Group #34183576 — subgroups

Subgroups — #34183576

Order 20224.

570 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 155 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	#23766490	C₂	1	1	yes	maximal, characteristic
2	#23764349	C₂	1	2	yes	maximal
3	C₂×#19098312	C₂	1	1	yes	maximal, characteristic
4	#23761240	C₂	1	2	yes	maximal
5	C₂×#494×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
7	#19098470	—	2	2	no	—
8	#19098462	—	2	2	no	—
9	C₄⋊C₄×Dic₇₉	—	2	2	no	—
10	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
11	#19098325	—	2	2	no	—
12	#19098325	—	2	2	no	—
13	#19098312	—	2	2	no	—
14	C₂²×Q₁₆×C₇₉	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
17	#494×C₇₉	—	2	2	no	—
18	#494×C₇₉	C₄	1	4	yes	complemented
19	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×C₇₉⋊C₈	—	2	2	no	—
21	C₂×C₄⋊Dic₇₉	—	2	2	no	—
22	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
23	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
24	C₂×C₄×Dic₇₉	—	2	2	no	—
25	C₂×C₄×Dic₇₉	—	2	2	no	—
26	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
27	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
28	C₇₉⋊#95	—	2	4	no	—
29	C₇₉⋊#95	—	2	2	no	—
30	C₂²×Q₈×C₇₉	—	2	1	no	—
31	C₂²×Q₈×C₇₉	D₄	1	2	yes	—
32	C₂×Q₁₆×C₇₉	—	2	8	no	—
33	C₂×Q₁₆×C₇₉	—	4	4	no	—
34	C₂×Q₁₆×C₇₉	—	4	4	no	—
35	C₂²×C₈×C₇₉	—	2	1	no	—
36	C₄⋊Q₈×C₇₉	—	2	1	no	—
37	C₄⋊Q₈×C₇₉	—	2	2	no	—
38	C₄⋊Q₈×C₇₉	—	2	2	no	—
39	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
40	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
41	C₄⋊Q₈×C₇₉	D₄	1	2	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	1	no	—
46	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
47	C₂²×Dic₇₉	—	2	2	no	—
48	C₂²×Dic₇₉	—	2	2	no	—
49	C₂×C₇₉⋊C₈	—	4	2	no	—
50	C₂×C₇₉⋊C₈	—	4	2	no	—
51	C₂×C₇₉⋊C₈	—	4	2	no	—
52	C₄⋊Dic₇₉	—	2	2	no	—
53	C₄⋊Dic₇₉	—	2	2	no	—
54	C₄⋊Dic₇₉	—	2	2	no	—
55	C₄⋊Dic₇₉	—	8	2	no	—
56	C₄⋊Dic₇₉	Q₁₆	1	4	yes	complemented
57	C₄×Dic₇₉	—	4	2	no	—
58	C₄×Dic₇₉	—	4	2	no	—
59	C₄×Dic₇₉	—	8	2	no	—
60	C₂×Q₈×C₇₉	—	2	2	no	—
61	C₂×Q₈×C₇₉	—	2	2	no	—
62	C₂×Q₈×C₇₉	—	4	2	no	—
63	C₂×Q₈×C₇₉	—	4	2	no	—
64	C₂×Q₈×C₇₉	—	4	2	no	—
65	C₂×Q₈×C₇₉	—	4	2	no	—
66	C₂×Q₈×C₇₉	—	4	1	no	—
67	C₂×Q₈×C₇₉	C₂²⋊C₄	1	4	yes	—
68	C₂²×C₄×C₇₉	—	2	2	no	—
69	C₂²×C₄×C₇₉	—	4	1	no	—
70	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
72	Q₁₆×C₇₉	—	4	16	no	—
73	C₂×C₈×C₇₉	—	2	2	no	—
74	C₂×C₈×C₇₉	—	2	2	no	—
75	C₂×C₈×C₇₉	—	2	2	no	—
76	C₄⋊C₄×C₇₉	—	2	4	no	—
77	C₄⋊C₄×C₇₉	—	2	4	no	—
78	C₄⋊C₄×C₇₉	—	2	4	no	—
79	C₄⋊C₄×C₇₉	—	4	2	no	—
80	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₇₉	#41	1	2	yes	—
