Subgroups — C₂×#22559651 #30838221

Order 17152.

754 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863742	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863606	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₈×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559651	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863148	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863143	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863140	C₂	1	1	yes	maximal, characteristic
8	C₂×#460×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11761618	—	2	1	no	—
10	C₂×#14524043	C₂²	1	1	yes	characteristic
11	#16863742	—	2	2	no	—
12	#16863742	C₂²	1	4	yes	—
13	#16863606	—	2	2	no	—
14	#16863606	C₂²	1	4	yes	complemented
15	Q₈×C₆₇⋊C₈	—	2	2	no	—
16	Q₈×C₆₇⋊C₈	C₂²	1	4	yes	complemented
17	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
18	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#14523966	—	2	1	no	—
21	C₂×#14523964	—	2	1	no	—
22	C₂×#14523964	—	2	1	no	—
23	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
24	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
25	#16863148	C₂²	1	4	yes	complemented
26	#16863143	C₂²	1	4	yes	complemented
27	#16863140	C₂²	1	4	yes	—
28	C₂²×SD₁₆×C₆₇	—	2	1	no	—
29	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	#460×C₆₇	—	2	2	no	—
32	#460×C₆₇	C₂²	1	4	yes	—
33	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₇	—	2	1	no	—
35	C₂²×Dic₁₃₄	—	2	1	no	—
36	C₂×#11761618	—	2	4	no	—
37	C₂×#11761618	—	4	4	no	—
38	C₂²×C₆₇⋊C₈	—	2	1	no	—
39	C₂²×C₆₇⋊C₈	—	2	1	no	—
40	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
41	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
42	#14524043	—	2	1	no	—
43	#14524043	—	2	1	no	—
44	#14524043	—	2	1	no	—
45	#14524043	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₆₇	—	2	1	no	—
47	C₂×C₄⋊Dic₆₇	—	2	1	no	—
48	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
49	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
51	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
52	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
53	#14523966	—	2	4	no	—
54	#14523964	—	2	4	no	—
55	#14523964	—	2	4	no	—
56	C₄×C₆₇⋊C₈	—	2	4	no	—
57	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
58	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
59	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₆₇	—	2	1	no	—
61	C₂²×D₄×C₆₇	—	2	1	no	—
62	C₂²×D₄×C₆₇	—	2	1	no	—
63	C₂×SD₁₆×C₆₇	—	2	4	no	—
64	C₂×SD₁₆×C₆₇	—	4	4	no	—
65	C₂²×C₈×C₆₇	—	2	1	no	—
66	#127×C₆₇	—	2	1	no	—
67	#127×C₆₇	—	2	1	no	—
68	#127×C₆₇	—	2	1	no	—
69	#127×C₆₇	C₂³	1	2	yes	—
70	C₄×Q₈×C₆₇	—	2	1	no	—
71	C₄×Q₈×C₆₇	—	2	1	no	—
72	C₄×Q₈×C₆₇	D₄	1	2	yes	—
73	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₆₇	—	2	1	no	—
77	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₆₇	—	2	1	no	—
79	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
80	#102×C₆₇	—	2	4	no	—
81	C₂×Dic₁₃₄	—	2	2	no	—
82	C₂×Dic₁₃₄	—	4	2	no	—
83	C₂×Dic₁₃₄	—	4	2	no	—
