Group #34205016 — subgroups

Subgroups — #34205016

Order 20224.

396 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19098669	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098385	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098380	C₂	1	1	yes	maximal, characteristic
4	#23765119	C₂	1	1	yes	maximal, characteristic
5	#23764154	C₂	1	1	yes	maximal, characteristic
6	#23761479	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1386	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₁₆	C₂²	1	1	yes	characteristic
9	C₂×#14579126	—	2	1	no	—
10	C₂×#14579101	C₂²	1	1	yes	characteristic
11	#19098669	—	2	2	no	—
12	#19098669	—	2	2	no	—
13	C₂×#14579097	C₂²	1	1	yes	characteristic
14	#19098590	—	2	1	no	—
15	C₂×#14579084	—	2	1	no	—
16	C₂×#14579071	C₂²	1	1	yes	characteristic
17	#19098385	—	2	2	no	—
18	#19098380	—	2	2	no	—
19	#19098366	C₄	1	4	yes	complemented
20	#19098322	—	2	1	no	—
21	C₂×M₃₂×C₇₉	C₂²	1	1	yes	characteristic
22	#427×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
24	C₂²×Dic₁₅₈	—	2	1	no	—
25	C₂×Dic₃₁₆	—	2	1	no	—
26	C₂×Dic₃₁₆	—	2	1	no	—
27	C₂×Dic₃₁₆	—	2	1	no	—
28	C₂×Dic₃₁₆	C₂×C₄	1	2	yes	—
29	C₂×Dic₃₁₆	D₄	1	2	yes	—
30	C₂×Dic₃₁₆	Q₈	1	2	yes	—
31	C₂×#11929608	—	2	1	no	—
32	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
33	#14579126	—	2	4	no	—
34	#14579126	—	4	2	no	—
35	C₂×Dic₇₉⋊C₄	—	4	1	no	—
36	C₂×C₄×Dic₇₉	—	4	1	no	—
37	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
38	#14579101	—	2	1	no	—
39	#14579101	—	2	1	no	—
40	C₂×C₇₉⋊C₁₆	C₂×C₄	1	2	yes	—
41	#14579097	—	2	1	no	—
42	#14579097	—	2	1	no	—
43	C₄⋊(C₇₉⋊C₈)	—	4	2	no	—
44	#14579084	—	2	4	no	—
45	#14579071	—	2	1	no	—
46	#14579071	—	2	1	no	—
47	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
48	#117×C₇₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
50	M₃₂×C₇₉	—	2	1	no	—
51	M₃₂×C₇₉	—	2	1	no	—
52	C₂×C₁₆×C₇₉	—	2	1	no	—
53	#107×C₇₉	C₂×C₄	1	2	yes	—
54	#106×C₇₉	—	2	1	no	—
55	#106×C₇₉	—	2	1	no	—
56	#106×C₇₉	D₄	1	2	yes	—
57	C₂×Dic₁₅₈	—	2	2	no	—
58	C₂×Dic₁₅₈	—	2	2	no	—
59	C₂×Dic₁₅₈	—	2	2	no	—
60	C₂×Dic₁₅₈	—	4	1	no	—
61	C₂×Dic₁₅₈	—	4	1	no	—
62	C₂×Dic₁₅₈	—	4	1	no	—
63	C₂²×Dic₇₉	—	2	1	no	—
64	C₂²×Dic₇₉	—	4	1	no	—
65	Dic₃₁₆	—	2	2	no	—
66	Dic₃₁₆	—	2	2	no	—
67	Dic₃₁₆	—	2	2	no	—
68	Dic₃₁₆	C₄⋊C₄	1	4	yes	—
69	#11929608	—	4	1	no	—
70	#11929608	—	4	1	no	—
71	C₂×C₇₉⋊C₈	—	2	1	no	—
72	C₂×C₇₉⋊C₈	—	2	1	no	—
73	C₂×C₇₉⋊C₈	—	2	1	no	—
74	C₂×C₇₉⋊C₈	—	4	1	no	—
75	Dic₇₉⋊C₄	—	4	4	no	—
76	C₄×Dic₇₉	—	2	1	no	—
77	C₄×Dic₇₉	—	4	4	no	—
78	C₄×Dic₇₉	SD₁₆	1	2	yes	—
79	C₇₉⋊C₁₆	—	2	2	no	—
80	C₂²×C₄×C₇₉	—	4	1	no	—
81	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
86	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
