Group #34190799 — subgroups

Subgroups — #34190799

Order 20224.

626 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 139 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×#19098968	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098768	C₂	1	2	yes	maximal
3	C₂×#19098308	C₂	1	2	yes	maximal, complemented
4	#23761235	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11929612	—	2	2	no	—
7	C₂×#14579161	C₂²	1	2	yes	—
8	#19098968	—	2	4	no	—
9	#19098768	—	2	4	no	—
10	#19098768	—	2	4	no	—
11	C₂×#14579095	—	2	2	no	—
12	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
13	C₂×#14579084	—	2	2	no	—
14	#19098308	—	2	4	no	—
15	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₈×C₇₉	—	2	2	no	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₅₈	—	2	2	no	—
20	C₂×#11929612	—	2	8	no	—
21	C₂×#11929612	—	4	4	no	—
22	C₂×#11929612	—	4	4	no	—
23	C₂²×C₇₉⋊C₈	—	2	2	no	—
24	#14579161	—	2	2	no	—
25	#14579161	—	2	2	no	—
26	#14579161	—	2	2	no	—
27	#14579161	D₄	1	4	yes	—
28	C₂×C₄⋊Dic₇₉	—	2	2	no	—
29	C₂×C₄⋊Dic₇₉	—	2	2	no	—
30	#14579095	—	2	8	no	—
31	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
33	#14579084	—	2	8	no	—
34	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₇₉	—	2	1	no	—
36	C₂²×C₈×C₇₉	—	2	1	no	—
37	C₂²×C₈×C₇₉	D₄	1	2	yes	—
38	C₄×D₄×C₇₉	—	2	2	no	—
39	C₄×D₄×C₇₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
42	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₉	—	2	2	no	—
44	C₂²⋊C₈×C₇₉	—	4	4	no	—
45	C₄×C₈×C₇₉	—	2	2	no	—
46	C₂×Dic₁₅₈	—	2	4	no	—
47	C₂×Dic₁₅₈	—	4	2	no	—
48	C₂×Dic₁₅₈	—	4	2	no	—
49	C₂×Dic₁₅₈	—	4	2	no	—
50	C₂×Dic₁₅₈	—	4	2	no	—
51	C₂×Dic₁₅₈	—	4	2	no	—
52	C₂²×Dic₇₉	—	4	2	no	—
53	#11929612	—	4	16	no	—
54	C₂×C₇₉⋊C₈	—	2	4	no	—
55	C₂×C₇₉⋊C₈	—	4	2	no	—
56	C₂×C₇₉⋊C₈	—	4	2	no	—
57	C₄⋊Dic₇₉	—	2	4	no	—
58	C₄⋊Dic₇₉	—	2	4	no	—
59	C₄⋊Dic₇₉	—	4	2	no	—
60	C₄⋊Dic₇₉	—	4	2	no	—
61	C₂⁴×C₇₉	—	2	1	no	—
62	C₂×D₄×C₇₉	—	2	2	no	—
63	C₂×D₄×C₇₉	—	2	1	no	—
64	C₂×D₄×C₇₉	—	2	2	no	—
65	C₂×D₄×C₇₉	D₈	1	2	yes	—
66	C₂²×C₄×C₇₉	—	2	1	no	—
67	C₂²×C₄×C₇₉	—	4	1	no	—
68	C₂²×C₄×C₇₉	—	4	1	no	—
69	C₂²×C₄×C₇₉	—	4	2	no	—
70	C₂²×C₄×C₇₉	—	4	2	no	—
71	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
74	C₂×C₈×C₇₉	—	2	2	no	—
75	C₂×C₈×C₇₉	—	2	2	no	—
76	C₂×C₈×C₇₉	—	4	1	no	—
77	C₂×C₈×C₇₉	—	4	2	no	—
78	C₂×C₈×C₇₉	SD₁₆	1	4	yes	complemented
79	C₄⋊C₄×C₇₉	—	2	2	no	—
80	C₂²⋊C₄×C₇₉	—	4	2	no	—
81	C₄²×C₇₉	C₂×D₄	1	2	yes	—
82	C₄²×C₇₉	C₂×D₄	1	2	yes	—
83	C₂³×C₇₉	—	2	2	no	—
84	C₂³×C₇₉	—	4	1	no	—
85	C₂³×C₇₉	—	4	2	no	—
86	C₂³×C₇₉	—	4	1	no	—
87	C₂³×C₇₉	—	4	2	no	—
88	C₂³×C₇₉	#121	1	1	yes	characteristic
89	D₄×C₇₉	—	2	4	no	—
90	D₄×C₇₉	—	4	2	no	—
91	C₂×C₄×C₇₉	—	2	2	no	—
92	C₂×C₄×C₇₉	—	4	1	no	—
93	C₂×C₄×C₇₉	—	4	2	no	—
94	C₂×C₄×C₇₉	—	8	2	no	—
