Subgroups — C₂²⋊Q₈×#10597010 #34061157

Order 19072.

656 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×#10597010	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×#10597010	C₂	1	1	yes	maximal, characteristic
3	(C₂×#10597010)⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750576	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750574	C₂	1	2	yes	maximal, complemented
6	#23750572	C₂	1	2	yes	maximal
7	#23750567	C₂	1	1	yes	maximal, characteristic
8	C₄⋊C₄×#10597010	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₄×#10597010	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²⋊C₄×#10597010	C₂	1	2	yes	maximal
11	C₂²⋊Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic
12	C₂³×#10597010	C₂²	1	1	yes	characteristic
13	C₂³×#10597010	C₂²	1	1	yes	characteristic
14	Q₈×#10597010	—	2	4	no	—
15	C₂×C₄⋊#10597010	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#10597010	C₂²	1	2	yes	—
17	C₂×C₄⋊#10597010	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#10597010	C₂²	1	2	yes	—
19	C₂×C₂²⋊#10597010	C₂²	1	2	yes	—
20	C₂×C₄×#10597010	—	2	4	no	—
21	C₂×C₄×#10597010	C₂²	1	1	yes	characteristic
22	C₂×C₄×#10597010	C₂²	1	1	yes	characteristic
23	C₂×C₄×#10597010	C₂²	1	1	yes	characteristic
24	C₂×C₄×#10597010	C₂²	1	2	yes	—
25	C₂×C₄×#10597010	C₂²	1	2	yes	—
26	C₂×C₄×#10597010	C₂²	1	1	yes	characteristic
27	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
28	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
29	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
30	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
31	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
32	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
34	#18011891	C₄	1	1	yes	characteristic, complemented
35	#18011890	C₄	1	1	yes	characteristic, complemented
36	#18011889	C₄	1	2	yes	complemented
37	#18011888	C₄	1	2	yes	complemented
38	#18011887	C₄	1	1	yes	characteristic, complemented
39	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
40	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
41	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
42	C₂²⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic, complemented
43	C₂²×#10597010	—	2	2	no	—
44	C₂²×#10597010	—	2	2	no	—
45	C₂²×#10597010	—	2	2	no	—
46	C₂²×#10597010	—	2	2	no	—
47	C₂²×#10597010	—	2	2	no	—
48	C₂²×#10597010	Q₈	1	4	yes	complemented
49	C₂²×#10597010	C₂³	1	2	yes	—
50	C₂²×#10597010	C₂³	1	2	yes	—
51	C₂²×#10597010	C₂³	1	1	yes	characteristic
52	C₂²×#10597010	C₂³	1	1	yes	characteristic
53	C₂²×#10597010	C₂³	1	1	yes	characteristic
54	C₂²×#10597010	C₂³	1	1	yes	characteristic
55	C₄⋊#10597010	—	2	4	no	—
56	C₄⋊#10597010	—	2	4	no	—
