Subgroups — #107×D₃₅₆ #36572547

Order 22784.

1126 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#107×D₈₉	C₂	1	2	yes	maximal, complemented
3	C₄⋊C₄×D₃₅₆	C₂	1	2	yes	maximal
4	#26021010	C₂	1	2	yes	maximal, complemented
5	#26020441	C₂	1	4	yes	maximal, complemented
6	#26020412	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020278	C₂	1	2	yes	maximal, complemented
8	C₄×#107×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₈×D₈₉	C₂²	1	2	yes	—
10	C₂×C₄×D₃₅₆	—	2	2	no	—
11	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×D₈₉	C₂²	1	4	yes	—
13	C₈×D₃₅₆	C₄	1	8	yes	complemented
14	C₂×#15667946	C₂²	1	2	yes	—
15	C₂×#15667946	C₂²	1	2	yes	—
16	C₂×#15667945	C₂²	1	4	yes	—
17	#107×D₈₉	—	2	8	no	—
18	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
19	C₂×#15667924	C₂²	1	2	yes	—
20	#19151496	—	2	2	no	—
21	#19151472	—	2	4	no	—
22	#19151468	C₂²	1	2	yes	—
23	#19151455	C₂²	1	4	yes	—
24	#19151360	C₂²	1	4	yes	—
25	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
29	#340×C₈₉	C₂²	1	2	yes	—
30	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₈₉	—	2	4	no	—
32	C₂²×C₄×D₈₉	C₂³	1	2	yes	—
33	C₂²×#10623494	C₂³	1	2	yes	—
34	C₂×C₈×D₈₉	—	2	4	no	—
35	C₂×C₈×D₈₉	—	2	4	no	—
36	C₂×C₈×D₈₉	C₂×C₄	1	8	yes	complemented
37	C₄×D₃₅₆	—	4	8	no	—
38	C₄×D₃₅₆	C₂×C₄	1	4	yes	—
39	C₄×D₃₅₆	Q₈	1	4	yes	—
40	C₂×C₄⋊Dic₈₉	—	2	2	no	—
41	C₂×C₄⋊Dic₈₉	—	2	2	no	—
42	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₈₉	C₂³	1	4	yes	—
44	C₂×#13083553	—	2	4	no	—
45	C₄⋊C₄×D₈₉	—	2	8	no	—
46	C₄⋊C₄×D₈₉	—	4	4	no	—
47	C₂×#13083551	—	2	4	no	—
48	C₂×#13083551	D₄	1	2	yes	—
49	#15667946	—	2	4	no	—
50	#15667946	—	4	2	no	—
51	#15667945	—	2	8	no	—
52	C₄⋊#10623494	C₂×C₄	1	4	yes	complemented
53	#15667924	C₂×C₄	1	8	yes	complemented
54	#15667919	—	2	4	no	—
55	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
59	C₂×C₄²×C₈₉	—	2	2	no	—
60	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
61	#107×C₈₉	—	2	2	no	—
62	#107×C₈₉	D₄	1	4	yes	complemented
63	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	complemented
64	#95×C₈₉	—	2	2	no	—
65	C₂³×D₈₉	C₂×D₄	1	2	yes	—
66	C₂×D₃₅₆	C₄⋊C₄	1	4	yes	—
67	C₂×D₃₅₆	D₈	1	4	yes	—
68	C₂×D₃₅₆	Q₁₆	1	4	yes	—
69	C₂²×Dic₈₉	—	2	4	no	—
70	C₂²×Dic₈₉	C₂×D₄	1	2	yes	—
71	C₂×C₄×D₈₉	—	2	2	no	—
72	C₂×C₄×D₈₉	—	2	2	no	—
73	C₂×C₄×D₈₉	—	2	2	no	—
74	C₂×C₄×D₈₉	—	2	2	no	—
75	C₂×C₄×D₈₉	—	4	8	no	—
76	C₂×C₄×D₈₉	—	4	8	no	—
77	C₂×C₄×D₈₉	—	8	4	no	—
78	C₂×C₄×D₈₉	C₂²×C₄	1	4	yes	—
79	C₂×C₄×D₈₉	C₂×Q₈	1	4	yes	—
80	C₂×#10623494	—	2	2	no	—
81	C₂×#10623494	—	2	2	no	—
82	C₂×#10623494	C₂²×C₄	1	4	yes	—
83	C₈×D₈₉	—	2	16	no	—
84	C₄⋊Dic₈₉	—	2	4	no	—
85	C₄⋊Dic₈₉	—	2	4	no	—
86	C₄⋊Dic₈₉	—	4	4	no	—
87	C₄⋊Dic₈₉	—	8	2	no	—
88	C₄⋊Dic₈₉	C₄⋊C₄	1	4	yes	—
89	#13083553	—	4	8	no	—
90	#13083551	—	4	8	no	—
91	#13083551	C₄⋊C₄	1	8	yes	—
92	C₂²×C₄×C₈₉	—	2	2	no	—
93	C₂²×C₄×C₈₉	—	2	2	no	—
94	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₈₉	—	2	1	no	—
98	C₂×C₈×C₈₉	—	2	1	no	—
99	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₈₉	#41	1	2	yes	—
103	C₄⋊C₄×C₈₉	—	2	2	no	—