95	C₂×C₄×C₇₉	—	8	1	no	—
96	C₂×C₄×C₇₉	—	8	1	no	—
97	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
98	C₂×C₄×C₇₉	#120	1	2	yes	—
99	C₂×C₄×C₇₉	#121	1	2	yes	—
100	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
101	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
103	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
104	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
105	C₂×C₄×C₇₉	#137	1	2	yes	—
106	C₂×Dic₇₉	—	4	4	no	—
107	C₂×Dic₇₉	—	8	2	no	—
108	C₂×Dic₇₉	—	8	2	no	—
109	Dic₁₅₈	—	4	4	no	—
110	Dic₁₅₈	—	4	4	no	—
111	Dic₁₅₈	—	8	2	no	—
112	Dic₁₅₈	—	8	2	no	—
113	C₈×C₇₉	—	2	4	no	—
114	C₈×C₇₉	—	8	1	no	—
115	C₇₉⋊C₈	—	4	4	no	—
116	C₂²×C₇₉	—	4	4	no	—
117	C₂²×C₇₉	—	4	2	no	—
118	C₂²×C₇₉	—	8	2	no	—
119	C₂²×C₇₉	—	8	1	no	—
120	C₂²×C₇₉	—	8	1	no	—
121	C₂²×C₇₉	#392	1	1	yes	characteristic
122	C₂²×C₇₉	#461	1	2	yes	—
123	C₂²×C₇₉	#466	1	1	yes	characteristic
124	C₂²×C₇₉	#469	1	1	yes	characteristic
125	C₂²×C₇₉	#473	1	2	yes	—
126	C₄×C₇₉	—	2	2	no	—
127	C₄×C₇₉	—	8	1	no	—
128	C₄×C₇₉	#447	1	2	yes	—
129	C₄×C₇₉	#448	1	2	yes	—
130	C₄×C₇₉	#449	1	2	yes	—
131	C₄×C₇₉	#492	1	1	yes	characteristic
132	C₄×C₇₉	#497	1	1	yes	characteristic
133	Dic₇₉	—	8	4	no	—
134	#10264	—	79	1	no	maximal, Sylow
135	C₂×C₇₉	—	8	2	no	—
136	C₂×C₇₉	#1673	1	2	yes	—
137	C₂×C₇₉	#1693	1	2	yes	—
138	C₂×C₇₉	#1999	1	1	yes	characteristic
139	C₂×C₇₉	#2013	1	1	yes	characteristic
140	C₂×C₇₉	#2020	1	1	yes	characteristic
141	C₂×#500	—	79	1	no	—
142	C₂×#461	—	79	2	no	—
143	#1954	D₇₉	1	1	yes	characteristic
144	C₂×#332	—	79	2	no	—
145	#1277	—	79	1	no	—
146	C₇₉	#10264	1	1	yes	characteristic, complemented, Sylow
147	C₂²×SD₁₆	—	158	2	no	—
148	C₂×C₄⋊Q₈	—	79	2	no	—
149	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
150	#500	—	158	4	no	—
151	#461	—	158	4	no	—
152	#461	—	158	4	no	—
153	C₂×#107	—	158	2	no	—
154	C₂×C₄⋊C₈	—	79	2	no	—
155	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
156	C₂×#103	—	158	2	no	—
157	C₂×C₂²⋊C₈	—	2	2	no	—
158	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
159	#332	—	158	4	no	—
160	C₂²×Q₈	—	158	2	no	—
161	C₂²×D₄	D₃₁₆	1	1	yes	characteristic
162	C₂³×C₄	—	2	1	no	—
163	C₂×SD₁₆	—	316	4	no	—
164	C₂×SD₁₆	—	316	4	no	—
165	C₂×SD₁₆	—	158	8	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	158	2	no	—
168	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
169	C₄⋊Q₈	—	79	4	no	—
170	C₄⋊Q₈	—	158	2	no	—
171	C₄⋊Q₈	—	158	2	no	—
172	C₄⋊Q₈	—	158	2	no	—
173	C₄×D₄	—	2	2	no	—
174	C₄×D₄	—	2	2	no	—
175	C₂×C₄⋊C₄	—	158	2	no	—
176	C₂×C₄⋊C₄	—	158	2	no	—
177	C₂×C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
178	C₂×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
180	#107	—	158	8	no	—
181	C₄⋊C₈	—	2	2	no	—
182	C₄⋊C₈	—	79	4	no	—