57	C₄⋊#10597010	—	2	2	no	—
58	C₄⋊#10597010	—	2	2	no	—
59	C₂²⋊#10597010	—	2	4	no	—
60	C₄×#10597010	—	2	2	no	—
61	C₄×#10597010	—	2	2	no	—
62	C₄×#10597010	—	2	4	no	—
63	C₄×#10597010	—	2	4	no	—
64	C₄×#10597010	—	2	2	no	—
65	C₄×#10597010	D₄	1	4	yes	—
66	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
67	C₂×Dic₂₉₈	C₂×C₄	1	2	yes	complemented
68	C₂×Dic₂₉₈	C₂×C₄	1	1	yes	characteristic, complemented
69	Q₈×D₁₄₉	—	2	2	no	—
70	Q₈×D₁₄₉	—	2	2	no	—
71	C₂²×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₁₄₉	—	2	2	no	—
73	C₂×C₄×D₁₄₉	—	2	2	no	—
74	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
78	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
79	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
80	C₄⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
81	C₄⋊Dic₁₄₉	C₂×C₄	1	2	yes	complemented
82	#14558715	C₂×C₄	1	2	yes	complemented
83	#14558715	C₂×C₄	1	2	yes	complemented
84	#14558715	C₂×C₄	1	2	yes	complemented
85	C₂²⋊Dic₁₄₉	C₂×C₄	1	2	yes	—
86	#14558713	C₂×C₄	1	2	yes	—
87	#14558713	C₂×C₄	1	2	yes	—
88	C₂×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
89	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	complemented
91	C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
92	C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
93	C₂×#10597010	—	2	8	no	—
94	C₂×#10597010	—	2	1	no	—
95	C₂×#10597010	—	2	1	no	—
96	C₂×#10597010	—	2	1	no	—
97	C₂×#10597010	—	2	1	no	—
98	C₂×#10597010	—	2	1	no	—
99	C₂×#10597010	—	2	1	no	—
100	C₂×#10597010	—	2	8	no	—
101	C₂×#10597010	—	2	2	no	—
102	C₂×#10597010	—	2	2	no	—
103	C₂×#10597010	—	2	2	no	—
104	C₂×#10597010	—	2	2	no	—
105	C₂×#10597010	—	2	2	no	—
106	C₂×#10597010	—	2	2	no	—
107	C₂×#10597010	C₂×D₄	1	2	yes	—
108	C₂×#10597010	C₂×D₄	1	2	yes	—
109	C₂×#10597010	C₂×Q₈	1	2	yes	—
110	C₂×#10597010	C₂×Q₈	1	2	yes	—
111	C₂×#10597010	#41	1	2	yes	—
112	C₂×#10597010	#41	1	2	yes	—
113	C₂²×D₁₄₉	—	2	1	no	—
114	C₂²×D₁₄₉	—	2	1	no	—
115	C₂²×D₁₄₉	—	2	1	no	—
116	C₂²×D₁₄₉	—	2	1	no	—
117	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×D₁₄₉	C₂×Q₈	1	2	yes	—
119	C₂²×D₁₄₉	#41	1	2	yes	—
120	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
121	Dic₂₉₈	—	2	2	no	—
122	Dic₂₉₈	—	2	4	no	—
123	C₂×Dic₁₄₉	—	2	2	no	—
124	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×Dic₁₄₉	C₂²×C₄	1	2	yes	—
126	C₂×Dic₁₄₉	C₂²×C₄	1	2	yes	—
127	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
128	C₄×D₁₄₉	—	2	1	no	—
129	C₄×D₁₄₉	—	2	2	no	—
130	C₄×D₁₄₉	—	2	1	no	—
131	C₄×D₁₄₉	—	2	2	no	—
132	C₄×D₁₄₉	—	2	2	no	—
133	C₄×D₁₄₉	—	2	2	no	—
134	C₄×D₁₄₉	—	2	2	no	—
135	C₄×D₁₄₉	—	2	2	no	—
136	C₄×D₁₄₉	C₂×D₄	1	2	yes	—
137	C₄×D₁₄₉	#41	1	2	yes	—
