Group #34444718 — subgroups

Subgroups — #34444718

Order 20224.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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	#23774039	C₂	1	2	yes	maximal, complemented
2	#23765548	C₂	1	2	yes	maximal, complemented
3	#23765543	C₂	1	2	yes	maximal, complemented
4	#23765508	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765503	C₂	1	1	yes	maximal, characteristic
6	#23765496	C₂	1	2	yes	maximal, complemented
7	#23765463	C₂	1	2	yes	maximal, complemented
8	#23765456	C₂	1	2	yes	maximal, complemented
9	C₇₉×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	#19099184	—	2	2	no	—
11	C₂×Dic₆₃₂	C₂²	1	1	yes	characteristic
12	C₂×#14579106	C₂²	1	2	yes	—
13	C₂×D₁₂₆₄	C₂²	1	1	yes	characteristic
14	#19098968	C₂²	1	2	yes	—
15	#19098947	C₂²	1	2	yes	—
16	#19098923	—	2	2	no	—
17	#19098809	—	2	2	no	—
18	#19098804	C₂²	1	2	yes	—
19	#19098799	C₂²	1	2	yes	—
20	#19098665	—	2	2	no	—
21	C₄×Dic₃₁₆	C₂²	1	2	yes	—
22	C₄×D₆₃₂	C₂²	1	2	yes	—
23	#19098391	C₂²	1	1	yes	characteristic
24	#19098391	C₂²	1	1	yes	characteristic
25	#19098391	C₂²	1	2	yes	—
26	#19098368	C₂²	1	2	yes	—
27	#19098368	C₂²	1	2	yes	—
28	#19098365	C₂²	1	2	yes	—
29	#19098365	C₂²	1	2	yes	—
30	C₂×M₃₂×C₇₉	C₂²	1	1	yes	characteristic
31	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
32	#405×C₇₉	C₂²	1	1	yes	characteristic
33	C₄⋊C₁₆×C₇₉	C₂²	1	2	yes	—
34	C₄⋊C₁₆×C₇₉	C₂²	1	2	yes	—
35	C₂×Dic₃₁₆	C₂³	1	2	yes	—
36	C₂×#11929613	—	2	2	no	—
37	C₂×D₆₃₂	C₂³	1	2	yes	—
38	#14579161	—	2	2	no	—
39	#14579156	—	4	2	no	—
40	#14579149	—	2	2	no	—
41	#14579147	—	4	2	no	—
42	#14579143	—	4	2	no	—
43	#14579140	—	2	2	no	—
44	#14579139	—	4	2	no	—
45	#14579135	—	2	2	no	—
46	C₄×Dic₁₅₈	—	2	2	no	—
47	C₄×D₃₁₆	—	2	2	no	—
48	Dic₆₃₂	—	4	1	no	—
49	#14579106	—	4	2	no	—
50	D₁₂₆₄	—	4	1	no	—
51	#14579095	—	2	2	no	—
52	#14579095	C₂³	1	2	yes	—
53	#14579095	C₂³	1	2	yes	—
54	#14579086	—	2	2	no	—
55	#14579086	—	2	2	no	—
56	#14579083	—	2	2	no	—
57	#14579083	—	2	2	no	—
58	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
60	#117×C₇₉	D₄	1	1	yes	characteristic
61	M₃₂×C₇₉	—	4	1	no	—
62	C₂×C₁₆×C₇₉	—	4	1	no	—
63	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
64	C₂×C₁₆×C₇₉	C₂³	1	2	yes	—
65	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
66	#97×C₇₉	D₄	1	2	yes	—
67	C₄×C₈×C₇₉	C₂³	1	2	yes	—
68	C₂×Dic₁₅₈	—	2	2	no	—
69	C₂×Dic₁₅₈	—	4	2	no	—
70	C₂×D₃₁₆	—	2	2	no	—
71	C₂×C₂²⋊D₇₉	—	4	2	no	—
72	C₂×C₄×D₇₉	—	4	2	no	—
73	Dic₃₁₆	—	2	2	no	—
74	Dic₃₁₆	—	2	2	no	—
75	#11929613	—	4	4	no	—
76	D₆₃₂	—	2	2	no	—
77	D₆₃₂	—	2	2	no	—
