1	4	yes	—
21	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#97×C₆₇	C₂²	1	2	yes	—
23	#390×C₆₇	—	2	4	no	—
24	#390×C₆₇	C₂²	1	4	yes	—
25	#380×C₆₇	—	2	2	no	—
26	#380×C₆₇	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₆₇	—	2	2	no	—
28	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	#340×C₆₇	C₂²	1	2	yes	—
30	#336×C₆₇	C₂²	1	2	yes	—
31	C₂×#41×C₆₇	—	2	4	no	—
32	C₂×#41×C₆₇	—	2	8	no	—
33	C₂×#41×C₆₇	—	4	4	no	—
34	C₂×#41×C₆₇	C₂×C₄	1	8	yes	—
35	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
36	C₂²×D₄×C₆₇	—	2	2	no	—
37	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₆₇	—	2	2	no	—
39	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
40	#135×C₆₇	—	2	32	no	—
41	C₂×Q₁₆×C₆₇	C₂×C₄	1	4	yes	—
42	C₂×Q₁₆×C₆₇	D₄	1	8	yes	—
43	C₂×SD₁₆×C₆₇	—	2	8	no	—
44	C₂×SD₁₆×C₆₇	C₂×C₄	1	8	yes	—
45	C₂×D₈×C₆₇	—	2	4	no	—
46	C₂×D₈×C₆₇	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₆₇	—	2	4	no	—
48	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₆₇	—	2	8	no	—
53	C₄×Q₈×C₆₇	—	4	4	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
60	C₂×C₄²×C₆₇	—	2	4	no	—
61	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
62	#106×C₆₇	—	2	4	no	—
63	#103×C₆₇	—	2	8	no	—
64	#102×C₆₇	—	4	4	no	—
65	C₂²⋊C₈×C₆₇	—	2	2	no	—
66	#97×C₆₇	—	2	4	no	—
67	#95×C₆₇	—	2	2	no	—
68	#95×C₆₇	D₄	1	2	yes	—
69	C₂⁴×C₆₇	—	2	2	no	—
70	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
71	#41×C₆₇	—	2	16	no	—
72	#41×C₆₇	—	4	8	no	—
73	#41×C₆₇	—	4	16	no	—
74	C₂×Q₈×C₆₇	—	2	2	no	—
75	C₂×Q₈×C₆₇	—	2	4	no	—
76	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
77	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
78	C₂×D₄×C₆₇	—	2	8	no	—
79	C₂×D₄×C₆₇	—	2	4	no	—
80	C₂×D₄×C₆₇	—	2	2	no	—
81	C₂×D₄×C₆₇	—	2	4	no	—
82	C₂×D₄×C₆₇	—	4	8	no	—
83	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₆₇	—	2	2	no	—
85	C₂²×C₄×C₆₇	—	2	2	no	—
86	C₂²×C₄×C₆₇	—	2	2	no	—
87	C₂²×C₄×C₆₇	—	2	8	no	—
88	C₂²×C₄×C₆₇	—	2	4	no	—
89	C₂²×C₄×C₆₇	—	4	8	no	—
90	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	#41	1	2	yes	—
94	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
95	Q₁₆×C₆₇	C₂²⋊C₄	1	16	yes	complemented
96	SD₁₆×C₆₇	—	2	16	no	—
97	D₈×C₆₇	—	2	8	no	—
98	C₂×C₈×C₆₇	—	2	2	no	—
99	C₂×C₈×C₆₇	—	2	8	no	—
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	—	2	2	no	—
102	C₂×C₈×C₆₇	—	2	2	no	—
103	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
106	C₄⋊C₄×C₆₇	—	2	4	no	—
107	C₄⋊C₄×C₆₇	—	2	4	no	—
108	C₄⋊C₄×C₆₇	—	4	8	no	—
109	C₂²⋊C₄×C₆₇	—	4	2	no	—
110	C₂²⋊C₄×C₆₇	—	4	8	no	—
111	C₂²⋊C₄×C₆₇	—	8	4	no	—
112	C₂²⋊C₄×C₆₇	—	8	2	no	—
113	C₄²×C₆₇	—	2	2	no	—
114	C₄²×C₆₇	—	2	2	no	—
115	C₄²×C₆₇	—	4	8	no	—
116	C₂³×C₆₇	—	2	2	no	—
117	C₂³×C₆₇	—	2	2	no	—
118	C₂³×C₆₇	—	2	2	no	—
119	C₂³×C₆₇	—	2	4	no	—
120	C₂³×C₆₇	—	4	4	no	—
121	C₂³×C₆₇	—	4	4	no	—
122	C₂³×C₆₇	—	4	2	no	—
123	C₂³×C₆₇	—	4	2	no	—
124	C₂³×C₆₇	C₄×D₄	1	2	yes	—
125	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₆₇	—	2	4	no	—
127	Q₈×C₆₇	—	2	8	no	—
128	Q₈×C₆₇	C₂×C₂²⋊C₄	1	8	yes	—
129	D₄×C₆₇	—	2	4	no	—
130	D₄×C₆₇	—	2	4	no	—
131	D₄×C₆₇	—	4	16	no	—
132	D₄×C₆₇	—	4	4	no	—
133	C₂×C₄×C₆₇	—	2	4	no	—
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	2	4	no	—
139	C₂×C₄×C₆₇	—	2	4	no	—
140	C₂×C₄×C₆₇	—	2	4	no	—
141	C₂×C₄×C₆₇	—	2	4	no	—
142	C₂×C₄×C₆₇	—	4	16	no	—
143	C₂×C₄×C₆₇	—	4	4	no	—
144	C₂×C₄×C₆₇	—	4	4	no	—
145	C₂×C₄×C₆₇	—	4	4	no	—
