Subgroups — C₂×#69875 #10798707

Order 768.

938 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×C₃×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×#822	C₂	1	2	yes	maximal
3	C₂×#4924	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	C₂×#4558	C₂	1	2	yes	maximal
6	#69875	C₂	1	8	yes	maximal, direct product factor
7	C₂×#1950	—	3	1	no	maximal, Sylow
8	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
11	C₂²×#208	C₂²	1	2	yes	—
12	C₂³×C₃⋊C₈	C₂²	1	2	yes	—
13	C₃×C₄×M₁₆	—	2	2	no	—
14	C₃×C₄×M₁₆	C₂²	1	4	yes	—
15	C₂×C₃×#97	—	2	1	no	—
16	C₂×C₃×C₄×C₈	—	2	1	no	—
17	C₂×#822	—	2	8	no	—
18	C₂×#822	C₂²	1	8	yes	—
19	#4924	—	2	2	no	—
20	#4924	C₂²	1	4	yes	—
21	C₂×C₄⋊(C₃⋊C₈)	—	2	1	no	—
22	C₂×C₄⋊(C₃⋊C₈)	—	2	1	no	—
23	C₂×C₄⋊(C₃⋊C₈)	C₄	1	2	yes	—
24	C₂×C₄⋊(C₃⋊C₈)	C₄	1	4	yes	—
25	C₂×C₄⋊(C₃⋊C₈)	C₄	1	2	yes	—
26	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	—
27	#4558	C₂²	1	8	yes	—
28	C₂²×#108	—	3	2	no	—
29	C₂×#423	—	3	1	no	—
30	C₂²×C₄⋊C₈	—	3	1	no	—
31	C₂×C₄×M₁₆	D₃	1	1	yes	characteristic
32	#1950	—	3	8	no	—
33	C₂×#341	—	3	2	no	—
34	C₂³×C₃×C₄	Q₈	1	1	yes	characteristic
35	C₂³×C₃×C₄	Q₈	1	1	yes	characteristic
36	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
37	C₂×C₃×M₁₆	—	2	1	no	—
38	C₂×C₃×M₁₆	—	2	1	no	—
39	C₂×C₃×M₁₆	—	2	2	no	—
40	C₂×C₃×M₁₆	—	2	2	no	—
41	C₂×C₃×M₁₆	D₄	1	4	yes	—
42	C₂×C₃×M₁₆	Q₈	1	4	yes	—
43	C₂×C₃×M₁₆	C₂³	1	2	yes	—
44	C₂×C₃×M₁₆	C₂³	1	2	yes	—
45	C₂²×C₃×C₈	—	2	1	no	—
46	C₂²×C₃×C₈	—	2	1	no	—
47	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
51	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
52	C₂×C₃×C₄²	D₄	1	2	yes	—
53	C₂×C₃×C₄²	Q₈	1	2	yes	—
54	C₂×C₃×C₄²	C₂³	1	2	yes	—
55	C₂×#208	—	2	2	no	—
56	C₂×#208	—	2	4	no	—
57	C₂×#208	—	2	4	no	—
58	C₂×#208	C₂³	1	4	yes	—
59	C₂²×C₃⋊C₈	—	2	4	no	—
60	C₂²×C₃⋊C₈	—	2	4	no	—
61	C₂²×C₃⋊C₈	—	2	2	no	—
62	C₂²×C₃⋊C₈	C₂×C₄	1	4	yes	—
63	C₂²×C₃⋊C₈	C₂×C₄	1	4	yes	—
64	C₂²×C₃⋊C₈	C₂³	1	4	yes	—
65	C₃×#97	—	2	4	no	—
66	C₃×C₄×C₈	—	2	4	no	—
67	#822	—	2	16	no	—
68	C₄⋊(C₃⋊C₈)	—	2	4	no	—
69	C₄⋊(C₃⋊C₈)	—	2	4	no	—
70	C₄⋊(C₃⋊C₈)	C₂×C₄	1	8	yes	—
71	C₄⋊(C₃⋊C₈)	C₂×C₄	1	8	yes	—
72	C₂²×M₁₆	—	3	2	no	—
73	C₂²×M₁₆	C₂×D₃	1	1	yes	characteristic
74	C₂²×M₁₆	C₂×D₃	1	1	yes	characteristic
75	C₂³×C₈	—	3	2	no	—
76	C₂²×C₄²	C₂×D₃	1	1	yes	characteristic
