Group #34444713 — subgroups

Subgroups — #34444713

Order 20224.

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

normal subgroups only

This group has 488 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	#23774040	C₂	1	2	yes	maximal, complemented
2	#23765546	C₂	1	2	yes	maximal, complemented
3	#23765540	C₂	1	2	yes	maximal, complemented
4	#23765503	C₂	1	1	yes	maximal, characteristic
5	#23765498	C₂	1	2	yes	maximal, complemented
6	#23765464	C₂	1	2	yes	maximal, complemented
7	#23765458	C₂	1	2	yes	maximal, complemented
8	#23765160	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2219	C₂	1	1	yes	maximal, characteristic, complemented
10	#19099186	—	2	2	no	—
11	C₂×#14579104	C₂²	1	2	yes	—
12	C₂×D₁₂₆₄	C₂²	1	1	yes	characteristic
13	C₂²×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
14	#19098967	C₂²	1	2	yes	—
15	#19098948	C₂²	1	2	yes	—
16	#19098924	—	2	2	no	—
17	#19098811	—	2	2	no	—
18	#19098799	C₂²	1	2	yes	—
19	#19098666	—	2	2	no	—
20	Q₁₆×Dic₇₉	C₂²	1	2	yes	—
21	#19098645	C₂²	1	2	yes	—
22	#19098518	C₂²	1	1	yes	characteristic
23	#19098391	C₂²	1	1	yes	characteristic
24	#19098390	C₂²	1	2	yes	—
25	Dic₇₉⋊C₁₆	C₂²	1	2	yes	—
26	Dic₇₉⋊C₁₆	C₂²	1	2	yes	—
27	#19098367	C₂²	1	2	yes	—
28	#19098365	C₂²	1	2	yes	—
29	#19098363	C₂²	1	2	yes	—
30	C₂×Q₃₂×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×M₃₂×C₇₉	C₂²	1	1	yes	characteristic
32	#467×C₇₉	C₂²	1	2	yes	—
33	#367×C₇₉	C₂²	1	1	yes	characteristic
34	#358×C₇₉	C₂²	1	2	yes	—
35	C₂×#11929611	—	2	2	no	—
36	C₂×D₆₃₂	C₂³	1	2	yes	—
37	C₂×#11929608	D₄	1	1	yes	characteristic
38	#14579160	—	2	2	no	—
39	#14579156	—	4	2	no	—
40	#14579150	—	2	2	no	—
41	#14579147	—	4	2	no	—
42	#14579143	—	4	2	no	—
43	#14579141	—	4	2	no	—
44	#14579135	—	2	2	no	—
45	Q₈×Dic₇₉	—	2	2	no	—
46	#14579123	—	2	2	no	—
47	#14579120	D₄	1	1	yes	characteristic
48	#14579104	—	4	2	no	—
49	D₁₂₆₄	—	4	1	no	—
50	C₂×C₇₉⋊C₁₆	—	4	1	no	—
51	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
52	#14579095	C₂³	1	2	yes	—
53	#14579094	—	2	2	no	—
54	#14579085	—	2	2	no	—
55	#14579083	—	2	2	no	—
56	#14579081	—	2	2	no	—
57	#14579071	D₄	1	2	yes	—
58	C₈×Dic₇₉	C₂³	1	2	yes	—
59	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
61	C₂²⋊Q₈×C₇₉	—	2	2	no	—
62	Q₃₂×C₇₉	—	4	1	no	—
63	M₃₂×C₇₉	—	4	1	no	—
64	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
65	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
66	#107×C₇₉	C₂³	1	2	yes	—
67	#103×C₇₉	—	2	2	no	—
68	C₂×Dic₁₅₈	—	4	2	no	—
69	C₂×D₃₁₆	—	2	2	no	—
70	C₂×C₂²⋊D₇₉	—	4	2	no	—
71	C₂×C₄×D₇₉	—	4	2	no	—
72	#11929611	—	4	4	no	—
73	D₆₃₂	—	2	2	no	—
74	D₆₃₂	—	2	2	no	—
75	#11929608	—	4	1	no	—
76	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
77	C₄⋊Dic₇₉	—	2	2	no	—
78	C₄⋊Dic₇₉	—	4	2	no	—
79	C₄⋊Dic₇₉	D₈	1	2	yes	—
80	Dic₇₉⋊C₄	—	4	2	no	—
81	C₂²⋊Dic₇₉	D₈	1	1	yes	characteristic
