Subgroups — C₂×#23762763 #34270502

Order 20224.

790 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098942	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098843	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#23762763	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19098315	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19098309	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19098308	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#474×C₇₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11929614	—	2	1	no	—
10	C₂²×#11929614	—	2	1	no	—
11	C₂³×C₇₉⋊C₈	—	2	1	no	—
12	C₂×#14579161	C₂²	1	1	yes	characteristic
13	#19098942	—	2	2	no	—
14	#19098942	C₂²	1	4	yes	complemented
15	#19098843	—	2	2	no	—
16	#19098843	C₂²	1	4	yes	—
17	D₄×C₇₉⋊C₈	—	2	2	no	—
18	D₄×C₇₉⋊C₈	C₂²	1	4	yes	—
19	C₂×#14579094	—	2	1	no	—
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#14579082	—	2	1	no	—
23	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
24	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
25	#19098315	C₂²	1	4	yes	complemented
26	#19098309	C₂²	1	4	yes	complemented
27	#19098308	C₂²	1	4	yes	complemented
28	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
30	#474×C₇₉	—	2	2	no	—
31	#474×C₇₉	C₂²	1	4	yes	—
32	C₂×#107×C₇₉	—	2	1	no	—
33	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#102×C₇₉	—	2	1	no	—
35	C₂²×Dic₁₅₈	—	2	1	no	—
36	C₂×#11929614	—	2	4	no	—
37	C₂×#11929614	—	2	4	no	—
38	C₂×#11929614	—	4	4	no	—
39	C₂×#11929614	—	4	4	no	—
40	C₂²×C₇₉⋊C₈	—	2	1	no	—
41	C₂²×C₇₉⋊C₈	—	2	1	no	—
42	C₂²×C₇₉⋊C₈	—	2	4	no	—
43	C₂²×C₇₉⋊C₈	—	4	4	no	—
44	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
45	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
46	#14579161	—	2	1	no	—
47	#14579161	—	2	1	no	—
48	#14579161	—	2	1	no	—
49	#14579161	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₇₉	—	2	1	no	—
51	C₂×C₄⋊Dic₇₉	—	2	1	no	—
52	#14579094	—	2	4	no	—
53	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
57	#14579082	—	2	4	no	—
58	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
59	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
60	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
61	C₂²×Q₈×C₇₉	—	2	1	no	—
62	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₇₉	—	2	1	no	—
64	C₂²×C₈×C₇₉	—	2	1	no	—
65	C₄⋊Q₈×C₇₉	—	2	1	no	—
66	C₄⋊Q₈×C₇₉	—	2	1	no	—
67	C₄⋊Q₈×C₇₉	—	2	1	no	—
68	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
69	C₄×D₄×C₇₉	—	2	1	no	—
70	C₄×D₄×C₇₉	—	2	1	no	—
71	C₄×D₄×C₇₉	D₄	1	2	yes	—
72	C₄×D₄×C₇₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
77	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
78	#107×C₇₉	—	2	4	no	—
79	C₄⋊C₈×C₇₉	—	2	1	no	—
80	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
81	#102×C₇₉	—	2	4	no	—
82	C₂×Dic₁₅₈	—	2	2	no	—
83	C₂×Dic₁₅₈	—	4	1	no	—
84	C₂×Dic₁₅₈	—	4	2	no	—
85	C₂×Dic₁₅₈	—	4	2	no	—
86	C₂²×Dic₇₉	—	4	1	no	—
87	#11929614	—	4	8	no	—
88	#11929614	—	4	8	no	—
