Group #34176483 — subgroups

Subgroups — #34176483

Order 20224.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₄×#14579161	C₂	1	1	yes	maximal, characteristic
2	#23763543	C₂	1	1	yes	maximal, characteristic
3	#23761225	C₂	1	4	yes	maximal
4	C₇₉×#1767	C₂	1	1	yes	maximal, characteristic
5	C₂×#14579161	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₁₅₈	C₄	1	2	yes	—
7	#19098469	C₂²	1	2	yes	—
8	#19098461	—	2	1	no	—
9	#19098461	—	2	1	no	—
10	#19098433	C₄	1	1	yes	characteristic
11	C₄×C₄⋊Dic₇₉	—	2	1	no	—
12	C₄×C₄⋊Dic₇₉	—	2	1	no	—
13	#19098318	—	2	1	no	—
14	#19098318	—	2	1	no	—
15	#19098318	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₇₉	—	2	1	no	—
17	C₂×#97×C₇₉	—	2	1	no	—
18	C₄³×C₇₉	C₂²	1	1	yes	characteristic
19	#336×C₇₉	C₂²	1	2	yes	—
20	C₂²×Dic₁₅₈	C₂×C₄	1	2	yes	—
21	C₂²×C₇₉⋊C₈	—	2	2	no	—
22	#14579161	—	2	4	no	—
23	C₄×Dic₁₅₈	—	4	4	no	—
24	C₂×C₄⋊Dic₇₉	—	2	1	no	—
25	C₂×C₄⋊Dic₇₉	—	2	1	no	—
26	C₂×C₄⋊Dic₇₉	—	2	1	no	—
27	C₂×C₄⋊Dic₇₉	—	2	1	no	—
28	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
29	C₂×Dic₇₉⋊C₄	—	2	2	no	—
30	C₂×C₄×Dic₇₉	—	2	2	no	—
31	C₇₉⋊#95	—	2	2	no	—
32	C₇₉⋊#95	—	2	2	no	—
33	C₂²×C₈×C₇₉	—	2	2	no	—
34	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₇₉	D₄	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	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₇₉	—	2	4	no	—
42	#97×C₇₉	—	4	2	no	—
43	C₂×Dic₁₅₈	—	2	2	no	—
44	C₂×Dic₁₅₈	—	4	2	no	—
45	C₂×Dic₁₅₈	—	4	2	no	—
46	C₂×Dic₁₅₈	M₁₆	1	4	yes	—
47	C₂²×Dic₇₉	—	2	2	no	—
48	C₂²×Dic₇₉	—	2	2	no	—
49	C₂×C₇₉⋊C₈	—	4	2	no	—
50	C₂×C₇₉⋊C₈	—	4	2	no	—
51	C₂×C₇₉⋊C₈	—	4	2	no	—
52	C₄⋊Dic₇₉	—	2	4	no	—
53	C₄⋊Dic₇₉	—	2	4	no	—
54	C₄⋊Dic₇₉	—	4	2	no	—
55	C₄⋊Dic₇₉	—	4	2	no	—
56	C₄⋊Dic₇₉	—	4	2	no	—
57	Dic₇₉⋊C₄	—	4	4	no	—
58	C₄×Dic₇₉	—	4	4	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₇₉	—	2	4	no	—
67	C₂×C₈×C₇₉	—	4	2	no	—
68	C₂×C₈×C₇₉	—	4	2	no	—
69	C₄²×C₇₉	—	2	2	no	—
70	C₄²×C₇₉	—	2	2	no	—
71	C₄²×C₇₉	—	2	2	no	—
72	C₄²×C₇₉	—	2	2	no	—
73	C₄²×C₇₉	—	4	1	no	—
74	C₄²×C₇₉	—	4	1	no	—
75	C₄²×C₇₉	SD₁₆	1	2	yes	—
76	C₄²×C₇₉	Q₁₆	1	2	yes	—
77	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
92	C₂×C₄×C₇₉	#100	1	2	yes	—
93	C₂×C₄×C₇₉	#103	1	2	yes	—
94	C₂×C₄×C₇₉	#103	1	2	yes	—
95	C₂×C₄×C₇₉	#104	1	2	yes	—
96	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×C₄×C₇₉	#137	1	2	yes	—
100	C₂×Dic₇₉	—	2	4	no	—
101	C₂×Dic₇₉	—	4	2	no	—
102	C₂×Dic₇₉	—	4	2	no	—
103	C₂×Dic₇₉	—	4	2	no	—
104	C₂×Dic₇₉	—	4	2	no	—
105	C₂×Dic₇₉	—	4	2	no	—
106	Dic₁₅₈	—	4	4	no	—
107	Dic₁₅₈	—	4	4	no	—
108	C₈×C₇₉	—	4	4	no	—
109	C₇₉⋊C₈	—	8	2	no	—
110	C₂²×C₇₉	#407	1	1	yes	characteristic
111	C₂²×C₇₉	#410	1	1	yes	characteristic
112	C₂²×C₇₉	C₂×#100	1	1	yes	characteristic
113	C₂²×C₇₉	C₂×#103	1	1	yes	characteristic
114	C₂²×C₇₉	#419	1	1	yes	characteristic
115	C₂²×C₇₉	C₂×#104	1	1	yes	characteristic
116	C₂²×C₇₉	#421	1	1	yes	characteristic
117	C₄×C₇₉	—	2	2	no	—
118	C₄×C₇₉	—	2	2	no	—
119	C₄×C₇₉	—	2	2	no	—
120	C₄×C₇₉	—	2	2	no	—
121	C₄×C₇₉	—	2	1	no	—
122	C₄×C₇₉	—	2	1	no	—
123	C₄×C₇₉	—	2	2	no	—
124	C₄×C₇₉	—	2	2	no	—
125	Dic₇₉	—	4	4	no	—
126	Dic₇₉	—	8	2	no	—
127	#7624	—	79	1	no	maximal, Sylow
128	C₂×C₇₉	#1466	1	1	yes	characteristic
129	C₂×C₇₉	#1487	1	1	yes	characteristic
130	C₂×C₇₉	#1491	1	1	yes	characteristic
131	C₂×C₇₉	#1503	1	1	yes	characteristic
132	C₂×C₇₉	#1515	1	1	yes	characteristic
133	C₂×C₇₉	#1530	1	1	yes	characteristic
134	C₂×C₇₉	#1548	1	1	yes	characteristic
135	C₄×C₄⋊Q₈	—	79	1	no	—
136	#1839	—	79	1	no	—
137	#1767	D₇₉	1	1	yes	characteristic
138	#1272	—	79	4	no	—