78	C₄⋊Dic₇₉	—	2	2	no	—
79	C₄⋊Dic₇₉	—	2	2	no	—
80	C₄⋊Dic₇₉	—	4	2	no	—
81	Dic₇₉⋊C₄	—	4	2	no	—
82	Dic₇₉⋊C₄	—	4	2	no	—
83	C₂²⋊Dic₇₉	—	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	(C₂×D₇₉)⋊C₄	—	4	2	no	—
88	C₄×Dic₇₉	—	4	2	no	—
89	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
90	M₁₆×C₇₉	—	4	1	no	—
91	C₂×C₈×C₇₉	—	2	1	no	—
92	C₂×C₈×C₇₉	—	2	1	no	—
93	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
94	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
96	C₄⋊C₄×C₇₉	D₈	1	2	yes	—
97	C₂²⋊C₄×C₇₉	D₈	1	1	yes	characteristic
98	C₂²⋊C₄×C₇₉	D₈	1	1	yes	characteristic
99	C₄²×C₇₉	C₂×D₄	1	2	yes	—
100	C₁₆×C₇₉	—	2	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	C₂×C₄×C₇₉	—	2	1	no	—
106	C₂×C₄×C₇₉	—	2	1	no	—
107	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
108	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
109	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
110	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
111	C₂²⋊D₇₉	—	16	2	no	—
112	C₂×Dic₇₉	—	4	2	no	—
113	C₂×Dic₇₉	—	4	2	no	—
114	C₂×Dic₇₉	—	4	2	no	—
115	D₃₁₆	—	4	2	no	—
116	D₃₁₆	—	4	2	no	—
117	C₄×D₇₉	—	16	2	no	—
118	Dic₁₅₈	—	4	2	no	—
119	Dic₁₅₈	—	4	2	no	—
120	Dic₁₅₈	—	16	2	no	—
121	C₈×C₇₉	—	2	1	no	—
122	C₈×C₇₉	—	2	2	no	—
123	C₈×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
124	C₈×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
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	2	no	—
132	C₄×C₇₉	—	2	2	no	—
133	C₄×C₇₉	—	2	1	no	—
134	C₄×C₇₉	#537	1	1	yes	characteristic
135	C₄×C₇₉	#575	1	1	yes	characteristic
136	Dic₇₉	—	8	2	no	—
137	Dic₇₉	—	8	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	—	79	1	no	—
148	#2218	—	79	1	no	—
149	#2217	—	79	2	no	—
150	#2211	—	79	2	no	—
151	#2210	—	79	2	no	—
152	#2151	D₇₉	1	1	yes	characteristic, complemented
153	C₇₉	#33829	1	1	yes	characteristic, complemented, Sylow
154	#542	—	158	2	no	—
155	C₂×Q₃₂	—	79	1	no	—
156	C₂×SD₃₂	—	79	2	no	—
157	C₂×D₁₆	—	79	1	no	—
158	C₂×M₃₂	C₂×D₇₉	1	1	yes	characteristic
159	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic
160	#500	—	79	2	no	—
161	#495	—	79	2	no	—
162	#489	—	158	2	no	—
163	#468	—	158	2	no	—
164	#467	—	79	2	no	—
165	#466	—	79	2	no	—
166	#440	—	158	2	no	—
167	C₄×Q₁₆	—	79	2	no	—
168	C₄×D₈	—	79	2	no	—
169	#405	C₂×D₇₉	1	1	yes	characteristic
170	#367	—	79	2	no	—
171	#367	—	79	1	no	—
172	#367	—	79	1	no	—
173	C₄⋊C₁₆	C₂×D₇₉	1	2	yes	—
174	C₄⋊C₁₆	C₂×D₇₉	1	2	yes	—
175	#358	—	79	2	no	—
176	#358	—	79	2	no	—
177	#357	—	79	2	no	—
178	#357	—	79	2	no	—
179	C₂×Q₁₆	—	79	2	no	—
180	C₂×SD₁₆	—	158	2	no	—
