Group #34191935 — subgroups

Subgroups — #34191935

Order 20224.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 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	C₂×#19098859	C₂	1	1	yes	maximal, characteristic
2	#23763393	C₂	1	1	yes	maximal, characteristic
3	#23762086	C₂	1	1	yes	maximal, characteristic
4	#23762080	C₂	1	1	yes	maximal, characteristic
5	#23761794	C₂	1	1	yes	maximal, characteristic
6	#23761297	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1570	C₂	1	1	yes	maximal, characteristic
8	C₂×#14579161	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
10	#19098859	—	2	2	no	—
11	#19098859	—	2	2	no	—
12	#19098616	C₂²	1	1	yes	characteristic
13	C₂×#14579095	—	2	1	no	—
14	#19098587	C₂²	1	1	yes	characteristic
15	C₂×#14579086	—	2	1	no	—
16	C₂×#14579079	—	2	1	no	—
17	#19098331	—	2	1	no	—
18	#19098311	—	2	2	no	—
19	#19098308	—	2	2	no	—
20	#19098293	—	2	2	no	—
21	#431×C₇₉	C₂²	1	1	yes	characteristic
22	#423×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
24	#334×C₇₉	—	2	2	no	—
25	C₂²×Dic₁₅₈	—	2	1	no	—
26	C₂²×Dic₁₅₈	D₄	1	1	yes	characteristic
27	C₂×#11929608	—	2	1	no	—
28	#14579161	—	2	1	no	—
29	#14579161	—	2	1	no	—
30	#14579161	—	2	1	no	—
31	#14579161	D₄	1	2	yes	—
32	C₄×Dic₁₅₈	—	2	1	no	—
33	C₄×Dic₁₅₈	—	2	1	no	—
34	C₄×Dic₁₅₈	—	2	1	no	—
35	C₄×Dic₁₅₈	—	2	1	no	—
36	C₂×C₄⋊Dic₇₉	—	2	1	no	—
37	C₂×C₄⋊Dic₇₉	—	2	1	no	—
38	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
39	C₂×Dic₇₉⋊C₄	—	2	1	no	—
40	C₂×C₄×Dic₇₉	—	2	1	no	—
41	#14579095	—	2	4	no	—
42	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
45	#14579086	—	2	4	no	—
46	#14579079	—	4	2	no	—
47	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
48	C₄×C₇₉⋊C₈	—	2	1	no	—
49	C₂×M₁₆×C₇₉	—	2	1	no	—
50	C₂²×C₈×C₇₉	—	2	1	no	—
51	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
52	C₄⋊C₈×C₇₉	—	2	1	no	—
53	C₄⋊C₈×C₇₉	—	2	1	no	—
54	C₄⋊C₈×C₇₉	—	2	1	no	—
55	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
56	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
57	C₂²⋊C₈×C₇₉	—	2	1	no	—
58	C₄×C₈×C₇₉	—	2	1	no	—
59	C₂×Dic₁₅₈	—	2	1	no	—
60	C₂×Dic₁₅₈	—	2	1	no	—
61	C₂×Dic₁₅₈	—	2	2	no	—
62	C₂×Dic₁₅₈	—	2	1	no	—
63	C₂×Dic₁₅₈	—	2	1	no	—
64	C₂×Dic₁₅₈	—	2	1	no	—
65	C₂×Dic₁₅₈	—	4	1	no	—
66	C₂×Dic₁₅₈	—	8	2	no	—
67	C₂×Dic₁₅₈	SD₁₆	1	2	yes	—
68	C₂²×Dic₇₉	—	2	1	no	—
