Group #34197563 — subgroups

Subgroups — #34197563

Order 20224.

460 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 119 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	#23761718	C₂	1	2	yes	maximal
2	#23761346	C₂	1	2	yes	maximal, complemented
3	#23761334	C₂	1	2	yes	maximal, complemented
4	C₇₉×#2326	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
6	#19098289	C₂²	1	4	yes	—
7	#19098287	—	2	2	no	—
8	C₂×#124×C₇₉	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₇₉	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
11	#391×C₇₉	C₂²	1	1	yes	characteristic
12	#390×C₇₉	C₄	1	1	yes	characteristic
13	#388×C₇₉	—	2	2	no	—
14	#385×C₇₉	—	2	2	no	—
15	#384×C₇₉	C₂²	1	1	yes	characteristic
16	#376×C₇₉	C₄	1	1	yes	characteristic
17	C₂²×C₇₉⋊C₈	—	4	2	no	—
18	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
19	C₂²⋊(C₇₉⋊C₈)	—	4	2	no	—
20	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₇₉	D₄	1	2	yes	—
23	#124×C₇₉	—	2	2	no	—
24	#124×C₇₉	C₈	1	4	yes	complemented
25	C₄×Q₈×C₇₉	—	4	2	no	—
26	C₄×D₄×C₇₉	—	4	2	no	—
27	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
32	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
33	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
34	C₂×C₄²×C₇₉	—	2	1	no	—
35	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
38	#95×C₇₉	—	2	1	no	—
39	#95×C₇₉	—	2	1	no	—
40	#95×C₇₉	—	2	2	no	—
41	C₂×C₇₉⋊C₈	—	4	4	no	—
42	C₂×C₇₉⋊C₈	—	8	4	no	—
43	C₂⁴×C₇₉	C₂²⋊C₄	1	2	yes	—
44	C₂×Q₈×C₇₉	—	2	1	no	—
45	C₂×Q₈×C₇₉	—	4	1	no	—
46	C₂×Q₈×C₇₉	—	4	1	no	—
47	C₂×Q₈×C₇₉	C₂×C₈	1	2	yes	complemented
48	C₂×D₄×C₇₉	—	4	1	no	—
49	C₂×D₄×C₇₉	—	4	1	no	—
50	C₂×D₄×C₇₉	C₂×C₈	1	2	yes	—
51	C₂×D₄×C₇₉	M₁₆	1	2	yes	—
52	C₂²×C₄×C₇₉	—	2	1	no	—
53	C₂²×C₄×C₇₉	—	2	1	no	—
54	C₂²×C₄×C₇₉	—	2	2	no	—
55	C₂²×C₄×C₇₉	—	2	2	no	—
56	C₂²×C₄×C₇₉	—	2	1	no	—
57	C₂²×C₄×C₇₉	—	2	1	no	—
58	C₂²×C₄×C₇₉	—	8	2	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	C₂×D₄	1	2	yes	—
63	C₄⋊C₄×C₇₉	—	4	1	no	—
64	C₄⋊C₄×C₇₉	—	4	1	no	—
65	C₄⋊C₄×C₇₉	—	4	2	no	—
66	C₄⋊C₄×C₇₉	—	8	2	no	—
67	C₂²⋊C₄×C₇₉	—	2	8	no	—
68	C₂²⋊C₄×C₇₉	—	4	2	no	—
69	C₂²⋊C₄×C₇₉	—	8	2	no	—
70	C₄²×C₇₉	—	2	2	no	—
71	C₄²×C₇₉	—	2	1	no	—
72	C₄²×C₇₉	—	4	2	no	—
73	C₄²×C₇₉	—	4	1	no	—
74	C₄²×C₇₉	C₂×C₈	1	2	yes	complemented
75	C₂³×C₇₉	—	2	2	no	—
76	C₂³×C₇₉	—	2	2	no	—
77	C₂³×C₇₉	—	4	2	no	—
78	C₂³×C₇₉	—	4	2	no	—
79	C₂³×C₇₉	C₂²⋊C₈	1	4	yes	—
80	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	Q₈×C₇₉	—	4	2	no	—
82	Q₈×C₇₉	—	4	2	no	—
83	D₄×C₇₉	—	4	2	no	—
84	D₄×C₇₉	—	4	2	no	—