84	C₂×Dic₁₃₄	—	4	1	no	—
85	C₂²×Dic₆₇	—	4	1	no	—
86	#11761618	—	4	8	no	—
87	C₂×C₆₇⋊C₈	—	2	2	no	—
88	C₂×C₆₇⋊C₈	—	2	2	no	—
89	C₂×C₆₇⋊C₈	—	2	2	no	—
90	C₂×C₆₇⋊C₈	—	2	2	no	—
91	C₂×C₆₇⋊C₈	—	4	2	no	—
92	C₂×C₆₇⋊C₈	—	4	2	no	—
93	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
94	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
95	C₄⋊Dic₆₇	—	2	2	no	—
96	C₄⋊Dic₆₇	—	2	2	no	—
97	C₄⋊Dic₆₇	—	4	1	no	—
98	C₄⋊Dic₆₇	—	4	1	no	—
99	C₂⁴×C₆₇	—	4	1	no	—
100	C₂×Q₈×C₆₇	—	2	1	no	—
101	C₂×Q₈×C₆₇	—	2	2	no	—
102	C₂×Q₈×C₆₇	D₈	1	4	yes	—
103	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₆₇	—	2	2	no	—
105	C₂×D₄×C₆₇	—	2	2	no	—
106	C₂×D₄×C₆₇	—	2	2	no	—
107	C₂×D₄×C₆₇	—	4	1	no	—
108	C₂×D₄×C₆₇	—	4	1	no	—
109	C₂×D₄×C₆₇	—	4	1	no	—
110	C₂×D₄×C₆₇	—	4	2	no	—
111	C₂×D₄×C₆₇	—	4	2	no	—
112	C₂×D₄×C₆₇	—	4	2	no	—
113	C₂×D₄×C₆₇	—	4	2	no	—
114	C₂×D₄×C₆₇	—	8	2	no	—
115	C₂²×C₄×C₆₇	—	2	1	no	—
116	C₂²×C₄×C₆₇	—	2	1	no	—
117	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
120	SD₁₆×C₆₇	—	4	8	no	—
121	C₂×C₈×C₆₇	—	2	2	no	—
122	C₂×C₈×C₆₇	—	4	2	no	—
123	C₄⋊C₄×C₆₇	—	2	2	no	—
124	C₄⋊C₄×C₆₇	—	2	1	no	—
125	C₄⋊C₄×C₆₇	—	2	2	no	—
126	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
127	C₄²×C₆₇	—	2	2	no	—
128	C₄²×C₆₇	—	2	2	no	—
129	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₆₇	#41	1	1	yes	characteristic
132	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
133	C₂³×C₆₇	—	4	2	no	—
134	C₂³×C₆₇	—	8	2	no	—
135	C₂³×C₆₇	—	8	2	no	—
136	C₂³×C₆₇	—	8	2	no	—
137	C₂³×C₆₇	#121	1	1	yes	characteristic
138	Q₈×C₆₇	—	2	2	no	—
139	Q₈×C₆₇	—	2	4	no	—
140	Q₈×C₆₇	C₂×D₈	1	4	yes	—
141	D₄×C₆₇	—	4	2	no	—
142	D₄×C₆₇	—	4	2	no	—
143	D₄×C₆₇	—	4	2	no	—
144	D₄×C₆₇	—	4	2	no	—
145	D₄×C₆₇	—	8	2	no	—
146	D₄×C₆₇	—	8	2	no	—
147	D₄×C₆₇	—	8	2	no	—
148	D₄×C₆₇	—	8	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	4	no	—
151	C₂×C₄×C₆₇	—	2	2	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
155	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
158	C₂×C₄×C₆₇	#135	1	2	yes	—
159	C₂×C₄×C₆₇	#135	1	2	yes	—
160	C₂×C₄×C₆₇	#137	1	2	yes	—
161	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₆₇	—	4	2	no	—
165	C₂×Dic₆₇	—	8	2	no	—
166	Dic₁₃₄	—	4	2	no	—
167	Dic₁₃₄	—	4	2	no	—
168	Dic₁₃₄	—	8	2	no	—
169	C₈×C₆₇	—	4	2	no	—
170	C₆₇⋊C₈	—	2	2	no	—
171	C₆₇⋊C₈	—	2	2	no	—
172	C₆₇⋊C₈	—	4	2	no	—
173	C₆₇⋊C₈	—	4	2	no	—
174	C₂²×C₆₇	—	8	2	no	—
175	C₂²×C₆₇	—	8	2	no	—
176	C₂²×C₆₇	—	8	2	no	—
177	C₂²×C₆₇	—	16	4	no	—
178	C₂²×C₆₇	#464	1	2	yes	—
179	C₂²×C₆₇	#466	1	2	yes	—
180	C₂²×C₆₇	#471	1	2	yes	—
181	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
182	C₄×C₆₇	—	2	4	no	—
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	4	2	no	—
186	C₄×C₆₇	#464	1	2	yes	—
187	C₄×C₆₇	#466	1	2	yes	—
188	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
190	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
191	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
192	Dic₆₇	—	8	2	no	—
193	C₂×#1682	—	67	1	no	maximal, Sylow
194	C₂×C₆₇	—	16	2	no	—
195	C₂×C₆₇	#1682	1	4	yes	complemented