69	C₂²×Dic₇₉	—	2	1	no	—
70	C₂²×Dic₇₉	—	4	1	no	—
71	#11929608	—	4	1	no	—
72	#11929608	—	4	1	no	—
73	C₂×C₇₉⋊C₈	—	4	1	no	—
74	C₂×C₇₉⋊C₈	—	4	1	no	—
75	C₄⋊Dic₇₉	—	2	2	no	—
76	C₄⋊Dic₇₉	—	2	1	no	—
77	C₄⋊Dic₇₉	—	2	1	no	—
78	C₄⋊Dic₇₉	—	2	2	no	—
79	C₄⋊Dic₇₉	—	4	1	no	—
80	C₄⋊Dic₇₉	—	4	1	no	—
81	Dic₇₉⋊C₄	—	4	1	no	—
82	Dic₇₉⋊C₄	—	4	1	no	—
83	C₄×Dic₇₉	—	4	1	no	—
84	C₄×Dic₇₉	—	4	1	no	—
85	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
88	M₁₆×C₇₉	—	4	1	no	—
89	M₁₆×C₇₉	—	4	1	no	—
90	C₂×C₈×C₇₉	—	2	2	no	—
91	C₂×C₈×C₇₉	—	2	2	no	—
92	C₂×C₈×C₇₉	—	4	1	no	—
93	C₂×C₈×C₇₉	—	4	1	no	—
94	C₂×C₈×C₇₉	—	4	1	no	—
95	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
96	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
97	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
98	C₄²×C₇₉	#41	1	1	yes	characteristic
99	C₂³×C₇₉	#123	1	1	yes	characteristic
100	C₂×C₄×C₇₉	—	2	2	no	—
101	C₂×C₄×C₇₉	—	4	1	no	—
102	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
103	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
104	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
105	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
106	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
107	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
108	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
109	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
110	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
111	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
112	C₂×Dic₇₉	—	2	2	no	—
113	C₂×Dic₇₉	—	4	1	no	—
114	C₂×Dic₇₉	—	4	1	no	—
115	C₂×Dic₇₉	—	4	1	no	—
116	C₂×Dic₇₉	—	4	2	no	—
117	C₂×Dic₇₉	—	8	2	no	—
118	C₂×Dic₇₉	—	8	1	no	—
119	Dic₁₅₈	—	2	2	no	—
120	Dic₁₅₈	—	2	2	no	—
121	Dic₁₅₈	—	4	1	no	—
122	Dic₁₅₈	—	4	1	no	—
123	Dic₁₅₈	—	8	2	no	—
124	Dic₁₅₈	—	8	2	no	—
125	C₈×C₇₉	—	4	2	no	—
126	C₈×C₇₉	—	4	2	no	—
127	C₈×C₇₉	—	8	1	no	—
128	C₇₉⋊C₈	—	8	1	no	—
129	C₇₉⋊C₈	—	8	1	no	—
130	C₂²×C₇₉	—	2	1	no	—
131	C₂²×C₇₉	—	2	1	no	—
132	C₂²×C₇₉	#394	1	1	yes	characteristic
133	C₂²×C₇₉	#483	1	1	yes	characteristic
134	C₂²×C₇₉	#485	1	1	yes	characteristic
135	C₄×C₇₉	—	2	1	no	—
136	C₄×C₇₉	—	2	1	no	—
137	C₄×C₇₉	—	2	1	no	—
138	C₄×C₇₉	#448	1	1	yes	characteristic
139	C₄×C₇₉	#452	1	1	yes	characteristic
140	C₄×C₇₉	#465	1	1	yes	characteristic
