Group #34190863 — subgroups

Subgroups — #34190863

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×#19098840	C₂	1	2	yes	maximal
2	#23764194	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098309	C₂	1	2	yes	maximal, complemented
4	#23761235	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#494×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
7	#19098840	—	2	4	no	—
8	#19098840	—	2	4	no	—
9	C₂×#14579094	—	2	2	no	—
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×#14579081	—	2	2	no	—
13	C₂×(C₂×D₇₉)⋊C₈	—	2	2	no	—
14	#19098309	—	2	4	no	—
15	C₂²×Q₁₆×C₇₉	—	2	2	no	—
16	C₂×C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
17	#494×C₇₉	—	2	4	no	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
20	C₂²×C₄×D₇₉	—	2	1	no	—
21	C₂²×C₇₉⋊C₈	—	2	2	no	—
22	C₂²×C₇₉⋊C₈	—	2	1	no	—
23	C₄×D₃₁₆	—	2	2	no	—
24	C₄×D₃₁₆	—	2	2	no	—
25	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
26	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
27	#14579094	—	2	8	no	—
28	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
31	#14579081	—	2	8	no	—
32	(C₂×D₇₉)⋊C₈	—	4	4	no	—
33	C₂²×Q₈×C₇₉	—	2	2	no	—
34	C₂×Q₁₆×C₇₉	—	2	8	no	—
35	C₂×Q₁₆×C₇₉	—	4	4	no	—
36	C₂×Q₁₆×C₇₉	—	4	4	no	—
37	C₂²×C₈×C₇₉	D₄	1	2	yes	—
38	C₄⋊Q₈×C₇₉	—	2	2	no	—
39	C₄⋊Q₈×C₇₉	—	2	2	no	—
40	C₄⋊Q₈×C₇₉	—	2	2	no	—
41	C₄⋊Q₈×C₇₉	D₄	1	4	yes	—
42	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
44	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
45	C₄×C₈×C₇₉	—	2	2	no	—
46	C₂³×D₇₉	—	2	1	no	—
47	C₂×D₃₁₆	—	2	2	no	—
48	C₂×D₃₁₆	—	2	1	no	—
49	C₂×D₃₁₆	—	2	2	no	—
50	C₂×D₃₁₆	Q₁₆	1	2	yes	complemented
51	C₂²×Dic₇₉	—	2	1	no	—
52	C₂×C₄×D₇₉	—	4	1	no	—
53	C₂×C₄×D₇₉	—	4	1	no	—
54	C₂×C₄×D₇₉	—	4	2	no	—
55	C₂×C₄×D₇₉	—	4	2	no	—
56	C₂×C₇₉⋊C₈	—	2	4	no	—
57	C₂×C₇₉⋊C₈	—	4	1	no	—
58	C₂×C₇₉⋊C₈	—	4	2	no	—
59	C₂×C₇₉⋊C₈	—	4	2	no	—
60	C₂×C₇₉⋊C₈	—	4	2	no	—
61	C₄⋊Dic₇₉	—	2	2	no	—
62	(C₂×D₇₉)⋊C₄	—	4	2	no	—
63	C₂×Q₈×C₇₉	—	2	4	no	—
64	C₂×Q₈×C₇₉	—	4	2	no	—
65	C₂×Q₈×C₇₉	—	4	4	no	—
66	C₂×Q₈×C₇₉	—	4	4	no	—
67	C₂²×C₄×C₇₉	—	4	2	no	—
68	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
71	Q₁₆×C₇₉	—	4	16	no	—
72	C₂×C₈×C₇₉	—	2	2	no	—
73	C₂×C₈×C₇₉	—	2	2	no	—
74	C₂×C₈×C₇₉	D₈	1	4	yes	—
75	C₄⋊C₄×C₇₉	—	2	4	no	—
76	C₄⋊C₄×C₇₉	—	2	4	no	—
77	C₄⋊C₄×C₇₉	—	4	2	no	—
78	C₄⋊C₄×C₇₉	—	4	2	no	—
79	C₄²×C₇₉	C₂×D₄	1	2	yes	—
80	C₄²×C₇₉	C₂×D₄	1	2	yes	—
81	C₂³×C₇₉	#121	1	1	yes	characteristic
82	C₂²×D₇₉	—	2	2	no	—
83	C₂²×D₇₉	—	4	1	no	—
84	C₂²×D₇₉	—	4	2	no	—
85	C₂²×D₇₉	—	4	1	no	—
86	C₂²×D₇₉	—	4	2	no	—
87	Q₈×C₇₉	—	4	8	no	—
88	Q₈×C₇₉	—	8	2	no	—
89	Q₈×C₇₉	—	8	2	no	—
90	C₂×C₄×C₇₉	—	2	2	no	—
91	C₂×C₄×C₇₉	—	4	4	no	—
