Subgroups — C₃×D₇×C₂²⋊Q₈ #13060972

Order 1344.

644 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₇	C₂	1	1	yes	maximal, characteristic
3	C₃×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6460	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6459	C₂	1	2	yes	maximal, complemented
8	C₃×D₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₇×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×D₇×C₂²⋊C₄	C₂	1	2	yes	maximal
11	C₃×#6441	C₂	1	2	yes	maximal, complemented
12	D₇×C₂²⋊Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic
17	C₃×Q₈×D₇	—	2	4	no	—
18	C₂×C₃×C₄×D₇	—	2	4	no	—
19	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
20	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
21	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
25	C₂×C₃×Dic₁₄	C₂²	1	2	yes	complemented
26	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
28	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	—
31	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
32	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
33	C₃×C₄⋊Dic₇	C₂²	1	2	yes	complemented
34	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
35	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
36	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
37	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
38	C₂×Q₈×D₇	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×C₄×D₇	C₂×C₃	1	1	yes	characteristic
40	C₇×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
41	#6509	C₂×C₃	1	1	yes	characteristic, complemented
42	#6487	C₂×C₃	1	1	yes	characteristic, complemented
43	#6460	C₂×C₃	1	1	yes	characteristic, complemented
44	#6459	C₂×C₃	1	2	yes	complemented
45	D₇×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
46	D₇×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
47	D₇×C₂²⋊C₄	C₂×C₃	1	2	yes	—
48	#6441	C₂×C₃	1	2	yes	complemented
49	C₂×C₃×C₂²⋊Q₈	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
51	C₂²×C₃×D₇	—	2	2	no	—
52	C₂²×C₃×D₇	—	2	2	no	—
53	C₂²×C₃×D₇	Q₈	1	4	yes	complemented
54	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
55	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
56	C₃×C₇×Q₈	—	2	2	no	—
57	C₂×C₃×C₄×C₇	—	2	2	no	—
58	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
62	C₂×C₃×Dic₇	—	2	2	no	—
63	C₂×C₃×Dic₇	C₂³	1	2	yes	—
64	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
65	C₂×C₃×Dic₇	C₂³	1	2	yes	—
66	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
67	C₃×C₄×D₇	—	2	2	no	—
68	C₃×C₄×D₇	—	2	4	no	—
69	C₃×C₄×D₇	—	2	4	no	—
70	C₃×C₄×D₇	—	2	2	no	—
71	C₃×C₄×D₇	—	2	2	no	—
72	C₃×C₄×D₇	D₄	1	4	yes	—
73	C₃×Dic₁₄	—	2	2	no	—
74	C₃×Dic₁₄	—	2	4	no	—
75	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
77	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