77	C₂×#108	—	3	8	no	—
78	C₂×#108	—	6	8	no	—
79	#423	—	3	4	no	—
80	#423	—	6	2	no	—
81	C₂×C₄⋊C₈	—	3	2	no	—
82	C₂×C₄⋊C₈	—	3	4	no	—
83	C₂×C₄⋊C₈	—	3	2	no	—
84	C₂×C₄⋊C₈	—	3	4	no	—
85	C₂×C₄⋊C₈	—	6	1	no	—
86	C₂×C₄⋊C₈	—	6	1	no	—
87	C₄×M₁₆	—	2	2	no	—
88	C₄×M₁₆	C₂×D₃	1	4	yes	—
89	C₂×#97	—	2	1	no	—
90	C₂×C₄×C₈	—	2	1	no	—
91	#341	—	3	8	no	—
92	C₂⁴×C₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₃×C₄	—	2	4	no	—
94	C₂²×C₃×C₄	—	4	2	no	—
95	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
98	C₂²×C₃×C₄	C₄⋊C₄	1	2	yes	—
99	C₂²×C₃×C₄	C₄⋊C₄	1	2	yes	—
100	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
104	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₃×C₄	C₂×Q₈	1	2	yes	—
107	C₂²×C₃×C₄	C₂×Q₈	1	2	yes	—
108	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₂×Q₈	1	2	yes	—
110	C₂²×C₃×C₄	#41	1	2	yes	—
111	C₂²×C₃×C₄	#41	1	2	yes	—
112	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
113	C₃×M₁₆	—	2	4	no	—
114	C₃×M₁₆	—	2	4	no	—
115	C₃×M₁₆	—	2	2	no	—
116	C₃×M₁₆	—	2	2	no	—
117	C₃×M₁₆	C₂×D₄	1	4	yes	—
118	C₃×M₁₆	C₂×Q₈	1	4	yes	—
119	C₂×C₃×C₈	—	2	4	no	—
120	C₂×C₃×C₈	—	2	4	no	—
121	C₂×C₃×C₈	—	2	2	no	—
122	C₂×C₃×C₈	—	2	2	no	—
123	C₃×C₄²	C₄⋊C₄	1	2	yes	—
124	C₃×C₄²	C₄⋊C₄	1	2	yes	—
125	C₃×C₄²	C₄⋊C₄	1	2	yes	—
126	C₃×C₄²	C₄⋊C₄	1	2	yes	—
127	C₃×C₄²	C₂²×C₄	1	2	yes	—
128	C₃×C₄²	C₂²×C₄	1	2	yes	—
129	C₃×C₄²	C₂×D₄	1	2	yes	—
130	C₃×C₄²	C₂×D₄	1	2	yes	—
131	#208	—	2	4	no	—
132	#208	—	2	4	no	—
133	#208	—	4	4	no	—
134	C₂×C₃⋊C₈	—	2	8	no	—
135	C₂×C₃⋊C₈	—	2	8	no	—
136	C₂×C₃⋊C₈	—	2	4	no	—
137	C₂×C₃⋊C₈	—	2	4	no	—
138	C₂×C₃⋊C₈	—	2	4	no	—
139	C₂×C₃⋊C₈	—	4	4	no	—
140	C₂×C₃⋊C₈	C₂²×C₄	1	8	yes	—
141	C₂³×C₄	Dic₆	1	1	yes	characteristic
142	C₂³×C₄	Dic₆	1	1	yes	characteristic
143	C₂³×C₄	C₂²×D₃	1	1	yes	characteristic
144	C₂×M₁₆	—	2	2	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	—	2	1	no	—
147	C₂×M₁₆	—	2	1	no	—
148	C₂×M₁₆	—	3	4	no	—
149	C₂×M₁₆	—	6	2	no	—
150	C₂×M₁₆	—	6	4	no	—
151	C₂×M₁₆	—	6	4	no	—
152	C₂×M₁₆	Dic₆	1	4	yes	—
153	C₂×M₁₆	D₁₂	1	4	yes	—
154	C₂×M₁₆	C₂²×D₃	1	2	yes	—
155	C₂×M₁₆	C₂²×D₃	1	2	yes	—
156	C₂²×C₈	—	2	1	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	3	4	no	—
159	C₂²×C₈	—	3	4	no	—
160	C₂²×C₈	—	3	4	no	—
161	C₂²×C₈	—	6	4	no	—
162	C₂²×C₈	—	6	4	no	—
163	C₂²×C₈	—	6	2	no	—
164	C₂×C₄²	Dic₆	1	2	yes	—