141	C₄×C₇₉	#470	1	1	yes	characteristic
142	C₄×C₇₉	#473	1	2	yes	—
143	Dic₇₉	—	4	2	no	—
144	Dic₇₉	—	8	2	no	—
145	Dic₇₉	—	8	1	no	—
146	#10454	—	79	1	no	maximal, Sylow
147	C₂×C₇₉	—	2	1	no	—
148	C₂×C₇₉	—	2	1	no	—
149	C₂×C₇₉	#2035	1	1	yes	characteristic
150	C₂×C₇₉	#2047	1	1	yes	characteristic
151	C₂×C₇₉	#2048	1	1	yes	characteristic
152	C₂×#477	—	79	1	no	—
153	#1801	—	79	1	no	—
154	#1570	D₇₉	1	1	yes	characteristic
155	#1549	—	79	1	no	—
156	#1548	—	79	1	no	—
157	#1479	—	79	1	no	—
158	#1301	—	79	1	no	—
159	C₇₉	#10454	1	1	yes	characteristic, complemented, Sylow
160	C₂×C₄⋊Q₈	—	79	1	no	—
161	C₂×C₄×Q₈	—	79	1	no	—
162	#477	—	158	2	no	—
163	#477	—	158	2	no	—
164	#431	—	79	1	no	—
165	#431	C₂×D₇₉	1	1	yes	characteristic
166	C₂×#107	—	158	1	no	—
167	#423	—	79	1	no	—
168	#423	C₂×D₇₉	1	1	yes	characteristic
169	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
170	C₂×#103	—	158	1	no	—
171	C₂×#101	—	158	1	no	—
172	#343	—	158	1	no	—
173	#334	—	2	2	no	—
174	#333	—	158	2	no	—
175	#332	—	158	2	no	—
176	Q₈⋊C₈	—	158	2	no	—
177	C₂²×Q₈	—	79	1	no	—
178	C₂²×Q₈	—	158	1	no	—
179	C₂×M₁₆	—	2	1	no	—
180	C₂×M₁₆	—	158	1	no	—
181	C₂²×C₈	—	2	1	no	—
182	C₄⋊Q₈	—	79	2	no	—
183	C₄⋊Q₈	—	158	1	no	—
184	C₄⋊Q₈	—	158	1	no	—
185	C₄⋊Q₈	—	158	1	no	—
186	C₄×Q₈	—	158	1	no	—
187	C₄×Q₈	—	158	1	no	—
188	C₄×Q₈	—	158	1	no	—
189	C₄×Q₈	—	158	1	no	—
190	C₂×C₄⋊C₄	—	79	1	no	—
191	C₂×C₄⋊C₄	—	158	1	no	—
192	C₂×C₄⋊C₄	—	158	1	no	—
193	C₂×C₄⋊C₄	—	158	1	no	—
194	C₂×C₄²	—	158	1	no	—
195	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
196	#107	—	158	4	no	—
197	C₄⋊C₈	—	2	1	no	—
198	C₄⋊C₈	—	2	1	no	—
199	C₄⋊C₈	—	2	1	no	—
200	C₄⋊C₈	—	158	1	no	—
201	C₄⋊C₈	—	158	1	no	—
202	C₄⋊C₈	—	158	1	no	—
203	C₄⋊C₈	D₃₁₆	1	2	yes	—
204	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
205	#103	—	158	4	no	—
206	#101	—	316	2	no	—
207	C₂²⋊C₈	—	2	1	no	—
208	C₂²⋊C₈	—	158	1	no	—
209	C₄×C₈	—	2	1	no	—
210	C₄×C₈	—	158	1	no	—
211	C₂×Q₈	—	316	1	no	—
212	C₂×Q₈	—	79	2	no	—
213	C₂×Q₈	—	632	2	no	—
214	C₂×Q₈	—	158	1	no	—
215	C₂×Q₈	—	158	1	no	—
216	C₂×Q₈	—	158	2	no	—
217	C₂×Q₈	—	158	1	no	—
218	C₂×Q₈	—	158	1	no	—
219	C₂×Q₈	—	158	1	no	—
220	C₂²×C₄	—	316	1	no	—
221	C₂²×C₄	—	158	1	no	—
222	C₂²×C₄	—	158	1	no	—
223	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
224	C₂²×C₄	#11929624	1	1	yes	characteristic