78	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
79	Q₈×D₇	—	2	4	no	—
80	C₂×C₄×D₇	—	2	4	no	—
81	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
82	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
83	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
87	C₂×Dic₁₄	C₂²×C₃	1	2	yes	complemented
88	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
90	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
91	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	—
93	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
94	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	—
95	C₄⋊Dic₇	C₂²×C₃	1	2	yes	complemented
96	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
97	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
98	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
99	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
100	C₂²×C₃×Q₈	—	7	1	no	—
101	C₂³×C₃×C₄	—	7	1	no	—
102	C₃×C₂²⋊Q₈	—	7	1	no	—
103	C₃×C₂²⋊Q₈	—	7	1	no	—
104	C₃×C₂²⋊Q₈	—	7	2	no	—
105	C₃×C₂²⋊Q₈	—	7	1	no	—
106	C₃×C₂²⋊Q₈	—	7	2	no	—
107	C₃×C₂²⋊Q₈	D₇	1	1	yes	characteristic, direct product factor
108	C₂×C₃×C₄⋊C₄	—	7	1	no	—
109	C₂×C₃×C₄⋊C₄	—	7	2	no	—
110	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
111	C₂²×C₃×C₇	—	2	1	no	—
112	C₂²×C₃×C₇	—	2	1	no	—
113	C₂²×C₃×C₇	C₂×Q₈	1	2	yes	complemented
114	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
115	C₂×C₃×D₇	—	2	1	no	—
116	C₂×C₃×D₇	—	2	1	no	—
117	C₂×C₃×D₇	—	2	8	no	—
118	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
119	C₂×C₃×D₇	C₂×Q₈	1	2	yes	—
120	C₂×C₃×D₇	C₂×Q₈	1	2	yes	complemented
121	C₂×C₃×D₇	#41	1	2	yes	—
122	C₃×C₄×C₇	—	2	2	no	—
123	C₃×C₄×C₇	—	2	1	no	—
124	C₃×C₄×C₇	—	2	2	no	—
125	C₃×C₄×C₇	C₂×D₄	1	2	yes	—
126	C₃×Dic₇	—	2	2	no	—
127	C₃×Dic₇	—	2	1	no	—
128	C₃×Dic₇	—	2	2	no	—
129	C₃×Dic₇	C₂×D₄	1	2	yes	—
130	C₂×C₂²⋊Q₈	—	7	1	no	Sylow
131	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
132	C₂²×D₇	—	2	2	no	—
133	C₂²×D₇	—	2	2	no	—
134	C₂²×D₇	C₃×Q₈	1	4	yes	complemented
135	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
136	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
137	C₇×Q₈	—	2	2	no	—
138	C₂×C₄×C₇	—	2	2	no	—
139	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
140	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
141	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
142	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
143	C₂×Dic₇	—	2	2	no	—
144	C₂×Dic₇	C₂³×C₃	1	2	yes	—
145	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
146	C₂×Dic₇	C₂³×C₃	1	2	yes	—
147	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
148	C₄×D₇	—	2	2	no	—
149	C₄×D₇	—	2	4	no	—
150	C₄×D₇	—	2	4	no	—
151	C₄×D₇	—	2	2	no	—
152	C₄×D₇	—	2	2	no	—
153	C₄×D₇	C₃×D₄	1	4	yes	—