83	C₂³×C₇₉	#120	1	1	yes	characteristic
84	Q₈×C₇₉	—	4	4	no	—
85	Q₈×C₇₉	—	4	4	no	—
86	Q₈×C₇₉	—	8	2	no	—
87	Q₈×C₇₉	—	8	2	no	—
88	C₂×C₄×C₇₉	—	2	1	no	—
89	C₂×C₄×C₇₉	—	2	1	no	—
90	C₂×C₄×C₇₉	—	2	4	no	—
91	C₂×C₄×C₇₉	—	4	2	no	—
92	C₂×C₄×C₇₉	—	4	2	no	—
93	C₂×C₄×C₇₉	—	4	2	no	—
94	C₂×C₄×C₇₉	—	8	1	no	—
95	C₂×C₄×C₇₉	—	8	1	no	—
96	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₇₉	#121	1	2	yes	—
99	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
100	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
101	C₂×C₄×C₇₉	#135	1	2	yes	—
102	C₂×C₄×C₇₉	#137	1	2	yes	—
103	C₂×C₄×C₇₉	#137	1	2	yes	—
104	C₂×Dic₇₉	—	2	4	no	—
105	C₂×Dic₇₉	—	4	2	no	—
106	C₂×Dic₇₉	—	4	2	no	—
107	C₂×Dic₇₉	—	4	2	no	—
108	C₂×Dic₇₉	—	4	2	no	—
109	C₂×Dic₇₉	—	4	2	no	—
110	C₈×C₇₉	—	2	4	no	—
111	C₇₉⋊C₈	—	8	2	no	—
112	C₂²×C₇₉	#386	1	1	yes	characteristic
113	C₂²×C₇₉	#451	1	2	yes	—
114	C₂²×C₇₉	#452	1	2	yes	—
115	C₂²×C₇₉	#453	1	1	yes	characteristic
116	C₂²×C₇₉	#453	1	1	yes	characteristic
117	C₄×C₇₉	—	2	1	no	—
118	C₄×C₇₉	—	2	1	no	—
119	C₄×C₇₉	—	4	4	no	—
120	C₄×C₇₉	—	8	2	no	—
121	C₄×C₇₉	C₄×Q₁₆	1	2	yes	—
122	C₄×C₇₉	#441	1	2	yes	—
123	C₄×C₇₉	#462	1	2	yes	—
124	C₄×C₇₉	#464	1	2	yes	—
125	Dic₇₉	—	4	4	no	—
126	Dic₇₉	—	8	2	no	—
127	#9066	—	79	1	no	maximal, Sylow
128	C₂×C₇₉	#1632	1	2	yes	—
129	C₂×C₇₉	#1633	1	1	yes	characteristic
130	C₂×C₇₉	#1634	1	1	yes	characteristic
131	C₂×C₇₉	#1878	1	2	yes	—
132	C₂×C₇₉	#1887	1	1	yes	characteristic
133	C₂×#494	D₇₉	1	1	yes	characteristic
134	#2369	—	79	1	no	—
135	#1987	—	79	2	no	—
136	C₂×#333	—	79	1	no	—
137	#1279	—	79	2	no	—
138	C₇₉	#9066	1	1	yes	characteristic, complemented, Sylow
139	C₂²×Q₁₆	—	2	2	no	—
140	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
141	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
142	#494	—	2	2	no	—
143	#494	Dic₇₉	1	4	yes	complemented
144	C₂×C₄⋊C₈	—	79	2	no	—
145	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
146	#391	—	158	2	no	—
147	#389	—	158	2	no	—
148	C₄×C₄⋊C₄	—	79	2	no	—
149	C₄×C₄⋊C₄	—	158	2	no	—
150	#340	—	158	2	no	—
151	#340	—	158	2	no	—
152	#333	—	158	2	no	—
153	C₂²×Q₈	—	2	1	no	—
154	C₂²×Q₈	C₂²⋊D₇₉	1	2	yes	—
155	C₂×Q₁₆	—	2	8	no	—
156	C₂×Q₁₆	—	4	4	no	—
157	C₂×Q₁₆	—	4	4	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	158	2	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	—	2	2	no	—
162	C₄⋊Q₈	—	2	2	no	—
163	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
164	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
165	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	79	2	no	—