82	C₂²⋊Dic₇₉	D₈	1	1	yes	characteristic
83	(C₂×D₇₉)⋊C₄	—	4	2	no	—
84	(C₂×D₇₉)⋊C₄	—	4	2	no	—
85	(C₂×D₇₉)⋊C₄	—	4	2	no	—
86	(C₂×D₇₉)⋊C₄	—	4	2	no	—
87	C₄×Dic₇₉	—	4	2	no	—
88	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
89	C₇₉⋊C₁₆	—	2	2	no	—
90	C₂×Q₈×C₇₉	—	2	2	no	—
91	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
92	Q₁₆×C₇₉	—	2	2	no	—
93	Q₁₆×C₇₉	—	2	2	no	—
94	C₂×C₈×C₇₉	—	2	1	no	—
95	C₂×C₈×C₇₉	—	2	1	no	—
96	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
98	C₄⋊C₄×C₇₉	—	2	2	no	—
99	C₄⋊C₄×C₇₉	—	4	2	no	—
100	C₂²⋊C₄×C₇₉	—	4	2	no	—
101	C₁₆×C₇₉	—	2	1	no	—
102	C₁₆×C₇₉	—	2	1	no	—
103	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
104	C₂²×D₇₉	—	4	2	no	—
105	Q₈×C₇₉	—	4	2	no	—
106	Q₈×C₇₉	—	4	2	no	—
107	C₂×C₄×C₇₉	—	2	1	no	—
108	C₂×C₄×C₇₉	—	2	1	no	—
109	C₂×C₄×C₇₉	—	4	2	no	—
110	C₂×C₄×C₇₉	—	4	2	no	—
111	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
112	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
113	C₂²⋊D₇₉	—	16	2	no	—
114	C₂×Dic₇₉	—	4	2	no	—
115	C₂×Dic₇₉	C₂×D₈	1	2	yes	—
116	C₂×Dic₇₉	C₂×D₈	1	2	yes	—
117	D₃₁₆	—	4	2	no	—
118	D₃₁₆	—	4	2	no	—
119	C₄×D₇₉	—	16	2	no	—
120	Dic₁₅₈	—	16	2	no	—
121	C₈×C₇₉	—	2	1	no	—
122	C₈×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
123	C₈×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
124	C₇₉⋊C₈	—	2	2	no	—
125	C₂²×C₇₉	—	2	2	no	—
126	C₂²×C₇₉	—	2	1	no	—
127	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
128	C₂×D₇₉	—	8	2	no	—
129	C₂×D₇₉	—	8	2	no	—
130	C₂×D₇₉	—	8	2	no	—
131	C₄×C₇₉	—	2	1	no	—
132	C₄×C₇₉	—	8	2	no	—
133	C₄×C₇₉	—	8	2	no	—
134	C₄×C₇₉	#537	1	1	yes	characteristic
135	C₄×C₇₉	#575	1	1	yes	characteristic
136	Dic₇₉	—	2	2	no	—
137	Dic₇₉	—	2	2	no	—
138	Dic₇₉	—	8	2	no	—
139	#33829	—	79	1	no	maximal, Sylow
140	C₂×C₇₉	—	4	1	no	—
141	C₂×C₇₉	#3245	1	1	yes	characteristic
142	C₂×C₇₉	#3416	1	2	yes	—
143	D₇₉	—	16	2	no	—
144	#3175	—	79	2	no	—
145	#2226	—	79	2	no	—
146	#2225	—	79	2	no	—
147	#2219	D₇₉	1	1	yes	characteristic, complemented
148	#2218	—	79	1	no	—
149	#2217	—	79	2	no	—
150	#2211	—	79	2	no	—
151	#2210	—	79	2	no	—
152	#2151	—	79	1	no	—
153	C₇₉	#33829	1	1	yes	characteristic, complemented, Sylow
154	#542	—	158	2	no	—
155	C₂×Q₃₂	C₂×D₇₉	1	1	yes	characteristic
156	C₂×SD₃₂	—	79	2	no	—
157	C₂×D₁₆	—	79	1	no	—
158	C₂×M₃₂	C₂×D₇₉	1	1	yes	characteristic
159	C₂²×C₁₆	—	79	1	no	—
160	#500	—	79	2	no	—
161	#495	—	79	2	no	—
162	#489	—	158	2	no	—
163	#468	—	158	2	no	—
164	#467	C₂×D₇₉	1	2	yes	—
165	#466	—	79	2	no	—
166	#440	—	158	2	no	—
167	C₄×Q₁₆	—	79	2	no	—
168	C₄×D₈	—	79	2	no	—
169	#405	—	79	1	no	—
170	#367	—	79	1	no	—
171	#367	—	79	2	no	—
172	#367	C₂×D₇₉	1	1	yes	characteristic
173	C₄⋊C₁₆	—	79	2	no	—
174	C₄⋊C₁₆	—	79	2	no	—
175	#358	—	79	2	no	—
176	#358	C₂×D₇₉	1	2	yes	—
177	#357	—	79	2	no	—
178	#357	—	79	2	no	—
179	C₂×Q₁₆	C₂²×D₇₉	1	2	yes	—
