Group #34188377 — subgroups

Subgroups — #34188377

Order 20224.

424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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	#23771763	C₂	1	1	yes	maximal, characteristic
2	#23763149	C₂	1	1	yes	maximal, characteristic
3	#23761282	C₂	1	4	yes	maximal
4	C₇₉×#1767	C₂	1	1	yes	maximal, characteristic
5	C₂×#14579153	C₄	1	2	yes	—
6	C₂×#14579072	C₂²	1	2	yes	—
7	#19098461	—	2	1	no	—
8	#19098461	—	2	1	no	—
9	#19098461	—	2	1	no	—
10	#19098461	—	2	1	no	—
11	#19098433	C₄	1	1	yes	characteristic
12	#19098433	C₄	1	1	yes	characteristic
13	#19098429	C₂²	1	2	yes	—
14	#19098318	—	2	1	no	—
15	#19098318	—	2	1	no	—
16	C₂×C₄⋊C₈×C₇₉	—	2	1	no	—
17	C₂×#97×C₇₉	C₂²	1	2	yes	—
18	C₄³×C₇₉	C₂²	1	1	yes	characteristic
19	#336×C₇₉	—	2	1	no	—
20	C₂²×C₇₉⋊C₈	—	2	2	no	—
21	#14579153	—	4	4	no	—
22	C₂×C₄⋊Dic₇₉	—	2	1	no	—
23	C₂×C₄⋊Dic₇₉	—	2	1	no	—
24	C₂×C₄⋊Dic₇₉	—	2	1	no	—
25	C₂×C₄⋊Dic₇₉	—	2	1	no	—
26	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
27	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
28	C₂×Dic₇₉⋊C₄	—	2	2	no	—
29	C₂×Dic₇₉⋊C₄	—	2	2	no	—
30	#14579072	—	2	2	no	—
31	#14579072	Q₈	1	4	yes	—
32	C₇₉⋊#95	—	2	2	no	—
33	C₇₉⋊#95	—	2	2	no	—
34	C₂²×C₈×C₇₉	—	2	2	no	—
35	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₉	—	2	4	no	—
43	#97×C₇₉	—	2	4	no	—
44	C₂²×Dic₇₉	—	2	2	no	—
45	C₂²×Dic₇₉	—	2	2	no	—
46	C₂×C₇₉⋊C₈	—	2	4	no	—
47	C₂×C₇₉⋊C₈	—	4	2	no	—
48	C₂×C₇₉⋊C₈	—	4	2	no	—
49	C₄⋊Dic₇₉	—	4	2	no	—
50	C₄⋊Dic₇₉	—	4	2	no	—
51	C₄⋊Dic₇₉	—	4	2	no	—
52	C₄⋊Dic₇₉	—	4	2	no	—
53	C₄⋊Dic₇₉	—	4	2	no	—
54	C₄⋊Dic₇₉	—	4	2	no	—
55	Dic₇₉⋊C₄	—	4	4	no	—
56	Dic₇₉⋊C₄	—	4	4	no	—
57	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₇₉	—	2	4	no	—
65	C₂×C₈×C₇₉	—	4	2	no	—
66	C₂×C₈×C₇₉	—	4	2	no	—
67	C₄²×C₇₉	—	2	2	no	—
68	C₄²×C₇₉	—	2	2	no	—
69	C₄²×C₇₉	—	2	2	no	—
70	C₄²×C₇₉	—	4	1	no	—
71	C₄²×C₇₉	—	4	1	no	—
72	C₄²×C₇₉	—	4	1	no	—
73	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
74	C₄²×C₇₉	#41	1	2	yes	—
75	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₇₉	—	2	1	no	—
77	C₂×C₄×C₇₉	—	2	1	no	—
78	C₂×C₄×C₇₉	—	2	1	no	—
79	C₂×C₄×C₇₉	—	2	1	no	—
80	C₂×C₄×C₇₉	—	2	1	no	—
81	C₂×C₄×C₇₉	—	2	1	no	—
82	C₂×C₄×C₇₉	—	2	1	no	—
83	C₂×C₄×C₇₉	—	2	1	no	—
84	C₂×C₄×C₇₉	—	2	1	no	—
85	C₂×C₄×C₇₉	—	2	1	no	—
86	C₂×C₄×C₇₉	—	2	1	no	—
87	C₂×C₄×C₇₉	—	2	1	no	—
88	C₂×C₄×C₇₉	—	2	1	no	—
89	C₂×C₄×C₇₉	—	2	1	no	—
90	C₂×C₄×C₇₉	—	2	1	no	—
91	C₂×C₄×C₇₉	#100	1	2	yes	—
92	C₂×C₄×C₇₉	#101	1	2	yes	—
93	C₂×C₄×C₇₉	#104	1	2	yes	—
94	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
95	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
96	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
97	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
98	C₂×Dic₇₉	—	4	2	no	—
99	C₂×Dic₇₉	—	4	2	no	—
100	C₂×Dic₇₉	—	4	2	no	—
101	C₂×Dic₇₉	—	4	2	no	—
102	C₂×Dic₇₉	—	4	2	no	—
103	C₂×Dic₇₉	—	4	2	no	—
104	C₈×C₇₉	—	4	4	no	—
105	C₇₉⋊C₈	—	4	4	no	—
106	C₂²×C₇₉	#391	1	1	yes	characteristic
107	C₂²×C₇₉	C₂×#100	1	1	yes	characteristic
108	C₂²×C₇₉	C₂×#101	1	1	yes	characteristic
109	C₂²×C₇₉	C₂×#104	1	1	yes	characteristic
110	C₂²×C₇₉	#421	1	1	yes	characteristic
111	C₂²×C₇₉	#421	1	1	yes	characteristic
112	C₂²×C₇₉	#421	1	1	yes	characteristic
113	C₄×C₇₉	—	2	1	no	—
114	C₄×C₇₉	—	2	1	no	—
115	C₄×C₇₉	—	2	2	no	—
116	C₄×C₇₉	—	2	2	no	—
117	C₄×C₇₉	—	2	2	no	—
118	C₄×C₇₉	—	2	2	no	—
119	C₄×C₇₉	—	2	2	no	—
120	C₄×C₇₉	—	4	1	no	—
121	Dic₇₉	—	8	2	no	—
122	Dic₇₉	—	8	2	no	—
123	#9894	—	79	1	no	maximal, Sylow
124	C₂×C₇₉	#1528	1	1	yes	characteristic
125	C₂×C₇₉	#1530	1	1	yes	characteristic
126	C₂×C₇₉	#1534	1	1	yes	characteristic