87	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
88	C₄⋊C₄×C₇₉	—	2	2	no	—
89	C₄⋊C₄×C₇₉	—	2	2	no	—
90	C₄⋊C₄×C₇₉	—	4	1	no	—
91	C₂²⋊C₄×C₇₉	—	4	1	no	—
92	C₄²×C₇₉	—	4	1	no	—
93	C₁₆×C₇₉	—	4	1	no	—
94	C₂³×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₇₉	—	4	2	no	—
96	C₂×C₄×C₇₉	—	4	2	no	—
97	C₂×C₄×C₇₉	—	8	2	no	—
98	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
100	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
101	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
103	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂×Dic₇₉	—	2	2	no	—
105	C₂×Dic₇₉	—	4	2	no	—
106	C₂×Dic₇₉	—	4	2	no	—
107	C₂×Dic₇₉	—	4	2	no	—
108	C₂×Dic₇₉	—	4	2	no	—
109	Dic₁₅₈	—	2	4	no	—
110	Dic₁₅₈	—	4	2	no	—
111	Dic₁₅₈	—	4	2	no	—
112	Dic₁₅₈	—	4	2	no	—
113	C₈×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
115	C₈×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
116	C₈×C₇₉	#123	1	1	yes	characteristic
117	C₇₉⋊C₈	—	4	1	no	—
118	C₇₉⋊C₈	—	8	1	no	—
119	C₂²×C₇₉	—	2	2	no	—
120	C₂²×C₇₉	#442	1	1	yes	characteristic
121	C₂²×C₇₉	#450	1	1	yes	characteristic
122	C₂²×C₇₉	#478	1	1	yes	characteristic
123	C₄×C₇₉	—	8	2	no	—
124	C₄×C₇₉	—	8	2	no	—
125	C₄×C₇₉	#385	1	1	yes	characteristic
126	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
127	C₄×C₇₉	#449	1	1	yes	characteristic
128	C₄×C₇₉	#476	1	1	yes	characteristic
129	Dic₇₉	—	4	2	no	—
130	Dic₇₉	—	4	4	no	—
131	#12957	—	79	1	no	maximal, Sylow
132	C₂×C₇₉	—	2	1	no	—
133	C₂×C₇₉	—	2	1	no	—
134	C₂×C₇₉	#1864	1	1	yes	characteristic
135	C₂×C₇₉	#2180	1	2	yes	—
136	C₂×#441	—	79	1	no	—
137	C₂×#365	—	79	1	no	—
138	C₂×#362	—	79	1	no	—
139	#2141	—	79	1	no	—
140	#1946	—	79	1	no	—
141	#1386	D₇₉	1	1	yes	characteristic
142	#1375	—	79	1	no	—
143	C₇₉	#12957	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₁₆	—	79	1	no	—
145	C₂×C₄×Q₈	—	158	1	no	—
146	C₂×M₃₂	—	79	1	no	—
147	C₂×M₃₂	C₂×D₇₉	1	1	yes	characteristic
148	#441	—	158	2	no	—
149	#441	—	158	2	no	—
150	C₂×#108	—	79	1	no	—
151	#427	C₂×D₇₉	1	1	yes	characteristic
152	C₂×#106	C₂×D₇₉	1	1	yes	characteristic
153	#424	—	158	1	no	—
154	C₂×#103	—	158	1	no	—
155	C₂×#97	—	79	1	no	—
156	#365	—	158	2	no	—
157	#362	—	158	2	no	—
158	#358	—	79	4	no	—
159	#339	—	158	1	no	—
160	C₂²×Q₈	—	158	1	no	—
161	C₂×Q₁₆	—	79	2	no	—
162	C₂×Q₁₆	—	79	2	no	—
163	C₂×Q₁₆	—	79	2	no	—
164	C₂×Q₁₆	—	158	1	no	—
165	C₂×Q₁₆	—	158	1	no	—
166	C₂×Q₁₆	—	158	1	no	—
167	C₂×M₁₆	—	158	1	no	—
168	C₂²×C₈	—	79	1	no	—
169	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
170	C₄×Q₈	—	316	2	no	—
171	C₄×Q₈	—	158	4	no	—
172	#117	—	2	1	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	316	1	no	—
175	C₂×C₄²	—	316	1	no	—
176	C₂×C₄²	—	79	1	no	—
177	M₃₂	—	2	1	no	—
178	M₃₂	—	2	1	no	—
