Subgroups — #34347174

Order 20224.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773258	C₂	1	2	yes	maximal
2	#23771997	C₂	1	1	yes	maximal, characteristic
3	#23764913	C₂	1	2	yes	maximal, complemented
4	#23764747	C₂	1	2	yes	maximal, complemented
5	#23764185	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764149	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763630	C₂	1	2	yes	maximal
8	#23763563	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763465	C₂	1	1	yes	maximal, characteristic
10	#23763239	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579167	C₂²	1	1	yes	characteristic
13	#19099043	C₂²	1	2	yes	—
14	#19098867	—	2	2	no	—
15	#19098860	—	2	2	no	—
16	#19098850	—	2	2	no	—
17	#19098845	—	2	2	no	—
18	C₂×#14579097	C₂²	1	1	yes	characteristic
19	#19098606	C₂²	1	2	yes	—
20	#19098606	C₂²	1	2	yes	—
21	#19098602	—	2	2	no	—
22	#19098600	—	2	1	no	—
23	C₂×#14579095	C₂²	1	1	yes	characteristic
24	#107×D₇₉	—	2	1	no	—
25	C₂×#14579092	C₂²	1	2	yes	—
26	#19098590	C₂²	1	2	yes	—
27	C₂×#14579087	C₂²	1	1	yes	characteristic
28	#19098562	C₂²	1	2	yes	—
29	#19098557	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
31	#19098428	C₂²	1	2	yes	—
32	#19098332	C₂²	1	2	yes	—
33	#19098331	C₂²	1	2	yes	—
34	#19098327	C₂²	1	1	yes	characteristic
35	#19098322	C₂²	1	1	yes	characteristic
36	#19098322	C₂²	1	2	yes	—
37	#544×C₇₉	C₂²	1	2	yes	—
38	#501×C₇₉	—	2	2	no	—
39	#500×C₇₉	—	2	1	no	—
40	#499×C₇₉	—	2	1	no	—
41	#428×C₇₉	C₂²	1	2	yes	—
42	#427×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
44	#405×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×#11929624	C₂³	1	1	yes	characteristic
46	#14579167	—	2	2	no	—
47	#14579167	Q₈	1	4	yes	complemented
48	C₂×#11929608	C₂³	1	2	yes	—
49	C₂×#11929608	C₂³	1	1	yes	characteristic
50	C₂×#11929607	—	2	1	no	—
51	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₇₉	—	2	1	no	—
53	C₄×Dic₁₅₈	—	2	2	no	—
54	C₄×D₃₁₆	—	2	2	no	—
55	(C₂²⋊D₇₉)⋊C₄	—	4	2	no	—
56	#14579119	—	2	2	no	—
57	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
58	C₄⋊C₄×D₇₉	—	2	2	no	—
59	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
60	#14579097	—	2	2	no	—
61	#14579095	—	2	1	no	—
62	#14579095	—	2	1	no	—
63	#14579094	—	2	2	no	—
64	#14579094	—	2	2	no	—
65	#14579092	—	2	2	no	—
66	#14579092	—	2	2	no	—
67	#14579092	—	2	2	no	—
68	#14579092	—	2	2	no	—
69	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
70	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
71	#14579087	Q₈	1	4	yes	complemented
72	#14579084	—	2	2	no	—
73	#14579084	D₄	1	1	yes	characteristic
74	#14579084	D₄	1	1	yes	characteristic
75	#14579081	—	2	2	no	—
76	#14579081	D₄	1	1	yes	characteristic
77	#14579081	D₄	1	1	yes	characteristic
78	C₈×Dic₇₉	—	2	2	no	—
79	C₇₉⋊#95	—	4	2	no	—
80	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₇₉	—	2	2	no	—
83	C₄⋊Q₈×C₇₉	—	2	2	no	—
84	#125×C₇₉	—	2	2	no	—
85	#125×C₇₉	—	2	2	no	—
86	C₂²⋊Q₈×C₇₉	—	4	2	no	—
87	#117×C₇₉	C₂³	1	2	yes	—
88	#117×C₇₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
90	#107×C₇₉	—	2	1	no	—
91	#107×C₇₉	—	2	1	no	—
92	#107×C₇₉	—	2	2	no	—
93	#107×C₇₉	D₄	1	1	yes	characteristic
94	#107×C₇₉	D₄	1	1	yes	characteristic