139	C₇₉	#7624	1	1	yes	characteristic, complemented, Sylow
140	C₂×C₄⋊Q₈	—	79	1	no	—
141	C₂×C₄×Q₈	—	79	2	no	—
142	C₂×C₄⋊C₈	—	2	1	no	—
143	C₂×#97	—	2	1	no	—
144	#391	—	79	2	no	—
145	#389	—	158	1	no	—
146	#389	—	158	1	no	—
147	#384	—	79	1	no	—
148	C₄×C₄⋊C₄	—	158	1	no	—
149	C₄×C₄⋊C₄	—	158	1	no	—
150	C₄³	C₂×D₇₉	1	1	yes	characteristic
151	#336	—	79	2	no	—
152	#336	—	158	1	no	—
153	#336	—	158	1	no	—
154	#336	C₂×D₇₉	1	2	yes	—
155	C₂²×Q₈	—	79	2	no	—
156	C₂²×C₈	—	2	2	no	—
157	C₂²×C₈	—	158	2	no	—
158	C₄⋊Q₈	—	158	4	no	—
159	C₄×Q₈	—	316	4	no	—
160	C₂×C₄⋊C₄	—	79	2	no	—
161	C₂×C₄⋊C₄	—	158	2	no	—
162	C₂×C₄⋊C₄	—	158	1	no	—
163	C₂×C₄⋊C₄	—	158	1	no	—
164	C₂×C₄⋊C₄	—	158	1	no	—
165	C₂×C₄⋊C₄	—	158	1	no	—
166	C₂×C₄²	—	158	2	no	—
167	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
168	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
169	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
170	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
171	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
172	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
173	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
174	C₄⋊C₈	—	2	4	no	—
175	#97	—	4	2	no	—
176	#95	—	158	2	no	—
177	#95	—	158	2	no	—
178	C₂×Q₈	—	316	2	no	—
179	C₂×Q₈	—	316	2	no	—
180	C₂×Q₈	—	79	4	no	—
181	C₂×Q₈	—	158	2	no	—
182	C₂²×C₄	—	158	2	no	—
183	C₂²×C₄	—	158	2	no	—
184	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
185	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
186	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
187	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
191	C₂×C₈	—	2	4	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	316	2	no	—
195	C₂×C₈	—	316	2	no	—
196	C₂×C₈	—	316	2	no	—
197	C₄⋊C₄	—	316	2	no	—
198	C₄⋊C₄	—	316	2	no	—
199	C₄⋊C₄	—	316	4	no	—
200	C₄⋊C₄	—	316	2	no	—
201	C₄⋊C₄	—	158	4	no	—
202	C₄⋊C₄	—	158	4	no	—
203	C₄²	—	2	2	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	4	1	no	—
208	C₄²	—	4	1	no	—
209	C₄²	—	316	4	no	—
210	C₄²	#11929612	1	2	yes	—
211	C₄²	#11929614	1	2	yes	—
212	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
213	Q₈	—	316	4	no	—
214	Q₈	—	316	4	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	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	316	2	no	—
230	C₂×C₄	—	316	2	no	—
231	C₂×C₄	—	316	2	no	—
232	C₂×C₄	—	316	2	no	—
233	C₂×C₄	—	316	2	no	—
234	C₂×C₄	—	158	4	no	—
235	C₂×C₄	#14579077	1	2	yes	—
236	C₂×C₄	#14579084	1	2	yes	—
237	C₂×C₄	#14579084	1	2	yes	—
238	C₂×C₄	#14579089	1	2	yes	—
239	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
240	C₂×C₄	C₂×#11929612	1	1	yes	characteristic
241	C₂×C₄	C₂×#11929614	1	1	yes	characteristic
242	C₂×C₄	#14579194	1	2	yes	—
243	C₈	—	4	4	no	—
244	C₈	—	632	2	no	—
245	C₂²	#19098526	1	1	yes	characteristic
246	C₂²	#19098536	1	1	yes	characteristic
247	C₂²	C₂×#14579077	1	1	yes	characteristic
248	C₂²	C₂×#14579084	1	1	yes	characteristic
249	C₂²	#19098573	1	1	yes	characteristic
250	C₂²	C₂×#14579089	1	1	yes	characteristic
251	C₂²	#19098579	1	1	yes	characteristic
252	C₄	—	2	2	no	—
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	2	2	no	—
257	C₄	—	2	2	no	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	316	4	no	—
261	C₄	—	632	2	no	—
262	C₂	#23761740	1	1	yes	characteristic
263	C₂	#23761828	1	1	yes	characteristic
264	C₂	#23761848	1	1	yes	characteristic
265	C₂	#23761898	1	1	yes	characteristic
266	C₂	#23761952	1	1	yes	characteristic
267	C₂	#23762010	1	1	yes	characteristic
268	C₂	#23762082	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#14579161

