Group #34179832 — subgroups

Subgroups — #34179832

Order 20224.

686 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23764337	C₂	1	1	yes	maximal, characteristic
2	#23763396	C₂	1	1	yes	maximal, characteristic
3	#23762090	C₂	1	2	yes	maximal
4	#23761855	C₂	1	2	yes	maximal
5	C₇₉×#3502	C₂	1	1	yes	maximal, characteristic
6	#19098587	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×#14579080	—	2	1	no	—
9	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	#19098332	—	2	1	no	—
11	#19098318	—	2	2	no	—
12	#19098312	—	2	2	no	—
13	#19098309	—	2	2	no	—
14	Q₈⋊(C₇₉⋊C₈)	—	2	4	no	—
15	Q₈²×C₇₉	—	2	2	no	—
16	#557×C₇₉	—	2	2	no	—
17	#557×C₇₉	—	2	4	no	—
18	#544×C₇₉	—	2	1	no	—
19	#544×C₇₉	C₄	1	4	yes	—
20	#533×C₇₉	—	2	2	no	—
21	#533×C₇₉	C₂²	1	2	yes	—
22	#519×C₇₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#11929608	—	2	2	no	—
25	C₂²×C₇₉⋊C₈	—	2	1	no	—
26	C₂²×C₇₉⋊C₈	—	2	1	no	—
27	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
28	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
30	#14579080	—	4	2	no	—
31	C₄×C₇₉⋊C₈	—	2	2	no	—
32	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
33	C₄⋊Q₈×C₇₉	—	2	2	no	—
34	C₄⋊Q₈×C₇₉	—	2	2	no	—
35	C₄⋊Q₈×C₇₉	—	2	4	no	—
36	C₄⋊Q₈×C₇₉	—	2	8	no	—
37	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
38	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
39	#125×C₇₉	—	2	4	no	—
40	#125×C₇₉	—	2	4	no	—
41	#125×C₇₉	—	2	8	no	—
42	#125×C₇₉	—	2	2	no	—
43	C₂²⋊Q₈×C₇₉	—	2	4	no	—
44	C₂²⋊Q₈×C₇₉	—	2	2	no	—
45	C₂²⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
46	C₄×Q₈×C₇₉	—	2	4	no	—
47	C₄×Q₈×C₇₉	—	2	4	no	—
48	C₄×Q₈×C₇₉	—	2	4	no	—
49	C₄×Q₈×C₇₉	—	2	4	no	—
50	C₄×Q₈×C₇₉	—	2	2	no	—
51	C₄×Q₈×C₇₉	—	2	2	no	—
52	C₄×Q₈×C₇₉	—	2	2	no	—
53	C₄×Q₈×C₇₉	D₄	1	4	yes	—
54	#117×C₇₉	—	2	4	no	—
55	#117×C₇₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₇₉	D₄	1	2	yes	—
59	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
60	#11929608	—	4	2	no	—
61	#11929608	—	4	2	no	—
62	C₂×C₇₉⋊C₈	—	2	2	no	—
63	C₂×C₇₉⋊C₈	—	4	1	no	—
64	C₂×C₇₉⋊C₈	—	4	2	no	—
65	C₂×C₇₉⋊C₈	—	4	1	no	—
66	C₂×C₇₉⋊C₈	—	4	1	no	—
67	C₂×C₇₉⋊C₈	—	4	2	no	—
68	C₂×Q₈×C₇₉	—	2	4	no	—
69	C₂×Q₈×C₇₉	—	2	2	no	—
70	C₂×Q₈×C₇₉	—	2	2	no	—
71	C₂×Q₈×C₇₉	—	2	2	no	—
72	C₂×Q₈×C₇₉	C₂²⋊C₄	1	4	yes	—
73	C₂×Q₈×C₇₉	SD₁₆	1	2	yes	—
74	C₂×Q₈×C₇₉	Q₁₆	1	2	yes	—
75	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
77	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
80	C₄⋊C₄×C₇₉	—	2	4	no	—
81	C₄⋊C₄×C₇₉	—	2	4	no	—
82	C₄⋊C₄×C₇₉	—	2	4	no	—
83	C₄⋊C₄×C₇₉	—	2	8	no	—
84	C₄⋊C₄×C₇₉	—	2	4	no	—
85	C₄⋊C₄×C₇₉	—	2	4	no	—
86	C₄⋊C₄×C₇₉	—	2	2	no	—
87	C₄⋊C₄×C₇₉	—	2	2	no	—
88	C₄⋊C₄×C₇₉	—	2	2	no	—
89	C₄⋊C₄×C₇₉	—	2	2	no	—
90	C₄⋊C₄×C₇₉	—	2	4	no	—
91	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
92	C₂²⋊C₄×C₇₉	—	2	4	no	—
93	C₄²×C₇₉	—	2	8	no	—
94	C₄²×C₇₉	—	2	2	no	—
95	C₄²×C₇₉	—	2	2	no	—
96	C₄²×C₇₉	—	2	4	no	—
97	C₄²×C₇₉	C₂×D₄	1	2	yes	—