85	C₂×C₄×C₇₉	—	2	1	no	—
86	C₂×C₄×C₇₉	—	2	1	no	—
87	C₂×C₄×C₇₉	—	2	2	no	—
88	C₂×C₄×C₇₉	—	2	2	no	—
89	C₂×C₄×C₇₉	—	2	2	no	—
90	C₂×C₄×C₇₉	—	2	1	no	—
91	C₂×C₄×C₇₉	—	4	1	no	—
92	C₂×C₄×C₇₉	—	4	4	no	—
93	C₂×C₄×C₇₉	—	4	1	no	—
94	C₂×C₄×C₇₉	—	4	1	no	—
95	C₂×C₄×C₇₉	—	4	1	no	—
96	C₂×C₄×C₇₉	—	4	1	no	—
97	C₂×C₄×C₇₉	—	4	2	no	—
98	C₂×C₄×C₇₉	—	4	1	no	—
99	C₂×C₄×C₇₉	—	4	1	no	—
100	C₂×C₄×C₇₉	—	4	2	no	—
101	C₂×C₄×C₇₉	—	4	1	no	—
102	C₂×C₄×C₇₉	—	4	1	no	—
103	C₂×C₄×C₇₉	—	4	1	no	—
104	C₂×C₄×C₇₉	—	8	2	no	—
105	C₂×C₄×C₇₉	#99	1	2	yes	—
106	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
107	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
108	C₇₉⋊C₈	—	8	4	no	—
109	C₂²×C₇₉	—	2	1	no	—
110	C₂²×C₇₉	—	2	1	no	—
111	C₂²×C₇₉	—	2	4	no	—
112	C₂²×C₇₉	—	4	4	no	—
113	C₂²×C₇₉	—	4	2	no	—
114	C₂²×C₇₉	—	4	2	no	—
115	C₂²×C₇₉	—	8	2	no	—
116	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
117	C₂²×C₇₉	C₂×#99	1	1	yes	characteristic
118	C₂²×C₇₉	#413	1	1	yes	characteristic
119	C₄×C₇₉	—	2	2	no	—
120	C₄×C₇₉	—	2	1	no	—
121	C₄×C₇₉	—	2	1	no	—
122	C₄×C₇₉	—	4	2	no	—
123	C₄×C₇₉	—	4	2	no	—
124	C₄×C₇₉	—	4	1	no	—
125	C₄×C₇₉	—	4	2	no	—
126	C₄×C₇₉	—	8	1	no	—
127	C₄×C₇₉	—	8	1	no	—
128	#11481	—	79	1	no	maximal, Sylow
129	C₂×C₇₉	—	2	1	no	—
130	C₂×C₇₉	—	2	1	no	—
131	C₂×C₇₉	—	4	4	no	—
132	C₂×C₇₉	#1459	1	1	yes	characteristic
133	C₂×C₇₉	#2127	1	1	yes	characteristic
134	C₂×C₇₉	#2135	1	1	yes	characteristic
135	#2326	D₇₉	1	1	yes	characteristic
136	#1459	—	79	2	no	—
137	#1325	—	79	2	no	—
138	#1319	—	79	2	no	—
139	C₇₉	#11481	1	1	yes	characteristic, complemented, Sylow
140	C₂×#124	Dic₇₉	1	1	yes	characteristic
141	C₂×C₄×Q₈	Dic₇₉	1	1	yes	characteristic
142	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
143	C₂×C₂²⋊C₈	—	158	2	no	—
144	#391	C₂×D₇₉	1	1	yes	characteristic
145	#390	Dic₇₉	1	1	yes	characteristic
146	#388	—	2	2	no	—
147	#385	—	2	2	no	—
148	#384	C₂×D₇₉	1	1	yes	characteristic
149	#376	Dic₇₉	1	1	yes	characteristic
150	#324	—	79	4	no	—
151	#323	—	158	2	no	—
152	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
153	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
154	C₂³×C₄	C₂²⋊D₇₉	1	2	yes	—
155	C₂²×C₈	—	316	2	no	—
156	#124	—	2	2	no	—
157	#124	C₇₉⋊C₈	1	4	yes	complemented
158	C₄×Q₈	—	4	2	no	—
159	C₄×D₄	—	4	2	no	—
160	C₂×C₄⋊C₄	—	2	1	no	—
161	C₂×C₄⋊C₄	—	2	2	no	—
162	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
163	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
164	C₂×C₂²⋊C₄	—	2	2	no	—
165	C₂×C₂²⋊C₄	—	2	2	no	—