183	C₄⋊C₈	—	158	2	no	—
184	#103	—	158	8	no	—
185	C₂²⋊C₈	—	4	4	no	—
186	C₄×C₈	—	2	2	no	—
187	C₂⁴	—	2	1	no	—
188	C₂×Q₈	—	316	2	no	—
189	C₂×Q₈	—	316	2	no	—
190	C₂×Q₈	—	316	2	no	—
191	C₂×Q₈	—	316	2	no	—
192	C₂×Q₈	—	316	2	no	—
193	C₂×Q₈	—	158	4	no	—
194	C₂×D₄	—	2	2	no	—
195	C₂×D₄	—	2	1	no	—
196	C₂×D₄	—	2	2	no	—
197	C₂×D₄	D₆₃₂	1	2	yes	—
198	C₂²×C₄	—	2	1	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	4	1	no	—
201	C₂²×C₄	—	4	2	no	—
202	C₂²×C₄	—	4	2	no	—
203	C₂²×C₄	—	316	2	no	—
204	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
205	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
206	C₂²×C₄	#11929624	1	1	yes	characteristic
207	SD₁₆	—	316	16	no	—
208	C₂×C₈	—	2	2	no	—
209	C₂×C₈	—	2	2	no	—
210	C₂×C₈	—	4	1	no	—
211	C₂×C₈	—	4	2	no	—
212	C₂×C₈	—	316	2	no	—
213	C₂×C₈	—	316	2	no	—
214	C₂×C₈	—	158	4	no	—
215	C₂×C₈	#11929612	1	4	yes	complemented
216	C₄⋊C₄	—	2	2	no	—
217	C₄⋊C₄	—	316	2	no	—
218	C₄⋊C₄	—	316	2	no	—
219	C₄⋊C₄	—	158	4	no	—
220	C₄⋊C₄	—	158	4	no	—
221	C₂²⋊C₄	—	4	2	no	—
222	C₄²	D₄×D₇₉	1	2	yes	—
223	C₄²	D₄×D₇₉	1	2	yes	—
224	C₂³	—	2	2	no	—
225	C₂³	—	4	1	no	—
226	C₂³	—	4	2	no	—
227	C₂³	—	4	1	no	—
228	C₂³	—	4	2	no	—
229	C₂³	#14579135	1	1	yes	characteristic
230	Q₈	—	316	4	no	—
231	Q₈	—	316	4	no	—
232	Q₈	—	632	2	no	—
233	Q₈	—	632	2	no	—
234	D₄	—	2	4	no	—
235	D₄	—	4	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	4	1	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	—	8	1	no	—
240	C₂×C₄	—	8	2	no	—
241	C₂×C₄	—	8	1	no	—
242	C₂×C₄	—	316	4	no	—
243	C₂×C₄	—	632	2	no	—
244	C₂×C₄	—	632	2	no	—
245	C₂×C₄	#14579129	1	1	yes	characteristic
246	C₂×C₄	#14579131	1	2	yes	—
247	C₂×C₄	#14579134	1	2	yes	—
248	C₂×C₄	#14579157	1	1	yes	characteristic
249	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
250	C₂×C₄	C₂×#11929612	1	2	yes	—
251	C₂×C₄	#14579183	1	1	yes	characteristic
252	C₂×C₄	#14579189	1	2	yes	—
253	C₂×C₄	#14579191	1	2	yes	—
254	C₈	—	2	4	no	—
255	C₈	—	8	1	no	—
256	C₈	—	316	4	no	—
257	C₂²	—	4	4	no	—
258	C₂²	—	4	2	no	—
259	C₂²	—	8	1	no	—
260	C₂²	—	8	1	no	—
261	C₂²	—	8	2	no	—
262	C₂²	#19098472	1	1	yes	characteristic
263	C₂²	#19098768	1	2	yes	—
264	C₂²	#19098799	1	1	yes	characteristic
265	C₂²	#19098816	1	1	yes	characteristic
266	C₂²	#19098838	1	2	yes	—
267	C₄	—	2	2	no	—
268	C₄	—	8	1	no	—
269	C₄	—	632	4	no	—
270	C₄	#19098699	1	2	yes	—
271	C₄	#19098701	1	2	yes	—
272	C₄	#19098710	1	2	yes	—
273	C₄	#19098935	1	1	yes	characteristic
274	C₄	#19098958	1	1	yes	characteristic
275	C₂	—	8	2	no	—
276	C₂	#23762789	1	2	yes	—
277	C₂	#23762913	1	2	yes	—
278	C₂	#23764398	1	1	yes	characteristic
279	C₂	#23764482	1	1	yes	characteristic
280	C₂	#23764521	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098968