165	C₂×C₄²	C₄×D₃	1	1	yes	characteristic
166	C₂×C₄²	C₄×D₃	1	2	yes	—
167	C₂×C₄²	C₄×D₃	1	1	yes	characteristic
168	C₂×C₄²	#67	1	2	yes	—
169	C₂×C₄²	#67	1	1	yes	characteristic
170	C₂×C₄²	#67	1	1	yes	characteristic
171	C₂×C₄²	C₂²×D₃	1	2	yes	—
172	#108	—	6	16	no	—
173	C₄⋊C₈	—	3	8	no	—
174	C₄⋊C₈	—	3	8	no	—
175	C₄⋊C₈	—	6	4	no	—
176	C₄⋊C₈	—	6	4	no	—
177	#97	—	2	4	no	—
178	C₄×C₈	—	2	4	no	—
179	C₂³×C₃	—	2	2	no	—
180	C₂³×C₃	—	2	2	no	—
181	C₂³×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂³×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂³×C₃	#125	1	2	yes	—
184	C₂³×C₃	C₄⋊Q₈	1	2	yes	—
185	C₂³×C₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₃×C₄	—	2	2	no	—
187	C₂×C₃×C₄	—	2	2	no	—
188	C₂×C₃×C₄	—	2	2	no	—
189	C₂×C₃×C₄	—	2	4	no	—
190	C₂×C₃×C₄	—	2	4	no	—
191	C₂×C₃×C₄	—	4	2	no	—
192	C₂×C₃×C₄	—	4	2	no	—
193	C₂×C₃×C₄	#108	1	4	yes	complemented
194	C₂×C₃×C₄	C₂×C₄⋊C₄	1	2	yes	—
195	C₂×C₃×C₄	C₂×C₄⋊C₄	1	2	yes	—
196	C₂×C₃×C₄	C₂×C₄⋊C₄	1	2	yes	—
197	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₃×C₄	C₂×C₄⋊C₄	1	2	yes	—
200	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
201	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
202	C₂×C₃×C₄	C₄×Q₈	1	2	yes	—
203	C₂×C₃×C₄	C₄×Q₈	1	2	yes	—
204	C₂×C₃×C₄	#121	1	2	yes	—
205	C₂×C₃×C₄	#121	1	2	yes	—
206	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₃×C₄	#125	1	2	yes	—
209	C₂×C₃×C₄	C₄⋊Q₈	1	2	yes	—
210	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
215	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
216	C₃×C₈	—	2	4	no	—
217	C₃×C₈	—	2	4	no	—
218	C₃⋊C₈	—	2	8	no	—
219	C₃⋊C₈	—	4	4	no	—
220	C₂⁴	C₂×Dic₆	1	1	yes	characteristic
221	C₂²×C₄	—	2	4	no	—
222	C₂²×C₄	—	4	2	no	—
223	C₂²×C₄	Dic₃⋊C₄	1	1	yes	characteristic
224	C₂²×C₄	Dic₃⋊C₄	1	1	yes	characteristic
225	C₂²×C₄	Dic₃⋊C₄	1	1	yes	characteristic
226	C₂²×C₄	Dic₃⋊C₄	1	2	yes	—
227	C₂²×C₄	Dic₃⋊C₄	1	2	yes	—
228	C₂²×C₄	Dic₃⋊C₄	1	1	yes	characteristic
229	C₂²×C₄	C₂×Dic₆	1	2	yes	—
230	C₂²×C₄	C₂×Dic₆	1	2	yes	—
231	C₂²×C₄	C₂×Dic₆	1	2	yes	—
232	C₂²×C₄	C₂×Dic₆	1	1	yes	characteristic
233	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
234	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
235	C₂²×C₄	C₂×D₁₂	1	2	yes	—
236	C₂²×C₄	#235	1	2	yes	—
237	C₂²×C₄	#235	1	2	yes	—
