Group #34207622 — subgroups

Subgroups — #34207622

Order 20224.

462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19098367	C₂	1	2	yes	maximal
2	C₂×#19098367	C₂	1	2	yes	maximal
3	#23764133	C₂	1	1	yes	maximal, characteristic
4	#23761478	C₂	1	1	yes	maximal, characteristic
5	C₂×#494×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇₉⋊C₁₆	C₂²	1	2	yes	—
7	C₂×#14579095	C₂²	1	1	yes	characteristic
8	C₂×#14579095	C₂²	1	1	yes	characteristic
9	#19098461	—	2	1	no	—
10	#19098367	—	2	4	no	—
11	#19098367	—	2	4	no	—
12	#19098326	—	2	1	no	—
13	C₂²×Q₁₆×C₇₉	—	2	1	no	—
14	C₂²×Q₁₆×C₇₉	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
16	#494×C₇₉	—	2	4	no	—
17	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Dic₇₉	—	2	1	no	—
19	C₂×C₄⋊Dic₇₉	—	2	1	no	—
20	C₂×Dic₇₉⋊C₄	—	4	1	no	—
21	C₂×C₇₉⋊C₁₆	—	2	2	no	—
22	C₂×C₇₉⋊C₁₆	—	2	2	no	—
23	C₂×C₇₉⋊C₁₆	—	2	2	no	—
24	#14579095	—	2	1	no	—
25	#14579095	—	2	2	no	—
26	#14579095	D₄	1	2	yes	—
27	C₇₉⋊#95	—	4	1	no	—
28	C₂²×Q₈×C₇₉	—	2	2	no	—
29	C₂×Q₁₆×C₇₉	—	2	4	no	—
30	C₂×Q₁₆×C₇₉	—	2	2	no	—
31	C₂×Q₁₆×C₇₉	—	2	2	no	—
32	C₂×Q₁₆×C₇₉	—	2	2	no	—
33	C₂×Q₁₆×C₇₉	—	2	2	no	—
34	C₂×Q₁₆×C₇₉	—	2	2	no	—
35	C₂×Q₁₆×C₇₉	—	4	2	no	—
36	C₂×Q₁₆×C₇₉	—	4	2	no	—
37	C₂×Q₁₆×C₇₉	D₄	1	4	yes	—
38	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
40	C₄⋊Q₈×C₇₉	—	2	4	no	—
41	C₄⋊Q₈×C₇₉	—	4	2	no	—
42	C₂×C₄⋊C₄×C₇₉	—	4	1	no	—
43	C₂×C₄⋊C₄×C₇₉	—	4	1	no	—
44	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
45	C₄×C₈×C₇₉	—	2	2	no	—
46	C₂²×Dic₇₉	—	4	1	no	—
47	C₂²×Dic₇₉	—	4	1	no	—
48	C₄⋊Dic₇₉	—	2	2	no	—
49	C₄⋊Dic₇₉	—	4	1	no	—
50	C₄⋊Dic₇₉	—	4	1	no	—
51	C₄⋊Dic₇₉	—	4	1	no	—
52	Dic₇₉⋊C₄	—	8	2	no	—
53	C₇₉⋊C₁₆	—	4	2	no	—
54	C₂×Q₈×C₇₉	—	2	4	no	—
55	C₂×Q₈×C₇₉	—	4	2	no	—
56	C₂×Q₈×C₇₉	—	4	2	no	—
57	C₂×Q₈×C₇₉	—	4	2	no	—
58	C₂×Q₈×C₇₉	—	4	2	no	—
59	C₂×Q₈×C₇₉	—	4	2	no	—
60	C₂²×C₄×C₇₉	—	4	2	no	—
61	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
62	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
63	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
64	Q₁₆×C₇₉	—	2	4	no	—
65	Q₁₆×C₇₉	—	2	4	no	—
66	Q₁₆×C₇₉	—	4	8	no	—
67	Q₁₆×C₇₉	—	4	2	no	—
68	Q₁₆×C₇₉	—	4	2	no	—
69	C₂×C₈×C₇₉	—	2	1	no	—
70	C₂×C₈×C₇₉	—	2	1	no	—
71	C₂×C₈×C₇₉	SD₁₆	1	2	yes	—
72	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
73	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
75	C₂×C₈×C₇₉	#41	1	2	yes	—
76	C₄⋊C₄×C₇₉	—	4	4	no	—
77	C₄⋊C₄×C₇₉	—	4	4	no	—
78	C₄²×C₇₉	—	2	1	no	—
79	C₄²×C₇₉	—	2	1	no	—
80	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
81	Q₈×C₇₉	—	4	4	no	—
82	Q₈×C₇₉	—	4	4	no	—
83	Q₈×C₇₉	—	8	2	no	—
84	Q₈×C₇₉	—	8	2	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	—	4	4	no	—
90	C₂×C₄×C₇₉	—	8	2	no	—