C₂

yes

maximal, characteristic, complemented

C₂×#19098768

C₂

yes

maximal

C₂×#19098308

C₂

yes

maximal, complemented

#23761235

C₂

yes

maximal, characteristic, complemented

C₇₉×#1954

C₂

yes

maximal, characteristic

C₂²×#11929612

—

C₂×#14579161

C₂²

yes

—

—

—

—

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₂×#14579084

—

#19098308

—

C₂×C₄×D₄×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₇₉

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

—

C₂×#11929612

—

C₂×#11929612

—

C₂×#11929612

—

C₂²×C₇₉⋊C₈

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

#14579095

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579084

—

C₂²×D₄×C₇₉

D₄

yes

characteristic

C₂³×C₄×C₇₉

—

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄×D₄×C₇₉

—

C₄×D₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

#11929612

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂⁴×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

D₈

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

SD₁₆

yes

complemented

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

#121

yes

characteristic

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

#120

yes

characteristic

C₂×C₄×C₇₉

#120

yes

—

C₂×C₄×C₇₉

#121

yes

—

100

C₂×C₄×C₇₉

#127

yes

characteristic

101

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

102

C₂×C₄×C₇₉

C₂×SD₁₆

yes

—

103

C₂×C₄×C₇₉

#135

yes

characteristic

104

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

105

C₂×C₄×C₇₉

#137

yes

—

106

C₂×Dic₇₉

—

107

C₂×Dic₇₉

—

108

C₂×Dic₇₉

—

109

Dic₁₅₈

—

110

Dic₁₅₈

—

111

Dic₁₅₈

—

112

Dic₁₅₈

—

113

C₈×C₇₉

—

114

C₈×C₇₉

—

115

C₇₉⋊C₈

—

116

C₂²×C₇₉

—

117

C₂²×C₇₉

—

118

C₂²×C₇₉

—

119

C₂²×C₇₉

—

120

C₂²×C₇₉

—

121

C₂²×C₇₉

#392

yes

characteristic

122

C₂²×C₇₉

#461

yes

—

123

C₂²×C₇₉

#466

yes

characteristic

124

C₂²×C₇₉

#469

yes

characteristic

125

C₂²×C₇₉

#473

yes

—

126

C₄×C₇₉

—

127

C₄×C₇₉

—

128

C₄×C₇₉

#447

yes

—

129

C₄×C₇₉

#448

yes

—

130

C₄×C₇₉

#449

yes

—

131

C₄×C₇₉

#492

yes

characteristic

132

C₄×C₇₉

#497

yes

characteristic

133

Dic₇₉

—

134

#10264

—

maximal, Sylow

135

C₂×C₇₉

—

136

C₂×C₇₉

#1673

yes

—

137

C₂×C₇₉

#1693

yes

—

138

C₂×C₇₉

#1999

yes

characteristic

139

C₂×C₇₉

#2013

yes

characteristic

140

C₂×C₇₉

#2020

yes

characteristic

141

C₂×#500

—

142

C₂×#461

—

143

#1954

D₇₉

yes

characteristic

144

C₂×#332

—

145

#1277

—

146

C₇₉

#10264

yes

characteristic, complemented, Sylow

147

C₂²×SD₁₆

—

158

—

148

C₂×C₄⋊Q₈

—

149

C₂×C₄×D₄

C₂×D₇₉

yes

characteristic

150

#500

—

158

—

151

#461

—

158

—

152

#461

—

158

—

153

C₂×#107

—

158

—

154

C₂×C₄⋊C₈

—

155

C₂×C₄⋊C₈

C₂×D₇₉

yes

characteristic

156

C₂×#103

—

158

—

157

C₂×C₂²⋊C₈

—

158

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

159

#332

—

158

—

160

C₂²×Q₈

—

158

—

161

C₂²×D₄

D₃₁₆

yes

characteristic

162

C₂³×C₄

—

163

C₂×SD₁₆

—

316

—

164

C₂×SD₁₆

—

316

—

165

C₂×SD₁₆

—

158

—

166

C₂²×C₈

—

167

C₂²×C₈

—

158

—

168

C₂²×C₈

C₂²⋊D₇₉

yes

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

158

—

171

C₄⋊Q₈

—

158

—

172

C₄⋊Q₈

—

158

—

173

C₄×D₄

—

174

C₄×D₄

—

175

C₂×C₄⋊C₄

—

158

—

176

C₂×C₄⋊C₄

—

158

—

177

C₂×C₄⋊C₄

D₃₁₆

yes