181	C₂×D₈	—	79	2	no	—
182	C₂×M₁₆	D₃₁₆	1	1	yes	characteristic
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	—	316	2	no	—
190	C₂²⋊Q₈	—	158	2	no	—
191	#121	—	158	2	no	—
192	C₄×Q₈	—	158	2	no	—
193	C₄×D₄	—	158	2	no	—
194	#117	D₃₁₆	1	1	yes	characteristic
195	Q₃₂	—	316	1	no	—
196	SD₃₂	—	316	2	no	—
197	D₁₆	—	316	1	no	—
198	M₃₂	—	4	1	no	—
199	C₂×C₁₆	—	4	1	no	—
200	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
201	C₂×C₁₆	C₂²×D₇₉	1	2	yes	—
202	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
203	#107	—	79	2	no	—
204	#107	—	79	2	no	—
205	#107	—	158	2	no	—
206	#103	—	158	2	no	—
207	#103	—	158	2	no	—
208	#102	—	158	2	no	—
209	#102	—	158	2	no	—
210	#97	D₃₁₆	1	2	yes	—
211	C₄×C₈	C₂²×D₇₉	1	2	yes	—
212	C₂×Q₈	—	316	2	no	—
213	C₂×Q₈	—	158	2	no	—
214	C₂×D₄	—	316	2	no	—
215	C₂×D₄	—	158	2	no	—
216	C₂²×C₄	—	316	2	no	—
217	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
218	Q₁₆	—	158	2	no	—
219	Q₁₆	—	158	2	no	—
220	SD₁₆	—	316	4	no	—
221	D₈	—	158	2	no	—
222	D₈	—	158	2	no	—
223	M₁₆	—	4	1	no	—
224	C₂×C₈	—	2	1	no	—
225	C₂×C₈	—	2	1	no	—
226	C₂×C₈	C₂×D₃₁₆	1	2	yes	—
227	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
228	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
229	C₄⋊C₄	—	316	2	no	—
230	C₄⋊C₄	—	316	2	no	—
231	C₄⋊C₄	—	316	2	no	—
232	C₄⋊C₄	—	158	2	no	—
233	C₄⋊C₄	—	158	2	no	—
234	C₄⋊C₄	D₆₃₂	1	2	yes	—
235	C₂²⋊C₄	—	316	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	D₆₃₂	1	1	yes	characteristic
241	C₂²⋊C₄	D₆₃₂	1	1	yes	characteristic
242	C₄²	—	316	2	no	—
243	C₄²	C₂×D₃₁₆	1	2	yes	—
244	C₁₆	—	2	2	no	—
245	C₁₆	—	2	1	no	—
246	C₁₆	—	2	1	no	—
247	C₂³	—	316	2	no	—
248	C₂³	C₂×D₆₃₂	1	1	yes	characteristic
249	Q₈	—	316	2	no	—
250	Q₈	—	316	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	—	316	2	no	—
258	C₂×C₄	—	316	2	no	—
259	C₂×C₄	—	316	2	no	—
260	C₂×C₄	—	1264	2	no	—
261	C₂×C₄	C₂×D₆₃₂	1	2	yes	—
262	C₂×C₄	C₂×D₆₃₂	1	2	yes	—
263	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
264	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
265	C₈	—	2	1	no	—
266	C₈	—	2	2	no	—
267	C₈	#14579206	1	1	yes	characteristic
268	C₈	#14579209	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	C₂²×D₆₃₂	1	1	yes	characteristic
275	C₄	—	2	2	no	—
276	C₄	—	2	2	no	—
277	C₄	—	2	1	no	—
278	C₄	—	632	2	no	—
279	C₄	—	632	2	no	—
280	C₄	—	632	2	no	—
281	C₄	#19099144	1	1	yes	characteristic
282	C₄	#19099363	1	1	yes	characteristic
283	C₂	—	4	1	no	—
284	C₂	—	1264	2	no	—
285	C₂	#23774710	1	1	yes	characteristic
286	C₂	#23776548	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#23774039