154	Dic₁₄	—	2	2	no	—
155	Dic₁₄	—	2	4	no	—
156	C₂⁴×C₃	—	7	1	no	—
157	C₂×C₃×Q₈	—	7	2	no	—
158	C₂×C₃×Q₈	—	7	1	no	—
159	C₂×C₃×Q₈	—	14	4	no	—
160	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
161	C₂²×C₃×C₄	—	7	1	no	—
162	C₂²×C₃×C₄	—	7	1	no	—
163	C₂²×C₃×C₄	—	7	2	no	—
164	C₂²×C₃×C₄	—	7	2	no	—
165	C₂²×C₃×C₄	—	7	1	no	—
166	C₂²×C₃×C₄	—	7	1	no	—
167	C₂²×C₃×C₄	—	7	1	no	—
168	C₂²×C₃×C₄	—	14	4	no	—
169	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic
170	C₃×C₄⋊C₄	—	7	2	no	—
171	C₃×C₄⋊C₄	—	7	2	no	—
172	C₃×C₄⋊C₄	—	7	2	no	—
173	C₃×C₄⋊C₄	—	7	1	no	—
174	C₃×C₄⋊C₄	—	7	2	no	—
175	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
176	C₃×C₄⋊C₄	C₂×D₇	1	2	yes	complemented
177	C₃×C₂²⋊C₄	—	7	2	no	—
178	C₃×C₂²⋊C₄	—	7	2	no	—
179	C₃×C₂²⋊C₄	—	7	2	no	—
180	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	—
181	C₂×C₃×C₇	—	2	2	no	—
182	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₃×C₇	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
185	C₃×D₇	—	2	2	no	—
186	C₃×D₇	C₂²⋊Q₈	1	4	yes	direct product factor
187	C₂²×Q₈	—	7	1	no	—
188	C₂³×C₄	—	7	1	no	—
189	C₂²⋊Q₈	—	7	1	no	—
190	C₂²⋊Q₈	—	7	1	no	—
191	C₂²⋊Q₈	—	7	2	no	—
192	C₂²⋊Q₈	—	7	1	no	—
193	C₂²⋊Q₈	—	7	2	no	—
194	C₂²⋊Q₈	C₃×D₇	1	1	yes	characteristic, direct product factor
195	C₂×C₄⋊C₄	—	7	1	no	—
196	C₂×C₄⋊C₄	—	7	2	no	—
197	C₂×C₂²⋊C₄	—	7	2	no	—
198	C₂²×C₇	—	2	1	no	—
199	C₂²×C₇	—	2	1	no	—
200	C₂²×C₇	C₂×C₃×Q₈	1	2	yes	complemented
201	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
202	C₂×D₇	—	2	1	no	—
203	C₂×D₇	—	2	1	no	—
204	C₂×D₇	—	2	8	no	—
205	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
206	C₂×D₇	C₂×C₃×Q₈	1	2	yes	—
207	C₂×D₇	C₂×C₃×Q₈	1	2	yes	complemented
208	C₂×D₇	C₃×#41	1	2	yes	—
209	C₄×C₇	—	2	2	no	—
210	C₄×C₇	—	2	1	no	—
211	C₄×C₇	—	2	2	no	—
212	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
213	Dic₇	—	2	2	no	—
214	Dic₇	—	2	1	no	—
215	Dic₇	—	2	2	no	—
216	Dic₇	C₂×C₃×D₄	1	2	yes	—
217	C₂³×C₃	—	7	1	no	—
218	C₂³×C₃	—	7	4	no	—
219	C₂³×C₃	—	7	1	no	—
220	C₂³×C₃	—	14	2	no	—
221	C₂³×C₃	—	14	2	no	—
222	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
223	C₃×Q₈	—	2	2	no	—
224	C₃×Q₈	—	14	4	no	—
225	C₃×Q₈	—	14	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	7	1	no	—
228	C₂×C₃×C₄	—	7	4	no	—
229	C₂×C₃×C₄	—	7	2	no	—
230	C₂×C₃×C₄	—	7	2	no	—
231	C₂×C₃×C₄	—	7	1	no	—
232	C₂×C₃×C₄	—	14	2	no	—
233	C₂×C₃×C₄	—	14	4	no	—
234	C₂×C₃×C₄	—	14	2	no	—
235	C₂×C₃×C₄	—	14	4	no	—
236	C₂×C₃×C₄	—	14	2	no	—
237	C₂×C₃×C₄	—	14	2	no	—
238	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
239	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
240	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
242	C₃×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Hall
243	C₂⁴	—	7	1	no	—