127	C₂×C₇₉	#1536	1	1	yes	characteristic
128	C₂×C₇₉	#1986	1	1	yes	characteristic
129	C₂×C₇₉	#1995	1	1	yes	characteristic
130	C₂×C₇₉	#1997	1	1	yes	characteristic
131	#2859	—	79	1	no	—
132	#1767	D₇₉	1	1	yes	characteristic
133	#1745	—	79	1	no	—
134	#1295	—	79	4	no	—
135	C₇₉	#9894	1	1	yes	characteristic, complemented, Sylow
136	C₂×#125	—	79	2	no	—
137	C₂×C₄⋊C₈	—	2	1	no	—
138	C₂×#97	—	79	2	no	—
139	C₂×#97	C₂×D₇₉	1	2	yes	—
140	#389	—	158	1	no	—
141	#389	—	158	1	no	—
142	#389	—	158	1	no	—
143	#389	—	158	1	no	—
144	#384	—	79	1	no	—
145	#384	—	79	1	no	—
146	#382	—	79	2	no	—
147	C₄³	C₂×D₇₉	1	1	yes	characteristic
148	#336	—	2	1	no	—
149	#336	—	158	1	no	—
150	#336	—	158	1	no	—
151	C₂²×C₈	—	2	2	no	—
152	C₂²×C₈	—	158	2	no	—
153	#125	—	316	4	no	—
154	C₂×C₄⋊C₄	—	79	2	no	—
155	C₂×C₄⋊C₄	—	79	2	no	—
156	C₂×C₄⋊C₄	—	158	2	no	—
157	C₂×C₄⋊C₄	—	158	2	no	—
158	C₂×C₄⋊C₄	—	158	1	no	—
159	C₂×C₄⋊C₄	—	158	1	no	—
160	C₂×C₄⋊C₄	—	158	1	no	—
161	C₂×C₄⋊C₄	—	158	1	no	—
162	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
163	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
164	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
165	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
166	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
167	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
168	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
169	C₄⋊C₈	—	2	4	no	—
170	#97	—	2	4	no	—
171	#97	—	79	4	no	—
172	#97	—	158	2	no	—
173	#95	—	158	2	no	—
174	#95	—	158	2	no	—
175	C₂²×C₄	—	158	2	no	—
176	C₂²×C₄	—	158	2	no	—
177	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
178	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
179	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
180	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
181	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
183	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
184	C₂×C₈	—	2	4	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	316	2	no	—
188	C₂×C₈	—	316	2	no	—
189	C₂×C₈	—	158	4	no	—
190	C₄⋊C₄	—	316	2	no	—
191	C₄⋊C₄	—	316	2	no	—
192	C₄⋊C₄	—	316	4	no	—
193	C₄⋊C₄	—	316	2	no	—
194	C₄⋊C₄	—	316	2	no	—
195	C₄⋊C₄	—	316	2	no	—
196	C₄⋊C₄	—	316	4	no	—
197	C₄⋊C₄	—	316	2	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	4	1	no	—
202	C₄²	—	4	1	no	—
203	C₄²	—	4	1	no	—
204	C₄²	Q₈×D₇₉	1	2	yes	—
205	C₄²	#11929623	1	2	yes	—
206	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	316	2	no	—
223	C₂×C₄	—	316	2	no	—
224	C₂×C₄	—	316	2	no	—
225	C₂×C₄	—	316	2	no	—
226	C₂×C₄	—	316	2	no	—
227	C₂×C₄	—	316	2	no	—
228	C₂×C₄	#14579077	1	2	yes	—
229	C₂×C₄	#14579079	1	2	yes	—
230	C₂×C₄	#14579089	1	2	yes	—
231	C₂×C₄	#14579126	1	2	yes	—
232	C₂×C₄	#14579141	1	2	yes	—
233	C₂×C₄	#14579148	1	1	yes	characteristic
234	C₂×C₄	#14579159	1	1	yes	characteristic
235	C₈	—	4	4	no	—
236	C₈	—	316	4	no	—
237	C₂²	#19098468	1	1	yes	characteristic
238	C₂²	C₂×#14579077	1	1	yes	characteristic
239	C₂²	C₂×#14579079	1	1	yes	characteristic
240	C₂²	C₂×#14579089	1	1	yes	characteristic
241	C₂²	#19098579	1	1	yes	characteristic
242	C₂²	#19098579	1	1	yes	characteristic
243	C₂²	#19098581	1	1	yes	characteristic
244	C₄	—	2	2	no	—
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	4	1	no	—
252	C₄	—	632	2	no	—
253	C₄	—	632	2	no	—
254	C₂	#23762001	1	1	yes	characteristic
255	C₂	#23762010	1	1	yes	characteristic
256	C₂	#23762026	1	1	yes	characteristic
257	C₂	#23762034	1	1	yes	characteristic
258	C₂	#23764343	1	1	yes	characteristic
259	C₂	#23764380	1	1	yes	characteristic
260	C₂	#23764388	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23771763