91	C₂×C₄×C₇₉	—	8	2	no	—
92	C₂×C₄×C₇₉	SD₃₂	1	2	yes	—
93	C₂×C₄×C₇₉	Q₃₂	1	2	yes	—
94	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
95	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
97	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
99	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
100	C₂×Dic₇₉	—	4	2	no	—
101	C₂×Dic₇₉	—	8	1	no	—
102	C₂×Dic₇₉	—	8	1	no	—
103	C₂×Dic₇₉	—	8	1	no	—
104	C₂×Dic₇₉	—	8	1	no	—
105	C₂×Dic₇₉	—	8	1	no	—
106	C₈×C₇₉	—	2	2	no	—
107	C₈×C₇₉	#121	1	2	yes	—
108	C₈×C₇₉	#123	1	2	yes	—
109	C₂²×C₇₉	#447	1	1	yes	characteristic
110	C₂²×C₇₉	#459	1	1	yes	characteristic
111	C₂²×C₇₉	#486	1	1	yes	characteristic
112	C₂²×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
113	C₂²×C₇₉	C₂×Q₃₂	1	1	yes	characteristic
114	C₂²×C₇₉	#510	1	1	yes	characteristic
115	C₂²×C₇₉	#510	1	1	yes	characteristic
116	C₄×C₇₉	—	2	2	no	—
117	C₄×C₇₉	—	2	2	no	—
118	C₄×C₇₉	—	8	4	no	—
119	C₄×C₇₉	#394	1	1	yes	characteristic
120	C₄×C₇₉	#450	1	1	yes	characteristic
121	C₄×C₇₉	#460	1	1	yes	characteristic
122	C₄×C₇₉	#490	1	1	yes	characteristic
123	Dic₇₉	—	8	2	no	—
124	Dic₇₉	—	16	1	no	—
125	#13409	—	79	1	no	maximal, Sylow
126	C₂×C₇₉	#2041	1	1	yes	characteristic
127	C₂×C₇₉	#2185	1	1	yes	characteristic
128	C₂×C₇₉	#2188	1	1	yes	characteristic
129	C₂×C₇₉	#2208	1	1	yes	characteristic
130	C₂×C₇₉	#2209	1	1	yes	characteristic
131	C₂×C₇₉	#2241	1	1	yes	characteristic
132	C₂×C₇₉	#2245	1	1	yes	characteristic
133	C₂×#494	D₇₉	1	1	yes	characteristic
134	C₂×#358	—	79	2	no	—
135	C₂×#358	—	79	2	no	—
136	#1942	—	79	1	no	—
137	#1374	—	79	1	no	—
138	C₇₉	#13409	1	1	yes	characteristic, complemented, Sylow
139	C₂²×Q₁₆	—	2	1	no	—
140	C₂²×Q₁₆	C₂×D₇₉	1	2	yes	—
141	C₂×C₄⋊Q₈	—	2	1	no	—
142	C₂²×C₁₆	—	79	2	no	—
143	#494	—	2	4	no	—
144	C₂×#107	—	79	1	no	—
145	C₂×#107	—	79	1	no	—
146	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
147	#389	—	158	1	no	—
148	#358	—	158	4	no	—
149	#358	—	158	4	no	—
150	#340	—	158	1	no	—
151	C₂²×Q₈	—	2	2	no	—
152	C₂×Q₁₆	—	2	4	no	—
153	C₂×Q₁₆	—	2	2	no	—
154	C₂×Q₁₆	—	2	2	no	—
155	C₂×Q₁₆	—	2	2	no	—
156	C₂×Q₁₆	—	2	2	no	—
157	C₂×Q₁₆	—	2	2	no	—
158	C₂×Q₁₆	—	4	2	no	—
159	C₂×Q₁₆	—	4	2	no	—
160	C₂×Q₁₆	C₂²⋊D₇₉	1	4	yes	—
161	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
162	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
163	C₄⋊Q₈	—	2	4	no	—
164	C₄⋊Q₈	—	4	2	no	—
165	C₂×C₄⋊C₄	—	4	1	no	—
166	C₂×C₄⋊C₄	—	4	1	no	—
167	C₂×C₄⋊C₄	—	316	1	no	—
168	C₂×C₄⋊C₄	—	158	1	no	—
169	C₂×C₄⋊C₄	—	158	1	no	—
170	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
171	C₂×C₁₆	—	158	2	no	—
172	C₂×C₁₆	—	158	2	no	—
173	C₂×C₁₆	—	158	2	no	—
174	#107	—	79	2	no	—
175	#107	—	158	2	no	—
176	#107	—	158	1	no	—