244	C₂×Q₈	—	7	2	no	—
245	C₂×Q₈	—	7	1	no	—
246	C₂×Q₈	—	14	4	no	—
247	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic, complemented
248	C₂²×C₄	—	7	1	no	—
249	C₂²×C₄	—	7	1	no	—
250	C₂²×C₄	—	7	2	no	—
251	C₂²×C₄	—	7	2	no	—
252	C₂²×C₄	—	7	1	no	—
253	C₂²×C₄	—	7	1	no	—
254	C₂²×C₄	—	7	1	no	—
255	C₂²×C₄	—	14	4	no	—
256	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic
257	C₄⋊C₄	—	7	2	no	—
258	C₄⋊C₄	—	7	2	no	—
259	C₄⋊C₄	—	7	2	no	—
260	C₄⋊C₄	—	7	1	no	—
261	C₄⋊C₄	—	7	2	no	—
262	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
263	C₄⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
264	C₂²⋊C₄	—	7	2	no	—
265	C₂²⋊C₄	—	7	2	no	—
266	C₂²⋊C₄	—	7	2	no	—
267	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	—
268	C₂×C₇	—	2	2	no	—
269	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
270	C₂×C₇	C₂²×C₃×Q₈	1	1	yes	characteristic
271	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
272	D₇	—	2	2	no	—
273	D₇	C₃×C₂²⋊Q₈	1	4	yes	direct product factor
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	7	2	no	—
277	C₂²×C₃	—	7	2	no	—
278	C₂²×C₃	—	7	2	no	—
279	C₂²×C₃	—	7	2	no	—
280	C₂²×C₃	—	14	8	no	—
281	C₂²×C₃	—	14	1	no	—
282	C₂²×C₃	—	14	1	no	—
283	C₂²×C₃	Q₈×D₇	1	2	yes	complemented
284	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
285	C₃×C₄	—	2	1	no	—
286	C₃×C₄	—	2	2	no	—
287	C₃×C₄	—	2	2	no	—
288	C₃×C₄	—	7	2	no	—
289	C₃×C₄	—	14	1	no	—
290	C₃×C₄	—	14	2	no	—
291	C₃×C₄	—	14	2	no	—
292	C₃×C₄	D₄×D₇	1	2	yes	—
293	C₂³	—	7	1	no	—
294	C₂³	—	7	4	no	—
295	C₂³	—	7	1	no	—
296	C₂³	—	14	2	no	—
297	C₂³	—	14	2	no	—
298	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
299	Q₈	—	2	2	no	—
300	Q₈	—	14	4	no	—
301	Q₈	—	14	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	7	1	no	—
304	C₂×C₄	—	7	4	no	—
305	C₂×C₄	—	7	2	no	—
306	C₂×C₄	—	7	2	no	—
307	C₂×C₄	—	7	1	no	—
308	C₂×C₄	—	14	2	no	—
309	C₂×C₄	—	14	2	no	—
310	C₂×C₄	—	14	4	no	—
311	C₂×C₄	—	14	4	no	—
312	C₂×C₄	—	14	2	no	—
313	C₂×C₄	—	14	2	no	—
314	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
315	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
316	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
317	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
318	C₇	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
319	C₂×C₃	—	2	2	no	—
320	C₂×C₃	—	7	4	no	—
321	C₂×C₃	—	14	2	no	—
322	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
323	C₂×C₃	C₂×Q₈×D₇	1	1	yes	characteristic
324	C₂×C₃	D₇×#41	1	1	yes	characteristic
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	7	2	no	—
328	C₂²	—	7	2	no	—
329	C₂²	—	7	2	no	—
330	C₂²	—	7	2	no	—
331	C₂²	—	14	8	no	—
332	C₂²	—	14	1	no	—
333	C₂²	—	14	1	no	—
334	C₂²	C₃×Q₈×D₇	1	2	yes	complemented
335	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