225	C₂²×C₄	#11929625	1	1	yes	characteristic
226	M₁₆	—	4	1	no	—
227	M₁₆	—	4	1	no	—
228	M₁₆	—	316	1	no	—
229	M₁₆	—	316	1	no	—
230	C₂×C₈	—	2	2	no	—
231	C₂×C₈	—	2	2	no	—
232	C₂×C₈	—	4	1	no	—
233	C₂×C₈	—	4	1	no	—
234	C₂×C₈	—	4	1	no	—
235	C₂×C₈	—	316	1	no	—
236	C₂×C₈	—	316	1	no	—
237	C₄⋊C₄	—	316	1	no	—
238	C₄⋊C₄	—	316	1	no	—
239	C₄⋊C₄	—	316	1	no	—
240	C₄⋊C₄	—	316	1	no	—
241	C₄⋊C₄	—	158	2	no	—
242	C₄⋊C₄	—	158	1	no	—
243	C₄⋊C₄	—	158	1	no	—
244	C₄⋊C₄	—	158	2	no	—
245	C₄²	—	316	1	no	—
246	C₄²	—	316	1	no	—
247	C₄²	D₄×D₇₉	1	1	yes	characteristic
248	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
249	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
250	C₄²	#11929625	1	1	yes	characteristic
251	C₂³	#14579146	1	1	yes	characteristic
252	Q₈	—	316	1	no	—
253	Q₈	—	316	1	no	—
254	Q₈	—	632	2	no	—
255	Q₈	—	632	2	no	—
256	Q₈	—	158	2	no	—
257	Q₈	—	158	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	4	1	no	—
260	C₂×C₄	—	316	1	no	—
261	C₂×C₄	—	316	1	no	—
262	C₂×C₄	—	316	1	no	—
263	C₂×C₄	—	316	2	no	—
264	C₂×C₄	—	632	2	no	—
265	C₂×C₄	—	632	1	no	—
266	C₂×C₄	—	158	2	no	—
267	C₂×C₄	#14579129	1	1	yes	characteristic
268	C₂×C₄	#14579135	1	1	yes	characteristic
269	C₂×C₄	#14579136	1	1	yes	characteristic
270	C₂×C₄	#14579136	1	1	yes	characteristic
271	C₂×C₄	#14579146	1	1	yes	characteristic
272	C₂×C₄	#14579150	1	1	yes	characteristic
273	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
274	C₂×C₄	#14579182	1	1	yes	characteristic
275	C₂×C₄	#14579190	1	1	yes	characteristic
276	C₂×C₄	#14579190	1	1	yes	characteristic
277	C₈	—	4	2	no	—
278	C₈	—	4	2	no	—
279	C₈	—	8	1	no	—
280	C₈	—	632	1	no	—
281	C₈	—	632	1	no	—
282	C₂²	—	2	1	no	—
283	C₂²	—	2	1	no	—
284	C₂²	#19098480	1	1	yes	characteristic
285	C₂²	#19098895	1	1	yes	characteristic
286	C₂²	#19098907	1	1	yes	characteristic
287	C₄	—	2	1	no	—
288	C₄	—	2	1	no	—
289	C₄	—	2	1	no	—
290	C₄	—	316	2	no	—
291	C₄	—	632	2	no	—
292	C₄	—	632	1	no	—
293	C₄	#19098700	1	1	yes	characteristic
294	C₄	#19098722	1	1	yes	characteristic
295	C₄	#19098793	1	1	yes	characteristic
296	C₄	#19098822	1	1	yes	characteristic
297	C₄	#19098838	1	2	yes	—
298	C₂	—	2	1	no	—
299	C₂	—	2	1	no	—
300	C₂	#23764598	1	1	yes	characteristic
301	C₂	#23764668	1	1	yes	characteristic
302	C₂	#23764675	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098859