95	#106×C₇₉	—	2	2	no	—
96	#106×C₇₉	D₄	1	2	yes	—
97	#97×C₇₉	—	2	1	no	—
98	C₄×C₈×C₇₉	—	2	1	no	—
99	#11929624	—	2	1	no	—
100	#11929624	—	2	1	no	—
101	#11929624	C₂×Q₈	1	2	yes	—
102	#11929624	C₂×Q₈	1	2	yes	—
103	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
104	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
105	C₂×C₂²⋊D₇₉	—	2	1	no	—
106	C₂²×Dic₇₉	—	2	1	no	—
107	C₂²×Dic₇₉	—	2	2	no	—
108	C₂×C₄×D₇₉	—	2	1	no	—
109	C₂×C₄×D₇₉	—	4	2	no	—
110	#11929608	—	2	1	no	—
111	#11929608	—	2	2	no	—
112	#11929608	—	2	2	no	—
113	#11929608	C₂×Q₈	1	2	yes	—
114	#11929607	—	2	4	no	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	—	2	2	no	—
117	C₂×C₇₉⋊C₈	—	2	1	no	—
118	C₂×C₇₉⋊C₈	—	2	1	no	—
119	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
121	C₈×D₇₉	—	2	4	no	—
122	C₄⋊Dic₇₉	—	2	2	no	—
123	C₄⋊Dic₇₉	—	2	2	no	—
124	Dic₇₉⋊C₄	—	4	2	no	—
125	(C₂×D₇₉)⋊C₄	—	4	2	no	—
126	C₄×Dic₇₉	—	2	1	no	—
127	C₄×Dic₇₉	—	4	2	no	—
128	C₄×Dic₇₉	C₂×Q₈	1	2	yes	—
129	C₂×Q₈×C₇₉	—	4	2	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
132	M₁₆×C₇₉	—	2	1	no	—
133	M₁₆×C₇₉	C₂×Q₈	1	2	yes	—
134	C₂×C₈×C₇₉	—	2	1	no	—
135	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
138	C₂×C₈×C₇₉	#41	1	2	yes	—
139	C₄⋊C₄×C₇₉	—	2	2	no	—
140	C₄⋊C₄×C₇₉	—	2	2	no	—
141	C₄⋊C₄×C₇₉	—	4	2	no	—
142	C₄⋊C₄×C₇₉	—	4	2	no	—
143	C₄⋊C₄×C₇₉	—	4	2	no	—
144	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₇₉	—	2	1	no	—
149	C₂²⋊C₄×C₇₉	—	2	2	no	—
150	C₄²×C₇₉	—	2	1	no	—
151	C₄²×C₇₉	—	2	2	no	—
152	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂²×D₇₉	—	2	1	no	—
154	Q₈×C₇₉	—	16	2	no	—
155	C₂×C₄×C₇₉	—	2	2	no	—
156	C₂×C₄×C₇₉	—	2	2	no	—
157	C₂×C₄×C₇₉	—	2	1	no	—
158	C₂×C₄×C₇₉	—	2	1	no	—
159	C₂×C₄×C₇₉	—	4	2	no	—
160	C₂×C₄×C₇₉	—	8	2	no	—
161	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂²⋊D₇₉	—	2	2	no	—
168	C₂²⋊D₇₉	—	2	2	no	—
169	C₂×Dic₇₉	—	2	1	no	—
170	C₂×Dic₇₉	—	2	2	no	—
171	C₂×Dic₇₉	—	4	1	no	—
172	C₂×Dic₇₉	—	4	1	no	—
173	C₂×Dic₇₉	—	4	2	no	—
174	C₂×Dic₇₉	—	8	2	no	—
175	D₃₁₆	—	2	1	no	—
176	D₃₁₆	C₄⋊Q₈	1	2	yes	—
177	C₄×D₇₉	—	2	2	no	—
178	C₄×D₇₉	—	2	2	no	—
179	C₄×D₇₉	—	16	2	no	—
180	Dic₁₅₈	—	2	1	no	—
181	Dic₁₅₈	C₄⋊Q₈	1	2	yes	—
182	C₈×C₇₉	—	2	2	no	—
183	C₈×C₇₉	C₂²⋊Q₈	1	2	yes	—
184	C₈×C₇₉	C₂²⋊Q₈	1	2	yes	—
185	C₇₉⋊C₈	—	2	2	no	—
186	C₇₉⋊C₈	—	2	1	no	—
187	C₇₉⋊C₈	—	2	1	no	—
188	C₇₉⋊C₈	—	4	2	no	—
189	C₂²×C₇₉	—	2	1	no	—
190	C₂²×C₇₉	—	2	1	no	—
191	C₂²×C₇₉	#544	1	1	yes	characteristic
192	C₂²×C₇₉	D₄²	1	1	yes	characteristic
193	C₂²×C₇₉	#554	1	1	yes	characteristic
194	C₂×D₇₉	—	2	2	no	—
195	C₂×D₇₉	—	4	1	no	—
196	C₂×D₇₉	—	4	1	no	—
197	C₄×C₇₉	—	4	1	no	—
198	C₄×C₇₉	—	4	2	no	—
199	C₄×C₇₉	—	4	1	no	—
200	C₄×C₇₉	—	4	2	no	—
201	C₄×C₇₉	—	8	2	no	—
202	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
203	C₄×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
204	C₄×C₇₉	#547	1	1	yes	characteristic
205	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
206	Dic₇₉	—	2	2	no	—
207	Dic₇₉	—	4	2	no	—
208	Dic₇₉	—	8	2	no	—
209	#26082	—	79	1	no	maximal, Sylow
210	C₂×C₇₉	—	2	1	no	—
211	C₂×C₇₉	—	2	1	no	—
212	C₂×C₇₉	#2440	1	1	yes	characteristic
213	C₂×C₇₉	#3290	1	1	yes	characteristic
214	C₂×C₇₉	#3290	1	1	yes	characteristic