C₂

yes

maximal, characteristic

#23763543

C₂

yes

maximal, characteristic

#23761225

C₂

yes

maximal

C₇₉×#1767

C₂

yes

maximal, characteristic

C₂×#14579161

C₄

yes

characteristic

C₂×C₄×Dic₁₅₈

C₄

yes

—

#19098469

C₂²

yes

—

#19098461

—

#19098461

—

#19098433

C₄

yes

characteristic

C₄×C₄⋊Dic₇₉

—

C₄×C₄⋊Dic₇₉

—

#19098318

—

#19098318

—

#19098318

C₂²

yes

—

C₂×C₄⋊C₈×C₇₉

—

C₂×#97×C₇₉

—

C₄³×C₇₉

C₂²

yes

characteristic

#336×C₇₉

C₂²

yes

—

C₂²×Dic₁₅₈

C₂×C₄

yes

—

C₂²×C₇₉⋊C₈

—

#14579161

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂×C₄

yes

—

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

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

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

M₁₆

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

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

SD₁₆

yes

—

C₄²×C₇₉

Q₁₆

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

#100

yes

—

C₂×C₄×C₇₉

#103

yes

—

C₂×C₄×C₇₉

#103

yes

—

C₂×C₄×C₇₉

#104

yes

—

C₂×C₄×C₇₉

C₂×M₁₆

yes

—

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₇₉

#137

yes

—

100

C₂×Dic₇₉

—

101

C₂×Dic₇₉

—

102

C₂×Dic₇₉

—

103

C₂×Dic₇₉

—

104

C₂×Dic₇₉

—

105

C₂×Dic₇₉

—

106

Dic₁₅₈

—

107

Dic₁₅₈

—

108

C₈×C₇₉

—

109

C₇₉⋊C₈

—

110

C₂²×C₇₉

#407

yes

characteristic

111

C₂²×C₇₉

#410

yes

characteristic

112

C₂²×C₇₉

C₂×#100

yes

characteristic

113

C₂²×C₇₉

C₂×#103

yes

characteristic

114

C₂²×C₇₉

#419

yes

characteristic

115

C₂²×C₇₉

C₂×#104

yes

characteristic

116

C₂²×C₇₉

#421

yes

characteristic

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

—

120

C₄×C₇₉

—

121

C₄×C₇₉

—

122

C₄×C₇₉

—

123

C₄×C₇₉

—

124

C₄×C₇₉

—

125

Dic₇₉

—

126

Dic₇₉

—

127

#7624

—

maximal, Sylow

128

C₂×C₇₉

#1466

yes

characteristic

129

C₂×C₇₉

#1487

yes

characteristic

130

C₂×C₇₉

#1491

yes

characteristic

131

C₂×C₇₉

#1503

yes

characteristic

132

C₂×C₇₉

#1515

yes

characteristic

133

C₂×C₇₉

#1530

yes

characteristic

134

C₂×C₇₉

#1548

yes

characteristic

135

C₄×C₄⋊Q₈

—

136

#1839

—

137

#1767

D₇₉

yes

characteristic

138

#1272

—

139

C₇₉

#7624

yes

characteristic, complemented, Sylow

140

C₂×C₄⋊Q₈

—

141

C₂×C₄×Q₈

—

142

C₂×C₄⋊C₈

—

143

C₂×#97

—

144

#391

—

145

#389

—

158

—

146

#389

—

158

—

147

#384

—

148

C₄×C₄⋊C₄

—

158

—

149

C₄×C₄⋊C₄

—

158

—

150

C₄³

C₂×D₇₉

yes

characteristic

151

#336

—

152

#336

—

158

—

153

#336

—

158

—

154

#336

C₂×D₇₉

yes

—

155

C₂²×Q₈

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

—

158

C₄⋊Q₈

—

158

—

159

C₄×Q₈

—

316

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

158

—

162

C₂×C₄⋊C₄

—

158

—

163

C₂×C₄⋊C₄

—

158

—

164

C₂×C₄⋊C₄

—

158

—

165

C₂×C₄⋊C₄

—

158

—

166

C₂×C₄²

—

158

—

167

C₂×C₄²

C₄×D₇₉