196	C₂×C₆₇	C₂×#464	1	1	yes	characteristic
197	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
198	C₂×C₆₇	C₂×#471	1	1	yes	characteristic
199	C₂×#486	—	67	1	no	—
200	C₂×#462	—	67	1	no	—
201	C₂×#460	D₆₇	1	1	yes	characteristic
202	C₂×C₈×Q₈	—	67	1	no	—
203	#1682	—	67	8	no	—
204	C₂×#335	—	67	1	no	—
205	C₂×#332	—	67	1	no	—
206	C₂×#331	—	67	1	no	—
207	C₆₇	C₂×#1682	1	1	yes	characteristic, complemented, Sylow
208	C₂²×Q₁₆	—	134	1	no	—
209	C₂²×SD₁₆	—	2	1	no	—
210	C₂×C₄⋊Q₈	—	67	1	no	—
211	C₂×#127	C₂×D₆₇	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
213	#486	—	67	4	no	—
214	#486	—	134	2	no	—
215	#462	—	67	4	no	—
216	#462	—	134	2	no	—
217	#460	—	2	2	no	—
218	#460	C₂×D₆₇	1	4	yes	—
219	C₈×Q₈	—	67	4	no	—
220	C₈×Q₈	—	134	2	no	—
221	C₂×C₄⋊C₈	—	67	1	no	—
222	C₂×C₄⋊C₈	—	67	1	no	—
223	C₂×C₄⋊C₈	—	134	1	no	—
224	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
225	C₂×#103	—	134	1	no	—
226	C₂×#102	—	2	1	no	—
227	C₂×#102	—	134	1	no	—
228	C₂×#102	—	134	1	no	—
229	C₂×C₄×C₈	—	67	1	no	—
230	C₂×C₄×C₈	—	134	1	no	—
231	#335	—	67	4	no	—
232	#332	—	67	4	no	—
233	#331	—	67	4	no	—
234	C₂²×Q₈	—	134	1	no	—
235	C₂²×Q₈	C₂²⋊D₆₇	1	1	yes	characteristic
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂×Q₁₆	—	268	4	no	—
240	C₂×Q₁₆	—	134	4	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	4	4	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	67	1	no	—
245	C₂²×C₈	—	67	1	no	—
246	C₂²×C₈	—	134	1	no	—
247	C₂²×C₈	—	134	1	no	—
248	C₄⋊Q₈	—	67	2	no	—
249	C₄⋊Q₈	—	134	1	no	—
250	C₄⋊Q₈	—	134	1	no	—
251	C₄⋊Q₈	—	134	1	no	—
252	#127	—	2	1	no	—
253	#127	—	2	1	no	—
254	#127	—	2	1	no	—
255	#127	C₂²×D₆₇	1	2	yes	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	C₂²⋊D₆₇	1	2	yes	—
259	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	134	1	no	—
262	C₂×C₄⋊C₄	—	134	1	no	—
263	C₂×C₄⋊C₄	C₂²⋊D₆₇	1	1	yes	characteristic
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	67	2	no	—
268	C₄⋊C₈	—	67	2	no	—
269	C₄⋊C₈	—	134	4	no	—
270	C₄⋊C₈	—	134	1	no	—
271	C₄⋊C₈	—	134	1	no	—
272	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
273	#103	—	134	4	no	—
274	#102	—	2	4	no	—
275	#102	—	134	4	no	—
276	#102	—	134	4	no	—
277	C₄×C₈	—	67	2	no	—
278	C₄×C₈	—	67	2	no	—
279	C₄×C₈	—	134	4	no	—
280	C₂⁴	—	4	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	268	1	no	—
284	C₂×Q₈	—	268	2	no	—
285	C₂×Q₈	—	268	2	no	—
286	C₂×Q₈	—	134	2	no	—
287	C₂×Q₈	#11761613	1	4	yes	—
288	C₂×Q₈	C₂×C₂²⋊D₆₇	1	2	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	8	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	268	1	no	—
303	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
305	C₂²×C₄	#11761627	1	1	yes	characteristic
306	Q₁₆	—	268	8	no	—
307	SD₁₆	—	4	8	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	—	268	2	no	—
311	C₂×C₈	—	268	2	no	—
312	C₂×C₈	—	67	2	no	—
313	C₂×C₈	—	67	2	no	—
314	C₂×C₈	—	134	2	no	—
315	C₂×C₈	—	134	2	no	—
316	C₂×C₈	—	134	2	no	—
317	C₂×C₈	—	134	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	268	1	no	—
