Group #34180432 — subgroups

Subgroups — #34180432

Order 20224.

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

normal subgroups only

This group has 658 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	#23764341	C₂	1	1	yes	maximal, characteristic
2	#23762100	C₂	1	2	yes	maximal
3	#23762015	C₂	1	2	yes	maximal
4	#23761744	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#3502	C₂	1	1	yes	maximal, characteristic
6	#19098620	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×#14579072	C₂²	1	1	yes	characteristic
9	#19098318	—	2	2	no	—
10	#19098309	—	2	2	no	—
11	#19098309	—	2	2	no	—
12	#19098305	—	2	4	no	—
13	#19098289	—	2	2	no	—
14	Q₈²×C₇₉	—	2	2	no	—
15	#557×C₇₉	—	2	2	no	—
16	#557×C₇₉	—	2	4	no	—
17	#544×C₇₉	—	2	2	no	—
18	#544×C₇₉	C₄	1	2	yes	—
19	#533×C₇₉	—	2	2	no	—
20	#533×C₇₉	C₂²	1	2	yes	—
21	#519×C₇₉	C₄	1	2	yes	—
22	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂²×C₇₉⋊C₈	—	2	1	no	—
24	C₂²×C₇₉⋊C₈	—	2	1	no	—
25	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
26	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
27	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
28	#14579072	—	2	2	no	—
29	#14579072	—	2	2	no	—
30	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
31	C₄⋊Q₈×C₇₉	—	2	2	no	—
32	C₄⋊Q₈×C₇₉	—	2	2	no	—
33	C₄⋊Q₈×C₇₉	—	2	8	no	—
34	C₄⋊Q₈×C₇₉	—	2	4	no	—
35	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
36	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
37	#125×C₇₉	—	2	4	no	—
38	#125×C₇₉	—	2	8	no	—
39	#125×C₇₉	—	2	4	no	—
40	#125×C₇₉	D₄	1	4	yes	—
41	C₂²⋊Q₈×C₇₉	—	2	4	no	—
42	C₂²⋊Q₈×C₇₉	—	2	2	no	—
43	C₂²⋊Q₈×C₇₉	—	2	2	no	—
44	C₄×Q₈×C₇₉	—	2	4	no	—
45	C₄×Q₈×C₇₉	—	2	4	no	—
46	C₄×Q₈×C₇₉	—	2	4	no	—
47	C₄×Q₈×C₇₉	—	2	4	no	—
48	C₄×Q₈×C₇₉	—	2	2	no	—
49	C₄×Q₈×C₇₉	—	2	2	no	—
50	C₄×Q₈×C₇₉	—	2	2	no	—
51	C₄×Q₈×C₇₉	—	2	2	no	—
52	#117×C₇₉	—	2	4	no	—
53	#117×C₇₉	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
56	C₂×C₄²×C₇₉	D₄	1	2	yes	—
57	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
58	C₂×C₇₉⋊C₈	—	2	2	no	—
59	C₂×C₇₉⋊C₈	—	4	1	no	—
60	C₂×C₇₉⋊C₈	—	4	2	no	—
61	C₂×C₇₉⋊C₈	—	4	1	no	—
62	C₂×C₇₉⋊C₈	—	4	2	no	—
63	C₂×C₇₉⋊C₈	—	4	1	no	—
64	C₂×Q₈×C₇₉	—	2	4	no	—
65	C₂×Q₈×C₇₉	—	2	4	no	—
66	C₂×Q₈×C₇₉	—	2	2	no	—
67	C₂×Q₈×C₇₉	—	2	2	no	—
68	C₂×Q₈×C₇₉	—	2	2	no	—
69	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
74	C₄⋊C₄×C₇₉	—	2	4	no	—
75	C₄⋊C₄×C₇₉	—	2	4	no	—
76	C₄⋊C₄×C₇₉	—	2	4	no	—
77	C₄⋊C₄×C₇₉	—	2	8	no	—
78	C₄⋊C₄×C₇₉	—	2	2	no	—
79	C₄⋊C₄×C₇₉	—	2	4	no	—
80	C₄⋊C₄×C₇₉	—	2	4	no	—
81	C₄⋊C₄×C₇₉	—	2	2	no	—
82	C₄⋊C₄×C₇₉	—	2	2	no	—
83	C₄⋊C₄×C₇₉	—	2	4	no	—
84	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