177	C₄×C₈	—	2	2	no	—
178	#95	—	316	1	no	—
179	C₂×Q₈	—	2	4	no	—
180	C₂×Q₈	—	4	2	no	—
181	C₂×Q₈	—	4	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	2	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	—	316	1	no	—
187	C₂²×C₄	—	316	1	no	—
188	C₂²×C₄	#11929609	1	1	yes	characteristic
189	C₂²×C₄	#11929609	1	1	yes	characteristic
190	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
191	Q₁₆	—	2	4	no	—
192	Q₁₆	—	2	4	no	—
193	Q₁₆	—	4	8	no	—
194	Q₁₆	—	4	2	no	—
195	Q₁₆	—	4	2	no	—
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	—	2	1	no	—
198	C₂×C₈	#11929612	1	2	yes	—
199	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
200	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
201	C₂×C₈	#11929623	1	2	yes	—
202	C₂×C₈	#11929623	1	1	yes	characteristic
203	C₄⋊C₄	—	4	4	no	—
204	C₄⋊C₄	—	4	4	no	—
205	C₄⋊C₄	—	316	1	no	—
206	C₄⋊C₄	—	316	1	no	—
207	C₄⋊C₄	—	316	1	no	—
208	C₄⋊C₄	—	632	2	no	—
209	C₄⋊C₄	—	158	2	no	—
210	C₄²	—	2	1	no	—
211	C₄²	—	2	1	no	—
212	C₁₆	—	316	2	no	—
213	C₂³	C₂×#11929609	1	1	yes	characteristic
214	Q₈	—	4	4	no	—
215	Q₈	—	4	4	no	—
216	Q₈	—	8	2	no	—
217	Q₈	—	8	2	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	—	4	4	no	—
223	C₂×C₄	—	8	2	no	—
224	C₂×C₄	—	8	2	no	—
225	C₂×C₄	—	316	2	no	—
226	C₂×C₄	—	632	1	no	—
227	C₂×C₄	—	632	1	no	—
228	C₂×C₄	—	632	1	no	—
229	C₂×C₄	—	632	1	no	—
230	C₂×C₄	—	632	1	no	—
231	C₂×C₄	#14579104	1	2	yes	—
232	C₂×C₄	#14579107	1	2	yes	—
233	C₂×C₄	#14579130	1	1	yes	characteristic
234	C₂×C₄	#14579132	1	1	yes	characteristic
235	C₂×C₄	#14579148	1	1	yes	characteristic
236	C₂×C₄	C₂×#11929612	1	1	yes	characteristic
237	C₂×C₄	#14579187	1	1	yes	characteristic
238	C₂×C₄	#14579187	1	1	yes	characteristic
239	C₈	—	2	2	no	—
240	C₈	#14579133	1	2	yes	—
241	C₈	#14579142	1	2	yes	—
242	C₂²	#19098697	1	1	yes	characteristic
243	C₂²	#19098755	1	1	yes	characteristic
244	C₂²	#19098909	1	1	yes	characteristic
245	C₂²	C₂×#14579104	1	1	yes	characteristic
246	C₂²	C₂×#14579107	1	1	yes	characteristic
247	C₂²	#19099004	1	1	yes	characteristic
248	C₂²	#19099004	1	1	yes	characteristic
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	8	4	no	—
252	C₄	—	632	2	no	—
253	C₄	—	1264	1	no	—
254	C₄	#19098477	1	1	yes	characteristic
255	C₄	#19098714	1	1	yes	characteristic
256	C₄	#19098760	1	1	yes	characteristic
257	C₄	#19098927	1	1	yes	characteristic
258	C₂	#23764631	1	1	yes	characteristic
259	C₂	#23765317	1	1	yes	characteristic
260	C₂	#23765334	1	1	yes	characteristic
261	C₂	#23765442	1	1	yes	characteristic
262	C₂	#23765447	1	1	yes	characteristic
263	C₂	#23765627	1	1	yes	characteristic
264	C₂	#23765645	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098367