98	C₄²×C₇₉	C₂×D₄	1	2	yes	—
99	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	Q₈×C₇₉	—	2	4	no	—
101	Q₈×C₇₉	—	2	4	no	—
102	Q₈×C₇₉	—	4	4	no	—
103	Q₈×C₇₉	—	4	2	no	—
104	Q₈×C₇₉	—	4	2	no	—
105	Q₈×C₇₉	—	8	4	no	—
106	C₂×C₄×C₇₉	—	2	2	no	—
107	C₂×C₄×C₇₉	—	2	2	no	—
108	C₂×C₄×C₇₉	—	2	1	no	—
109	C₂×C₄×C₇₉	—	2	1	no	—
110	C₂×C₄×C₇₉	—	2	4	no	—
111	C₂×C₄×C₇₉	—	2	4	no	—
112	C₂×C₄×C₇₉	—	2	2	no	—
113	C₂×C₄×C₇₉	—	4	1	no	—
114	C₂×C₄×C₇₉	—	4	2	no	—
115	C₂×C₄×C₇₉	#103	1	4	yes	—
116	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
118	C₂×C₄×C₇₉	#120	1	2	yes	—
119	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
120	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
121	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
122	C₂×C₄×C₇₉	#137	1	2	yes	—
123	C₇₉⋊C₈	—	4	2	no	—
124	C₇₉⋊C₈	—	8	2	no	—
125	C₇₉⋊C₈	—	8	1	no	—
126	C₂²×C₇₉	—	2	1	no	—
127	C₂²×C₇₉	—	2	1	no	—
128	C₂²×C₇₉	#379	1	1	yes	characteristic
129	C₂²×C₇₉	C₂×#103	1	1	yes	characteristic
130	C₂²×C₇₉	#419	1	1	yes	characteristic
131	C₄×C₇₉	—	2	1	no	—
132	C₄×C₇₉	—	2	4	no	—
133	C₄×C₇₉	—	2	2	no	—
134	C₄×C₇₉	—	4	4	no	—
135	C₄×C₇₉	—	4	2	no	—
136	C₄×C₇₉	—	4	4	no	—
137	C₄×C₇₉	#448	1	2	yes	—
138	C₄×C₇₉	#451	1	2	yes	—
139	C₄×C₇₉	#454	1	1	yes	characteristic
140	C₄×C₇₉	#456	1	1	yes	characteristic
141	#8356	—	79	1	no	maximal, Sylow
142	C₂×C₇₉	—	2	1	no	—
143	C₂×C₇₉	—	2	1	no	—
144	C₂×C₇₉	#1787	1	1	yes	characteristic
145	C₂×C₇₉	#1791	1	1	yes	characteristic
146	C₂×C₇₉	#1793	1	1	yes	characteristic
147	#3502	D₇₉	1	1	yes	characteristic
148	#1984	—	79	1	no	—
149	#1801	—	79	1	no	—
150	#1550	—	79	2	no	—
151	#1493	—	79	2	no	—
152	C₇₉	#8356	1	1	yes	characteristic, complemented, Sylow
153	Q₈²	—	2	2	no	—
154	#557	—	2	2	no	—
155	#557	—	2	4	no	—
156	#544	—	2	1	no	—
157	#544	Dic₇₉	1	4	yes	—
158	#533	—	2	2	no	—
159	#533	C₂×D₇₉	1	2	yes	—
160	#519	—	2	1	no	—
161	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
162	#423	—	79	2	no	—
163	C₂×C₄⋊C₈	—	79	1	no	—
164	C₂×#101	—	158	1	no	—
165	C₂×C₄×C₈	—	79	1	no	—
166	#343	—	158	1	no	—
167	#336	—	158	2	no	—
168	#333	—	158	2	no	—
169	#332	—	158	2	no	—
170	Q₈⋊C₈	—	158	4	no	—
171	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
172	C₂×M₁₆	—	158	2	no	—
173	C₂²×C₈	—	158	1	no	—
174	C₂²×C₈	—	158	1	no	—
175	C₄⋊Q₈	—	2	2	no	—
176	C₄⋊Q₈	—	2	2	no	—
177	C₄⋊Q₈	—	2	4	no	—
178	C₄⋊Q₈	—	2	8	no	—
179	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
180	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
181	#125	—	2	4	no	—
182	#125	—	2	4	no	—
183	#125	—	2	8	no	—
184	#125	—	2	2	no	—
185	C₂²⋊Q₈	—	2	4	no	—
186	C₂²⋊Q₈	—	2	2	no	—
187	C₂²⋊Q₈	C₂×Dic₇₉	1	4	yes	—
188	C₄×Q₈	—	2	4	no	—
189	C₄×Q₈	—	2	4	no	—
190	C₄×Q₈	—	2	4	no	—
191	C₄×Q₈	—	2	4	no	—
192	C₄×Q₈	—	2	2	no	—
193	C₄×Q₈	—	2	2	no	—
194	C₄×Q₈	—	2	2	no	—
195	C₄×Q₈	C₂²⋊D₇₉	1	4	yes	—
196	#117	—	2	4	no	—
197	#117	—	2	2	no	—