89	C₂×C₇₉⋊C₈	—	2	2	no	—
90	C₂×C₇₉⋊C₈	—	2	2	no	—
91	C₂×C₇₉⋊C₈	—	2	2	no	—
92	C₂×C₇₉⋊C₈	—	4	8	no	—
93	C₂×C₇₉⋊C₈	—	4	2	no	—
94	C₂×C₇₉⋊C₈	—	4	2	no	—
95	C₂×C₇₉⋊C₈	D₈	1	4	yes	—
96	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
97	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
98	C₄⋊Dic₇₉	—	2	2	no	—
99	C₄⋊Dic₇₉	—	2	2	no	—
100	C₄⋊Dic₇₉	—	4	1	no	—
101	C₄⋊Dic₇₉	—	4	1	no	—
102	C₂⁴×C₇₉	—	2	1	no	—
103	C₂×Q₈×C₇₉	—	2	2	no	—
104	C₂×Q₈×C₇₉	—	4	1	no	—
105	C₂×Q₈×C₇₉	—	4	2	no	—
106	C₂×Q₈×C₇₉	—	4	2	no	—
107	C₂×D₄×C₇₉	—	2	1	no	—
108	C₂×D₄×C₇₉	—	2	2	no	—
109	C₂×D₄×C₇₉	Q₁₆	1	4	yes	complemented
110	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₇₉	—	2	1	no	—
112	C₂²×C₄×C₇₉	—	2	2	no	—
113	C₂²×C₄×C₇₉	—	2	2	no	—
114	C₂²×C₄×C₇₉	—	4	2	no	—
115	C₂²×C₄×C₇₉	—	4	2	no	—
116	C₂²×C₄×C₇₉	—	4	1	no	—
117	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
120	C₂×C₈×C₇₉	—	2	2	no	—
121	C₂×C₈×C₇₉	—	4	2	no	—
122	C₄⋊C₄×C₇₉	—	2	1	no	—
123	C₄⋊C₄×C₇₉	—	2	2	no	—
124	C₄⋊C₄×C₇₉	—	2	2	no	—
125	C₄⋊C₄×C₇₉	—	4	1	no	—
126	C₄⋊C₄×C₇₉	—	4	1	no	—
127	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
128	C₂²⋊C₄×C₇₉	—	2	2	no	—
129	C₂²⋊C₄×C₇₉	—	2	2	no	—
130	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₇₉	#41	1	1	yes	characteristic
133	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
134	C₂³×C₇₉	—	2	2	no	—
135	C₂³×C₇₉	—	2	4	no	—
136	C₂³×C₇₉	—	4	2	no	—
137	C₂³×C₇₉	—	4	2	no	—
138	C₂³×C₇₉	#121	1	1	yes	characteristic
139	Q₈×C₇₉	—	4	2	no	—
140	Q₈×C₇₉	—	4	2	no	—
141	Q₈×C₇₉	—	8	2	no	—
142	D₄×C₇₉	—	2	2	no	—
143	D₄×C₇₉	—	2	4	no	—
144	D₄×C₇₉	C₂×Q₁₆	1	4	yes	complemented
145	C₂×C₄×C₇₉	—	2	2	no	—
146	C₂×C₄×C₇₉	—	2	2	no	—
147	C₂×C₄×C₇₉	—	4	2	no	—
148	C₂×C₄×C₇₉	—	4	2	no	—
149	C₂×C₄×C₇₉	—	4	2	no	—
150	C₂×C₄×C₇₉	—	4	4	no	—
151	C₂×C₄×C₇₉	—	4	2	no	—
152	C₂×C₄×C₇₉	—	8	2	no	—
153	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
158	C₂×C₄×C₇₉	#135	1	2	yes	—
159	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
160	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
163	C₂×Dic₇₉	—	4	2	no	—
164	C₂×Dic₇₉	—	8	2	no	—
165	Dic₁₅₈	—	4	2	no	—
166	Dic₁₅₈	—	4	2	no	—
167	Dic₁₅₈	—	8	2	no	—
168	C₈×C₇₉	—	4	2	no	—
169	C₇₉⋊C₈	—	2	2	no	—
170	C₇₉⋊C₈	—	4	2	no	—
171	C₇₉⋊C₈	—	4	2	no	—
172	C₇₉⋊C₈	C₂×D₈	1	4	yes	—
173	C₂²×C₇₉	—	2	4	no	—
174	C₂²×C₇₉	—	4	8	no	—
175	C₂²×C₇₉	—	4	2	no	—
176	C₂²×C₇₉	—	4	2	no	—
177	C₂²×C₇₉	#459	1	2	yes	—
178	C₂²×C₇₉	#467	1	2	yes	—
179	C₂²×C₇₉	#473	1	2	yes	—
180	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
181	C₄×C₇₉	—	2	1	no	—
182	C₄×C₇₉	—	2	1	no	—
183	C₄×C₇₉	—	4	2	no	—
184	C₄×C₇₉	—	8	2	no	—
185	C₄×C₇₉	#459	1	2	yes	—
186	C₄×C₇₉	#467	1	2	yes	—
187	C₄×C₇₉	C₂²×D₈	1	1	yes	characteristic
188	C₄×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
189	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
190	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	Dic₇₉	—	8	2	no	—
192	C₂×#1669	—	79	1	no	maximal, Sylow
193	C₂×C₇₉	—	4	4	no	—
194	C₂×C₇₉	#1669	1	4	yes	complemented