characteristic

178

C₂×C₂²⋊C₄

—

179

C₂×C₄²

C₂²×D₇₉

yes

characteristic

180

#107

—

158

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

158

—

184

#103

—

158

—

185

C₂²⋊C₈

—

186

C₄×C₈

—

187

C₂⁴

—

188

C₂×Q₈

—

316

—

189

C₂×Q₈

—

316

—

190

C₂×Q₈

—

316

—

191

C₂×Q₈

—

316

—

192

C₂×Q₈

—

316

—

193

C₂×Q₈

—

158

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

D₆₃₂

yes

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

316

—

204

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

205

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

206

C₂²×C₄

#11929624

yes

characteristic

207

SD₁₆

—

316

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

316

—

213

C₂×C₈

—

316

—

214

C₂×C₈

—

158

—

215

C₂×C₈

#11929612

yes

complemented

216

C₄⋊C₄

—

217

C₄⋊C₄

—

316

—

218

C₄⋊C₄

—

316

—

219

C₄⋊C₄

—

158

—

220

C₄⋊C₄

—

158

—

221

C₂²⋊C₄

—

222

C₄²

D₄×D₇₉

yes

—

223

C₄²

D₄×D₇₉

yes

—

224

C₂³

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

—

229

C₂³

#14579135

yes

characteristic

230

Q₈

—

316

—

231

Q₈

—

316

—

232

Q₈

—

632

—

233

Q₈

—

632

—

234

D₄

—

235

D₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

316

—

243

C₂×C₄

—

632

—

244

C₂×C₄

—

632

—

245

C₂×C₄

#14579129

yes

characteristic

246

C₂×C₄

#14579131

yes

—

247

C₂×C₄

#14579134

yes

—

248

C₂×C₄

#14579157

yes

characteristic

249

C₂×C₄

C₂×D₆₃₂

yes

characteristic

250

C₂×C₄

C₂×#11929612

yes

—

251

C₂×C₄

#14579183

yes

characteristic

252

C₂×C₄

#14579189

yes

—

253

C₂×C₄

#14579191

yes

—

254

C₈

—

255

C₈

—

256

C₈

—

316

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

#19098472

yes

characteristic

263

C₂²

#19098768

yes

—

264

C₂²

#19098799

yes

characteristic

265

C₂²

#19098816

yes

characteristic

266

C₂²

#19098838

yes

—

267

C₄

—

268

C₄

—

269

C₄

—

632

—

270

C₄

#19098699

yes

—

271

C₄

#19098701

yes

—

272

C₄

#19098710

yes

—

273

C₄

#19098935

yes

characteristic

274

C₄

#19098958

yes

characteristic

275

C₂

—

276

C₂

#23762789

yes

—

277

C₂

#23762913

yes

—

278

C₂

#23764398

yes

characteristic

279

C₂

#23764482

yes

characteristic

280

C₂

#23764521

yes

characteristic

	subgroup	G/H
center	C₂³	#14579135
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1954	C₂
socle	C₂³×C₇₉	#121
prime radical	C₂²×D₄×C₇₉	D₄
hypercenter	#1954	D₇₉
hypocenter	C₇₉	#10264
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#14579135

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1954

C₂

socle

C₂³×C₇₉

#121

prime radical

C₂²×D₄×C₇₉

D₄

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. C₂×#19098968	C₂	semidirect
3. C₂×#19098308	C₂	semidirect
4. #23761235	C₂	semidirect
78. C₂×C₈×C₇₉	SD₁₆	semidirect
146. C₇₉	#10264	semidirect
215. C₂×C₈	#11929612	semidirect

H ≅ G/N

type

1. C₂×#19098968

C₂

semidirect

3. C₂×#19098308

C₂

semidirect

4. #23761235

C₂

semidirect

78. C₂×C₈×C₇₉

SD₁₆

semidirect

146. C₇₉

#10264

semidirect

215. C₂×C₈

#11929612

semidirect

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

subgroup	index
C₂×#19098968	2
C₂×#19098768	2
C₂×#19098308	2
#23761235	2
C₇₉×#1954	2
#10264	79

subgroup

index

C₇₉×#1954

Subgroups — #34190799

Conjugacy classes of subgroups

Complements

Maximal subgroups