85	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
86	C₂²⋊C₄×C₇₉	—	2	4	no	—
87	C₄²×C₇₉	—	2	8	no	—
88	C₄²×C₇₉	—	2	4	no	—
89	C₄²×C₇₉	—	2	2	no	—
90	C₄²×C₇₉	—	2	2	no	—
91	C₄²×C₇₉	C₂×D₄	1	2	yes	—
92	C₄²×C₇₉	C₂×D₄	1	2	yes	—
93	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	Q₈×C₇₉	—	2	8	no	—
95	Q₈×C₇₉	—	4	2	no	—
96	Q₈×C₇₉	—	4	2	no	—
97	Q₈×C₇₉	—	8	2	no	—
98	Q₈×C₇₉	—	8	4	no	—
99	C₂×C₄×C₇₉	—	2	2	no	—
100	C₂×C₄×C₇₉	—	2	2	no	—
101	C₂×C₄×C₇₉	—	2	2	no	—
102	C₂×C₄×C₇₉	—	2	1	no	—
103	C₂×C₄×C₇₉	—	2	1	no	—
104	C₂×C₄×C₇₉	—	2	4	no	—
105	C₂×C₄×C₇₉	—	2	4	no	—
106	C₂×C₄×C₇₉	—	2	2	no	—
107	C₂×C₄×C₇₉	—	4	1	no	—
108	C₂×C₄×C₇₉	—	4	2	no	—
109	C₂×C₄×C₇₉	#101	1	4	yes	—
110	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
111	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
112	C₂×C₄×C₇₉	#120	1	2	yes	—
113	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
114	C₇₉⋊C₈	—	4	2	no	—
115	C₇₉⋊C₈	—	8	2	no	—
116	C₇₉⋊C₈	—	8	1	no	—
117	C₂²×C₇₉	—	2	1	no	—
118	C₂²×C₇₉	—	2	1	no	—
119	C₂²×C₇₉	#379	1	1	yes	characteristic
120	C₂²×C₇₉	C₂×#101	1	2	yes	—
121	C₄×C₇₉	—	2	1	no	—
122	C₄×C₇₉	—	2	2	no	—
123	C₄×C₇₉	—	2	4	no	—
124	C₄×C₇₉	—	2	2	no	—
125	C₄×C₇₉	—	4	4	no	—
126	C₄×C₇₉	—	4	2	no	—
127	C₄×C₇₉	—	4	4	no	—
128	C₄×C₇₉	#454	1	1	yes	characteristic
129	C₄×C₇₉	#456	1	1	yes	characteristic
130	#8460	—	79	1	no	maximal, Sylow
131	C₂×C₇₉	—	2	2	no	—
132	C₂×C₇₉	#1784	1	1	yes	characteristic
133	C₂×C₇₉	#1793	1	1	yes	characteristic
134	C₂×C₇₉	#1794	1	1	yes	characteristic
135	#3502	D₇₉	1	1	yes	characteristic
136	#1985	—	79	1	no	—
137	#1552	—	79	2	no	—
138	#1531	—	79	2	no	—
139	#1467	—	79	1	no	—
140	C₇₉	#8460	1	1	yes	characteristic, complemented, Sylow
141	Q₈²	—	2	2	no	—
142	#557	—	2	2	no	—
143	#557	—	2	4	no	—
144	#544	—	2	2	no	—
145	#544	Dic₇₉	1	2	yes	—
146	#533	—	2	2	no	—
147	#533	C₂×D₇₉	1	2	yes	—
148	#519	Dic₇₉	1	2	yes	—
149	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
150	#432	—	79	2	no	—
151	C₂×C₄⋊C₈	—	79	1	no	—
152	C₂×#97	—	79	1	no	—
153	#336	—	158	2	no	—
154	#332	—	158	2	no	—
155	#332	—	158	2	no	—
156	#330	—	158	4	no	—
157	#324	—	158	2	no	—
158	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
159	C₂²×C₈	—	158	1	no	—
160	C₂²×C₈	—	158	1	no	—
161	C₄⋊Q₈	—	2	2	no	—
162	C₄⋊Q₈	—	2	2	no	—
163	C₄⋊Q₈	—	2	8	no	—
164	C₄⋊Q₈	—	2	4	no	—
165	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
166	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
167	#125	—	2	4	no	—
168	#125	—	2	8	no	—
169	#125	—	2	4	no	—
170	#125	C₂²⋊D₇₉	1	4	yes	—
171	C₂²⋊Q₈	—	2	4	no	—
172	C₂²⋊Q₈	—	2	2	no	—
173	C₂²⋊Q₈	—	2	2	no	—
174	C₄×Q₈	—	2	4	no	—
175	C₄×Q₈	—	2	4	no	—
176	C₄×Q₈	—	2	4	no	—
177	C₄×Q₈	—	2	4	no	—