C₂

yes

maximal, complemented

#23765548

C₂

yes

maximal, complemented

#23765543

C₂

yes

maximal, complemented

#23765508

C₂

yes

maximal, characteristic, complemented

#23765503

C₂

yes

maximal, characteristic

#23765496

C₂

yes

maximal, complemented

#23765463

C₂

yes

maximal, complemented

#23765456

C₂

yes

maximal, complemented

C₇₉×#2151

C₂

yes

maximal, characteristic, complemented

#19099184

—

C₂×Dic₆₃₂

C₂²

yes

characteristic

C₂×#14579106

C₂²

yes

—

C₂×D₁₂₆₄

C₂²

yes

characteristic

#19098968

C₂²

yes

—

#19098947

C₂²

yes

—

#19098923

—

#19098809

—

#19098804

C₂²

yes

—

#19098799

C₂²

yes

—

#19098665

—

C₄×Dic₃₁₆

C₂²

yes

—

C₄×D₆₃₂

C₂²

yes

—

#19098391

C₂²

yes

characteristic

#19098391

C₂²

yes

characteristic

#19098391

C₂²

yes

—

#19098368

C₂²

yes

—

#19098368

C₂²

yes

—

#19098365

C₂²

yes

—

#19098365

C₂²

yes

—

C₂×M₃₂×C₇₉

C₂²

yes

characteristic

C₂²×C₁₆×C₇₉

C₂²

yes

characteristic

#405×C₇₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₉

C₂²

yes

—

C₄⋊C₁₆×C₇₉

C₂²

yes

—

C₂×Dic₃₁₆

C₂³

yes

—

C₂×#11929613

—

C₂×D₆₃₂

C₂³

yes

—

—

—

—

—

—

—

—

—

C₄×Dic₁₅₈

—

C₄×D₃₁₆

—

Dic₆₃₂

—

#14579106

—

D₁₂₆₄

—

#14579095

—

#14579095

C₂³

yes

—

#14579095

C₂³

yes

—

—

—

—

—

C₂×M₁₆×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

#117×C₇₉

D₄

yes

characteristic

M₃₂×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

C₂³

yes

characteristic

C₂×C₁₆×C₇₉

C₂³

yes

—

C₂×C₁₆×C₇₉

C₂³

yes

characteristic

#97×C₇₉

D₄

yes

—

C₄×C₈×C₇₉

C₂³

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

C₂×C₄×D₇₉

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929613

—

D₆₃₂

—

D₆₃₂

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂⁴

yes

characteristic

C₄⋊C₄×C₇₉

D₈

yes

—

C₂²⋊C₄×C₇₉

D₈

yes

characteristic

C₂²⋊C₄×C₇₉

D₈

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

—

100

C₁₆×C₇₉

—

101

C₁₆×C₇₉

—

102

C₁₆×C₇₉

—

103

C₂³×C₇₉

C₂×D₈

yes

characteristic

104

C₂²×D₇₉

—

105

C₂×C₄×C₇₉

—

106

C₂×C₄×C₇₉

—

107

C₂×C₄×C₇₉

C₂×D₈

yes

—

108

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

109

C₂×C₄×C₇₉

C₂×D₈

yes

—

110

C₂×C₄×C₇₉

C₂²×D₄

yes

characteristic

111

C₂²⋊D₇₉

—

112

C₂×Dic₇₉

—

113

C₂×Dic₇₉

—

114

C₂×Dic₇₉

—

115

D₃₁₆

—

116

D₃₁₆

—

117

C₄×D₇₉

—

118

Dic₁₅₈

—

119

Dic₁₅₈

—

120

Dic₁₅₈

—

121

C₈×C₇₉

—

122

C₈×C₇₉

—

123

C₈×C₇₉

H(5,𝔽₂)