166	C₂×C₂²⋊C₄	C₂²⋊D₇₉	1	2	yes	—
167	C₂×C₄²	—	2	1	no	—
168	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
169	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
170	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
171	C₂²⋊C₈	—	316	2	no	—
172	C₂²⋊C₈	—	158	4	no	—
173	#95	—	2	1	no	—
174	#95	—	2	1	no	—
175	#95	—	2	2	no	—
176	C₂⁴	C₂²⋊Dic₇₉	1	2	yes	—
177	C₂×Q₈	—	2	1	no	—
178	C₂×Q₈	—	4	1	no	—
179	C₂×Q₈	—	4	1	no	—
180	C₂×Q₈	C₂×C₇₉⋊C₈	1	2	yes	complemented
181	C₂×D₄	—	4	1	no	—
182	C₂×D₄	—	4	1	no	—
183	C₂×D₄	C₂×C₇₉⋊C₈	1	2	yes	—
184	C₂×D₄	#11929608	1	2	yes	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	8	2	no	—
192	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
193	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
194	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
195	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
196	C₂×C₈	—	316	4	no	—
197	C₂×C₈	—	632	4	no	—
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₄⋊C₄	—	8	2	no	—
202	C₂²⋊C₄	—	2	8	no	—
203	C₂²⋊C₄	—	4	2	no	—
204	C₂²⋊C₄	—	8	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	1	no	—
207	C₄²	—	4	1	no	—
208	C₄²	—	4	2	no	—
209	C₄²	C₂×C₇₉⋊C₈	1	2	yes	complemented
210	C₂³	—	2	2	no	—
211	C₂³	—	2	2	no	—
212	C₂³	—	4	2	no	—
213	C₂³	—	4	2	no	—
214	C₂³	C₂²⋊(C₇₉⋊C₈)	1	4	yes	—
215	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
216	Q₈	—	4	2	no	—
217	Q₈	—	4	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	4	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	4	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	4	1	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	1	no	—
239	C₂×C₄	—	8	2	no	—
240	C₂×C₄	#14579076	1	2	yes	—
241	C₂×C₄	C₂²×C₇₉⋊C₈	1	1	yes	characteristic
242	C₂×C₄	C₂×#11929608	1	1	yes	characteristic
243	C₈	—	632	4	no	—
244	C₂²	—	2	1	no	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	4	no	—
247	C₂²	—	4	4	no	—
248	C₂²	—	4	2	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	8	2	no	—
251	C₂²	C₂×C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
252	C₂²	C₂×#14579076	1	1	yes	characteristic
253	C₂²	#19098547	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	2	no	—
257	C₄	—	4	2	no	—
258	C₄	—	4	2	no	—
259	C₄	—	4	2	no	—
260	C₄	—	4	1	no	—
261	C₄	—	8	1	no	—
262	C₄	—	8	1	no	—
263	C₂	—	2	1	no	—
264	C₂	—	2	1	no	—
265	C₂	—	4	4	no	—
266	C₂	#23761718	1	1	yes	characteristic
267	C₂	#23765069	1	1	yes	characteristic
268	C₂	#23765095	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23761718