198	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
199	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
200	C₂×C₄²	C₂²⋊D₇₉	1	2	yes	—
201	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
202	C₄⋊C₈	—	158	2	no	—
203	C₄⋊C₈	—	158	2	no	—
204	C₄⋊C₈	—	158	2	no	—
205	#101	—	316	2	no	—
206	C₄×C₈	—	158	2	no	—
207	C₂×Q₈	—	2	4	no	—
208	C₂×Q₈	—	2	2	no	—
209	C₂×Q₈	—	2	2	no	—
210	C₂×Q₈	—	2	2	no	—
211	C₂×Q₈	C₂²⋊Dic₇₉	1	4	yes	—
212	C₂×Q₈	#11929611	1	2	yes	—
213	C₂×Q₈	#11929614	1	2	yes	—
214	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
215	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
216	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
217	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
218	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
219	M₁₆	—	316	2	no	—
220	M₁₆	—	316	2	no	—
221	C₂×C₈	—	316	1	no	—
222	C₂×C₈	—	316	1	no	—
223	C₂×C₈	—	316	2	no	—
224	C₂×C₈	—	316	1	no	—
225	C₂×C₈	—	316	2	no	—
226	C₂×C₈	—	158	2	no	—
227	C₄⋊C₄	—	2	4	no	—
228	C₄⋊C₄	—	2	4	no	—
229	C₄⋊C₄	—	2	4	no	—
230	C₄⋊C₄	—	2	8	no	—
231	C₄⋊C₄	—	2	4	no	—
232	C₄⋊C₄	—	2	4	no	—
233	C₄⋊C₄	—	2	2	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	2	2	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	2	4	no	—
238	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
239	C₂²⋊C₄	—	2	4	no	—
240	C₄²	—	2	8	no	—
241	C₄²	—	2	2	no	—
242	C₄²	—	2	2	no	—
243	C₄²	—	2	4	no	—
244	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
245	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
246	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
247	Q₈	—	2	4	no	—
248	Q₈	—	2	4	no	—
249	Q₈	—	4	4	no	—
250	Q₈	—	4	2	no	—
251	Q₈	—	4	2	no	—
252	Q₈	—	8	4	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	4	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	4	1	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	#14579085	1	4	yes	—
263	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
264	C₂×C₄	#14579130	1	1	yes	characteristic
265	C₂×C₄	#14579130	1	2	yes	—
266	C₂×C₄	#14579130	1	1	yes	characteristic
267	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
268	C₂×C₄	C₂×#11929614	1	1	yes	characteristic
269	C₂×C₄	#14579192	1	2	yes	—
270	C₈	—	316	2	no	—
271	C₈	—	632	2	no	—
272	C₈	—	632	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	2	1	no	—
275	C₂²	#19098419	1	1	yes	characteristic
276	C₂²	C₂×#14579085	1	1	yes	characteristic
277	C₂²	#19098572	1	1	yes	characteristic
278	C₄	—	2	4	no	—
279	C₄	—	2	2	no	—
280	C₄	—	2	1	no	—
281	C₄	—	4	2	no	—
282	C₄	—	4	4	no	—
283	C₄	—	4	4	no	—
284	C₄	#19098702	1	2	yes	—
285	C₄	#19098719	1	2	yes	—
286	C₄	#19098736	1	1	yes	characteristic
287	C₄	#19098746	1	1	yes	characteristic
288	C₂	—	2	1	no	—
289	C₂	—	2	1	no	—
290	C₂	#23763335	1	1	yes	characteristic
291	C₂	#23763351	1	1	yes	characteristic
292	C₂	#23763359	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764337