180	C₂×SD₁₆	—	158	2	no	—
181	C₂×D₈	—	79	2	no	—
182	C₂×M₁₆	—	79	1	no	—
183	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
184	C₄⋊Q₈	—	158	2	no	—
185	#126	—	316	2	no	—
186	#124	—	316	2	no	—
187	#124	—	158	2	no	—
188	#123	—	316	2	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	—	316	2	no	—
191	#121	—	158	2	no	—
192	C₄×Q₈	—	158	2	no	—
193	C₄×D₄	—	158	2	no	—
194	#117	—	79	1	no	—
195	Q₃₂	—	4	1	no	—
196	SD₃₂	—	316	2	no	—
197	D₁₆	—	316	1	no	—
198	M₃₂	—	4	1	no	—
199	C₂×C₁₆	—	316	1	no	—
200	C₂×C₁₆	—	79	2	no	—
201	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
202	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
203	#107	—	79	2	no	—
204	#107	—	158	2	no	—
205	#107	C₂²×D₇₉	1	2	yes	—
206	#103	—	2	2	no	—
207	#103	—	158	2	no	—
208	#102	—	158	2	no	—
209	#102	—	158	2	no	—
210	#97	—	79	2	no	—
211	C₄×C₈	—	79	2	no	—
212	C₂×Q₈	—	2	2	no	—
213	C₂×Q₈	—	316	2	no	—
214	C₂×D₄	—	316	2	no	—
215	C₂×D₄	—	158	2	no	—
216	C₂²×C₄	—	316	2	no	—
217	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
218	Q₁₆	—	2	2	no	—
219	Q₁₆	—	2	2	no	—
220	SD₁₆	—	316	4	no	—
221	D₈	—	158	2	no	—
222	D₈	—	158	2	no	—
223	M₁₆	—	316	1	no	—
224	C₂×C₈	—	2	1	no	—
225	C₂×C₈	—	2	1	no	—
226	C₂×C₈	—	79	2	no	—
227	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
228	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
229	C₄⋊C₄	—	2	2	no	—
230	C₄⋊C₄	—	4	2	no	—
231	C₄⋊C₄	—	316	2	no	—
232	C₄⋊C₄	—	316	2	no	—
233	C₄⋊C₄	—	79	2	no	—
234	C₄⋊C₄	—	158	2	no	—
235	C₂²⋊C₄	—	4	2	no	—
236	C₂²⋊C₄	—	316	2	no	—
237	C₂²⋊C₄	—	316	2	no	—
238	C₂²⋊C₄	—	316	2	no	—
239	C₂²⋊C₄	—	316	2	no	—
240	C₂²⋊C₄	—	79	1	no	—
241	C₂²⋊C₄	—	79	1	no	—
242	C₄²	—	316	2	no	—
243	C₄²	—	79	2	no	—
244	C₁₆	—	2	1	no	—
245	C₁₆	—	2	1	no	—
246	C₁₆	—	158	2	no	—
247	C₂³	—	316	2	no	—
248	C₂³	D₈×D₇₉	1	1	yes	characteristic
249	Q₈	—	4	2	no	—
250	Q₈	—	4	2	no	—
251	Q₈	—	1264	2	no	—
252	D₄	—	316	2	no	—
253	D₄	—	316	2	no	—
254	D₄	—	1264	2	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	316	2	no	—
260	C₂×C₄	—	79	2	no	—
261	C₂×C₄	—	79	2	no	—
262	C₂×C₄	—	1264	2	no	—
263	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
264	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
265	C₈	—	2	1	no	—
266	C₈	—	158	2	no	—
267	C₈	#14579206	1	1	yes	characteristic
268	C₈	#14579208	1	1	yes	characteristic
269	C₂²	—	2	2	no	—
270	C₂²	—	2	1	no	—
271	C₂²	—	632	2	no	—
272	C₂²	—	632	2	no	—
273	C₂²	—	632	2	no	—
274	C₂²	C₂×D₈×D₇₉	1	1	yes	characteristic
275	C₄	—	2	1	no	—
276	C₄	—	8	2	no	—
277	C₄	—	8	2	no	—
278	C₄	—	632	2	no	—
279	C₄	—	158	2	no	—
280	C₄	—	158	2	no	—
281	C₄	#19099140	1	1	yes	characteristic
282	C₄	#19099360	1	1	yes	characteristic
283	C₂	—	4	1	no	—
284	C₂	—	1264	2	no	—
285	C₂	#23774706	1	1	yes	characteristic
286	C₂	#23776545	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#23774040