yes

characteristic

168

C₂×C₄²

C₄×D₇₉

yes

characteristic

169

C₂×C₄²

D₃₁₆

yes

characteristic

170

C₂×C₄²

D₃₁₆

yes

characteristic

171

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

172

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

173

C₂×C₄²

C₂²×D₇₉

yes

characteristic

174

C₄⋊C₈

—

175

#97

—

176

#95

—

158

—

177

#95

—

158

—

178

C₂×Q₈

—

316

—

179

C₂×Q₈

—

316

—

180

C₂×Q₈

—

181

C₂×Q₈

—

158

—

182

C₂²×C₄

—

158

—

183

C₂²×C₄

—

158

—

184

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

185

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

186

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

187

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

188

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

189

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

190

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

316

—

195

C₂×C₈

—

316

—

196

C₂×C₈

—

316

—

197

C₄⋊C₄

—

316

—

198

C₄⋊C₄

—

316

—

199

C₄⋊C₄

—

316

—

200

C₄⋊C₄

—

316

—

201

C₄⋊C₄

—

158

—

202

C₄⋊C₄

—

158

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

316

—

210

C₄²

#11929612

yes

—

211

C₄²

#11929614

yes

—

212

C₂³

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

213

Q₈

—

316

—

214

Q₈

—

316

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

316

—

230

C₂×C₄

—

316

—

231

C₂×C₄

—

316

—

232

C₂×C₄

—

316

—

233

C₂×C₄

—

316

—

234

C₂×C₄

—

158

—

235

C₂×C₄

#14579077

yes

—

236

C₂×C₄

#14579084

yes

—

237

C₂×C₄

#14579084

yes

—

238

C₂×C₄

#14579089

yes

—

239

C₂×C₄

M₁₆×D₇₉

yes

—

240

C₂×C₄

C₂×#11929612

yes

characteristic

241

C₂×C₄

C₂×#11929614

yes

characteristic

242

C₂×C₄

#14579194

yes

—

243

C₈

—

244

C₈

—

632

—

245

C₂²

#19098526

yes

characteristic

246

C₂²

#19098536

yes

characteristic

247

C₂²

C₂×#14579077

yes

characteristic

248

C₂²

C₂×#14579084

yes

characteristic

249

C₂²

#19098573

yes

characteristic

250

C₂²

C₂×#14579089

yes

characteristic

251

C₂²

#19098579

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

316

—

261

C₄

—

632

—

262

C₂

#23761740

yes

characteristic

263

C₂

#23761828

yes

characteristic

264

C₂

#23761848

yes

characteristic

265

C₂

#23761898

yes

characteristic

266

C₂

#23761952

yes

characteristic

267

C₂

#23762010

yes

characteristic

268

C₂

#23762082

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	#7624
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
139. C₇₉	#7624	semidirect

H ≅ G/N

type

139. C₇₉

#7624

semidirect

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

subgroup	index
C₄×#14579161	2
#23763543	2
#23761225	2
C₇₉×#1767	2
#7624	79

subgroup

index

C₇₉×#1767

Subgroups — #34176483

Conjugacy classes of subgroups

Complements

Maximal subgroups