178	C₄×Q₈	—	2	2	no	—
179	C₄×Q₈	—	2	2	no	—
180	C₄×Q₈	—	2	2	no	—
181	C₄×Q₈	—	2	2	no	—
182	#117	—	2	4	no	—
183	#117	C₂×Dic₇₉	1	4	yes	—
184	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
185	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
186	C₂×C₄²	C₂²⋊D₇₉	1	2	yes	—
187	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
188	C₄⋊C₈	—	158	2	no	—
189	C₄⋊C₈	—	158	2	no	—
190	C₂²⋊C₈	—	158	2	no	—
191	#97	—	158	2	no	—
192	#97	—	158	2	no	—
193	C₂×Q₈	—	2	4	no	—
194	C₂×Q₈	—	2	4	no	—
195	C₂×Q₈	—	2	2	no	—
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	2	2	no	—
198	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
199	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
200	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
201	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
202	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
203	C₂×C₈	—	316	1	no	—
204	C₂×C₈	—	316	1	no	—
205	C₂×C₈	—	316	2	no	—
206	C₂×C₈	—	316	2	no	—
207	C₂×C₈	—	316	1	no	—
208	C₂×C₈	—	158	2	no	—
209	C₄⋊C₄	—	2	4	no	—
210	C₄⋊C₄	—	2	4	no	—
211	C₄⋊C₄	—	2	4	no	—
212	C₄⋊C₄	—	2	8	no	—
213	C₄⋊C₄	—	2	2	no	—
214	C₄⋊C₄	—	2	4	no	—
215	C₄⋊C₄	—	2	4	no	—
216	C₄⋊C₄	—	2	2	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	2	4	no	—
219	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
220	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
221	C₂²⋊C₄	—	2	4	no	—
222	C₄²	—	2	8	no	—
223	C₄²	—	2	4	no	—
224	C₄²	—	2	2	no	—
225	C₄²	—	2	2	no	—
226	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
227	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
228	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
229	Q₈	—	2	8	no	—
230	Q₈	—	4	2	no	—
231	Q₈	—	4	2	no	—
232	Q₈	—	8	2	no	—
233	Q₈	—	8	4	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	4	no	—
240	C₂×C₄	—	2	4	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	#14579080	1	4	yes	—
245	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
246	C₂×C₄	#14579130	1	1	yes	characteristic
247	C₂×C₄	#14579130	1	2	yes	—
248	C₂×C₄	#14579130	1	1	yes	characteristic
249	C₈	—	316	2	no	—
250	C₈	—	632	2	no	—
251	C₈	—	632	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	#19098419	1	1	yes	characteristic
255	C₂²	C₂×#14579080	1	2	yes	—
256	C₄	—	2	4	no	—
257	C₄	—	2	2	no	—
258	C₄	—	2	1	no	—
259	C₄	—	2	2	no	—
260	C₄	—	4	4	no	—
261	C₄	—	4	2	no	—
262	C₄	—	4	4	no	—
263	C₄	#19098736	1	1	yes	characteristic
264	C₄	#19098746	1	1	yes	characteristic
265	C₂	—	2	2	no	—
266	C₂	#23763324	1	1	yes	characteristic
267	C₂	#23763359	1	1	yes	characteristic
268	C₂	#23763364	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23764341