195	C₂×C₇₉	C₂×#459	1	1	yes	characteristic
196	C₂×C₇₉	C₂×#467	1	1	yes	characteristic
197	C₂×C₇₉	C₂×#473	1	1	yes	characteristic
198	C₂×#494	—	79	1	no	—
199	C₂×#474	—	79	1	no	—
200	C₂×#474	D₇₉	1	1	yes	characteristic
201	C₂×C₈×D₄	—	79	1	no	—
202	#1669	—	79	8	no	—
203	C₂×#335	—	79	1	no	—
204	C₂×#332	—	79	1	no	—
205	C₂×#332	—	79	1	no	—
206	C₇₉	C₂×#1669	1	1	yes	characteristic, complemented, Sylow
207	C₂²×Q₁₆	—	158	1	no	—
208	C₂²×Q₁₆	—	158	1	no	—
209	C₂³×C₈	—	158	1	no	—
210	C₂×C₄⋊Q₈	—	79	1	no	—
211	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
213	#494	—	79	4	no	—
214	#494	—	158	2	no	—
215	#474	—	2	2	no	—
216	#474	—	79	4	no	—
217	#474	—	158	2	no	—
218	#474	C₂×D₇₉	1	4	yes	—
219	C₈×D₄	—	79	4	no	—
220	C₈×D₄	—	158	2	no	—
221	C₂×#107	—	2	1	no	—
222	C₂×#107	—	158	1	no	—
223	C₂×C₄⋊C₈	—	79	1	no	—
224	C₂×C₄⋊C₈	—	79	1	no	—
225	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
226	C₂×#102	—	2	1	no	—
227	C₂×#102	—	158	1	no	—
228	C₂×C₂²⋊C₈	—	158	1	no	—
229	C₂×C₄×C₈	—	79	1	no	—
230	#335	—	79	4	no	—
231	#332	—	79	4	no	—
232	#332	—	79	4	no	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	—	158	1	no	—
235	C₂²×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
236	C₂³×C₄	—	2	1	no	—
237	C₂×Q₁₆	—	316	4	no	—
238	C₂×Q₁₆	—	316	4	no	—
239	C₂×Q₁₆	—	158	4	no	—
240	C₂×Q₁₆	—	158	4	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	316	4	no	—
243	C₂²×C₈	—	79	1	no	—
244	C₂²×C₈	—	79	1	no	—
245	C₂²×C₈	—	158	4	no	—
246	C₂²×C₈	—	158	1	no	—
247	C₂²×C₈	—	158	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	79	2	no	—
252	C₄⋊Q₈	—	158	1	no	—
253	C₄⋊Q₈	—	158	1	no	—
254	C₄⋊Q₈	—	158	1	no	—
255	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	C₂²⋊D₇₉	1	2	yes	—
259	C₄×D₄	C₂²×D₇₉	1	2	yes	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	158	1	no	—
263	C₂×C₄⋊C₄	—	158	1	no	—
264	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
267	#107	—	2	4	no	—
268	#107	—	158	4	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	79	2	no	—
271	C₄⋊C₈	—	79	2	no	—
272	C₄⋊C₈	—	158	1	no	—
273	C₄⋊C₈	—	158	1	no	—
274	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
275	#102	—	2	4	no	—
276	#102	—	158	4	no	—
277	C₂²⋊C₈	—	158	4	no	—
278	C₄×C₈	—	79	2	no	—
279	C₄×C₈	—	79	2	no	—
280	C₂⁴	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	316	1	no	—
286	C₂×Q₈	—	316	2	no	—
287	C₂×Q₈	—	316	2	no	—
288	C₂×Q₈	—	158	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	#11929614	1	4	yes	complemented
292	C₂×D₄	C₂×C₂²⋊D₇₉	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	316	1	no	—
300	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
302	C₂²×C₄	#11929623	1	1	yes	characteristic
303	Q₁₆	—	316	8	no	—
304	Q₁₆	—	316	8	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	316	2	no	—
308	C₂×C₈	—	316	2	no	—
309	C₂×C₈	—	316	8	no	—
310	C₂×C₈	—	79	4	no	—
311	C₂×C₈	—	79	2	no	—
312	C₂×C₈	—	79	2	no	—
313	C₂×C₈	—	158	2	no	—
314	C₂×C₈	—	158	2	no	—
315	C₂×C₈	—	158	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	316	1	no	—