C₂

yes

maximal, complemented

#23765546

C₂

yes

maximal, complemented

#23765540

C₂

yes

maximal, complemented

#23765503

C₂

yes

maximal, characteristic

#23765498

C₂

yes

maximal, complemented

#23765464

C₂

yes

maximal, complemented

#23765458

C₂

yes

maximal, complemented

#23765160

C₂

yes

maximal, characteristic, complemented

C₇₉×#2219

C₂

yes

maximal, characteristic, complemented

#19099186

—

C₂×#14579104

C₂²

yes

—

C₂×D₁₂₆₄

C₂²

yes

characteristic

C₂²×C₇₉⋊C₁₆

C₂²

yes

characteristic

#19098967

C₂²

yes

—

#19098948

C₂²

yes

—

#19098924

—

#19098811

—

#19098799

C₂²

yes

—

#19098666

—

Q₁₆×Dic₇₉

C₂²

yes

—

#19098645

C₂²

yes

—

#19098518

C₂²

yes

characteristic

#19098391

C₂²

yes

characteristic

#19098390

C₂²

yes

—

Dic₇₉⋊C₁₆

C₂²

yes

—

Dic₇₉⋊C₁₆

C₂²

yes

—

#19098367

C₂²

yes

—

#19098365

C₂²

yes

—

#19098363

C₂²

yes

—

C₂×Q₃₂×C₇₉

C₂²

yes

characteristic

C₂×M₃₂×C₇₉

C₂²

yes

characteristic

#467×C₇₉

C₂²

yes

—

#367×C₇₉

C₂²

yes

characteristic

#358×C₇₉

C₂²

yes

—

C₂×#11929611

—

C₂×D₆₃₂

C₂³

yes

—

C₂×#11929608

D₄

yes

—

—

—

—

—

—

—

Q₈×Dic₇₉

—

#14579123

—

#14579120

D₄

yes

characteristic

#14579104

—

D₁₂₆₄

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

C₂³

yes

—

#14579095

C₂³

yes

—

—

—

—

—

D₄

yes

—

C₈×Dic₇₉

C₂³

yes

—

C₂×Q₁₆×C₇₉

C₂³

yes

—

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₂²⋊Q₈×C₇₉

—

Q₃₂×C₇₉

—

M₃₂×C₇₉

—

C₂×C₁₆×C₇₉

C₂³

yes

characteristic

C₂×C₁₆×C₇₉

C₂³

yes

characteristic

#107×C₇₉

C₂³

yes

—

#103×C₇₉

—

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

C₂×C₄×D₇₉

—

#11929611

—

D₆₃₂

—

D₆₃₂

—

#11929608

—

C₂×C₇₉⋊C₈

C₂×D₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₈

yes

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

D₈

yes

characteristic

C₂²⋊Dic₇₉

D₈

yes

characteristic

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₂×D₄

yes

—

C₇₉⋊C₁₆

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂⁴

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

100

C₂²⋊C₄×C₇₉

—

101

C₁₆×C₇₉

—

102

C₁₆×C₇₉

—

103

C₂³×C₇₉

C₂×D₈

yes

characteristic

104

C₂²×D₇₉

—

105

Q₈×C₇₉

—

106

Q₈×C₇₉

—

107

C₂×C₄×C₇₉

—

108

C₂×C₄×C₇₉

—

109

C₂×C₄×C₇₉

—

110

C₂×C₄×C₇₉

—

111

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

112

C₂×C₄×C₇₉

C₂²×D₄

yes

characteristic

113

C₂²⋊D₇₉

—

114

C₂×Dic₇₉

—

115

C₂×Dic₇₉

C₂×D₈

yes

—

116

C₂×Dic₇₉

C₂×D₈

yes

—

117

D₃₁₆

—

118

D₃₁₆

—

119

C₄×D₇₉

—

120

Dic₁₅₈

—

121

C₈×C₇₉

—

122

C₈×C₇₉

H(5,𝔽₂)