104	C₄⋊C₄×C₈₉	—	2	2	no	—
105	C₄⋊C₄×C₈₉	—	2	2	no	—
106	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
107	C₄²×C₈₉	—	4	4	no	—
108	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
109	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
110	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
111	C₂²×D₈₉	—	2	2	no	—
112	C₂²×D₈₉	—	2	2	no	—
113	C₂²×D₈₉	—	2	2	no	—
114	C₂²×D₈₉	—	2	2	no	—
115	C₂²×D₈₉	C₂×C₄⋊C₄	1	4	yes	—
116	C₂²×D₈₉	C₂×D₈	1	4	yes	—
117	C₂²×D₈₉	C₂×Q₁₆	1	4	yes	—
118	C₂×C₄×C₈₉	—	2	1	no	—
119	C₂×C₄×C₈₉	—	2	1	no	—
120	C₂×C₄×C₈₉	—	2	4	no	—
121	C₂×C₄×C₈₉	—	4	2	no	—
122	C₂×C₄×C₈₉	—	4	2	no	—
123	C₂×C₄×C₈₉	—	4	2	no	—
124	C₂×C₄×C₈₉	—	4	2	no	—
125	C₂×C₄×C₈₉	—	4	2	no	—
126	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
129	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
130	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
134	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
135	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
136	C₂×Dic₈₉	—	2	2	no	—
137	C₂×Dic₈₉	—	2	2	no	—
138	C₂×Dic₈₉	—	4	4	no	—
139	C₂×Dic₈₉	—	4	4	no	—
140	C₂×Dic₈₉	—	4	4	no	—
141	C₂×Dic₈₉	C₂×C₄⋊C₄	1	4	yes	—
142	D₃₅₆	#107	1	16	yes	direct product factor
143	C₄×D₈₉	—	2	4	no	—
144	C₄×D₈₉	—	2	4	no	—
145	C₄×D₈₉	—	2	4	no	—
146	C₄×D₈₉	—	2	4	no	—
147	C₄×D₈₉	—	8	16	no	—
148	C₈×C₈₉	—	2	2	no	—
149	C₈×C₈₉	C₄×D₄	1	4	yes	complemented
150	#10623494	—	2	4	no	—
151	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
152	C₂²×C₈₉	D₄²	1	1	yes	characteristic
153	C₂²×C₈₉	#547	1	1	yes	characteristic
154	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
155	C₂²×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
156	C₂²×C₈₉	#576	1	1	yes	characteristic
157	C₂²×C₈₉	#578	1	1	yes	characteristic
158	C₂×D₈₉	—	2	4	no	—
159	C₂×D₈₉	—	2	4	no	—
160	C₂×D₈₉	—	2	4	no	—
161	C₂×D₈₉	—	2	4	no	—
162	C₂×D₈₉	—	2	4	no	—
163	C₂×D₈₉	—	2	4	no	—
164	C₂×D₈₉	C₂×#107	1	8	yes	complemented
165	C₄×C₈₉	—	2	2	no	—
166	C₄×C₈₉	—	4	4	no	—
167	C₄×C₈₉	—	8	2	no	—
168	C₄×C₈₉	C₂×#107	1	4	yes	complemented
169	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
170	C₄×C₈₉	#520	1	1	yes	characteristic
171	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
172	C₄×C₈₉	#554	1	1	yes	characteristic
173	Dic₈₉	—	2	4	no	—
174	Dic₈₉	—	8	4	no	—
175	D₄×#107	—	89	1	no	maximal, Sylow
176	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₈₉	C₂²×#107	1	1	yes	characteristic
178	C₂×C₈₉	#2913	1	1	yes	characteristic
179	C₂×C₈₉	D₄×D₈	1	1	yes	characteristic
180	C₂×C₈₉	D₄×Q₁₆	1	1	yes	characteristic
181	C₂×C₈₉	#3334	1	1	yes	characteristic
182	C₂×C₈₉	#3338	1	1	yes	characteristic
183	D₈₉	—	2	8	no	—
184	C₂×C₈×D₄	—	89	1	no	—
185	C₂²×#107	—	89	2	no	—
186	D₄×C₄⋊C₄	—	89	2	no	—
187	#1947	—	89	2	no	—
188	#1852	—	89	4	no	—
189	#1845	—	89	1	no	—
190	#1808	—	89	2	no	—
191	C₄×#107	D₈₉	1	1	yes	characteristic, complemented
192	C₈₉	D₄×#107	1	1	yes	characteristic, complemented, Sylow
193	C₂³×C₈	—	89	2	no	—
194	C₂×C₄×D₄	—	89	1	no	—
195	C₂×C₄×D₄	—	178	2	no	—
196	C₂²×C₄⋊C₄	—	89	4	no	—