169	C₂×C₄⋊C₄	—	79	2	no	—
170	C₂×C₄⋊C₄	—	158	2	no	—
171	C₂×C₄²	—	158	2	no	—
172	C₂×C₄²	—	158	2	no	—
173	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
174	C₄⋊C₈	—	158	2	no	—
175	C₄⋊C₈	—	158	2	no	—
176	C₄×C₈	—	2	1	no	—
177	C₄×C₈	C₂×Dic₇₉	1	2	yes	—
178	#95	—	158	4	no	—
179	#95	—	158	2	no	—
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	2	no	—
185	C₂×Q₈	—	4	2	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂×Q₈	C₂²⋊Dic₇₉	1	4	yes	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	—	4	1	no	—
190	C₂²×C₄	—	158	2	no	—
191	C₂²×C₄	—	158	2	no	—
192	C₂²×C₄	D₄×D₇₉	1	2	yes	—
193	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
194	Q₁₆	—	4	16	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	316	2	no	—
199	C₂×C₈	—	316	2	no	—
200	C₂×C₈	—	316	2	no	—
201	C₄⋊C₄	—	2	4	no	—
202	C₄⋊C₄	—	2	4	no	—
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	79	4	no	—
206	C₄⋊C₄	—	632	2	no	—
207	C₄⋊C₄	—	158	2	no	—
208	C₄⋊C₄	—	158	2	no	—
209	C₄⋊C₄	—	158	2	no	—
210	C₄²	—	316	2	no	—
211	C₄²	—	316	2	no	—
212	C₄²	—	632	2	no	—
213	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
214	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
215	C₄²	#11929623	1	2	yes	—
216	C₂³	#14579129	1	1	yes	characteristic
217	Q₈	—	4	4	no	—
218	Q₈	—	4	4	no	—
219	Q₈	—	8	2	no	—
220	Q₈	—	8	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	4	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	8	1	no	—
228	C₂×C₄	—	8	1	no	—
229	C₂×C₄	—	316	2	no	—
230	C₂×C₄	—	316	2	no	—
231	C₂×C₄	—	316	2	no	—
232	C₂×C₄	—	316	2	no	—
233	C₂×C₄	—	316	2	no	—
234	C₂×C₄	—	158	4	no	—
235	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
236	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
237	C₂×C₄	#14579133	1	2	yes	—
238	C₂×C₄	#14579142	1	1	yes	characteristic
239	C₂×C₄	Q₁₆×D₇₉	1	2	yes	—
240	C₂×C₄	#14579184	1	2	yes	—
241	C₂×C₄	#14579193	1	2	yes	—
242	C₂×C₄	#14579193	1	2	yes	—
243	C₈	—	2	4	no	—
244	C₈	—	632	2	no	—
245	C₂²	#19098443	1	1	yes	characteristic
246	C₂²	#19098717	1	2	yes	—
247	C₂²	#19098724	1	2	yes	—
248	C₂²	#19098730	1	1	yes	characteristic
249	C₂²	#19098730	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	4	4	no	—
253	C₄	—	8	2	no	—
254	C₄	—	316	4	no	—
255	C₄	—	632	2	no	—
256	C₄	Q₁₆×Dic₇₉	1	2	yes	—
257	C₄	#19098670	1	2	yes	—
258	C₄	#19098771	1	2	yes	—
259	C₄	#19098787	1	2	yes	—
260	C₂	#23762531	1	2	yes	—
261	C₂	#23762538	1	1	yes	characteristic
262	C₂	#23762543	1	1	yes	characteristic
263	C₂	#23763743	1	2	yes	—
264	C₂	#23763799	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23766490