322	C₄⋊C₄	—	268	1	no	—
323	C₄⋊C₄	—	134	2	no	—
324	C₄⋊C₄	—	134	2	no	—
325	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	2	yes	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	D₄×D₆₇	1	1	yes	characteristic
329	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
330	C₄²	#11761627	1	1	yes	characteristic
331	C₄²	C₂³×D₆₇	1	1	yes	characteristic
332	C₂³	—	4	2	no	—
333	C₂³	—	8	2	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	8	2	no	—
336	C₂³	#14524015	1	1	yes	characteristic
337	Q₈	—	2	4	no	—
338	Q₈	—	2	2	no	—
339	Q₈	—	268	2	no	—
340	Q₈	—	268	2	no	—
341	Q₈	—	536	2	no	—
342	Q₈	C₂×#11761613	1	4	yes	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	8	2	no	—
348	D₄	—	8	2	no	—
349	D₄	—	8	2	no	—
350	D₄	—	8	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	268	2	no	—
357	C₂×C₄	—	536	2	no	—
358	C₂×C₄	#14524015	1	1	yes	characteristic
359	C₂×C₄	#14524015	1	1	yes	characteristic
360	C₂×C₄	#14524015	1	1	yes	characteristic
361	C₂×C₄	C₂×#11761613	1	2	yes	—
362	C₂×C₄	#14524063	1	2	yes	—
363	C₂×C₄	#14524064	1	2	yes	—
364	C₂×C₄	#14524072	1	2	yes	—
365	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
367	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
368	C₈	—	4	2	no	—
369	C₈	—	268	2	no	—
370	C₈	—	268	2	no	—
371	C₈	—	134	2	no	—
372	C₈	—	134	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	16	4	no	—
377	C₂²	#16863616	1	2	yes	—
378	C₂²	#16863630	1	2	yes	—
379	C₂²	#16863657	1	2	yes	—
380	C₂²	C₂×#14524015	1	1	yes	characteristic
381	C₄	—	2	4	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	536	2	no	—
386	C₄	#16863616	1	2	yes	—
387	C₄	#16863630	1	2	yes	—
388	C₄	C₂²×#11761613	1	1	yes	characteristic
389	C₄	C₂×#14524063	1	1	yes	characteristic
390	C₄	C₂×#14524064	1	1	yes	characteristic
391	C₄	C₂×#14524072	1	1	yes	characteristic
392	C₂	—	16	2	no	—
393	C₂	#22559651	1	4	yes	direct product factor
394	C₂	C₂×#16863616	1	1	yes	characteristic
395	C₂	C₂×#16863630	1	1	yes	characteristic
396	C₂	C₂×#16863657	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14524015
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×#460×C₆₇	C₂
socle	C₂³×C₆₇	#121
prime radical	C₂×#127×C₆₇	C₂²
hypercenter	C₂×#460	D₆₇
hypocenter	C₆₇	C₂×#1682
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#460

Complements

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

N	H ≅ G/N	type
2. C₂×#16863606	C₂	semidirect
3. C₂×Q₈×C₆₇⋊C₈	C₂	semidirect
4. #22559651	C₂	direct (N × H)
5. C₂×#16863148	C₂	semidirect
6. C₂×#16863143	C₂	semidirect
14. #16863606	C₂²	semidirect
16. Q₈×C₆₇⋊C₈	C₂²	semidirect
25. #16863148	C₂²	semidirect
26. #16863143	C₂²	semidirect
195. C₂×C₆₇	#1682	semidirect
207. C₆₇	C₂×#1682	semidirect
393. C₂	#22559651	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×#16863742	2
C₂×#16863606	2
C₂×Q₈×C₆₇⋊C₈	2
#22559651	2
C₂×#16863148	2
C₂×#16863143	2
C₂×#16863140	2
C₂×#460×C₆₇	2
C₂×#1682	67

Subgroups — C2×#22559651 #30838221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22559651 #30838221