197	C₈×D₄	—	89	8	no	—
198	C₂×#107	—	89	2	no	—
199	C₂×#107	—	89	2	no	—
200	C₂×#107	—	89	4	no	—
201	C₂×#107	—	178	8	no	—
202	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
203	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
204	C₂×C₄⋊C₈	—	89	1	no	—
205	C₂×C₂²⋊C₈	—	89	2	no	—
206	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
207	#389	—	178	2	no	—
208	#385	—	178	4	no	—
209	#384	—	89	2	no	—
210	#380	—	89	4	no	—
211	C₄×C₄⋊C₄	C₂×D₈₉	1	2	yes	—
212	#340	—	89	4	no	—
213	#340	C₂×D₈₉	1	2	yes	—
214	C₂²×D₄	—	89	1	no	—
215	C₂³×C₄	—	89	2	no	—
216	C₂³×C₄	—	178	4	no	—
217	C₂²×C₈	—	89	2	no	—
218	C₂²×C₈	—	89	8	no	—
219	C₂²×C₈	—	178	4	no	—
220	C₂²×C₈	—	178	4	no	—
221	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
222	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
223	C₄×D₄	—	89	4	no	—
224	C₄×D₄	—	89	4	no	—
225	C₄×D₄	—	356	8	no	—
226	C₂×C₄⋊C₄	—	89	1	no	—
227	C₂×C₄⋊C₄	—	89	4	no	—
228	C₂×C₄⋊C₄	—	356	4	no	—
229	C₂×C₄⋊C₄	—	178	4	no	—
230	C₂×C₄⋊C₄	—	178	2	no	—
231	C₂×C₄⋊C₄	—	178	8	no	—
232	C₂×C₄⋊C₄	—	178	2	no	—
233	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
235	C₂×C₂²⋊C₄	—	89	2	no	—
236	C₂×C₂²⋊C₄	—	178	4	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
239	#107	—	2	2	no	—
240	#107	—	356	2	no	—
241	#107	—	178	4	no	—
242	#107	—	178	8	no	—
243	#107	D₃₅₆	1	4	yes	direct product factor
244	C₄⋊C₈	—	89	4	no	—
245	C₂²⋊C₈	—	89	8	no	—
246	C₄×C₈	C₄×D₈₉	1	4	yes	complemented
247	#95	—	2	2	no	—
248	#95	—	178	4	no	—
249	C₂⁴	—	89	2	no	—
250	C₂×D₄	—	89	4	no	—
251	C₂×D₄	—	89	4	no	—
252	C₂×D₄	—	89	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	89	2	no	—
256	C₂²×C₄	—	89	4	no	—
257	C₂²×C₄	—	89	4	no	—
258	C₂²×C₄	—	356	8	no	—
259	C₂²×C₄	—	356	8	no	—
260	C₂²×C₄	—	178	4	no	—
261	C₂²×C₄	—	178	2	no	—
262	C₂²×C₄	—	178	2	no	—
263	C₂²×C₄	—	178	2	no	—
264	C₂²×C₄	—	178	2	no	—
265	C₂²×C₄	—	712	4	no	—
266	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
267	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
268	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	89	4	no	—
272	C₂×C₈	—	178	2	no	—
273	C₂×C₈	—	178	2	no	—
274	C₂×C₈	—	178	16	no	—
275	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
276	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
277	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
278	C₂×C₈	#13083574	1	2	yes	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	89	4	no	—
283	C₄⋊C₄	—	356	8	no	—
284	C₄⋊C₄	—	356	4	no	—
285	C₄⋊C₄	—	178	4	no	—
286	C₄⋊C₄	—	178	4	no	—
287	C₄⋊C₄	—	712	2	no	—
288	C₄⋊C₄	C₂×D₃₅₆	1	4	yes	—
289	C₂²⋊C₄	—	89	8	no	—
290	C₂²⋊C₄	—	356	8	no	—
291	C₄²	—	4	4	no	—
292	C₄²	C₂×C₄×D₈₉	1	2	yes	—
293	C₄²	Q₈×D₈₉	1	2	yes	—
294	C₂³	—	89	4	no	—
295	C₂³	—	89	4	no	—
296	C₂³	—	89	4	no	—
297	C₂³	—	178	2	no	—
298	C₂³	—	178	2	no	—
299	C₂³	—	178	2	no	—
300	C₂³	—	178	2	no	—
301	C₂³	C₂×D₄×D₈₉	1	1	yes	characteristic
302	D₄	—	89	16	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	89	4	no	—
312	C₂×C₄	—	356	4	no	—
313	C₂×C₄	—	356	4	no	—
314	C₂×C₄	—	356	4	no	—