C₂

yes

maximal, characteristic

#23762100

C₂

yes

maximal

#23762015

C₂

yes

maximal

#23761744

C₂

yes

maximal, characteristic

C₇₉×#3502

C₂

yes

maximal, characteristic

#19098620

C₂²

yes

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×#14579072

C₂²

yes

—

—

—

—

—

Q₈²×C₇₉

—

#557×C₇₉

—

#557×C₇₉

—

#544×C₇₉

—

#544×C₇₉

C₄

yes

—

#533×C₇₉

—

#533×C₇₉

C₂²

yes

—

#519×C₇₉

C₄

yes

—

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

#14579072

—

C₂²×Q₈×C₇₉

C₂×C₄

yes

characteristic

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

D₄

yes

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

—

#125×C₇₉

D₄

yes

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

#117×C₇₉

—

#117×C₇₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×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

—

106

C₂×C₄×C₇₉

—

107

C₂×C₄×C₇₉

—

108

C₂×C₄×C₇₉

—

109

C₂×C₄×C₇₉

#101

yes

—

110

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

—

111

C₂×C₄×C₇₉

#120

yes

characteristic

112

C₂×C₄×C₇₉

#120

yes

—

113

C₂×C₄×C₇₉

#120

yes

characteristic

114

C₇₉⋊C₈

—

115

C₇₉⋊C₈

—

116

C₇₉⋊C₈

—

117

C₂²×C₇₉

—

118

C₂²×C₇₉

—

119

C₂²×C₇₉

#379

yes

characteristic

120

C₂²×C₇₉

C₂×#101

yes

—

121

C₄×C₇₉

—

122

C₄×C₇₉

—

123

C₄×C₇₉

—

124

C₄×C₇₉

—

125

C₄×C₇₉

—

126

C₄×C₇₉

—

127

C₄×C₇₉

—

128

C₄×C₇₉

#454

yes

characteristic

129

C₄×C₇₉

yes

130

—

131

C₂×C₇₉

—

132

C₂×C₇₉

#1784

yes

characteristic

133

C₂×C₇₉

#1793

yes

characteristic

134

C₂×C₇₉

#1794

yes

characteristic

135

#3502

D₇₉

yes

characteristic

136

#1985

—

137

#1552

—

138

#1531

—

139

#1467

—

140

C₇₉

#8460

yes

characteristic, complemented, Sylow

141

Q₈²

—

142

#557

—

143

#557

—

144

#544

—

145

#544

Dic₇₉

yes

—

146

#533

—

147

#533

C₂×D₇₉

yes

—

148

#519

Dic₇₉

yes

—

149

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

150

#432

—

151

C₂×C₄⋊C₈

—

152

C₂×#97

—

153

#336

—

158

—

154

#332

—

158

—

155

#332

—

158

—

156

#330

—

158

—

157

#324

—

158

—

158

C₂²×Q₈

C₂×Dic₇₉

yes

characteristic

159

C₂²×C₈

—

158

—

160

C₂²×C₈

—

158

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

164

C₄⋊Q₈

—

165

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

166

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

167

#125

—

168

#125

—

169

#125

—

170

#125

C₂²⋊D₇₉

yes

—

171

C₂²⋊Q₈

—

172

C₂²⋊Q₈

—

173

C₂²⋊Q₈

—

174

C₄×Q₈

—

175

C₄×Q₈

—

176

C₄×Q₈

—

177

C₄×Q₈

—

178

C₄×Q₈

—

179

C₄×Q₈

—

180

C₄×Q₈

—

181

C₄×Q₈

—

182

#117

—

183

#117

C₂×Dic₇₉

yes

—

184

C₂×C₄⋊C₄

C₂×Dic₇₉

yes

characteristic

185

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

—

186

C₂×C₄²

C₂²⋊D₇₉

yes

—

187

C₂×C₄²

C₂²×D₇₉

yes

characteristic

188

C₄⋊C₈

—

158

—

189

C₄⋊C₈

—

158

—

190

C₂²⋊C₈

—

158

—

191

#97

—

158

—

192

#97

—

158

—

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

199

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

200

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

201

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

202

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

203

C₂×C₈

—

316

—

204

C₂×C₈

—

316

—

205

C₂×C₈

—

316

—

206

C₂×C₈

—

316

—

207

C₂×C₈

—

316

—

208

C₂×C₈

—

158

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

C₂²⋊Dic₇₉

yes

—

220

C₄⋊C₄

C₂²⋊Dic₇₉

yes

—

221

C₂²⋊C₄

—

222

C₄²

—

223

C₄²

—

224

C₄²

—

225

C₄²

—

226

C₄²

C₂×C₂²⋊D₇₉

yes

—

227

C₄²

C₂×C₂²⋊D₇₉

yes

—

228

C₂³

C₂×C₂²⋊Dic₇₉

yes

characteristic

229

Q₈

—

230

Q₈

—

231

Q₈

—

232

Q₈

—

233

Q₈

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

#14579080

yes

—

245

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

—

246

C₂×C₄

#14579130

yes

characteristic

247

C₂×C₄

#14579130

yes

—

248

C₂×C₄

#14579130

yes

characteristic

249

C₈

—

316

—

250

C₈

—

632

—

251

C₈

—

632

—

252

C₂²

—

253

C₂²

—

254

C₂²

#19098419

yes

characteristic

255

C₂²

C₂×#14579080

yes

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

#19098736

yes

characteristic

264

C₄

#19098746

yes

characteristic

265

C₂

—

266

C₂

#23763324

yes

characteristic

267

C₂

#23763359

yes

characteristic

268

C₂

#23763364

yes

characteristic

	subgroup	G/H
center	C₂²	#19098419
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#3502	C₂
socle	C₂²×C₇₉	#379
prime radical	C₂³×C₇₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#3502	D₇₉
hypocenter	C₇₉	#8460
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3502

subgroup

G/H

center

C₂²

#19098419

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#3502

C₂

socle

C₂²×C₇₉

#379

prime radical

C₂³×C₇₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3502

N	H ≅ G/N	type
140. C₇₉	#8460	semidirect

H ≅ G/N

type

140. C₇₉

#8460

semidirect

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

subgroup	index
#23764341	2
#23762100	2
#23762015	2
#23761744	2
C₇₉×#3502	2
#8460	79

subgroup

index

C₇₉×#3502

Subgroups — #34180432

Conjugacy classes of subgroups

Complements

Maximal subgroups