C₂

yes

maximal, characteristic

#23763393

C₂

yes

maximal, characteristic

#23762086

C₂

yes

maximal, characteristic

#23762080

C₂

yes

maximal, characteristic

#23761794

C₂

yes

maximal, characteristic

#23761297

C₂

yes

maximal, characteristic

C₇₉×#1570

C₂

yes

maximal, characteristic

C₂×#14579161

C₂²

yes

characteristic

C₂×C₄×Dic₁₅₈

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#14579095

—

#19098587

C₂²

yes

—

—

—

—

—

—

#431×C₇₉

C₂²

yes

characteristic

#423×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#334×C₇₉

—

C₂²×Dic₁₅₈

—

C₂²×Dic₁₅₈

D₄

yes

—

—

—

—

D₄

yes

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

D₄

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

#14579095

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

#14579086

—

#14579079

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

—

C₂×M₁₆×C₇₉

—

C₂²×C₈×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

D₄

yes

—

C₄⋊C₈×C₇₉

D₄

yes

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

SD₁₆

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

C₂²×C₄×C₇₉

yes

C₂²×C₄×C₇₉

yes

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

C₄²×C₇₉

yes

C₂³×C₇₉

yes

100

C₂×C₄×C₇₉

—

101

C₂×C₄×C₇₉

—

102

C₂×C₄×C₇₉

#120

yes

characteristic

103

C₂×C₄×C₇₉

#121

yes

characteristic

104

C₂×C₄×C₇₉

#121

yes

characteristic

105

C₂×C₄×C₇₉

#121

yes

characteristic

106

C₂×C₄×C₇₉

#123

yes

characteristic

107

C₂×C₄×C₇₉

#124

yes

characteristic

108

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

109

C₂×C₄×C₇₉

#135

yes

characteristic

110

C₂×C₄×C₇₉

#137

yes

characteristic

111

C₂×C₄×C₇₉

#137

yes

characteristic

112

C₂×Dic₇₉

—

113

C₂×Dic₇₉

—

114

C₂×Dic₇₉

—

115

C₂×Dic₇₉

—

116

C₂×Dic₇₉

—

117

C₂×Dic₇₉

—

118

C₂×Dic₇₉

—

119

Dic₁₅₈

—

120

Dic₁₅₈

—

121

Dic₁₅₈

—

122

Dic₁₅₈

—

123

Dic₁₅₈

—

124

Dic₁₅₈

—

125

C₈×C₇₉

—

126

C₈×C₇₉

—

127

C₈×C₇₉

—

128

C₇₉⋊C₈

—

129

C₇₉⋊C₈

—

130

C₂²×C₇₉

—

131

C₂²×C₇₉

—

132

C₂²×C₇₉

#394

yes

characteristic

133

C₂²×C₇₉

#483

yes

characteristic

134

C₂²×C₇₉

#485

yes

characteristic

135

C₄×C₇₉

—

136

C₄×C₇₉

—

137

C₄×C₇₉

—

138

C₄×C₇₉

#448

yes

characteristic

139

C₄×C₇₉

#452

yes

characteristic

140

C₄×C₇₉

#465

yes

characteristic

141

C₄×C₇₉

#470

yes

characteristic

142

C₄×C₇₉

#473

yes

—

143

Dic₇₉

—

144

Dic₇₉

—

145

Dic₇₉

—

146

#10454

—

maximal, Sylow

147

C₂×C₇₉

—

148

C₂×C₇₉

—

149

C₂×C₇₉

#2035

yes

characteristic

150

C₂×C₇₉

#2047

yes

characteristic

151

C₂×C₇₉

#2048

yes

characteristic

152

C₂×#477

—

153

#1801

—

154

#1570

D₇₉

yes

characteristic

155

#1549

—

156

#1548

—

157

#1479

—

158

#1301

—

159

C₇₉

#10454

yes

characteristic, complemented, Sylow

160

C₂×C₄⋊Q₈

—

161

C₂×C₄×Q₈

—

162

#477

—

158

—

163

#477

—

158

—

164

#431

—

165

#431

C₂×D₇₉

yes

characteristic

166

C₂×#107

—

158

—

167

#423

—

168

#423

C₂×D₇₉

yes

characteristic

169

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

170

C₂×#103

—

158

—

171

C₂×#101

—

158

—

172

#343

—

158

—

173

#334

—

174

#333

—

158

—

175

#332

—

158

—

176

Q₈⋊C₈

—

158

—

177

C₂²×Q₈

—

178

C₂²×Q₈

—

158

—

179

C₂×M₁₆

—

180

C₂×M₁₆

—

158

—

181

C₂²×C₈

—

182

C₄⋊Q₈

—

183

C₄⋊Q₈

—

158

—

184

C₄⋊Q₈

—

158

—

185

C₄⋊Q₈

—

158

—

186

C₄×Q₈

—

158

—

187

C₄×Q₈

—

158

—

188

C₄×Q₈

—

158

—

189

C₄×Q₈

—

158

—

190

C₂×C₄⋊C₄

—

191

C₂×C₄⋊C₄

—

158

—

192

C₂×C₄⋊C₄

—

158

—

193

C₂×C₄⋊C₄

—

158