92	C₂×C₄×C₇₉	—	8	4	no	—
93	C₂×C₄×C₇₉	#120	1	2	yes	—
94	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
95	C₂×C₄×C₇₉	#121	1	2	yes	—
96	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
97	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
98	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
99	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
100	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
101	C₂×C₄×C₇₉	#137	1	2	yes	—
102	C₂×Dic₇₉	—	4	1	no	—
103	C₂×Dic₇₉	—	4	2	no	—
104	D₃₁₆	—	2	4	no	—
105	D₃₁₆	—	4	2	no	—
106	C₄×D₇₉	—	8	2	no	—
107	C₄×D₇₉	—	8	1	no	—
108	C₄×D₇₉	—	8	1	no	—
109	C₈×C₇₉	—	2	4	no	—
110	C₇₉⋊C₈	—	4	4	no	—
111	C₇₉⋊C₈	—	8	1	no	—
112	C₂²×C₇₉	#392	1	1	yes	characteristic
113	C₂²×C₇₉	#459	1	2	yes	—
114	C₂²×C₇₉	#467	1	1	yes	characteristic
115	C₂²×C₇₉	#470	1	1	yes	characteristic
116	C₂²×C₇₉	#473	1	2	yes	—
117	C₂×D₇₉	—	4	4	no	—
118	C₂×D₇₉	—	4	2	no	—
119	C₂×D₇₉	—	8	2	no	—
120	C₂×D₇₉	—	8	1	no	—
121	C₂×D₇₉	—	8	1	no	—
122	C₄×C₇₉	—	2	2	no	—
123	C₄×C₇₉	—	8	4	no	—
124	C₄×C₇₉	#447	1	2	yes	—
125	C₄×C₇₉	#451	1	2	yes	—
126	C₄×C₇₉	#452	1	2	yes	—
127	C₄×C₇₉	#493	1	1	yes	characteristic
128	C₄×C₇₉	#496	1	1	yes	characteristic
129	Dic₇₉	—	8	1	no	—
130	#10274	—	79	1	no	maximal, Sylow
131	C₂×C₇₉	#1669	1	2	yes	—
132	C₂×C₇₉	#1689	1	2	yes	—
133	C₂×C₇₉	#2001	1	1	yes	characteristic
134	C₂×C₇₉	#2011	1	1	yes	characteristic
135	C₂×C₇₉	#2020	1	1	yes	characteristic
136	D₇₉	—	8	2	no	—
137	C₂×#494	D₇₉	1	1	yes	characteristic, complemented
138	C₂×#474	—	79	2	no	—
139	#1954	—	79	1	no	—
140	C₂×#332	—	79	2	no	—
141	#1277	—	79	1	no	—
142	C₇₉	#10274	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₁₆	—	2	2	no	—
144	C₂×C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
145	C₂×C₄×D₄	—	79	1	no	—
146	#494	—	2	4	no	—
147	#474	—	158	4	no	—
148	#474	—	158	4	no	—
149	C₂×#107	—	158	2	no	—
150	C₂×C₄⋊C₈	—	79	2	no	—
151	C₂×C₄⋊C₈	—	79	1	no	—
152	C₂×#102	—	158	2	no	—
153	C₂×C₂²⋊C₈	—	158	2	no	—
154	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
155	#332	—	158	4	no	—
156	C₂²×Q₈	—	2	2	no	—
157	C₂²×D₄	—	79	1	no	—
158	C₂³×C₄	—	158	1	no	—
159	C₂×Q₁₆	—	2	8	no	—
160	C₂×Q₁₆	—	4	4	no	—
161	C₂×Q₁₆	—	4	4	no	—
162	C₂²×C₈	—	158	1	no	—
163	C₂²×C₈	—	158	2	no	—
164	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
165	C₄⋊Q₈	—	2	2	no	—
166	C₄⋊Q₈	—	2	2	no	—
167	C₄⋊Q₈	—	2	2	no	—
168	C₄⋊Q₈	C₂²⋊D₇₉	1	4	yes	—
169	C₄×D₄	—	158	2	no	—
170	C₄×D₄	—	158	2	no	—
171	C₂×C₄⋊C₄	—	2	2	no	—
172	C₂×C₄⋊C₄	—	2	2	no	—
173	C₂×C₄⋊C₄	—	79	1	no	—
174	C₂×C₂²⋊C₄	—	158	1	no	—
175	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
176	#107	—	158	8	no	—