138	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
139	Q₈×C₁₄₉	—	2	2	no	—
140	C₂×C₄×C₁₄₉	—	2	2	no	—
141	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
143	C₂×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
144	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₁₄₉	—	2	1	no	—
146	C₂²×C₁₄₉	—	2	1	no	—
147	C₂²×C₁₄₉	C₄×Q₈	1	2	yes	complemented
148	C₂²×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
149	C₂×D₁₄₉	—	2	1	no	—
150	C₂×D₁₄₉	—	2	1	no	—
151	C₂×D₁₄₉	—	2	2	no	—
152	C₂×D₁₄₉	—	2	2	no	—
153	C₂×D₁₄₉	—	2	2	no	—
154	C₂×D₁₄₉	—	2	2	no	—
155	C₂×D₁₄₉	C₄×Q₈	1	2	yes	complemented
156	C₂×D₁₄₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×D₁₄₉	C₂²×Q₈	1	1	yes	characteristic
158	C₂×D₁₄₉	C₂×#41	1	1	yes	characteristic
159	C₂×D₁₄₉	C₂×#41	1	1	yes	characteristic
160	C₂×D₁₄₉	C₂×#41	1	1	yes	characteristic
161	C₂×D₁₄₉	C₂×#41	1	1	yes	characteristic
162	#10597010	—	2	2	no	—
163	#10597010	—	2	2	no	—
164	#10597010	—	2	2	no	—
165	#10597010	—	4	2	no	—
166	#10597010	—	4	2	no	—
167	#10597010	C₂²⋊Q₈	1	4	yes	direct product factor
168	C₄×C₁₄₉	—	2	1	no	—
169	C₄×C₁₄₉	—	2	2	no	—
170	C₄×C₁₄₉	—	2	2	no	—
171	C₄×C₁₄₉	C₄×D₄	1	2	yes	—
172	Dic₁₄₉	—	2	1	no	—
173	Dic₁₄₉	—	2	2	no	—
174	Dic₁₄₉	—	2	2	no	—
175	Dic₁₄₉	C₄×D₄	1	2	yes	—
176	C₂×C₁₄₉	—	2	2	no	—
177	C₂×C₁₄₉	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂×C₁₄₉	C₂×C₄×Q₈	1	1	yes	characteristic
179	C₂×C₁₄₉	C₄×#41	1	1	yes	characteristic
180	D₁₄₉	—	2	2	no	—
181	D₁₄₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
182	D₁₄₉	#525	1	1	yes	characteristic
183	D₁₄₉	#529	1	1	yes	characteristic
184	D₁₄₉	#533	1	1	yes	characteristic
185	C₁₄₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
186	C₄×C₂²⋊Q₈	—	149	1	no	maximal, Sylow
187	C₂×C₂²⋊Q₈	—	149	1	no	—
188	C₂×C₄×Q₈	—	149	1	no	—
189	C₂²×C₄²	—	149	1	no	—
190	#391	—	149	1	no	—
191	#389	—	149	1	no	—
192	#387	—	149	2	no	—
193	#385	—	149	2	no	—
194	#380	—	149	1	no	—
195	C₄×C₄⋊C₄	—	149	2	no	—
196	C₄×C₄⋊C₄	—	149	1	no	—
197	C₄×C₂²⋊C₄	—	149	2	no	—
198	C₂²×Q₈	—	149	1	no	—
199	C₂³×C₄	—	149	1	no	—
200	C₂³×C₄	—	149	1	no	—
201	C₂³×C₄	—	149	1	no	—
202	C₂²⋊Q₈	—	149	1	no	—
203	C₂²⋊Q₈	—	149	1	no	—
204	C₂²⋊Q₈	—	149	2	no	—
205	C₂²⋊Q₈	—	149	1	no	—
206	C₂²⋊Q₈	—	149	2	no	—
207	C₂²⋊Q₈	#10597010	1	1	yes	characteristic, direct product factor
208	C₄×Q₈	—	298	4	no	—
209	C₂×C₄⋊C₄	—	149	1	no	—
210	C₂×C₄⋊C₄	—	149	2	no	—
211	C₂×C₄⋊C₄	—	149	1	no	—
212	C₂×C₄⋊C₄	—	149	2	no	—
213	C₂×C₄⋊C₄	—	149	2	no	—
214	C₂×C₄⋊C₄	—	149	1	no	—
215	C₂×C₂²⋊C₄	—	149	2	no	—
216	C₂×C₂²⋊C₄	—	149	2	no	—
217	C₂×C₄²	—	298	4	no	—
218	C₂×C₄²	—	149	2	no	—
219	C₂×C₄²	—	149	2	no	—
220	C₂×C₄²	—	149	1	no	—
221	C₂×C₄²	—	149	1	no	—
222	C₂×C₄²	—	149	1	no	—