215	D₇₉	—	4	2	no	—
216	#3164	D₇₉	1	1	yes	characteristic, complemented
217	#3084	—	79	2	no	—
218	#2913	—	79	1	no	—
219	#2090	—	79	2	no	—
220	#2061	—	79	2	no	—
221	#1952	—	79	1	no	—
222	#1945	—	79	1	no	—
223	#1860	—	79	2	no	—
224	#1846	—	79	1	no	—
225	#1816	—	79	1	no	—
226	#1764	—	79	1	no	—
227	C₇₉	#26082	1	1	yes	characteristic, complemented, Sylow
228	C₂×#131	—	79	1	no	—
229	#544	C₂×D₇₉	1	2	yes	—
230	#520	—	79	2	no	—
231	#501	—	2	2	no	—
232	#500	—	2	1	no	—
233	#499	—	2	1	no	—
234	#479	—	158	2	no	—
235	#478	—	158	2	no	—
236	#476	—	158	2	no	—
237	#475	—	158	2	no	—
238	C₂×#108	—	79	1	no	—
239	#428	—	79	2	no	—
240	#428	—	79	2	no	—
241	#428	—	158	2	no	—
242	#428	C₂×D₇₉	1	2	yes	—
243	#427	—	158	1	no	—
244	#427	C₂×D₇₉	1	1	yes	characteristic
245	C₂×#107	—	79	1	no	—
246	C₂×#107	—	158	1	no	—
247	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
248	C₂×#106	—	79	2	no	—
249	#424	—	79	2	no	—
250	C₂×#104	—	79	1	no	—
251	#417	—	79	2	no	—
252	#416	—	79	1	no	—
253	#405	C₂×D₇₉	1	1	yes	characteristic
254	C₂×C₄×C₈	—	79	1	no	—
255	#382	—	79	2	no	—
256	#343	—	79	2	no	—
257	#343	—	79	2	no	—
258	#341	—	79	1	no	—
259	#339	—	79	1	no	—
260	#339	—	79	2	no	—
261	C₂×#41	—	79	1	no	—
262	#131	—	79	4	no	—
263	#131	—	158	2	no	—
264	C₂×M₁₆	—	79	1	no	—
265	C₂×M₁₆	—	79	2	no	—
266	C₂×M₁₆	—	158	1	no	—
267	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
268	C₂²×C₈	—	79	1	no	—
269	C₂²×C₈	—	158	1	no	—
270	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	2	2	no	—
273	#125	—	2	2	no	—
274	#125	—	2	2	no	—
275	C₂²⋊Q₈	—	4	2	no	—
276	C₄×Q₈	—	158	2	no	—
277	C₄×D₄	—	316	2	no	—
278	C₄×D₄	—	158	2	no	—
279	#117	—	158	2	no	—
280	#117	C₂²×D₇₉	1	1	yes	characteristic
281	#117	C₂²×D₇₉	1	2	yes	—
282	C₂×C₄⋊C₄	—	79	2	no	—
283	C₂×C₄⋊C₄	—	158	2	no	—
284	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
285	C₂×C₄²	—	79	1	no	—
286	#108	—	158	2	no	—
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	2	no	—
290	#107	—	158	1	no	—
291	#107	—	158	1	no	—
292	#107	—	158	2	no	—
293	#107	—	158	2	no	—
294	#107	C₂²⋊D₇₉	1	1	yes	characteristic
295	#107	C₂²⋊D₇₉	1	1	yes	characteristic
296	#106	—	2	2	no	—
297	#106	—	158	2	no	—
298	#106	—	158	2	no	—
299	#106	—	158	2	no	—
300	#106	—	158	2	no	—
301	#106	C₂²⋊D₇₉	1	2	yes	—
302	C₄⋊C₈	—	158	2	no	—
303	C₄⋊C₈	—	158	2	no	—
304	#104	—	79	4	no	—
305	#103	—	79	1	no	—
306	#103	—	79	1	no	—
307	#103	—	158	2	no	—
308	#102	—	79	1	no	—
309	#102	—	79	1	no	—
310	#102	—	158	2	no	—
311	#97	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	158	2	no	—
314	#95	—	316	2	no	—
315	#41	—	79	2	no	—
316	#41	—	79	2	no	—
317	#41	—	158	1	no	—
318	#41	—	158	1	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	79	1	no	—
321	C₂×D₄	—	79	1	no	—
322	C₂×D₄	—	158	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	316	2	no	—
325	C₂²×C₄	—	158	1	no	—
326	C₂²×C₄	—	158	2	no	—
327	C₂²×C₄	—	158	1	no	—
328	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
329	M₁₆	—	2	1	no	—
330	M₁₆	—	79	2	no	—
331	M₁₆	—	158	2	no	—
332	M₁₆	—	158	2	no	—
333	M₁₆	—	158	1	no	—
334	M₁₆	—	158	4	no	—
335	M₁₆	Q₈×D₇₉	1	2	yes	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	79	1	no	—