322	C₄⋊C₄	—	316	1	no	—
323	C₄⋊C₄	—	158	2	no	—
324	C₄⋊C₄	—	158	2	no	—
325	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₄²	D₄×D₇₉	1	1	yes	characteristic
329	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
330	C₄²	#11929623	1	1	yes	characteristic
331	C₄²	C₂³×D₇₉	1	1	yes	characteristic
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	#14579133	1	1	yes	characteristic
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	8	2	no	—
340	Q₈	—	316	2	no	—
341	Q₈	—	316	2	no	—
342	Q₈	—	632	2	no	—
343	D₄	—	2	4	no	—
344	D₄	—	2	2	no	—
345	D₄	C₂×#11929614	1	4	yes	complemented
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	—	316	2	no	—
355	C₂×C₄	—	632	2	no	—
356	C₂×C₄	#14579133	1	1	yes	characteristic
357	C₂×C₄	#14579133	1	1	yes	characteristic
358	C₂×C₄	#14579133	1	1	yes	characteristic
359	C₂×C₄	D₈×D₇₉	1	2	yes	—
360	C₂×C₄	C₂×#11929614	1	2	yes	—
361	C₂×C₄	#14579181	1	2	yes	—
362	C₂×C₄	#14579185	1	2	yes	—
363	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
365	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
366	C₈	—	4	2	no	—
367	C₈	—	316	2	no	—
368	C₈	—	316	2	no	—
369	C₈	—	79	4	no	—
370	C₈	—	158	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	#19098756	1	2	yes	—
376	C₂²	#19098802	1	2	yes	—
377	C₂²	#19098836	1	2	yes	—
378	C₂²	C₂×#14579133	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	632	2	no	—
384	C₄	#19098756	1	2	yes	—
385	C₄	#19098802	1	2	yes	—
386	C₄	C₂×D₈×D₇₉	1	1	yes	characteristic
387	C₄	C₂²×#11929614	1	1	yes	characteristic
388	C₄	C₂×#14579181	1	1	yes	characteristic
389	C₄	C₂×#14579185	1	1	yes	characteristic
390	C₂	—	4	4	no	—
391	C₂	#23762763	1	4	yes	direct product factor
392	C₂	C₂×#19098756	1	1	yes	characteristic
393	C₂	C₂×#19098802	1	1	yes	characteristic
394	C₂	C₂×#19098836	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579133
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₂×#474×C₇₉	C₂
socle	C₂³×C₇₉	#121
prime radical	C₂²×D₄×C₇₉	D₄
hypercenter	C₂×#474	D₇₉
hypocenter	C₇₉	C₂×#1669
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#474

Complements

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

N	H ≅ G/N	type
1. C₂×#19098942	C₂	semidirect
4. #23762763	C₂	direct (N × H)
5. C₂×#19098315	C₂	semidirect
6. C₂×#19098309	C₂	semidirect
7. C₂×#19098308	C₂	semidirect
14. #19098942	C₂²	semidirect
25. #19098315	C₂²	semidirect
26. #19098309	C₂²	semidirect
27. #19098308	C₂²	semidirect
109. C₂×D₄×C₇₉	Q₁₆	semidirect
144. D₄×C₇₉	C₂×Q₁₆	semidirect
194. C₂×C₇₉	#1669	semidirect
206. C₇₉	C₂×#1669	semidirect
291. C₂×D₄	#11929614	semidirect
345. D₄	C₂×#11929614	semidirect
391. C₂	#23762763	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×#19098942	2
C₂×#19098843	2
C₂×D₄×C₇₉⋊C₈	2
#23762763	2
C₂×#19098315	2
C₂×#19098309	2
C₂×#19098308	2
C₂×#474×C₇₉	2
C₂×#1669	79

Subgroups — C2×#23762763 #34270502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23762763 #34270502