223	C₂×C₄²	—	149	1	no	—
224	#95	—	149	2	no	—
225	#95	—	149	2	no	—
226	#95	—	149	2	no	—
227	#95	—	149	2	no	—
228	#95	—	149	2	no	—
229	C₂⁴	—	149	1	no	—
230	C₂×Q₈	—	298	2	no	—
231	C₂×Q₈	—	298	2	no	—
232	C₂×Q₈	—	149	1	no	—
233	C₂×Q₈	—	149	2	no	—
234	C₂×Q₈	C₂×#10597010	1	1	yes	characteristic, complemented
235	C₂²×C₄	—	298	2	no	—
236	C₂²×C₄	—	298	2	no	—
237	C₂²×C₄	—	298	2	no	—
238	C₂²×C₄	—	298	2	no	—
239	C₂²×C₄	—	298	2	no	—
240	C₂²×C₄	—	298	2	no	—
241	C₂²×C₄	—	298	2	no	—
242	C₂²×C₄	—	149	2	no	—
243	C₂²×C₄	—	149	2	no	—
244	C₂²×C₄	—	149	4	no	—
245	C₂²×C₄	—	149	1	no	—
246	C₂²×C₄	—	149	1	no	—
247	C₂²×C₄	—	149	1	no	—
248	C₂²×C₄	—	149	1	no	—
249	C₂²×C₄	—	149	1	no	—
250	C₂²×C₄	—	149	1	no	—
251	C₂²×C₄	—	149	1	no	—
252	C₂²×C₄	—	149	2	no	—
253	C₂²×C₄	—	149	2	no	—
254	C₂²×C₄	—	149	1	no	—
255	C₂²×C₄	—	149	1	no	—
256	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
257	C₄⋊C₄	—	298	4	no	—
258	C₄⋊C₄	—	298	2	no	—
259	C₄⋊C₄	—	298	4	no	—
260	C₄⋊C₄	—	298	2	no	—
261	C₄⋊C₄	—	149	2	no	—
262	C₄⋊C₄	—	149	2	no	—
263	C₄⋊C₄	—	149	2	no	—
264	C₄⋊C₄	—	149	1	no	—
265	C₄⋊C₄	—	149	2	no	—
266	C₄⋊C₄	C₂×#10597010	1	1	yes	characteristic, complemented
267	C₄⋊C₄	C₂×#10597010	1	2	yes	complemented
268	C₂²⋊C₄	—	298	4	no	—
269	C₂²⋊C₄	—	149	2	no	—
270	C₂²⋊C₄	—	149	2	no	—
271	C₂²⋊C₄	—	149	2	no	—
272	C₂²⋊C₄	C₂×#10597010	1	2	yes	—
273	C₄²	—	298	2	no	—
274	C₄²	—	298	2	no	—
275	C₄²	—	298	2	no	—
276	C₄²	—	298	4	no	—
277	C₄²	—	298	4	no	—
278	C₄²	—	149	4	no	—
279	C₂³	—	298	1	no	—
280	C₂³	—	298	1	no	—
281	C₂³	—	298	1	no	—
282	C₂³	—	298	1	no	—
283	C₂³	—	149	2	no	—
284	C₂³	—	149	2	no	—
285	C₂³	—	149	1	no	—
286	C₂³	—	149	1	no	—
287	C₂³	C₂²×#10597010	1	1	yes	characteristic
288	Q₈	—	2	2	no	—
289	Q₈	—	298	4	no	—
290	Q₈	—	298	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	298	1	no	—
293	C₂×C₄	—	298	2	no	—
294	C₂×C₄	—	298	2	no	—
295	C₂×C₄	—	298	2	no	—
296	C₂×C₄	—	298	1	no	—
297	C₂×C₄	—	298	2	no	—
298	C₂×C₄	—	298	2	no	—
299	C₂×C₄	—	298	8	no	—
300	C₂×C₄	—	298	1	no	—
301	C₂×C₄	—	298	1	no	—
302	C₂×C₄	—	298	1	no	—
303	C₂×C₄	—	298	1	no	—
304	C₂×C₄	—	298	1	no	—
305	C₂×C₄	—	298	1	no	—
306	C₂×C₄	—	298	2	no	—
307	C₂×C₄	—	298	8	no	—
308	C₂×C₄	—	298	2	no	—
309	C₂×C₄	—	298	2	no	—
310	C₂×C₄	—	298	2	no	—
311	C₂×C₄	—	298	2	no	—
312	C₂×C₄	—	298	2	no	—
313	C₂×C₄	—	298	2	no	—
314	C₂×C₄	—	298	2	no	—
315	C₂×C₄	—	149	2	no	—
316	C₂×C₄	—	149	2	no	—
317	C₂×C₄	—	149	2	no	—
318	C₂×C₄	—	149	2	no	—
319	C₂×C₄	—	149	2	no	—
320	C₂×C₄	—	149	1	no	—
321	C₂×C₄	—	149	2	no	—
322	C₂×C₄	—	149	2	no	—
323	C₂×C₄	—	149	2	no	—
324	C₂×C₄	—	149	1	no	—
325	C₂×C₄	—	149	2	no	—
326	C₂×C₄	—	149	2	no	—
327	C₂×C₄	C₂²×#10597010	1	2	yes	—
328	C₂×C₄	C₂²×#10597010	1	2	yes	—