177	C₄⋊C₈	—	79	4	no	—
178	C₄⋊C₈	—	158	2	no	—
179	C₄⋊C₈	—	158	2	no	—
180	#102	—	158	8	no	—
181	C₂²⋊C₈	—	316	4	no	—
182	C₄×C₈	—	2	2	no	—
183	C₂⁴	—	158	1	no	—
184	C₂×Q₈	—	2	4	no	—
185	C₂×Q₈	—	4	2	no	—
186	C₂×Q₈	—	4	4	no	—
187	C₂×Q₈	—	4	4	no	—
188	C₂×D₄	—	79	2	no	—
189	C₂×D₄	—	158	2	no	—
190	C₂×D₄	—	158	1	no	—
191	C₂×D₄	—	158	2	no	—
192	C₂²×C₄	—	4	2	no	—
193	C₂²×C₄	—	316	1	no	—
194	C₂²×C₄	—	316	1	no	—
195	C₂²×C₄	—	316	2	no	—
196	C₂²×C₄	—	316	2	no	—
197	C₂²×C₄	—	158	1	no	—
198	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
200	C₂²×C₄	#11929623	1	1	yes	characteristic
201	Q₁₆	—	4	16	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	316	2	no	—
205	C₂×C₈	—	316	2	no	—
206	C₂×C₈	—	316	1	no	—
207	C₂×C₈	—	316	2	no	—
208	C₂×C₈	—	158	4	no	—
209	C₂×C₈	#11929609	1	4	yes	—
210	C₄⋊C₄	—	2	4	no	—
211	C₄⋊C₄	—	2	4	no	—
212	C₄⋊C₄	—	4	2	no	—
213	C₄⋊C₄	—	4	2	no	—
214	C₄⋊C₄	—	158	2	no	—
215	C₂²⋊C₄	—	316	2	no	—
216	C₄²	D₄×D₇₉	1	2	yes	—
217	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
218	C₂³	—	316	1	no	—
219	C₂³	—	316	2	no	—
220	C₂³	—	316	1	no	—
221	C₂³	—	316	2	no	—
222	C₂³	—	158	2	no	—
223	C₂³	#14579132	1	1	yes	characteristic
224	Q₈	—	4	8	no	—
225	Q₈	—	8	2	no	—
226	Q₈	—	8	2	no	—
227	D₄	—	316	2	no	—
228	D₄	—	158	4	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	4	4	no	—
231	C₂×C₄	—	8	4	no	—
232	C₂×C₄	—	316	1	no	—
233	C₂×C₄	—	316	2	no	—
234	C₂×C₄	—	632	1	no	—
235	C₂×C₄	—	632	1	no	—
236	C₂×C₄	—	632	2	no	—
237	C₂×C₄	#14579129	1	2	yes	—
238	C₂×C₄	#14579130	1	1	yes	characteristic
239	C₂×C₄	#14579133	1	2	yes	—
240	C₂×C₄	#14579157	1	1	yes	characteristic
241	C₂×C₄	C₂×#11929609	1	2	yes	—
242	C₂×C₄	Q₁₆×D₇₉	1	1	yes	characteristic
243	C₂×C₄	#14579184	1	1	yes	characteristic
244	C₂×C₄	#14579187	1	2	yes	—
245	C₂×C₄	#14579193	1	2	yes	—
246	C₈	—	2	4	no	—
247	C₈	—	316	4	no	—
248	C₈	—	632	1	no	—
249	C₂²	—	316	4	no	—
250	C₂²	—	316	2	no	—
251	C₂²	—	632	1	no	—
252	C₂²	—	632	2	no	—
253	C₂²	—	632	1	no	—
254	C₂²	#19098471	1	1	yes	characteristic
255	C₂²	#19098755	1	2	yes	—
256	C₂²	#19098801	1	1	yes	characteristic
257	C₂²	#19098818	1	1	yes	characteristic
258	C₂²	#19098835	1	2	yes	—
259	C₄	—	2	2	no	—
260	C₄	—	8	4	no	—
261	C₄	—	632	1	no	—
262	C₄	#19098697	1	2	yes	—
263	C₄	#19098717	1	2	yes	—
264	C₄	#19098724	1	2	yes	—
265	C₄	#19098939	1	1	yes	characteristic
266	C₄	#19098950	1	1	yes	characteristic
267	C₂	—	632	2	no	—
268	C₂	#23762762	1	2	yes	—
269	C₂	#23762886	1	2	yes	—
270	C₂	#23764407	1	1	yes	characteristic
271	C₂	#23764471	1	1	yes	characteristic
272	C₂	#23764519	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098840