C₂

yes

maximal, characteristic

#23763396

C₂

yes

maximal, characteristic

#23762090

C₂

yes

maximal

#23761855

C₂

yes

maximal

C₇₉×#3502

C₂

yes

maximal, characteristic

#19098587

C₂²

yes

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×#14579080

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

—

—

—

—

Q₈⋊(C₇₉⋊C₈)

—

Q₈²×C₇₉

—

#557×C₇₉

—

#557×C₇₉

—

#544×C₇₉

—

#544×C₇₉

C₄

yes

—

#533×C₇₉

—

#533×C₇₉

C₂²

yes

—

#519×C₇₉

—

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

#14579080

—

C₄×C₇₉⋊C₈

—

C₂²×Q₈×C₇₉

D₄

yes

characteristic

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

D₄

yes

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

C₂×C₄

yes

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

D₄

yes

—

#117×C₇₉

—

#117×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₇₉

SD₁₆

yes

—

C₂×Q₈×C₇₉

Q₁₆

yes

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

100

Q₈×C₇₉

—

101

Q₈×C₇₉

—

102

Q₈×C₇₉

—

103

Q₈×C₇₉

—

104

Q₈×C₇₉

—

105

Q₈×C₇₉

—

106

C₂×C₄×C₇₉

—

107

C₂×C₄×C₇₉

—

108

C₂×C₄×C₇₉

—

109

C₂×C₄×C₇₉

—

110

C₂×C₄×C₇₉

—

111

C₂×C₄×C₇₉

—

112

C₂×C₄×C₇₉

—

113

C₂×C₄×C₇₉

—

114

C₂×C₄×C₇₉

—

115

C₂×C₄×C₇₉

#103

yes

—

116

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

—

117

C₂×C₄×C₇₉

#120

yes

characteristic

118

C₂×C₄×C₇₉

#120

yes

—

119

C₂×C₄×C₇₉

#120

yes

characteristic

120

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

121

C₂×C₄×C₇₉

C₂×Q₁₆

yes

characteristic

122

C₂×C₄×C₇₉

#137

yes

—

123

C₇₉⋊C₈

—

124

C₇₉⋊C₈

—

125

C₇₉⋊C₈

—

126

C₂²×C₇₉

—

127

C₂²×C₇₉

—

128

C₂²×C₇₉

#379

yes

characteristic

129

C₂²×C₇₉

C₂×#103

yes

characteristic

130

C₂²×C₇₉

#419

yes

characteristic

131

C₄×C₇₉

—

132

C₄×C₇₉

—

133

C₄×C₇₉

—

134

C₄×C₇₉

—

135

C₄×C₇₉

—

136

C₄×C₇₉

—

137

C₄×C₇₉

#448

yes

—

138

C₄×C₇₉

#451

yes

—

139

C₄×C₇₉

#454

yes

characteristic

140

C₄×C₇₉

yes

141

—

142

C₂×C₇₉

—

143

C₂×C₇₉

—

144

C₂×C₇₉

#1787

yes

characteristic

145

C₂×C₇₉

#1791

yes

characteristic

146

C₂×C₇₉

#1793

yes

characteristic

147

#3502

D₇₉

yes

characteristic

148

#1984

—

149

#1801

—

150

#1550

—

151

#1493

—

152

C₇₉

#8356

yes

characteristic, complemented, Sylow

153

Q₈²

—

154

#557

—

155

#557

—

156

#544

—

157

#544

Dic₇₉

yes

—

158

#533

—

159

#533

C₂×D₇₉

yes

—

160

#519

—

161

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

162

#423

—

163

C₂×C₄⋊C₈

—

164

C₂×#101

—

158

—

165

C₂×C₄×C₈

—

166

#343

—

158

—

167

#336

—

158

—

168

#333

—

158

—

169

#332

—

158

—

170

Q₈⋊C₈

—

158

—

171

C₂²×Q₈

C₂²⋊D₇₉

yes

characteristic

172

C₂×M₁₆

—

158

—

173

C₂²×C₈

—

158

—

174

C₂²×C₈

—

158

—

175

C₄⋊Q₈

—

176

C₄⋊Q₈

—

177

C₄⋊Q₈

—

178

C₄⋊Q₈

—

179

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

180

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

181

#125

—

182

#125

—

183

#125

—

184

#125

—

185

C₂²⋊Q₈

—

186

C₂²⋊Q₈

—

187

C₂²⋊Q₈

C₂×Dic₇₉

yes

—

188

C₄×Q₈

—

189

C₄×Q₈

—

190

C₄×Q₈

—

191

C₄×Q₈

—

192