338	C₂×C₈	—	79	1	no	—
339	C₂×C₈	—	158	2	no	—
340	C₂×C₈	—	158	1	no	—
341	C₂×C₈	—	158	1	no	—
342	C₂×C₈	—	158	1	no	—
343	C₂×C₈	—	158	4	no	—
344	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
346	C₂×C₈	Q₈×D₇₉	1	2	yes	—
347	C₂×C₈	#11929625	1	2	yes	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	316	2	no	—
354	C₄⋊C₄	—	158	2	no	—
355	C₄⋊C₄	—	158	2	no	—
356	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
357	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
358	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
359	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	316	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	316	2	no	—
366	C₄²	—	79	2	no	—
367	C₄²	—	158	1	no	—
368	C₂³	—	158	1	no	—
369	C₂³	#14579206	1	1	yes	characteristic
370	Q₈	—	16	2	no	—
371	Q₈	—	79	2	no	—
372	Q₈	—	158	1	no	—
373	D₄	—	79	2	no	—
374	D₄	—	158	2	no	—
375	D₄	—	158	2	no	—
376	D₄	—	158	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	316	1	no	—
384	C₂×C₄	—	316	1	no	—
385	C₂×C₄	—	316	2	no	—
386	C₂×C₄	—	632	2	no	—
387	C₂×C₄	—	158	2	no	—
388	C₂×C₄	—	158	1	no	—
389	C₂×C₄	—	158	2	no	—
390	C₂×C₄	—	158	2	no	—
391	C₂×C₄	—	1264	2	no	—
392	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
394	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
395	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
397	C₂×C₄	#14579209	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	316	2	no	—
400	C₈	—	158	1	no	—
401	C₈	—	158	1	no	—
402	C₈	—	158	2	no	—
403	C₈	#14579137	1	2	yes	—
404	C₈	#14579137	1	2	yes	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	316	1	no	—
408	C₂²	—	316	1	no	—
409	C₂²	—	158	2	no	—
410	C₂²	#19099190	1	1	yes	characteristic
411	C₂²	D₄×C₂²⋊D₇₉	1	1	yes	characteristic
412	C₂²	#19099274	1	1	yes	characteristic
413	C₄	—	4	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	8	2	no	—
418	C₄	—	316	2	no	—
419	C₄	—	632	2	no	—
420	C₄	—	158	2	no	—
421	C₄	C₂×#14579137	1	1	yes	characteristic
422	C₄	C₄⋊Q₈×D₇₉	1	1	yes	characteristic
423	C₄	#19099216	1	1	yes	characteristic
424	C₄	Q₈×C₂²⋊D₇₉	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	316	2	no	—
428	C₂	#23767098	1	1	yes	characteristic
429	C₂	#23775182	1	1	yes	characteristic
430	C₂	#23775186	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₇₉
commutator, cosocle	C₂²×C₄×C₇₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#3164	C₂
socle	C₂²×C₇₉	D₄²
prime radical	C₂×#11929624	C₂³
hypercenter	#3164	D₇₉
hypocenter	C₇₉	#26082
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #3164

Complements

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

N	H ≅ G/N	type
3. #23764913	C₂	semidirect
4. #23764747	C₂	semidirect
5. #23764185	C₂	semidirect
6. #23764149	C₂	semidirect
8. #23763563	C₂	semidirect
11. C₇₉×#3164	C₂	semidirect
47. #14579167	Q₈	semidirect
71. #14579087	Q₈	semidirect
216. #3164	D₇₉	semidirect
227. C₇₉	#26082	semidirect

Maximal subgroups

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

subgroup	index
#23773258	2
#23771997	2
#23764913	2
#23764747	2
#23764185	2
#23764149	2
#23763630	2
#23763563	2
#23763465	2
#23763239	2
C₇₉×#3164	2
#26082	79