C₂

yes

maximal

C₂×#19098367

C₂

yes

maximal

#23764133

C₂

yes

maximal, characteristic

#23761478

C₂

yes

maximal, characteristic

C₂×#494×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₁₆

C₂²

yes

—

C₂×#14579095

C₂²

yes

characteristic

C₂×#14579095

C₂²

yes

—

—

—

—

C₂²×Q₁₆×C₇₉

—

C₂²×Q₁₆×C₇₉

C₂²

yes

—

C₂×C₄⋊Q₈×C₇₉

—

#494×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×Dic₇₉⋊C₄

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

—

#14579095

—

#14579095

—

#14579095

D₄

yes

—

C₇₉⋊#95

—

C₂²×Q₈×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

D₄

yes

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₇₉⋊C₁₆

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

D₈

yes

characteristic

C₂²×C₄×C₇₉

D₈

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

SD₁₆

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

C₂×C₈×C₇₉

yes

C₂×C₈×C₇₉

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂×D₈

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×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

SD₃₂

yes

—

C₂×C₄×C₇₉

Q₃₂

yes

—

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂×SD₁₆

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

100

C₂×Dic₇₉

—

101

C₂×Dic₇₉

—

102

C₂×Dic₇₉

—

103

C₂×Dic₇₉

—

104

C₂×Dic₇₉

—

105

C₂×Dic₇₉

—

106

C₈×C₇₉

—

107

C₈×C₇₉

#121

yes

—

108

C₈×C₇₉

#123

yes

—

109

C₂²×C₇₉

#447

yes

characteristic

110

C₂²×C₇₉

#459

yes

characteristic

111

C₂²×C₇₉

#486

yes

characteristic

112

C₂²×C₇₉

C₂×SD₃₂

yes

characteristic

113

C₂²×C₇₉

C₂×Q₃₂

yes

characteristic

114

C₂²×C₇₉

#510

yes

characteristic

115

C₂²×C₇₉

#510

yes

characteristic

116

C₄×C₇₉

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

#394

yes

characteristic

120

C₄×C₇₉

#450

yes

characteristic

121

C₄×C₇₉

#460

yes

characteristic

122

C₄×C₇₉

#490

yes

characteristic

123

Dic₇₉

—

124

Dic₇₉

—

125

#13409

—

maximal, Sylow

126

C₂×C₇₉

#2041

yes

characteristic

127

C₂×C₇₉

#2185

yes

characteristic

128

C₂×C₇₉

#2188

yes

characteristic

129

C₂×C₇₉

#2208

yes

characteristic

130

C₂×C₇₉

#2209

yes

characteristic

131

C₂×C₇₉

#2241

yes

characteristic

132

C₂×C₇₉

#2245

yes

characteristic

133

C₂×#494

D₇₉

yes

characteristic

134

C₂×#358

—

135

C₂×#358

—

136

#1942

—

137

#1374

—

138

C₇₉

#13409

yes

characteristic, complemented, Sylow

139

C₂²×Q₁₆

—

140

C₂²×Q₁₆

C₂×D₇₉

yes

—

141

C₂×C₄⋊Q₈

—

142

C₂²×C₁₆

—

143

#494

—

144

C₂×#107

—

145

C₂×#107

—

146

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

147

#389

—

158

—

148

#358

—

158

—

149

#358

—

158

—

150

#340

—

158

—

151

C₂²×Q₈

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂×Q₁₆

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

C₂²⋊D₇₉

yes

—

161

C₂²×C₈

C₂²⋊D₇₉

yes

characteristic

162

C₂²×C₈

C₂²×D₇₉

yes

characteristic

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

316

—

168

C₂×C₄⋊C₄

—

158

—

169

C₂×C₄⋊C₄

—

158

—

170

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

171

C₂×C₁₆

—

158

—

172

C₂×C₁₆

—

158

—

173

C₂×C₁₆

—

158

—

174

#107

—

175

#107

—

158

—