C₂

yes

maximal

#23761346

C₂

yes

maximal, complemented

#23761334

C₂

yes

maximal, complemented

C₇₉×#2326

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₇₉⋊C₈)

—

#19098289

C₂²

yes

—

#19098287

—

C₂×#124×C₇₉

C₄

yes

characteristic

C₂×C₄×Q₈×C₇₉

C₄

yes

characteristic

C₂×C₄×D₄×C₇₉

C₂²

yes

characteristic

#391×C₇₉

C₂²

yes

characteristic

#390×C₇₉

C₄

yes

characteristic

#388×C₇₉

—

#385×C₇₉

—

#384×C₇₉

C₂²

yes

characteristic

#376×C₇₉

C₄

yes

characteristic

C₂²×C₇₉⋊C₈

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²×Q₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×D₄×C₇₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₇₉

D₄

yes

—

#124×C₇₉

—

#124×C₇₉

C₈

yes

complemented

C₄×Q₈×C₇₉

—

C₄×D₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂³

yes

characteristic

C₂×C₂²⋊C₄×C₇₉

—

C₂×C₂²⋊C₄×C₇₉

—

C₂×C₂²⋊C₄×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

#95×C₇₉

—

#95×C₇₉

—

#95×C₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂⁴×C₇₉

C₂²⋊C₄

yes

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂×C₈

yes

complemented

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

C₂×C₈

yes

—

C₂×D₄×C₇₉

M₁₆

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

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

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×C₈

yes

complemented

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂²⋊C₈

yes

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×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