179	M₃₂	—	158	1	no	—
180	M₃₂	—	158	1	no	—
181	C₂×C₁₆	—	2	1	no	—
182	C₂×C₁₆	—	79	2	no	—
183	#108	—	158	1	no	—
184	#108	—	158	1	no	—
185	#107	C₄×D₇₉	1	2	yes	—
186	#106	—	2	1	no	—
187	#106	—	2	1	no	—
188	#106	D₃₁₆	1	2	yes	—
189	C₄⋊C₈	—	316	2	no	—
190	#103	—	158	4	no	—
191	#97	—	158	1	no	—
192	#97	—	158	1	no	—
193	C₂×Q₈	—	316	1	no	—
194	C₂×Q₈	—	316	1	no	—
195	C₂×Q₈	—	316	1	no	—
196	C₂×Q₈	—	158	2	no	—
197	C₂×Q₈	—	158	2	no	—
198	C₂×Q₈	—	158	2	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	316	1	no	—
201	C₂²×C₄	—	158	1	no	—
202	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
203	Q₁₆	—	79	4	no	—
204	Q₁₆	—	158	2	no	—
205	Q₁₆	—	158	2	no	—
206	Q₁₆	—	158	2	no	—
207	M₁₆	—	316	1	no	—
208	M₁₆	—	316	1	no	—
209	C₂×C₈	—	316	1	no	—
210	C₂×C₈	—	158	1	no	—
211	C₂×C₈	—	158	1	no	—
212	C₂×C₈	—	158	1	no	—
213	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
214	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
215	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
216	C₂×C₈	Q₈×D₇₉	1	1	yes	characteristic
217	C₂×C₈	#11929623	1	1	yes	characteristic
218	C₂×C₈	#11929624	1	1	yes	characteristic
219	C₄⋊C₄	—	2	2	no	—
220	C₄⋊C₄	—	2	2	no	—
221	C₄⋊C₄	—	4	1	no	—
222	C₄⋊C₄	—	316	4	no	—
223	C₂²⋊C₄	—	4	1	no	—
224	C₄²	—	4	1	no	—
225	C₄²	—	316	4	no	—
226	C₄²	—	79	2	no	—
227	C₄²	—	158	1	no	—
228	C₁₆	—	4	1	no	—
229	C₁₆	—	158	2	no	—
230	C₂³	#14579185	1	1	yes	characteristic
231	Q₈	—	316	2	no	—
232	Q₈	—	316	2	no	—
233	Q₈	—	316	2	no	—
234	Q₈	—	158	4	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	8	2	no	—
238	C₂×C₄	—	316	2	no	—
239	C₂×C₄	—	316	2	no	—
240	C₂×C₄	—	316	2	no	—
241	C₂×C₄	—	316	2	no	—
242	C₂×C₄	—	158	2	no	—
243	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
244	C₂×C₄	#14579131	1	1	yes	characteristic
245	C₂×C₄	#14579139	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
247	C₂×C₄	#14579184	1	1	yes	characteristic
248	C₂×C₄	#14579188	1	1	yes	characteristic
249	C₈	—	316	1	no	—
250	C₈	—	632	1	no	—
251	C₈	C₄⋊C₄×D₇₉	1	1	yes	characteristic
252	C₈	C₄×D₃₁₆	1	1	yes	characteristic
253	C₈	#14579141	1	1	yes	characteristic
254	C₈	#14579143	1	1	yes	characteristic
255	C₂²	—	2	2	no	—
256	C₂²	#19098672	1	1	yes	characteristic
257	C₂²	#19098715	1	1	yes	characteristic
258	C₂²	#19098866	1	1	yes	characteristic
259	C₄	—	8	2	no	—
260	C₄	—	8	2	no	—
261	C₄	—	316	2	no	—
262	C₄	—	316	4	no	—
263	C₄	#19098437	1	1	yes	characteristic
264	C₄	#19098648	1	1	yes	characteristic
265	C₄	#19098711	1	1	yes	characteristic
266	C₄	#19098852	1	1	yes	characteristic
267	C₂	—	2	1	no	—
268	C₂	—	2	1	no	—
269	C₂	#23763662	1	1	yes	characteristic
270	C₂	#23765288	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098669