176

#107

—

158

—

177

C₄×C₈

—

178

#95

—

316

—

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂²×C₄

—

186

C₂²×C₄

—

316

—

187

C₂²×C₄

—

316

—

188

C₂²×C₄

#11929609

yes

characteristic

189

C₂²×C₄

#11929609

yes

characteristic

190

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

191

Q₁₆

—

192

Q₁₆

—

193

Q₁₆

—

194

Q₁₆

—

195

Q₁₆

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

#11929612

yes

—

199

C₂×C₈

D₄×D₇₉

yes

characteristic

200

C₂×C₈

C₂×C₂²⋊D₇₉

yes

—

201

C₂×C₈

#11929623

yes

—

202

C₂×C₈

#11929623

yes

characteristic

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

316

—

206

C₄⋊C₄

—

316

—

207

C₄⋊C₄

—

316

—

208

C₄⋊C₄

—

632

—

209

C₄⋊C₄

—

158

—

210

C₄²

—

211

C₄²

—

212

C₁₆

—

316

—

213

C₂³

C₂×#11929609

yes

characteristic

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

Q₈

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

316

—

226

C₂×C₄

—

632

—

227

C₂×C₄

—

632

—

228

C₂×C₄

—

632

—

229

C₂×C₄

—

632

—

230

C₂×C₄

—

632

—

231

C₂×C₄

#14579104

yes

—

232

C₂×C₄

#14579107

yes

—

233

C₂×C₄

#14579130

yes

characteristic

234

C₂×C₄

#14579132

yes

characteristic

235

C₂×C₄

#14579148

yes

characteristic

236

C₂×C₄

C₂×#11929612

yes

characteristic

237

C₂×C₄

#14579187

yes

characteristic

238

C₂×C₄

#14579187

yes

characteristic

239

C₈

—

240

C₈

#14579133

yes

—

241

C₈

#14579142

yes

—

242

C₂²

#19098697

yes

characteristic

243

C₂²

#19098755

yes

characteristic

244

C₂²

#19098909

yes

characteristic

245

C₂²

C₂×#14579104

yes

characteristic

246

C₂²

C₂×#14579107

yes

characteristic

247

C₂²

#19099004

yes

characteristic

248

C₂²

#19099004

yes

characteristic

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

632

—

253

C₄

—

1264

—

254

C₄

#19098477

yes

characteristic

255

C₄

#19098714

yes

characteristic

256

C₄

#19098760

yes

characteristic

257

C₄

#19098927

yes

characteristic

258

C₂

#23764631

yes

characteristic

259

C₂

#23765317

yes

characteristic

260

C₂

#23765334

yes

characteristic

261

C₂

#23765442

yes

characteristic

262

C₂

#23765447

yes

characteristic

263

C₂

#23765627

yes

characteristic

264

C₂

#23765645

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#11929609
commutator, cosocle	C₂²×C₈×C₇₉	C₂³
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₂×#494×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₈
hypercenter	C₂×#494	D₇₉
hypocenter	C₇₉	#13409
LCS	G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#494

subgroup

G/H

center

C₂³

C₂×#11929609

commutator, cosocle

C₂²×C₈×C₇₉

C₂³

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₂×#494×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₈

D₇₉

C₇₉

G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#494

N	H ≅ G/N	type
138. C₇₉	#13409	semidirect

H ≅ G/N

type

138. C₇₉

#13409

semidirect

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

subgroup	index
C₂×#19098367	2
#23764133	2
#23761478	2
C₂×#494×C₇₉	2
#13409	79

subgroup

index

C₂×#494×C₇₉

Subgroups — #34207622

Conjugacy classes of subgroups

Complements

Maximal subgroups