329	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
330	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	298	2	no	—
334	C₂²	—	298	2	no	—
335	C₂²	—	298	2	no	—
336	C₂²	—	298	2	no	—
337	C₂²	—	298	1	no	—
338	C₂²	—	298	1	no	—
339	C₂²	—	149	2	no	—
340	C₂²	—	149	1	no	—
341	C₂²	—	149	1	no	—
342	C₂²	—	149	1	no	—
343	C₂²	—	149	1	no	—
344	C₂²	—	149	1	no	—
345	C₂²	—	149	1	no	—
346	C₂²	Q₈×#10597010	1	2	yes	complemented
347	C₂²	C₂³×#10597010	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	298	2	no	—
352	C₄	—	298	2	no	—
353	C₄	—	298	2	no	—
354	C₄	—	298	1	no	—
355	C₄	—	298	2	no	—
356	C₄	—	298	2	no	—
357	C₄	—	596	2	no	—
358	C₄	—	596	2	no	—
359	C₄	—	149	4	no	—
360	C₄	—	149	2	no	—
361	C₄	D₄×#10597010	1	2	yes	—
362	C₂	—	2	2	no	—
363	C₂	—	298	2	no	—
364	C₂	—	149	1	no	—
365	C₂	—	149	1	no	—
366	C₂	—	149	1	no	—
367	C₂	—	149	1	no	—
368	C₂	C₂×D₄×#10597010	1	1	yes	characteristic
369	C₂	C₂×Q₈×#10597010	1	1	yes	characteristic
370	C₂	#41×#10597010	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#10597010
commutator, socle	C₂²×C₁₄₉	C₂³×C₄
Fitting	C₂²⋊Q₈×C₁₄₉	C₄
prime radical	C₂³×D₁₄₉	C₂³
cosocle	C₂²×D₁₄₉	C₂⁴
hypercenter	C₂²⋊Q₈	#10597010
hypocenter	C₁₄₉	C₄×C₂²⋊Q₈
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×#10597010	C₂	semidirect
3. (C₂×#10597010)⋊Q₈	C₂	semidirect
4. #23750576	C₂	semidirect
5. #23750574	C₂	semidirect
8. C₄⋊C₄×#10597010	C₂	semidirect
9. C₄⋊C₄×#10597010	C₂	semidirect
34. #18011891	C₄	semidirect
35. #18011890	C₄	semidirect
36. #18011889	C₄	semidirect
37. #18011888	C₄	semidirect
38. #18011887	C₄	semidirect
42. C₂²⋊Q₈×C₁₄₉	C₄	semidirect
48. C₂²×#10597010	Q₈	semidirect
67. C₂×Dic₂₉₈	C₂×C₄	semidirect
68. C₂×Dic₂₉₈	C₂×C₄	semidirect
80. C₄⋊Dic₁₄₉	C₂×C₄	semidirect
81. C₄⋊Dic₁₄₉	C₂×C₄	semidirect
82. #14558715	C₂×C₄	semidirect
83. #14558715	C₂×C₄	semidirect
84. #14558715	C₂×C₄	semidirect
88. C₂×Q₈×C₁₄₉	C₂×C₄	semidirect
90. C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
91. C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
147. C₂²×C₁₄₉	C₄×Q₈	semidirect
155. C₂×D₁₄₉	C₄×Q₈	semidirect
167. #10597010	C₂²⋊Q₈	direct (N × H)
185. C₁₄₉	C₄×C₂²⋊Q₈	semidirect
207. C₂²⋊Q₈	#10597010	direct (N × H)
234. C₂×Q₈	C₂×#10597010	semidirect
266. C₄⋊C₄	C₂×#10597010	semidirect
267. C₄⋊C₄	C₂×#10597010	semidirect
346. C₂²	Q₈×#10597010	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×#10597010	2
C₂²×C₄×#10597010	2
(C₂×#10597010)⋊Q₈	2
#23750576	2
#23750574	2
#23750572	2
#23750567	2
C₄⋊C₄×#10597010	2
C₂²⋊C₄×#10597010	2
C₂²⋊Q₈×D₁₄₉	2
C₄×C₂²⋊Q₈	149

Subgroups — C22⋊Q8×#10597010 #34061157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊Q₈×#10597010 #34061157