C₂

yes

maximal, characteristic

#23763149

C₂

yes

maximal, characteristic

#23761282

C₂

yes

maximal

C₇₉×#1767

C₂

yes

maximal, characteristic

C₂×#14579153

C₄

yes

—

C₂×#14579072

C₂²

yes

—

—

—

—

—

C₄

yes

characteristic

#19098433

C₄

yes

characteristic

#19098429

C₂²

yes

—

#19098318

—

#19098318

—

C₂×C₄⋊C₈×C₇₉

—

C₂×#97×C₇₉

C₂²

yes

—

C₄³×C₇₉

C₂²

yes

characteristic

#336×C₇₉

—

C₂²×C₇₉⋊C₈

—

#14579153

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₇₉

C₂×C₄

yes

—

C₂×Dic₇₉⋊C₄

—

C₂×Dic₇₉⋊C₄

—

#14579072

—

#14579072

Q₈

yes

—

C₇₉⋊#95

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

—

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

#97×C₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×Q₈

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#100

yes

—

C₂×C₄×C₇₉

#101

yes

—

C₂×C₄×C₇₉

#104

yes

—

C₂×C₄×C₇₉

C₄×Q₈

yes

—

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₉

#124

yes

characteristic

C₂×C₄×C₇₉

C₄⋊Q₈

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

100

C₂×Dic₇₉

—

101

C₂×Dic₇₉

—

102

C₂×Dic₇₉

—

103

C₂×Dic₇₉

—

104

C₈×C₇₉

—

105

C₇₉⋊C₈

—

106

C₂²×C₇₉

#391

yes

characteristic

107

C₂²×C₇₉

C₂×#100

yes

characteristic

108

C₂²×C₇₉

C₂×#101

yes

characteristic

109

C₂²×C₇₉

C₂×#104

yes

characteristic

110

C₂²×C₇₉

#421

yes

characteristic

111

C₂²×C₇₉

#421

yes

characteristic

112

C₂²×C₇₉

#421

yes

characteristic

113

C₄×C₇₉

—

114

C₄×C₇₉

—

115

C₄×C₇₉

—

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

—

120

C₄×C₇₉

—

121

Dic₇₉

—

122

Dic₇₉

—

123

#9894

—

maximal, Sylow

124

C₂×C₇₉

#1528

yes

characteristic

125

C₂×C₇₉

#1530

yes

characteristic

126

C₂×C₇₉

#1534

yes

characteristic

127

C₂×C₇₉

#1536

yes

characteristic

128

C₂×C₇₉

#1986

yes

characteristic

129

C₂×C₇₉

#1995

yes

characteristic

130

C₂×C₇₉

#1997

yes

characteristic

131

#2859

—

132

#1767

D₇₉

yes

characteristic

133

#1745

—

134

#1295

—

135

C₇₉

#9894

yes

characteristic, complemented, Sylow

136

C₂×#125

—

137

C₂×C₄⋊C₈

—

138

C₂×#97

—

139

C₂×#97

C₂×D₇₉

yes

—

140

#389

—

158

—

141

#389

—

158

—

142

#389

—

158

—

143

#389

—

158

—

144

#384

—

145

#384

—

146

#382

—

147

C₄³

C₂×D₇₉

yes

characteristic

148

#336

—

149

#336

—

158

—

150

#336

—

158

—

151

C₂²×C₈

—

152

C₂²×C₈

—

158

—

153

#125

—

316

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

158

—

157

C₂×C₄⋊C₄

—

158

—

158

C₂×C₄⋊C₄

—

158

—

159

C₂×C₄⋊C₄

—

158

—

160

C₂×C₄⋊C₄

—

158

—

161

C₂×C₄⋊C₄

—

158

—

162

C₂×C₄²

C₄×D₇₉

yes

characteristic

163

C₂×C₄²

C₄×D₇₉

yes

characteristic

164

C₂×C₄²

D₃₁₆

yes

characteristic

165

C₂×C₄²

D₃₁₆

yes

characteristic

166

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

167