C₂

yes

maximal, characteristic

C₂×#19098385

C₂

yes

maximal, characteristic

C₂×#19098380

C₂

yes

maximal, characteristic

#23765119

C₂

yes

maximal, characteristic

#23764154

C₂

yes

maximal, characteristic

#23761479

C₂

yes

maximal, characteristic

C₇₉×#1386

C₂

yes

maximal, characteristic

C₂²×Dic₃₁₆

C₂²

yes

characteristic

C₂×#14579126

—

C₂×#14579101

C₂²

yes

—

—

C₂²

yes

—

—

C₂²

yes

—

—

C₄

yes

complemented

#19098322

—

C₂×M₃₂×C₇₉

C₂²

yes

characteristic

#427×C₇₉

C₂²

yes

characteristic

C₂×#106×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

C₂×C₄

yes

—

C₂×Dic₃₁₆

D₄

yes

—

C₂×Dic₃₁₆

Q₈

yes

—

C₂×#11929608

—

C₂²×C₇₉⋊C₈

D₄

yes

characteristic

#14579126

—

#14579126

—

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

D₄

yes

characteristic

#14579101

—

#14579101

—

C₂×C₇₉⋊C₁₆

C₂×C₄

yes

—

#14579097

—

#14579097

—

C₄⋊(C₇₉⋊C₈)