146	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
147	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
149	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
151	C₈×C₆₇	—	2	2	no	—
152	C₈×C₆₇	—	4	2	no	—
153	C₈×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
154	C₂²×C₆₇	—	2	2	no	—
155	C₂²×C₆₇	—	2	2	no	—
156	C₂²×C₆₇	—	2	2	no	—
157	C₂²×C₆₇	—	4	4	no	—
158	C₂²×C₆₇	—	4	4	no	—
159	C₂²×C₆₇	—	4	4	no	—
160	C₂²×C₆₇	—	4	4	no	—
161	C₂²×C₆₇	—	8	4	no	—
162	C₂²×C₆₇	—	8	4	no	—
163	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
164	C₂²×C₆₇	D₄²	1	2	yes	—
165	C₂²×C₆₇	#575	1	2	yes	—
166	C₂²×C₆₇	#577	1	2	yes	—
167	C₄×C₆₇	—	2	2	no	—
168	C₄×C₆₇	—	2	8	no	—
169	C₄×C₆₇	—	4	4	no	—
170	C₄×C₆₇	—	8	4	no	—
171	C₄×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₄×C₆₇	#518	1	1	yes	characteristic
173	C₄×C₆₇	#546	1	2	yes	—
174	#22441	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂×C₆₇	—	4	2	no	—
176	C₂×C₆₇	—	8	4	no	—
177	C₂×C₆₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₆₇	#2943	1	1	yes	characteristic
179	C₂×C₆₇	#2952	1	1	yes	characteristic
180	C₂×C₆₇	#3271	1	4	yes	—
181	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic
182	C₂×#441	C₂×C₆₇	1	2	yes	complemented
183	#2341	C₂×C₆₇	1	2	yes	complemented
184	#1972	C₂×C₆₇	1	2	yes	complemented
185	#1880	C₂×C₆₇	1	4	yes	complemented
186	#1807	C₂×C₆₇	1	1	yes	characteristic, complemented
187	#1788	C₂×C₆₇	1	2	yes	complemented
188	#1752	C₂×C₆₇	1	1	yes	characteristic, complemented
189	C₆₇	#22441	1	1	yes	characteristic, direct product factor, Sylow
190	C₂²×#41	C₂²×C₆₇	1	2	yes	—
191	C₂×#135	—	2	8	no	—
192	C₂×#135	C₄×C₆₇	1	8	yes	complemented
193	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
194	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
195	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	—
198	#441	—	2	8	no	—
199	C₂×#106	C₂²×C₆₇	1	2	yes	—
200	C₂×#103	C₂²×C₆₇	1	4	yes	—
201	C₂×#102	C₂²×C₆₇	1	4	yes	—
202	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
203	C₂×#97	C₂²×C₆₇	1	2	yes	—
204	#390	—	2	4	no	—
205	#390	C₂²×C₆₇	1	4	yes	—
206	#380	—	2	2	no	—
207	#380	C₂²×C₆₇	1	2	yes	—
208	C₄×C₂²⋊C₄	—	2	2	no	—
209	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
210	#340	C₂²×C₆₇	1	2	yes	—
211	#336	C₂²×C₆₇	1	2	yes	—
212	C₂×#41	—	2	4	no	—
213	C₂×#41	—	2	8	no	—
214	C₂×#41	—	4	4	no	—
215	C₂×#41	C₂×C₄×C₆₇	1	8	yes	—
216	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
219	C₂³×C₄	—	2	2	no	—
220	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
221	#135	—	2	32	no	—
222	C₂×Q₁₆	C₂×C₄×C₆₇	1	4	yes	—
223	C₂×Q₁₆	D₄×C₆₇	1	8	yes	—
224	C₂×SD₁₆	—	2	8	no	—
225	C₂×SD₁₆	C₂×C₄×C₆₇	1	8	yes	—
226	C₂×D₈	—	2	4	no	—
227	C₂×D₈	C₂×C₄×C₆₇	1	4	yes	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
230	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
231	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
233	C₄×Q₈	—	2	8	no	—
234	C₄×Q₈	—	4	4	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
237	C₂×C₂²⋊C₄	—	2	4	no	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₂²⋊C₄	—	2	4	no	—
240	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
241	C₂×C₄²	—	2	4	no	—
242	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
243	#106	—	2	4	no	—
244	#103	—	2	8	no	—
245	#102	—	4	4	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	#97	—	2	4	no	—
248	#95	—	2	2	no	—