C₄×Q₈

—

193

C₄×Q₈

—

194

C₄×Q₈

—

195

C₄×Q₈

C₂²⋊D₇₉

yes

—

196

#117

—

197

#117

—

198

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

—

199

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

200

C₂×C₄²

C₂²⋊D₇₉

yes

—

201

C₂×C₄²

C₂²×D₇₉

yes

characteristic

202

C₄⋊C₈

—

158

—

203

C₄⋊C₈

—

158

—

204

C₄⋊C₈

—

158

—

205

#101

—

316

—

206

C₄×C₈

—

158

—

207

C₂×Q₈

—

208

C₂×Q₈

—

209

C₂×Q₈

—

210

C₂×Q₈

—

211

C₂×Q₈

C₂²⋊Dic₇₉

yes

—

212

C₂×Q₈

#11929611

yes

—

213

C₂×Q₈

#11929614

yes

—

214

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

215

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

216

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

217

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

218

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

219

M₁₆

—

316

—

220

M₁₆

—

316

—

221

C₂×C₈

—

316

—

222

C₂×C₈

—

316

—

223

C₂×C₈

—

316

—

224

C₂×C₈

—

316

—

225

C₂×C₈

—

316

—

226

C₂×C₈

—

158

—

227

C₄⋊C₄

—

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₄⋊C₄

C₂²⋊Dic₇₉

yes

—

239

C₂²⋊C₄

—

240

C₄²

—

241

C₄²

—

242

C₄²

—

243

C₄²

—

244

C₄²

C₂×C₂²⋊D₇₉

yes

—

245

C₄²

C₂×C₂²⋊D₇₉

yes

—

246

C₂³

C₂×C₂²⋊Dic₇₉

yes

characteristic

247

Q₈

—

248

Q₈

—

249

Q₈

—

250

Q₈

—

251

Q₈

—

252

Q₈

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

#14579085

yes

—

263

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

—

264

C₂×C₄

#14579130

yes

characteristic

265

C₂×C₄

#14579130

yes

—

266

C₂×C₄

#14579130

yes

characteristic

267

C₂×C₄

C₂×#11929611

yes

characteristic

268

C₂×C₄

C₂×#11929614

yes

characteristic

269

C₂×C₄

#14579192

yes

—

270

C₈

—

316

—

271

C₈

—

632

—

272

C₈

—

632

—

273

C₂²

—

274

C₂²

—

275

C₂²

#19098419

yes

characteristic

276

C₂²

C₂×#14579085

yes

characteristic

277

C₂²

#19098572

yes

characteristic

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

282

C₄

—

283

C₄

—

284

C₄

#19098702

yes

—

285

C₄

#19098719

yes

—

286

C₄

#19098736

yes

characteristic

287

C₄

#19098746

yes

characteristic

288

C₂

—

289

C₂

—

290

C₂

#23763335

yes

characteristic

291

C₂

#23763351

yes

characteristic

292

C₂

#23763359

yes

characteristic

	subgroup	G/H
center	C₂²	#19098419
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#3502	C₂
socle	C₂²×C₇₉	#379
prime radical	C₂³×C₇₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#3502	D₇₉
hypocenter	C₇₉	#8356
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3502

subgroup

G/H

center

C₂²

#19098419

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#3502

C₂

socle

C₂²×C₇₉

#379

prime radical

C₂³×C₇₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3502

N	H ≅ G/N	type
152. C₇₉	#8356	semidirect

H ≅ G/N

type

152. C₇₉

#8356

semidirect

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

subgroup	index
#23764337	2
#23763396	2
#23762090	2
#23761855	2
C₇₉×#3502	2
#8356	79

subgroup

index

C₇₉×#3502

Subgroups — #34179832

Conjugacy classes of subgroups

Complements

Maximal subgroups