C₂

yes

maximal

#23764194

C₂

yes

maximal, characteristic

C₂×#19098309

C₂

yes

maximal, complemented

#23761235

C₂

yes

maximal, characteristic, complemented

C₂×#494×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₃₁₆

C₂²

yes

—

—

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

C₂×#14579081

—

C₂×(C₂×D₇₉)⋊C₈

—

#19098309

—

C₂²×Q₁₆×C₇₉

—

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

—

#494×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×D₃₁₆

D₄

yes

characteristic

C₂²×C₄×D₇₉

—

C₂²×C₇₉⋊C₈

—

C₂²×C₇₉⋊C₈

—

C₄×D₃₁₆

—

C₄×D₃₁₆

—

C₂×C₄⋊Dic₇₉

D₄

yes

characteristic

C₂×(C₂×D₇₉)⋊C₄

—

#14579094

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

#14579081

—

(C₂×D₇₉)⋊C₈

—

C₂²×Q₈×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄×C₈×C₇₉

—

C₂³×D₇₉

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

Q₁₆

yes

complemented

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₈

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#121

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#120

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

#127

yes

characteristic

C₂×C₄×C₇₉

C₂×D₈

yes

—

C₂×C₄×C₇₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₇₉

#135

yes

characteristic

100

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

101

C₂×C₄×C₇₉

#137

yes

—

102

C₂×Dic₇₉

—

103

C₂×Dic₇₉

—

104

D₃₁₆

—

105

D₃₁₆

—

106

C₄×D₇₉

—

107

C₄×D₇₉

—

108

C₄×D₇₉

—

109

C₈×C₇₉

—

110

C₇₉⋊C₈

—

111

C₇₉⋊C₈

—

112

C₂²×C₇₉

#392

yes

characteristic

113

C₂²×C₇₉

#459

yes

—

114

C₂²×C₇₉

#467

yes

characteristic

115

C₂²×C₇₉

#470

yes

characteristic

116

C₂²×C₇₉

#473

yes

—

117

C₂×D₇₉

—

118

C₂×D₇₉

—

119

C₂×D₇₉

—

120

C₂×D₇₉

—

121

C₂×D₇₉

—

122

C₄×C₇₉

—

123

C₄×C₇₉

—

124

C₄×C₇₉

#447

yes

—

125

C₄×C₇₉

#451

yes

—

126

C₄×C₇₉

#452

yes

—

127

C₄×C₇₉

#493

yes

characteristic

128

C₄×C₇₉

#496

yes

characteristic

129

Dic₇₉

—

130

#10274

—

maximal, Sylow

131

C₂×C₇₉

#1669

yes

—

132

C₂×C₇₉

#1689

yes

—

133

C₂×C₇₉

#2001

yes

characteristic

134

C₂×C₇₉

#2011

yes

characteristic

135

C₂×C₇₉

#2020

yes

characteristic

136

D₇₉

—

137

C₂×#494

D₇₉

yes

characteristic, complemented

138

C₂×#474

—

139

#1954

—

140

C₂×#332

—

141

#1277

—

142

C₇₉

#10274

yes

characteristic, complemented, Sylow

143

C₂²×Q₁₆

—

144

C₂×C₄⋊Q₈

C₂×D₇₉

yes

—

145

C₂×C₄×D₄

—

146

#494

—

147

#474

—

158

—

148

#474

—

158

—

149

C₂×#107

—

158

—

150

C₂×C₄⋊C₈

—

151

C₂×C₄⋊C₈

—

152

C₂×#102

—

158

—

153

C₂×C₂²⋊C₈

—

158

—

154

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

155

#332

—

158

—

156

C₂²×Q₈

—

157

C₂²×D₄

—

158

C₂³×C₄

—

158

—

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

161

C₂×Q₁₆

—

162

C₂²×C₈

—

158

—

163

C₂²×C₈

—

158

—

164

C₂²×C₈

C₂²⋊D₇₉

yes

—

165

C₄⋊Q₈

—

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

169

C₄×D₄

—

158

—

170

C₄×D₄

—

158

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

—

174

C₂×C₂²⋊C₄

—

158

—

175

C₂×C₄²

C₂²×D₇₉

yes

characteristic

176

#107

—

158

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

158

—

179

C₄⋊C₈

—

158

—

180

#102

—

158

—

181

C₂²⋊C₈

—

316

—