yes

characteristic

124

C₈×C₇₉

2₋¹⁺⁴

yes

characteristic

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

—

148

#2218

—

149

#2217

—

150

#2211

—

151

#2210

—

152

#2151

D₇₉

yes

characteristic, complemented

153

C₇₉

#33829

yes

characteristic, complemented, Sylow

154

#542

—

158

—

155

C₂×Q₃₂

—

156

C₂×SD₃₂

—

157

C₂×D₁₆

—

158

C₂×M₃₂

C₂×D₇₉

yes

characteristic

159

C₂²×C₁₆

C₂×D₇₉

yes

characteristic

160

#500

—

161

#495

—

162

#489

—

158

—

163

#468

—

158

—

164

#467

—

165

#466

—

166

#440

—

158

—

167

C₄×Q₁₆

—

168

C₄×D₈

—

169

#405

C₂×D₇₉

yes

characteristic

170

#367

—

171

#367

—

172

#367

—

173

C₄⋊C₁₆

C₂×D₇₉

yes

—

174

C₄⋊C₁₆

C₂×D₇₉

yes

—

175

#358

—

176

#358

—

177

#357

—

178

#357

—

179

C₂×Q₁₆

—

180

C₂×SD₁₆

—

158

—

181

C₂×D₈

—

182

C₂×M₁₆

D₃₁₆

yes

characteristic

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

—

316

—

190

C₂²⋊Q₈

—

158

—

191

#121

—

158

—

192

C₄×Q₈

—

158

—

193

C₄×D₄

—

158

—

194

#117

D₃₁₆

yes

characteristic

195

Q₃₂

—

316

—

196

SD₃₂

—

316

—

197

D₁₆

—

316

—

198

M₃₂

—

199

C₂×C₁₆

—

200

C₂×C₁₆

C₂²×D₇₉

yes

characteristic

201

C₂×C₁₆

C₂²×D₇₉

yes

—

202

C₂×C₁₆

C₂²×D₇₉

yes

characteristic

203

#107

—

204

#107

—

205

#107

—

158

—

206

#103

—

158

—

207

#103

—

158

—

208

#102

—

158

—

209

#102

—

158

—

210

#97

D₃₁₆

yes

—

211

C₄×C₈

C₂²×D₇₉

yes

—

212

C₂×Q₈

—

316

—

213

C₂×Q₈

—

158

—

214

C₂×D₄

—

316

—

215

C₂×D₄

—

158

—

216

C₂²×C₄

—

316

—

217

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

218

Q₁₆

—

158

—

219

Q₁₆

—

158

—

220

SD₁₆

—

316

—

221

D₈

—

158

—

222

D₈

—

158

—

223

M₁₆

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

C₂×D₃₁₆

yes

—

227

C₂×C₈

C₂×D₃₁₆

yes

characteristic

228

C₂×C₈

C₂³×D₇₉

yes

characteristic

229

C₄⋊C₄

—

316

—

230

C₄⋊C₄

—

316

—

231

C₄⋊C₄

—

316

—

232

C₄⋊C₄

—

158

—

233

C₄⋊C₄

—

158

—

234

C₄⋊C₄

D₆₃₂

yes

—

235

C₂²⋊C₄

—

316

—

236

C₂²⋊C₄

—

316

—

237

C₂²⋊C₄

—

316

—

238

C₂²⋊C₄

—

316

—

239

C₂²⋊C₄

—

316

—

240

C₂²⋊C₄

D₆₃₂

yes

characteristic

241

C₂²⋊C₄

D₆₃₂

yes

characteristic

242

C₄²

—

316

—

243

C₄²

C₂×D₃₁₆

yes

—

244

C₁₆

—

245

C₁₆

—

246

C₁₆

—

247

C₂³

—

316

—

248

C₂³

C₂×D₆₃₂

yes

characteristic

249

Q₈

—

316

—

250

Q₈

—

316

—

251

Q₈

—

1264

—

252

D₄

—

316

—

253

D₄

—

316

—

254

D₄

—

1264

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

316

—

258

C₂×C₄

—

316

—

259

C₂×C₄

—

316

—

260

C₂×C₄

—

1264

—

261

C₂×C₄

C₂×D₆₃₂

yes

—

262

C₂×C₄

C₂×D₆₃₂

yes

—

263

C₂×C₄

C₂×D₆₃₂

yes

characteristic

264

C₂×C₄

C₂²×D₃₁₆

yes

characteristic

265

C₈

—

266

C₈

—

267

C₈

#14579206

yes

characteristic

268

C₈

#14579209

yes

characteristic

269

C₂²

—

270

C₂²

—

271

C₂²

—

632

—

272

C₂²

—

632

—

273

C₂²

—

632

—

274

C₂²

C₂²×D₆₃₂

yes

characteristic

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

632

—

279

C₄

—

632

—

280

C₄

—

632

—

281

C₄

#19099144

yes

characteristic

282

C₄

#19099363

yes

characteristic

283

C₂

—

284

C₂

—

1264

—

285

C₂

#23774710

yes

characteristic

286

C₂

#23776548

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₆₃₂
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#2151	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	#23765503	C₂
hypercenter	#2151	D₇₉
hypocenter	C₇₉	#33829
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #2151

subgroup

G/H

center

C₂²

C₂²×D₆₃₂

commutator, cosocle

C₂×C₈×C₇₉

C₂⁴

Frattini

C₂×C₈

C₂³×D₇₉

Fitting

C₇₉×#2151

C₂

socle

C₂²×C₇₉

C₂²×D₈

C₂

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #2151

N	H ≅ G/N	type
1. #23774039	C₂	semidirect
2. #23765548	C₂	semidirect
3. #23765543	C₂	semidirect
4. #23765508	C₂	semidirect
6. #23765496	C₂	semidirect
7. #23765463	C₂	semidirect
8. #23765456	C₂	semidirect
9. C₇₉×#2151	C₂	semidirect
152. #2151	D₇₉	semidirect
153. C₇₉	#33829	semidirect

H ≅ G/N

type

1. #23774039

C₂

semidirect

2. #23765548

C₂

semidirect

3. #23765543

C₂

semidirect

4. #23765508

C₂

semidirect

6. #23765496

C₂

semidirect

7. #23765463

C₂

semidirect

8. #23765456

C₂

semidirect

9. C₇₉×#2151

C₂

semidirect

152. #2151

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
#23774039	2
#23765548	2
#23765543	2
#23765508	2
#23765503	2
#23765496	2
#23765463	2
#23765456	2
C₇₉×#2151	2
#33829	79

subgroup

index

C₇₉×#2151

Subgroups — #34444718

Conjugacy classes of subgroups

Complements

Maximal subgroups