249	#95	D₄×C₆₇	1	2	yes	—
250	C₂⁴	—	2	2	no	—
251	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
252	#41	—	2	16	no	—
253	#41	—	4	8	no	—
254	#41	—	4	16	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
258	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	4	8	no	—
264	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	8	no	—
271	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
272	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
273	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
274	C₂²×C₄	#41×C₆₇	1	2	yes	—
275	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
276	Q₁₆	C₂²⋊C₄×C₆₇	1	16	yes	complemented
277	SD₁₆	—	2	16	no	—
278	D₈	—	2	8	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
285	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
286	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	4	8	no	—
290	C₂²⋊C₄	—	4	2	no	—
291	C₂²⋊C₄	—	4	8	no	—
292	C₂²⋊C₄	—	8	4	no	—
293	C₂²⋊C₄	—	8	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	4	8	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	4	4	no	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	2	no	—
305	C₂³	C₄×D₄×C₆₇	1	2	yes	—
306	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
307	Q₈	—	2	4	no	—
308	Q₈	—	2	8	no	—
309	Q₈	C₂×C₂²⋊C₄×C₆₇	1	8	yes	—
310	D₄	—	2	4	no	—
311	D₄	—	2	4	no	—
312	D₄	—	4	16	no	—
313	D₄	—	4	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
328	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
330	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
331	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
332	C₈	—	2	2	no	—
333	C₈	—	4	2	no	—
334	C₈	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	4	4	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	8	4	no	—
343	C₂²	—	8	4	no	—
344	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
345	C₂²	D₄²×C₆₇	1	2	yes	—
346	C₂²	#575×C₆₇	1	2	yes	—
347	C₂²	#577×C₆₇	1	2	yes	—
348	C₄	—	2	2	no	—
349	C₄	—	2	8	no	—
350	C₄	—	4	4	no	—
351	C₄	—	8	4	no	—
352	C₄	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
353	C₄	#518×C₆₇	1	1	yes	characteristic
354	C₄	#546×C₆₇	1	2	yes	—
355	C₂	—	4	2	no	—
356	C₂	—	8	4	no	—
357	C₂	D₄×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
358	C₂	C₆₇×#2943	1	1	yes	characteristic
359	C₂	C₆₇×#2952	1	1	yes	characteristic
360	C₂	C₆₇×#3271	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×#135×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₄×C₂²⋊C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#441×C₆₇	C₂	semidirect
3. C₆₇×#2341	C₂	semidirect
4. C₆₇×#1972	C₂	semidirect
5. C₆₇×#1880	C₂	semidirect
6. C₆₇×#1807	C₂	semidirect
7. C₆₇×#1788	C₂	semidirect
8. C₆₇×#1752	C₂	semidirect
11. C₂×#135×C₆₇	C₄	semidirect
95. Q₁₆×C₆₇	C₂²⋊C₄	semidirect
174. #22441	C₆₇	direct (N × H)
182. C₂×#441	C₂×C₆₇	semidirect
183. #2341	C₂×C₆₇	semidirect
184. #1972	C₂×C₆₇	semidirect
185. #1880	C₂×C₆₇	semidirect
186. #1807	C₂×C₆₇	semidirect
187. #1788	C₂×C₆₇	semidirect
188. #1752	C₂×C₆₇	semidirect
189. C₆₇	#22441	direct (N × H)
192. C₂×#135	C₄×C₆₇	semidirect
276. Q₁₆	C₂²⋊C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₆₇	2
C₂×#441×C₆₇	2
C₆₇×#2341	2
C₆₇×#1972	2
C₆₇×#1880	2
C₆₇×#1807	2
C₆₇×#1788	2
C₆₇×#1752	2
#22441	67

Subgroups — C67×#22441 #30701692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22441 #30701692