336	C₄	—	2	1	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	7	2	no	—
340	C₄	—	14	1	no	—
341	C₄	—	14	2	no	—
342	C₄	—	14	2	no	—
343	C₄	C₃×D₄×D₇	1	2	yes	—
344	C₃	D₇×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
345	C₂	—	2	2	no	—
346	C₂	—	7	4	no	—
347	C₂	—	14	2	no	—
348	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
349	C₂	C₂×C₃×Q₈×D₇	1	1	yes	characteristic
350	C₂	C₃×D₇×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₃×C₇×C₂²⋊Q₈	C₂
socle	C₂²×C₃×C₇	C₂⁴
prime radical	C₂³×C₃×D₇	C₂²
hypercenter	C₃×C₂²⋊Q₈	D₇
hypocenter	C₇	C₂×C₃×C₂²⋊Q₈
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×D₇	C₂	semidirect
3. C₃×C₇×C₂²⋊Q₈	C₂	semidirect
4. C₃×#6509	C₂	semidirect
5. C₃×#6487	C₂	semidirect
6. C₃×#6460	C₂	semidirect
7. C₃×#6459	C₂	semidirect
8. C₃×D₇×C₄⋊C₄	C₂	semidirect
9. C₃×D₇×C₄⋊C₄	C₂	semidirect
11. C₃×#6441	C₂	semidirect
12. D₇×C₂²⋊Q₈	C₃	direct (N × H)
14. C₂×C₃×C₇×Q₈	C₂²	semidirect
25. C₂×C₃×Dic₁₄	C₂²	semidirect
26. C₂×C₃×Dic₁₄	C₂²	semidirect
27. C₃×C₇×C₄⋊C₄	C₂²	semidirect
28. C₃×C₇×C₄⋊C₄	C₂²	semidirect
33. C₃×C₄⋊Dic₇	C₂²	semidirect
34. C₃×C₄⋊Dic₇	C₂²	semidirect
35. C₃×Dic₇⋊C₄	C₂²	semidirect
36. C₃×Dic₇⋊C₄	C₂²	semidirect
37. C₃×Dic₇⋊C₄	C₂²	semidirect
38. C₂×Q₈×D₇	C₂×C₃	semidirect
40. C₇×C₂²⋊Q₈	C₂×C₃	semidirect
41. #6509	C₂×C₃	semidirect
42. #6487	C₂×C₃	semidirect
43. #6460	C₂×C₃	semidirect
44. #6459	C₂×C₃	semidirect
45. D₇×C₄⋊C₄	C₂×C₃	semidirect
46. D₇×C₄⋊C₄	C₂×C₃	semidirect
48. #6441	C₂×C₃	semidirect
53. C₂²×C₃×D₇	Q₈	semidirect
76. C₂×C₇×Q₈	C₂²×C₃	semidirect
87. C₂×Dic₁₄	C₂²×C₃	semidirect
88. C₂×Dic₁₄	C₂²×C₃	semidirect
89. C₇×C₄⋊C₄	C₂²×C₃	semidirect
90. C₇×C₄⋊C₄	C₂²×C₃	semidirect
95. C₄⋊Dic₇	C₂²×C₃	semidirect
96. C₄⋊Dic₇	C₂²×C₃	semidirect
97. Dic₇⋊C₄	C₂²×C₃	semidirect
98. Dic₇⋊C₄	C₂²×C₃	semidirect
99. Dic₇⋊C₄	C₂²×C₃	semidirect
107. C₃×C₂²⋊Q₈	D₇	direct (N × H)
113. C₂²×C₃×C₇	C₂×Q₈	semidirect
120. C₂×C₃×D₇	C₂×Q₈	semidirect
134. C₂²×D₇	C₃×Q₈	semidirect
160. C₂×C₃×Q₈	C₂×D₇	semidirect
175. C₃×C₄⋊C₄	C₂×D₇	semidirect
176. C₃×C₄⋊C₄	C₂×D₇	semidirect
186. C₃×D₇	C₂²⋊Q₈	direct (N × H)
194. C₂²⋊Q₈	C₃×D₇	direct (N × H)
200. C₂²×C₇	C₂×C₃×Q₈	semidirect
207. C₂×D₇	C₂×C₃×Q₈	semidirect
242. C₃×C₇	C₂×C₂²⋊Q₈	semidirect
247. C₂×Q₈	C₂×C₃×D₇	semidirect
262. C₄⋊C₄	C₂×C₃×D₇	semidirect
263. C₄⋊C₄	C₂×C₃×D₇	semidirect
273. D₇	C₃×C₂²⋊Q₈	direct (N × H)
283. C₂²×C₃	Q₈×D₇	semidirect
318. C₇	C₂×C₃×C₂²⋊Q₈	semidirect
334. C₂²	C₃×Q₈×D₇	semidirect
344. C₃	D₇×C₂²⋊Q₈	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×C₃×Q₈×D₇	2
C₂²×C₃×C₄×D₇	2
C₃×C₇×C₂²⋊Q₈	2
C₃×#6509	2
C₃×#6487	2
C₃×#6460	2
C₃×#6459	2
C₃×D₇×C₄⋊C₄	2
C₃×D₇×C₂²⋊C₄	2
C₃×#6441	2
D₇×C₂²⋊Q₈	3
C₂×C₃×C₂²⋊Q₈	7

Subgroups — C3×D7×C22⋊Q8 #13060972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×C₂²⋊Q₈ #13060972