182

C₄×C₈

—

183

C₂⁴

—

158

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×D₄

—

189

C₂×D₄

—

158

—

190

C₂×D₄

—

158

—

191

C₂×D₄

—

158

—

192

C₂²×C₄

—

193

C₂²×C₄

—

316

—

194

C₂²×C₄

—

316

—

195

C₂²×C₄

—

316

—

196

C₂²×C₄

—

316

—

197

C₂²×C₄

—

158

—

198

C₂²×C₄

D₄×D₇₉

yes

characteristic

199

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

200

C₂²×C₄

#11929623

yes

characteristic

201

Q₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

316

—

205

C₂×C₈

—

316

—

206

C₂×C₈

—

316

—

207

C₂×C₈

—

316

—

208

C₂×C₈

—

158

—

209

C₂×C₈

#11929609

yes

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

158

—

215

C₂²⋊C₄

—

316

—

216

C₄²

D₄×D₇₉

yes

—

217

C₄²

C₂×C₂²⋊D₇₉

yes

—

218

C₂³

—

316

—

219

C₂³

—

316

—

220

C₂³

—

316

—

221

C₂³

—

316

—

222

C₂³

—

158

—

223

C₂³

#14579132

yes

characteristic

224

Q₈

—

225

Q₈

—

226

Q₈

—

227

D₄

—

316

—

228

D₄

—

158

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

316

—

233

C₂×C₄

—

316

—

234

C₂×C₄

—

632

—

235

C₂×C₄

—

632

—

236

C₂×C₄

—

632

—

237

C₂×C₄

#14579129

yes

—

238

C₂×C₄

#14579130

yes

characteristic

239

C₂×C₄

#14579133

yes

—

240

C₂×C₄

#14579157

yes

characteristic

241

C₂×C₄

C₂×#11929609

yes

—

242

C₂×C₄

Q₁₆×D₇₉

yes

characteristic

243

C₂×C₄

#14579184

yes

characteristic

244

C₂×C₄

#14579187

yes

—

245

C₂×C₄

#14579193

yes

—

246

C₈

—

247

C₈

—

316

—

248

C₈

—

632

—

249

C₂²

—

316

—

250

C₂²

—

316

—

251

C₂²

—

632

—

252

C₂²

—

632

—

253

C₂²

—

632

—

254

C₂²

#19098471

yes

characteristic

255

C₂²

#19098755

yes

—

256

C₂²

#19098801

yes

characteristic

257

C₂²

#19098818

yes

characteristic

258

C₂²

#19098835

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

632

—

262

C₄

#19098697

yes

—

263

C₄

#19098717

yes

—

264

C₄

#19098724

yes

—

265

C₄

#19098939

yes

characteristic

266

C₄

#19098950

yes

characteristic

267

C₂

—

632

—

268

C₂

#23762762

yes

—

269

C₂

#23762886

yes

—

270

C₂

#23764407

yes

characteristic

271

C₂

#23764471

yes

characteristic

272

C₂

#23764519

yes

characteristic

	subgroup	G/H
center	C₂³	#14579132
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×#494×C₇₉	C₂
socle	C₂³×C₇₉	#121
prime radical	C₂²×D₃₁₆	D₄
hypercenter	C₂×#494	D₇₉
hypocenter	C₇₉	#10274
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#14579132

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₂×#494×C₇₉

C₂

socle

C₂³×C₇₉

#121

prime radical

C₂²×D₃₁₆

D₄

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
3. C₂×#19098309	C₂	semidirect
4. #23761235	C₂	semidirect
5. C₂×#494×C₇₉	C₂	semidirect
50. C₂×D₃₁₆	Q₁₆	semidirect
137. C₂×#494	D₇₉	semidirect
142. C₇₉	#10274	semidirect

H ≅ G/N

type

3. C₂×#19098309

C₂

semidirect

4. #23761235

C₂

semidirect

5. C₂×#494×C₇₉

C₂

semidirect

50. C₂×D₃₁₆

Q₁₆

semidirect

137. C₂×#494

D₇₉

semidirect

142. C₇₉

#10274

semidirect

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

subgroup	index
C₂×#19098840	2
#23764194	2
C₂×#19098309	2
#23761235	2
C₂×#494×C₇₉	2
#10274	79

subgroup

index

C₂×#494×C₇₉

Subgroups — #34190863

Conjugacy classes of subgroups

Complements

Maximal subgroups