238	C₂²×C₄	C₂×#67	1	1	yes	characteristic
239	C₂²×C₄	C₂×#67	1	1	yes	characteristic
240	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
241	M₁₆	—	2	4	no	—
242	M₁₆	—	2	4	no	—
243	M₁₆	—	2	2	no	—
244	M₁₆	—	2	2	no	—
245	M₁₆	—	6	4	no	—
246	M₁₆	—	6	4	no	—
247	M₁₆	—	12	4	no	—
248	M₁₆	C₂×Dic₆	1	4	yes	—
249	M₁₆	C₂×D₁₂	1	4	yes	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	4	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	3	8	no	—
255	C₂×C₈	—	6	8	no	—
256	C₂×C₈	—	6	8	no	—
257	C₂×C₈	—	6	4	no	—
258	C₂×C₈	—	6	4	no	—
259	C₂×C₈	—	6	4	no	—
260	C₂×C₈	—	12	4	no	—
261	C₄²	Dic₃⋊C₄	1	2	yes	—
262	C₄²	Dic₃⋊C₄	1	2	yes	—
263	C₄²	Dic₃⋊C₄	1	2	yes	—
264	C₄²	Dic₃⋊C₄	1	2	yes	—
265	C₄²	C₂×C₄×D₃	1	2	yes	—
266	C₄²	C₂×C₄×D₃	1	2	yes	—
267	C₄²	C₂×#67	1	2	yes	—
268	C₄²	C₂×#67	1	2	yes	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	4	no	—
274	C₂²×C₃	—	2	4	no	—
275	C₂²×C₃	#389	1	2	yes	—
276	C₂²×C₃	#389	1	2	yes	—
277	C₂²×C₃	C₂×#108	1	2	yes	—
278	C₂²×C₃	#430	1	2	yes	—
279	C₂²×C₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
280	C₂²×C₃	C₂×#125	1	1	yes	characteristic
281	C₂²×C₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
282	C₃×C₄	—	2	2	no	—
283	C₃×C₄	—	2	2	no	—
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	#389	1	2	yes	—
286	C₃×C₄	#389	1	2	yes	—
287	C₃×C₄	C₂×#108	1	4	yes	complemented
288	C₃×C₄	C₂×C₄×D₄	1	1	yes	characteristic
289	C₃×C₄	C₂×C₄×Q₈	1	1	yes	characteristic
290	C₃×C₄	C₂×#121	1	1	yes	characteristic
291	C₃×C₄	C₂×C₂²⋊Q₈	1	1	yes	characteristic
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	#869	1	2	yes	—
295	C₂³	#870	1	2	yes	—
296	C₂³	C₂×Dic₃⋊C₄	1	1	yes	characteristic
297	C₂³	C₂×Dic₃⋊C₄	1	1	yes	characteristic
298	C₂³	C₂²×Dic₆	1	1	yes	characteristic
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	#822	1	4	yes	complemented
307	C₂×C₄	C₄×Dic₆	1	2	yes	—
308	C₂×C₄	C₄×Dic₆	1	2	yes	—
309	C₂×C₄	#869	1	2	yes	—
310	C₂×C₄	#870	1	2	yes	—
311	C₂×C₄	C₄×D₁₂	1	2	yes	—
312	C₂×C₄	C₄×D₁₂	1	2	yes	—
313	C₂×C₄	C₂×Dic₃⋊C₄	1	2	yes	—
314	C₂×C₄	C₂×Dic₃⋊C₄	1	2	yes	—
315	C₂×C₄	C₂×Dic₃⋊C₄	1	2	yes	—
316	C₂×C₄	C₂×Dic₃⋊C₄	1	2	yes	—
317	C₂×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
318	C₂×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
319	C₂×C₄	#924	1	2	yes	—
320	C₂×C₄	#924	1	2	yes	—