—

C₂×C₄×C₇₉

—

100

C₂×C₄×C₇₉

—

101

C₂×C₄×C₇₉

—

102

C₂×C₄×C₇₉

—

103

C₂×C₄×C₇₉

—

104

C₂×C₄×C₇₉

—

105

C₂×C₄×C₇₉

#99

yes

—

106

C₂×C₄×C₇₉

C₂²×C₈

yes

characteristic

107

C₂×C₄×C₇₉

C₂×M₁₆

yes

characteristic

108

C₇₉⋊C₈

—

109

C₂²×C₇₉

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

—

112

C₂²×C₇₉

—

113

C₂²×C₇₉

—

114

C₂²×C₇₉

—

115

C₂²×C₇₉

—

116

C₂²×C₇₉

C₂×C₂²⋊C₈

yes

characteristic

117

C₂²×C₇₉

C₂×#99

yes

characteristic

118

C₂²×C₇₉

#413

yes

characteristic

119

C₄×C₇₉

—

120

C₄×C₇₉

—

121

C₄×C₇₉

—

122

C₄×C₇₉

—

123

C₄×C₇₉

—

124

C₄×C₇₉

—

125

C₄×C₇₉

—

126

C₄×C₇₉

—

127

C₄×C₇₉

—

128

#11481

—

maximal, Sylow

129

C₂×C₇₉

—

130

C₂×C₇₉

—

131

C₂×C₇₉

—

132

C₂×C₇₉

#1459

yes

characteristic

133

C₂×C₇₉

#2127

yes

characteristic

134

C₂×C₇₉

#2135

yes

characteristic

135

#2326

D₇₉

yes

characteristic

136

#1459

—

137

#1325

—

138

#1319

—

139

C₇₉

#11481

yes

characteristic, complemented, Sylow

140

C₂×#124

Dic₇₉

yes

characteristic

141

C₂×C₄×Q₈

Dic₇₉

yes

characteristic

142

C₂×C₄×D₄

C₂×D₇₉

yes

characteristic

143

C₂×C₂²⋊C₈

—

158

—

144

#391

C₂×D₇₉

yes

characteristic

145

#390

Dic₇₉

yes

characteristic

146

#388

—

147

#385

—

148

#384

C₂×D₇₉

yes

characteristic

149

#376

Dic₇₉

yes

characteristic

150

#324

—

151

#323

—

158

—

152

C₂²×Q₈

C₂×Dic₇₉

yes

characteristic

153

C₂²×D₄

C₂×Dic₇₉

yes

characteristic

154

C₂³×C₄

C₂²⋊D₇₉

yes

—

155

C₂²×C₈

—

316

—

156

#124

—

157

#124

C₇₉⋊C₈

yes

complemented

158

C₄×Q₈

—

159

C₄×D₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

characteristic

163

C₂×C₄⋊C₄

C₂²×D₇₉

yes

characteristic

164

C₂×C₂²⋊C₄

—

165

C₂×C₂²⋊C₄

—

166

C₂×C₂²⋊C₄

C₂²⋊D₇₉

yes

—

167

C₂×C₄²

—

168

C₂×C₄²

C₂×Dic₇₉

yes

characteristic

169

C₂×C₄²

C₂×Dic₇₉

yes

characteristic

170

C₂×C₄²

C₂×Dic₇₉

yes

characteristic

171

C₂²⋊C₈

—

316

—

172

C₂²⋊C₈

—

158

—

173

#95

—

174

#95

—

175

#95

—

176

C₂⁴

C₂²⋊Dic₇₉

yes

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×Q₈

C₂×C₇₉⋊C₈

yes

complemented

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

C₂×C₇₉⋊C₈

yes

—

184

C₂×D₄

#11929608

yes

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

C₂²⋊Dic₇₉

yes

characteristic

193

C₂²×C₄

C₂²⋊Dic₇₉

yes

characteristic

194

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

195

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

—

196

C₂×C₈

—

316

—

197

C₂×C₈

—

632

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₂²⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

209

C₄²

C₂×C₇₉⋊C₈

yes

complemented

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

C₂²⋊(C₇₉⋊C₈)

yes

—

215

C₂³

C₂×C₂²⋊Dic₇₉

yes

characteristic

216

Q₈

—

217

Q₈

—

218

D₄

—

219

D₄

—

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

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

#14579076

yes

—

241

C₂×C₄

C₂²×C₇₉⋊C₈

yes

characteristic

242

C₂×C₄

C₂×#11929608

yes

characteristic

243

C₈

—

632

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

C₂×C₂²⋊(C₇₉⋊C₈)

yes

characteristic

252

C₂²

C₂×#14579076

yes

characteristic

253

C₂²

#19098547

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₂

—

264

C₂

—

265

C₂

—

266

C₂

#23761718

yes

characteristic

267

C₂

#23765069

yes

characteristic

268

C₂

#23765095

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#14579076
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₄⋊C₄	C₂²×D₇₉
Fitting	C₇₉×#2326	C₂
socle	C₂²×C₇₉	C₂×#99
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂×C₄⋊C₄×C₇₉	C₂³
hypercenter	#2326	D₇₉
hypocenter	C₇₉	#11481
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×D₄ ◁ #2326

subgroup

G/H

center

C₂²

C₂×#14579076

commutator

C₂×C₄×C₇₉

C₂²×C₈

Frattini

C₂×C₄⋊C₄

C₂²×D₇₉

Fitting

C₇₉×#2326

C₂

socle

C₂²×C₇₉

C₂×#99

prime radical

C₂²×D₄×C₇₉

C₂×C₄

cosocle

C₂×C₄⋊C₄×C₇₉

C₂³

D₇₉

C₇₉

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

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×D₄ ◁ #2326

N	H ≅ G/N	type
2. #23761346	C₂	semidirect
3. #23761334	C₂	semidirect
24. #124×C₇₉	C₈	semidirect
47. C₂×Q₈×C₇₉	C₂×C₈	semidirect
74. C₄²×C₇₉	C₂×C₈	semidirect
139. C₇₉	#11481	semidirect
157. #124	C₇₉⋊C₈	semidirect
180. C₂×Q₈	C₂×C₇₉⋊C₈	semidirect
209. C₄²	C₂×C₇₉⋊C₈	semidirect

H ≅ G/N

type

2. #23761346

C₂

semidirect

3. #23761334

C₂

semidirect

24. #124×C₇₉

C₈

semidirect

47. C₂×Q₈×C₇₉

C₂×C₈

semidirect

74. C₄²×C₇₉

C₂×C₈

semidirect

139. C₇₉

#11481

semidirect

157. #124

C₇₉⋊C₈

semidirect

180. C₂×Q₈

C₂×C₇₉⋊C₈

semidirect

209. C₄²

C₂×C₇₉⋊C₈

semidirect

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

subgroup	index
#23761718	2
#23761346	2
#23761334	2
C₇₉×#2326	2
#11481	79

subgroup

index

C₇₉×#2326

Subgroups — #34197563

Conjugacy classes of subgroups

Complements

Maximal subgroups