yes

characteristic

123

C₈×C₇₉

2₋¹⁺⁴

yes

characteristic

124

C₇₉⋊C₈

—

125

C₂²×C₇₉

—

126

C₂²×C₇₉

—

127

C₂²×C₇₉

C₂²×D₈

yes

characteristic

128

C₂×D₇₉

—

129

C₂×D₇₉

—

130

C₂×D₇₉

—

131

C₄×C₇₉

—

132

C₄×C₇₉

—

133

C₄×C₇₉

—

134

C₄×C₇₉

#537

yes

characteristic

135

C₄×C₇₉

#575

yes

characteristic

136

Dic₇₉

—

137

Dic₇₉

—

138

Dic₇₉

—

139

#33829

—

maximal, Sylow

140

C₂×C₇₉

—

141

C₂×C₇₉

#3245

yes

characteristic

142

C₂×C₇₉

#3416

yes

—

143

D₇₉

—

144

#3175

—

145

#2226

—

146

#2225

—

147

#2219

D₇₉

yes

characteristic, complemented

148

#2218

—

149

#2217

—

150

#2211

—

151

#2210

—

152

#2151

—

153

C₇₉

#33829

yes

characteristic, complemented, Sylow

154

#542

—

158

—

155

C₂×Q₃₂

C₂×D₇₉

yes

characteristic

156

C₂×SD₃₂

—

157

C₂×D₁₆

—

158

C₂×M₃₂

C₂×D₇₉

yes

characteristic

159

C₂²×C₁₆

—

160

#500

—

161

#495

—

162

#489

—

158

—

163

#468

—

158

—

164

#467

C₂×D₇₉

yes

—

165

#466

—

166

#440

—

158

—

167

C₄×Q₁₆

—

168

C₄×D₈

—

169

#405

—

170

#367

—

171

#367

—

172

#367

C₂×D₇₉

yes

characteristic

173

C₄⋊C₁₆

—

174

C₄⋊C₁₆

—

175

#358

—

176

#358

C₂×D₇₉

yes

—

177

#357

—

178

#357

—

179

C₂×Q₁₆

C₂²×D₇₉

yes

—

180

C₂×SD₁₆

—

158

—

181

C₂×D₈

—

182

C₂×M₁₆

—

183

C₂²×C₈

C₂²×D₇₉

yes

characteristic

184

C₄⋊Q₈

—

158

—

185

#126

—

316

—

186

#124

—

316

—

187

#124

—

158

—

188

#123

—

316

—

189

C₂²⋊Q₈

—

190

C₂²⋊Q₈

—

316

—

191

#121

—

158

—

192

C₄×Q₈

—

158

—

193

C₄×D₄

—

158

—

194

#117

—

195

Q₃₂

—

196

SD₃₂

—

316

—

197

D₁₆

—

316

—

198

M₃₂

—

199

C₂×C₁₆

—

316

—

200

C₂×C₁₆

—

201

C₂×C₁₆

C₂²×D₇₉

yes

characteristic

202

C₂×C₁₆

C₂²×D₇₉

yes

characteristic

203

#107

—

204

#107

—

158

—

205

#107

C₂²×D₇₉

yes

—

206

#103

—

207

#103

—

158

—

208

#102

—

158

—

209

#102

—

158

—

210

#97

—

211

C₄×C₈

—

212

C₂×Q₈

—

213

C₂×Q₈

—

316

—

214

C₂×D₄

—

316

—

215

C₂×D₄

—

158

—

216

C₂²×C₄

—

316

—

217

C₂²×C₄

D₄×D₇₉

yes

characteristic

218

Q₁₆

—

219

Q₁₆

—

220

SD₁₆

—

316

—

221

D₈

—

158

—

222

D₈

—

158

—

223

M₁₆

—

316

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

D₄×D₇₉

yes

characteristic

228

C₂×C₈

C₂³×D₇₉

yes

characteristic

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

316

—

232

C₄⋊C₄

—

316

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