—

#14579084

—

#14579071

—

#14579071

—

C₂²×C₈×C₇₉

C₂³

yes

characteristic

#117×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

M₃₂×C₇₉

—

M₃₂×C₇₉

—

C₂×C₁₆×C₇₉

—

#107×C₇₉

C₂×C₄

yes

—

#106×C₇₉

—

#106×C₇₉

—

#106×C₇₉

D₄

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

C₄⋊C₄

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

SD₁₆

yes

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×Q₈

yes

C₂×C₈×C₇₉

yes

C₂×C₈×C₇₉

yes

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

C₂×C₄×C₇₉

#120

yes

characteristic

100

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

101

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

102

C₂×C₄×C₇₉

#135

yes

characteristic

103

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

104

C₂×Dic₇₉

—

105

C₂×Dic₇₉

—

106

C₂×Dic₇₉

—

107

C₂×Dic₇₉

—

108

C₂×Dic₇₉

—

109

Dic₁₅₈

—

110

Dic₁₅₈

—

111

Dic₁₅₈

—

112

Dic₁₅₈

—

113

C₈×C₇₉

C₂×C₄⋊C₄

yes

characteristic

114

C₈×C₇₉

C₄×D₄

yes

characteristic

115

C₈×C₇₉

C₂²⋊Q₈

yes

characteristic

116

C₈×C₇₉

#123

yes

characteristic

117

C₇₉⋊C₈

—

118

C₇₉⋊C₈

—

119

C₂²×C₇₉

—

120

C₂²×C₇₉

#442

yes

characteristic

121

C₂²×C₇₉

#450

yes

characteristic

122

C₂²×C₇₉

#478

yes

characteristic

123

C₄×C₇₉

—

124

C₄×C₇₉

—

125

C₄×C₇₉

#385

yes

characteristic

126

C₄×C₇₉

C₄×SD₁₆

yes

characteristic

127

C₄×C₇₉

#449

yes

characteristic

128

C₄×C₇₉

#476

yes

characteristic

129

Dic₇₉

—

130

Dic₇₉

—

131

#12957

—

maximal, Sylow

132

C₂×C₇₉

—

133

C₂×C₇₉

—

134

C₂×C₇₉

#1864

yes

characteristic

135

C₂×C₇₉

#2180

yes

—

136

C₂×#441

—

137

C₂×#365

—

138

C₂×#362

—

139

#2141

—

140

#1946

—

141

#1386

D₇₉

yes

characteristic

142

#1375

—

143

C₇₉

#12957

yes

characteristic, complemented, Sylow

144

C₂²×Q₁₆

—

145

C₂×C₄×Q₈

—

158

—

146

C₂×M₃₂

—

147

C₂×M₃₂

C₂×D₇₉

yes

characteristic

148

#441

—

158

—

149

#441

—

158

—

150

C₂×#108

—

151

#427

C₂×D₇₉

yes

characteristic

152

C₂×#106

C₂×D₇₉

yes

characteristic

153

#424

—

158

—

154

C₂×#103

—

158

—

155

C₂×#97

—

156

#365

—

158

—

157

#362

—

158

—

158

#358

—

159

#339

—

158

—

160

C₂²×Q₈

—

158

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

158

—

165

C₂×Q₁₆

—

158

—

166

C₂×Q₁₆

—

158

—

167

C₂×M₁₆

—

158

—

168

C₂²×C₈

—

169

C₂²×C₈

C₂²×D₇₉

yes

characteristic

170

C₄×Q₈

—

316

—

171

C₄×Q₈

—

158

—

172

#117

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

316

—

175

C₂×C₄²

—

316

—

176

C₂×C₄²

—

177

M₃₂

—

178

M₃₂

—

179

M₃₂

—

158

—

180

M₃₂

—

158

—

181

C₂×C₁₆

—

182

C₂×C₁₆

—

183

#108

—

158

—

184

#108

—

158

—

185

#107

C₄×D₇₉

yes

—

186

#106

—

187

#106

—

188

#106

D₃₁₆

yes

—

189

C₄⋊C₈

—

316

—

190

#103

—

158

—

191

#97

—

158

—

192

#97

—

158

—

193

C₂×Q₈

—

316

—

194

C₂×Q₈

—

316

—

195

C₂×Q₈

—

316

—

196

C₂×Q₈

—

158

—

197

C₂×Q₈

—

158

—

198

C₂×Q₈

—

158

—

199

C₂²×C₄

—

200

C₂²×C₄

—

316

—

201

C₂²×C₄

—

158

—

202

C₂²×C₄

D₄×D₇₉

yes

characteristic

203

Q₁₆

—

204

Q₁₆

—

158

—

205

Q₁₆

—

158

—

206

Q₁₆

—

158

—

207

M₁₆

—

316

—

208

M₁₆

—

316

—

209

C₂×C₈

—

316

—

210

C₂×C₈

—

158

—

211

C₂×C₈

—

158

—

212

C₂×C₈

—

158

—

213

C₂×C₈

C₂×C₄×D₇₉

yes

characteristic

214

C₂×C₈

D₄×D₇₉

yes

characteristic

215

C₂×C₈

C₂×D₃₁₆

yes

characteristic

216

C₂×C₈

Q₈×D₇₉

yes

characteristic

217

C₂×C₈

#11929623

yes

characteristic

218

C₂×C₈

#11929624

yes

characteristic

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

316

—

223

C₂²⋊C₄

—

224

C₄²

—

225

C₄²

—

316

—

226

C₄²

—

227

C₄²

—

158

—

228

C₁₆

—

229

C₁₆

—

158

—

230

C₂³

#14579185

yes

characteristic

231

Q₈

—

316

—

232

Q₈

—

316

—

233

Q₈

—

316

—

234

Q₈

—

158

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

316

—

239

C₂×C₄

—

316

—

240

C₂×C₄

—

316

—

241

C₂×C₄

—

316

—

242

C₂×C₄

—

158

—

243

C₂×C₄

(C₂²⋊D₇₉)⋊C₄

yes

characteristic

244

C₂×C₄

#14579131

yes

characteristic

245

C₂×C₄

#14579139

yes

characteristic

246

C₂×C₄

SD₁₆×D₇₉

yes

characteristic

247

C₂×C₄

#14579184

yes

characteristic

248

C₂×C₄

#14579188

yes

characteristic

249

C₈

—

316

—

250

C₈

—

632

—

251

C₈

C₄⋊C₄×D₇₉

yes

characteristic

252

C₈

C₄×D₃₁₆

yes

characteristic

253

C₈

#14579141

yes

characteristic

254

C₈

#14579143

yes

characteristic

255

C₂²

—

256

C₂²

#19098672

yes

characteristic

257

C₂²

#19098715

yes

characteristic

258

C₂²

#19098866

yes

characteristic

259

C₄

—

260

C₄

—

261

C₄

—

316

—

262

C₄

—

316

—

263

C₄

#19098437

yes

characteristic

264

C₄

#19098648

yes

characteristic

265

C₄

#19098711

yes

characteristic

266

C₄

#19098852

yes

characteristic

267

C₂

—

268

C₂

—

269

C₂

#23763662

yes

characteristic

270

C₂

#23765288

yes

—

	subgroup	G/H
center	C₂²	#19098672
commutator	C₂×C₈×C₇₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#1386	C₂
socle	C₂²×C₇₉	#442
prime radical	C₂³×C₇₉	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	#1386	D₇₉
hypocenter	C₇₉	#12957
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

subgroup

G/H

center

C₂²

#19098672

commutator

C₂×C₈×C₇₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#1386

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂²×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

N	H ≅ G/N	type
19. #19098366	C₄	semidirect
143. C₇₉	#12957	semidirect

H ≅ G/N

type

19. #19098366

C₄

semidirect

143. C₇₉

#12957

semidirect

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

subgroup	index
C₂×#19098669	2
C₂×#19098385	2
C₂×#19098380	2
#23765119	2
#23764154	2
#23761479	2
C₇₉×#1386	2
#12957	79

subgroup

index

C₇₉×#1386

Subgroups — #34205016

Conjugacy classes of subgroups

Complements

Maximal subgroups