C₂

yes

maximal, characteristic

#23764349

C₂

yes

maximal

C₂×#19098312

C₂

yes

maximal, characteristic

#23761240

C₂

yes

maximal

C₂×#494×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#19098470

—

#19098462

—

C₄⋊C₄×Dic₇₉

—

C₄×C₄⋊Dic₇₉

C₂²

yes

—

#19098325

—

#19098325

—

#19098312

—

C₂²×Q₁₆×C₇₉

—

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#494×C₇₉

—

#494×C₇₉

C₄

yes

complemented

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂²×C₇₉⋊C₈

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

D₄

yes

—

C₂×C₄⋊Dic₇₉

D₄

yes

—

C₂×C₄×Dic₇₉

—

C₂×C₄×Dic₇₉

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₇₉⋊#95

—

C₇₉⋊#95

—

C₂²×Q₈×C₇₉

—

C₂²×Q₈×C₇₉

D₄

yes

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

—

C₂²×C₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄×C₈×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

Q₁₆

yes

complemented

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

#120

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×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×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

—

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

#123

yes

characteristic

100

C₂×C₄×C₇₉

C₂×Q₁₆

yes

—

101

C₂×C₄×C₇₉

#135

yes

—

102

C₂×C₄×C₇₉

#137

yes

—

103

C₂×C₄×C₇₉

#137

yes

—

104

C₂×Dic₇₉

—

105

C₂×Dic₇₉

—

106

C₂×Dic₇₉

—

107

C₂×Dic₇₉

—

108

C₂×Dic₇₉

—

109

C₂×Dic₇₉

—

110

C₈×C₇₉

—

111

C₇₉⋊C₈

—

112

C₂²×C₇₉

#386

yes

characteristic

113

C₂²×C₇₉

#451

yes

—

114

C₂²×C₇₉

#452

yes

—

115

C₂²×C₇₉

#453

yes

characteristic

116

C₂²×C₇₉

#453

yes

characteristic

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

—

120

C₄×C₇₉

—

121

C₄×C₇₉

C₄×Q₁₆

yes

—

122

C₄×C₇₉

#441

yes

—

123

C₄×C₇₉

#462

yes

—

124

C₄×C₇₉

#464

yes

—

125

Dic₇₉

—

126

Dic₇₉

—

127

#9066

—

maximal, Sylow

128

C₂×C₇₉

#1632

yes

—

129

C₂×C₇₉

#1633

yes

characteristic

130

C₂×C₇₉

#1634

yes

characteristic

131

C₂×C₇₉

#1878

yes

—

132

C₂×C₇₉

#1887

yes

characteristic

133

C₂×#494

D₇₉

yes

characteristic

134

#2369

—

135

#1987

—

136

C₂×#333

—

137

#1279

—

138

C₇₉

#9066

yes

characteristic, complemented, Sylow

139

C₂²×Q₁₆

—

140

C₂×C₄⋊Q₈

C₂×D₇₉

yes

characteristic

141

C₂×C₄⋊Q₈

C₂×D₇₉

yes

characteristic

142

#494

—

143

#494

Dic₇₉

yes

complemented

144

C₂×C₄⋊C₈

—

145

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

146

#391

—

158

—

147

#389

—

158

—

148

C₄×C₄⋊C₄

—

149

C₄×C₄⋊C₄

—

158

—

150

#340

—

158

—

151

#340

—

158

—

152

#333

—

158

—

153

C₂²×Q₈

—

154

C₂²×Q₈

C₂²⋊D₇₉

yes

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂²×C₈

—

159

C₂²×C₈

—

158

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

C₂×Dic₇₉

yes

—

164

C₄⋊Q₈

C₂×Dic₇₉

yes

—

165

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

158

—

171

C₂×C₄²

—

158

—

172

C₂×C₄²

—

158

—

173

C₂×C₄²

C₂²×D₇₉

yes

characteristic

174

C₄⋊C₈

—

158

—

175

C₄⋊C₈

—

158

—

176

C₄×C₈

—

177

C₄×C₈

C₂×Dic₇₉

yes

—

178

#95

—

158

—

179

#95

—

158

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

C₂²⋊Dic₇₉

yes

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

158

—

191

C₂²×C₄

—

158

—

192

C₂²×C₄

D₄×D₇₉

yes

—

193

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

194

Q₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

316

—

199

C₂×C₈

—

316

—

200

C₂×C₈

—

316

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

632

—

207

C₄⋊C₄

—

158

—

208

C₄⋊C₄

—

158

—

209

C₄⋊C₄

—

158

—

210

C₄²

—

316

—

211

C₄²

—

316

—

212

C₄²

—

632

—

213

C₄²

C₂²×Dic₇₉

yes

characteristic

214

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

215

C₄²

#11929623

yes

—

216

C₂³

#14579129

yes

characteristic

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

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

—

316

—

230

C₂×C₄

—

316

—

231

C₂×C₄

—

316

—

232

C₂×C₄

—

316

—

233

C₂×C₄

—

316

—

234

C₂×C₄

—

158

—

235

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

236

C₂×C₄

D₄×Dic₇₉

yes

—

237

C₂×C₄

#14579133

yes

—

238

C₂×C₄

#14579142

yes

characteristic

239

C₂×C₄

Q₁₆×D₇₉

yes

—

240

C₂×C₄

#14579184

yes

—

241

C₂×C₄

#14579193

yes

—

242

C₂×C₄

#14579193

yes

—

243

C₈

—

244

C₈

—

632

—

245

C₂²

#19098443

yes

characteristic

246

C₂²

#19098717

yes

—

247

C₂²

#19098724

yes

—

248

C₂²

#19098730

yes

characteristic

249

C₂²

#19098730

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

316

—

255

C₄

—

632

—

256

C₄

Q₁₆×Dic₇₉

yes

—

257

C₄

#19098670

yes

—

258

C₄

#19098771

yes

—

259

C₄

#19098787

yes

—

260

C₂

#23762531

yes

—

261

C₂

#23762538

yes

characteristic

262

C₂

#23762543

yes

characteristic

263

C₂

#23763743

yes

—

264

C₂

#23763799

yes

characteristic

	subgroup	G/H
center	C₂³	#14579129
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×#494×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	#120
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₂×#494	D₇₉
hypocenter	C₇₉	#9066
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#14579129

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₂×#494×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

#120

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
18. #494×C₇₉	C₄	semidirect
56. C₄⋊Dic₇₉	Q₁₆	semidirect
138. C₇₉	#9066	semidirect
143. #494	Dic₇₉	semidirect

H ≅ G/N

type

18. #494×C₇₉

C₄

semidirect

56. C₄⋊Dic₇₉

Q₁₆

semidirect

138. C₇₉

#9066

semidirect

143. #494

Dic₇₉

semidirect

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

subgroup	index
#23766490	2
#23764349	2
C₂×#19098312	2
#23761240	2
C₂×#494×C₇₉	2
#9066	79

subgroup

index

C₂×#494×C₇₉

Subgroups — #34183576

Conjugacy classes of subgroups

Complements

Maximal subgroups