321	C₂×C₄	#930	1	2	yes	—
322	C₂×C₄	#930	1	2	yes	—
323	C₂×C₄	C₂²×Dic₆	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₁₂	1	1	yes	characteristic
326	C₂×C₄	C₂×#235	1	1	yes	characteristic
327	C₂×C₄	C₂×#235	1	1	yes	characteristic
328	C₂×C₄	C₂²×#67	1	1	yes	characteristic
329	C₈	—	2	4	no	—
330	C₈	—	2	4	no	—
331	C₈	—	6	8	no	—
332	C₈	—	12	4	no	—
333	C₂×C₃	—	2	1	no	—
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	—	2	2	no	—
336	C₂×C₃	#1950	1	4	yes	complemented
337	C₂×C₃	C₂×#389	1	1	yes	characteristic
338	C₂×C₃	C₂²×#108	1	1	yes	characteristic
339	C₂×C₃	C₂×#430	1	1	yes	characteristic
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	#4928	1	2	yes	—
347	C₂²	#4928	1	2	yes	—
348	C₂²	C₂×#822	1	2	yes	—
349	C₂²	#5124	1	2	yes	—
350	C₂²	C₂×#869	1	1	yes	characteristic
351	C₂²	C₂×#870	1	1	yes	characteristic
352	C₂²	C₂²×Dic₃⋊C₄	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	#4928	1	2	yes	—
357	C₄	#4928	1	2	yes	—
358	C₄	C₂×#822	1	4	yes	complemented
359	C₄	C₂×C₄×Dic₆	1	1	yes	characteristic
360	C₄	C₂×C₄×D₁₂	1	1	yes	characteristic
361	C₄	C₂×#924	1	1	yes	characteristic
362	C₄	C₂×#930	1	1	yes	characteristic
363	C₃	C₂×#1950	1	1	yes	characteristic, complemented, Sylow
364	C₂	—	2	2	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	#69875	1	4	yes	direct product factor
368	C₂	C₂×#4928	1	1	yes	characteristic
369	C₂	C₂²×#822	1	1	yes	characteristic
370	C₂	C₂×#5124	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×#67
commutator	C₂×C₃×C₄	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₃
Fitting	C₂×C₃×C₄×M₁₆	C₂
socle	C₂³×C₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₃	C₂×Q₈
cosocle	C₂²×C₃×C₄	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₃
hypocenter	C₃	C₂×#1950
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
6. #69875	C₂	direct (N × H)
193. C₂×C₃×C₄	#108	semidirect
287. C₃×C₄	C₂×#108	semidirect
306. C₂×C₄	#822	semidirect
336. C₂×C₃	#1950	semidirect
358. C₄	C₂×#822	semidirect
363. C₃	C₂×#1950	semidirect
367. C₂	#69875	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×C₄×M₁₆	2
C₂²×#822	2
C₂×#4924	2
C₂²×C₄⋊(C₃⋊C₈)	2
C₂×#4558	2
#69875	2
C₂×#1950	3

Subgroups — C2×#69875 #10798707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#69875 #10798707