315	C₂×C₄	—	178	2	no	—
316	C₂×C₄	—	178	2	no	—
317	C₂×C₄	—	178	4	no	—
318	C₂×C₄	—	178	4	no	—
319	C₂×C₄	—	178	4	no	—
320	C₂×C₄	—	178	4	no	—
321	C₂×C₄	—	712	16	no	—
322	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
323	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
324	C₂×C₄	D₈×D₈₉	1	2	yes	—
325	C₂×C₄	Q₁₆×D₈₉	1	2	yes	—
326	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
327	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
328	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
329	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
330	C₂×C₄	#15668058	1	1	yes	characteristic
331	C₂×C₄	#15668059	1	1	yes	characteristic
332	C₈	—	2	2	no	—
333	C₈	—	178	4	no	—
334	C₈	C₄×D₃₅₆	1	4	yes	complemented
335	C₂²	—	89	8	no	—
336	C₂²	—	178	4	no	—
337	C₂²	—	178	4	no	—
338	C₂²	—	178	4	no	—
339	C₂²	—	178	4	no	—
340	C₂²	—	178	4	no	—
341	C₂²	—	178	4	no	—
342	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
343	C₂²	D₄×D₃₅₆	1	1	yes	characteristic
344	C₂²	#19152253	1	1	yes	characteristic
345	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
346	C₂²	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
347	C₂²	#19152400	1	1	yes	characteristic
348	C₂²	#19152412	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	4	4	no	—
351	C₄	—	8	2	no	—
352	C₄	—	178	4	no	—
353	C₄	—	712	4	no	—
354	C₄	#107×D₈₉	1	4	yes	complemented
355	C₄	C₂×C₄×D₃₅₆	1	1	yes	characteristic
356	C₄	#19152078	1	1	yes	characteristic
357	C₄	Q₈×D₃₅₆	1	1	yes	characteristic
358	C₄	#19152308	1	1	yes	characteristic
359	C₂	—	178	8	no	—
360	C₂	C₄⋊C₄×D₃₅₆	1	1	yes	characteristic
361	C₂	C₂×#107×D₈₉	1	1	yes	characteristic
362	C₂	#26028849	1	1	yes	characteristic
363	C₂	D₈×D₃₅₆	1	1	yes	characteristic
364	C₂	Q₁₆×D₃₅₆	1	1	yes	characteristic
365	C₂	#26032601	1	1	yes	characteristic
366	C₂	#26032646	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#107×C₈₉	C₂
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂²×D₃₅₆	D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#107	D₈₉
hypocenter	C₈₉	D₄×#107
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
2. C₂×#107×D₈₉	C₂	semidirect
4. #26021010	C₂	semidirect
5. #26020441	C₂	semidirect
6. #26020412	C₂	semidirect
7. #26020278	C₂	semidirect
8. C₄×#107×C₈₉	C₂	semidirect
13. C₈×D₃₅₆	C₄	semidirect
36. C₂×C₈×D₈₉	C₂×C₄	semidirect
52. C₄⋊#10623494	C₂×C₄	semidirect
53. #15667924	C₂×C₄	semidirect
62. #107×C₈₉	D₄	semidirect
63. C₄×C₈×C₈₉	C₂×C₄	semidirect
142. D₃₅₆	#107	direct (N × H)
149. C₈×C₈₉	C₄×D₄	semidirect
164. C₂×D₈₉	C₂×#107	semidirect
168. C₄×C₈₉	C₂×#107	semidirect
191. C₄×#107	D₈₉	semidirect
192. C₈₉	D₄×#107	semidirect
243. #107	D₃₅₆	direct (N × H)
246. C₄×C₈	C₄×D₈₉	semidirect
334. C₈	C₄×D₃₅₆	semidirect
354. C₄	#107×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₃₅₆	2
C₂×#107×D₈₉	2
C₄⋊C₄×D₃₅₆	2
#26021010	2
#26020441	2
#26020412	2
#26020278	2
C₄×#107×C₈₉	2
D₄×#107	89

Subgroups — #107×D356 #36572547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #107×D₃₅₆ #36572547