—

194

C₂×C₄²

—

158

—

195

C₂×C₄²

C₂²×D₇₉

yes

characteristic

196

#107

—

158

—

197

C₄⋊C₈

—

198

C₄⋊C₈

—

199

C₄⋊C₈

—

200

C₄⋊C₈

—

158

—

201

C₄⋊C₈

—

158

—

202

C₄⋊C₈

—

158

—

203

C₄⋊C₈

D₃₁₆

yes

—

204

C₄⋊C₈

C₂²⋊D₇₉

yes

—

205

#103

—

158

—

206

#101

—

316

—

207

C₂²⋊C₈

—

208

C₂²⋊C₈

—

158

—

209

C₄×C₈

—

210

C₄×C₈

—

158

—

211

C₂×Q₈

—

316

—

212

C₂×Q₈

—

213

C₂×Q₈

—

632

—

214

C₂×Q₈

—

158

—

215

C₂×Q₈

—

158

—

216

C₂×Q₈

—

158

—

217

C₂×Q₈

—

158

—

218

C₂×Q₈

—

158

—

219

C₂×Q₈

—

158

—

220

C₂²×C₄

—

316

—

221

C₂²×C₄

—

158

—

222

C₂²×C₄

—

158

—

223

C₂²×C₄

D₄×D₇₉

yes

characteristic

224

C₂²×C₄

#11929624

yes

characteristic

225

C₂²×C₄

#11929625

yes

characteristic

226

M₁₆

—

227

M₁₆

—

228

M₁₆

—

316

—

229

M₁₆

—

316

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₂×C₈

—

234

C₂×C₈

—

235

C₂×C₈

—

316

—

236

C₂×C₈

—

316

—

237

C₄⋊C₄

—

316

—

238

C₄⋊C₄

—

316

—

239

C₄⋊C₄

—

316

—

240

C₄⋊C₄

—

316

—

241

C₄⋊C₄

—

158

—

242

C₄⋊C₄

—

158

—

243

C₄⋊C₄

—

158

—

244

C₄⋊C₄

—

158

—

245

C₄²

—

316

—

246

C₄²

—

316

—

247

C₄²

D₄×D₇₉

yes

characteristic

248

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

249

C₄²

C₂×D₃₁₆

yes

characteristic

250

C₄²

#11929625

yes

characteristic

251

C₂³

#14579146

yes

characteristic

252

Q₈

—

316

—

253

Q₈

—

316

—

254

Q₈

—

632

—

255

Q₈

—

632

—

256

Q₈

—

158

—

257

Q₈

—

158

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

316

—

261

C₂×C₄

—

316

—

262

C₂×C₄

—

316

—

263

C₂×C₄

—

316

—

264

C₂×C₄

—

632

—

265

C₂×C₄

—

632

—

266

C₂×C₄

—

158

—

267

C₂×C₄

#14579129

yes

characteristic

268

C₂×C₄

#14579135

yes

characteristic

269

C₂×C₄

#14579136

yes

characteristic

270

C₂×C₄

#14579136

yes

characteristic

271

C₂×C₄

#14579146

yes

characteristic

272

C₂×C₄

#14579150

yes

characteristic

273

C₂×C₄

SD₁₆×D₇₉

yes

characteristic

274

C₂×C₄

#14579182

yes

characteristic

275

C₂×C₄

#14579190

yes

characteristic

276

C₂×C₄

#14579190

yes

characteristic

277

C₈

—

278

C₈

—

279

C₈

—

280

C₈

—

632

—

281

C₈

—

632

—

282

C₂²

—

283

C₂²

—

284

C₂²

#19098480

yes

characteristic

285

C₂²

#19098895

yes

characteristic

286

C₂²

#19098907

yes

characteristic

287

C₄

—

288

C₄

—

289

C₄

—

290

C₄

—

316

—

291

C₄

—

632

—

292

C₄

—

632

—

293

C₄

#19098700

yes

characteristic

294

C₄

#19098722

yes

characteristic

295

C₄

#19098793

yes

characteristic

296

C₄

#19098822

yes

characteristic

297

C₄

#19098838

yes

—

298

C₂

—

299

C₂

—

300

C₂

#23764598

yes

characteristic

301

C₂

#23764668

yes

characteristic

302

C₂

#23764675

yes

characteristic

	subgroup	G/H
center	C₂²	#19098480
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1570	C₂
socle	C₂²×C₇₉	#394
prime radical	C₂³×C₇₉	#123
hypercenter	#1570	D₇₉
hypocenter	C₇₉	#10454
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1570

subgroup

G/H

center

C₂²

#19098480

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1570

C₂

C₂²×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1570

N	H ≅ G/N	type
159. C₇₉	#10454	semidirect

H ≅ G/N

type

159. C₇₉

#10454

semidirect

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

subgroup	index
C₂×#19098859	2
#23763393	2
#23762086	2
#23762080	2
#23761794	2
#23761297	2
C₇₉×#1570	2
#10454	79

subgroup

index

C₇₉×#1570

Subgroups — #34191935

Conjugacy classes of subgroups

Complements

Maximal subgroups