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

168

C₂×C₄²

C₂²×D₇₉

yes

characteristic

169

C₄⋊C₈

—

170

#97

—

171

#97

—

172

#97

—

158

—

173

#95

—

158

—

174

#95

—

158

—

175

C₂²×C₄

—

158

—

176

C₂²×C₄

—

158

—

177

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

178

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

179

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

180

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

181

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

182

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

183

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

316

—

188

C₂×C₈

—

316

—

189

C₂×C₈

—

158

—

190

C₄⋊C₄

—

316

—

191

C₄⋊C₄

—

316

—

192

C₄⋊C₄

—

316

—

193

C₄⋊C₄

—

316

—

194

C₄⋊C₄

—

316

—

195

C₄⋊C₄

—

316

—

196

C₄⋊C₄

—

316

—

197

C₄⋊C₄

—

316

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

Q₈×D₇₉

yes

—

205

C₄²

#11929623

yes

—

206

C₂³

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

316

—

223

C₂×C₄

—

316

—

224

C₂×C₄

—

316

—

225

C₂×C₄

—

316

—

226

C₂×C₄

—

316

—

227

C₂×C₄

—

316

—

228

C₂×C₄

#14579077

yes

—

229

C₂×C₄

#14579079

yes

—

230

C₂×C₄

#14579089

yes

—

231

C₂×C₄

#14579126

yes

—

232

C₂×C₄

#14579141

yes

—

233

C₂×C₄

#14579148

yes

characteristic

234

C₂×C₄

#14579159

yes

characteristic

235

C₈

—

236

C₈

—

316

—

237

C₂²

#19098468

yes

characteristic

238

C₂²

C₂×#14579077

yes

characteristic

239

C₂²

C₂×#14579079

yes

characteristic

240

C₂²

C₂×#14579089

yes

characteristic

241

C₂²

#19098579

yes

characteristic

242

C₂²

#19098579

yes

characteristic

243

C₂²

#19098581

yes

characteristic

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

632

—

253

C₄

—

632

—

254

C₂

#23762001

yes

characteristic

255

C₂

#23762010

yes

characteristic

256

C₂

#23762026

yes

characteristic

257

C₂

#23762034

yes

characteristic

258

C₂

#23764343

yes

characteristic

259

C₂

#23764380

yes

characteristic

260

C₂

#23764388

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₇₉)⋊C₄
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1767	C₂
socle, prime radical	C₂³×C₇₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1767	D₇₉
hypocenter	C₇₉	#9894
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

subgroup

G/H

center

C₂³

C₂×(C₂×D₇₉)⋊C₄

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1767

C₂

socle, prime radical

C₂³×C₇₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

N	H ≅ G/N	type
135. C₇₉	#9894	semidirect

H ≅ G/N

type

135. C₇₉

#9894

semidirect

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

subgroup	index
#23771763	2
#23763149	2
#23761282	2
C₇₉×#1767	2
#9894	79

subgroup

index

C₇₉×#1767

Subgroups — #34188377

Conjugacy classes of subgroups

Complements

Maximal subgroups