158

—

235

C₂²⋊C₄

—

236

C₂²⋊C₄

—

316

—

237

C₂²⋊C₄

—

316

—

238

C₂²⋊C₄

—

316

—

239

C₂²⋊C₄

—

316

—

240

C₂²⋊C₄

—

241

C₂²⋊C₄

—

242

C₄²

—

316

—

243

C₄²

—

244

C₁₆

—

245

C₁₆

—

246

C₁₆

—

158

—

247

C₂³

—

316

—

248

C₂³

D₈×D₇₉

yes

characteristic

249

Q₈

—

250

Q₈

—

251

Q₈

—

1264

—

252

D₄

—

316

—

253

D₄

—

316

—

254

D₄

—

1264

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

316

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

1264

—

263

C₂×C₄

D₈×D₇₉

yes

characteristic

264

C₂×C₄

C₂×D₄×D₇₉

yes

characteristic

265

C₈

—

266

C₈

—

158

—

267

C₈

#14579206

yes

characteristic

268

C₈

#14579208

yes

characteristic

269

C₂²

—

270

C₂²

—

271

C₂²

—

632

—

272

C₂²

—

632

—

273

C₂²

—

632

—

274

C₂²

C₂×D₈×D₇₉

yes

characteristic

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

632

—

279

C₄

—

158

—

280

C₄

—

158

—

281

C₄

#19099140

yes

characteristic

282

C₄

#19099360

yes

characteristic

283

C₂

—

284

C₂

—

1264

—

285

C₂

#23774706

yes

characteristic

286

C₂

#23776545

yes

—

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#2219	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	#23765503	C₂
hypercenter	#2219	D₇₉
hypocenter	C₇₉	#33829
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2219

subgroup

G/H

center

C₂²

C₂×D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂⁴

Frattini

C₂×C₈

C₂³×D₇₉

Fitting

C₇₉×#2219

C₂

socle

C₂²×C₇₉

C₂²×D₈

C₂

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2219

N	H ≅ G/N	type
1. #23774040	C₂	semidirect
2. #23765546	C₂	semidirect
3. #23765540	C₂	semidirect
5. #23765498	C₂	semidirect
6. #23765464	C₂	semidirect
7. #23765458	C₂	semidirect
8. #23765160	C₂	semidirect
9. C₇₉×#2219	C₂	semidirect
147. #2219	D₇₉	semidirect
153. C₇₉	#33829	semidirect

H ≅ G/N

type

1. #23774040

C₂

semidirect

2. #23765546

C₂

semidirect

3. #23765540

C₂

semidirect

5. #23765498

C₂

semidirect

6. #23765464

C₂

semidirect

7. #23765458

C₂

semidirect

8. #23765160

C₂

semidirect

9. C₇₉×#2219

C₂

semidirect

147. #2219

D₇₉

semidirect

153. C₇₉

#33829

semidirect

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

subgroup	index
#23774040	2
#23765546	2
#23765540	2
#23765503	2
#23765498	2
#23765464	2
#23765458	2
#23765160	2
C₇₉×#2219	2
#33829	79

subgroup

index

C₇₉×#2219

Subgroups — #34444713

Conjugacy classes of subgroups

Complements

Maximal subgroups