Group #34187850 — subgroups

Subgroups — #34187850

Order 20224.

426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 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×#19098959	C₂	1	1	yes	maximal, characteristic
2	#23764388	C₂	1	1	yes	maximal, characteristic
3	#23764245	C₂	1	1	yes	maximal, characteristic
4	#23762155	C₂	1	1	yes	maximal, characteristic
5	#23762084	C₂	1	1	yes	maximal, characteristic
6	#23761681	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1546	C₂	1	1	yes	maximal, characteristic
8	C₂×#14579161	C₂²	1	1	yes	characteristic
9	#19098959	—	2	1	no	—
10	#19098959	—	2	1	no	—
11	#19098959	—	2	2	no	—
12	C₂×#14579092	C₄	1	4	yes	—
13	#19098587	C₂²	1	1	yes	characteristic
14	C₂×#14579080	—	2	2	no	—
15	C₄×#11929608	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
17	#19098331	—	2	2	no	—
18	#19098313	—	2	2	no	—
19	#19098310	—	2	2	no	—
20	#19098285	—	2	1	no	—
21	C₈×C₇₉⋊C₈	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
23	#431×C₇₉	C₂²	1	1	yes	characteristic
24	#423×C₇₉	C₂²	1	1	yes	characteristic
25	#332×C₇₉	—	2	2	no	—
26	C₂²×Dic₁₅₈	—	2	1	no	—
27	C₂×#11929608	—	2	1	no	—
28	C₂×#11929608	D₄	1	2	yes	—
29	C₂²×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
30	#14579161	—	2	1	no	—
31	#14579161	—	2	1	no	—
32	#14579161	—	2	1	no	—
33	#14579161	—	2	1	no	—
34	C₂×C₄⋊Dic₇₉	—	2	1	no	—
35	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
36	#14579092	—	2	4	no	—
37	#14579092	—	2	4	no	—
38	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
39	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
40	#14579080	—	4	4	no	—
41	#14579072	—	2	1	no	—
42	C₄×C₇₉⋊C₈	—	2	1	no	—
43	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
44	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
45	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
46	C₂²×Q₈×C₇₉	—	2	1	no	—
47	C₂×M₁₆×C₇₉	—	2	1	no	—
48	C₄⋊Q₈×C₇₉	—	2	1	no	—
49	C₄⋊Q₈×C₇₉	—	2	1	no	—
50	C₄⋊Q₈×C₇₉	—	2	1	no	—
51	C₄⋊Q₈×C₇₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₇₉	—	2	1	no	—
56	C₄⋊C₈×C₇₉	—	2	1	no	—
57	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
58	C₂²⋊C₈×C₇₉	—	2	1	no	—
59	C₄×C₈×C₇₉	—	2	1	no	—
60	C₂×Dic₁₅₈	—	4	1	no	—
61	C₂×Dic₁₅₈	—	4	1	no	—
62	C₂×Dic₁₅₈	—	8	2	no	—
63	C₂²×Dic₇₉	—	2	2	no	—
64	#11929608	—	2	2	no	—
65	#11929608	—	4	2	no	—
66	#11929608	SD₁₆	1	4	yes	—
67	C₂×C₇₉⋊C₈	—	2	4	no	—
68	C₂×C₇₉⋊C₈	—	2	2	no	—
69	C₂×C₇₉⋊C₈	—	4	1	no	—
70	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
71	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
72	C₄⋊Dic₇₉	—	2	2	no	—
73	C₄⋊Dic₇₉	—	2	2	no	—
74	C₄⋊Dic₇₉	—	4	1	no	—
75	C₄⋊Dic₇₉	—	4	1	no	—
76	C₂×Q₈×C₇₉	—	4	1	no	—
77	C₂×Q₈×C₇₉	—	4	1	no	—
78	C₂×Q₈×C₇₉	—	4	2	no	—
79	C₂×Q₈×C₇₉	—	4	2	no	—
80	C₂²×C₄×C₇₉	—	2	2	no	—
81	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
84	M₁₆×C₇₉	—	4	2	no	—
85	C₂×C₈×C₇₉	—	2	2	no	—
86	C₂×C₈×C₇₉	—	4	1	no	—
87	C₄⋊C₄×C₇₉	—	2	2	no	—
88	C₄⋊C₄×C₇₉	—	2	2	no	—
89	C₄⋊C₄×C₇₉	—	4	1	no	—
90	C₄⋊C₄×C₇₉	—	4	1	no	—
91	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
92	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
93	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
94	C₄²×C₇₉	#41	1	1	yes	characteristic
95	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
96	Q₈×C₇₉	—	8	2	no	—
97	Q₈×C₇₉	—	8	1	no	—
98	Q₈×C₇₉	—	8	1	no	—
99	C₂×C₄×C₇₉	—	2	2	no	—
100	C₂×C₄×C₇₉	—	2	2	no	—
101	C₂×C₄×C₇₉	—	4	2	no	—
102	C₂×C₄×C₇₉	—	4	4	no	—
103	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
105	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
106	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
107	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
108	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
109	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
110	C₂×C₄×C₇₉	#135	1	2	yes	—
111	C₂×Dic₇₉	—	4	2	no	—
112	C₂×Dic₇₉	—	8	2	no	—
113	Dic₁₅₈	—	8	2	no	—
114	Dic₁₅₈	—	8	2	no	—
115	C₈×C₇₉	—	4	2	no	—
116	C₈×C₇₉	—	8	1	no	—
117	C₇₉⋊C₈	—	2	2	no	—
118	C₇₉⋊C₈	—	2	4	no	—
119	C₇₉⋊C₈	—	8	1	no	—
120	C₇₉⋊C₈	#101	1	4	yes	complemented
121	C₂²×C₇₉	—	2	1	no	—
122	C₂²×C₇₉	—	2	1	no	—
123	C₂²×C₇₉	#390	1	1	yes	characteristic
124	C₂²×C₇₉	C₄×SD₁₆	1	2	yes	—
125	C₄×C₇₉	—	2	1	no	—
126	C₄×C₇₉	—	2	1	no	—
127	C₄×C₇₉	—	8	2	no	—
128	C₄×C₇₉	C₂×#101	1	2	yes	—
129	C₄×C₇₉	#465	1	2	yes	—
130	C₄×C₇₉	#471	1	2	yes	—
131	C₄×C₇₉	#492	1	1	yes	characteristic
132	C₄×C₇₉	#495	1	1	yes	characteristic
133	Dic₇₉	—	8	2	no	—
134	#9794	—	79	1	no	maximal, Sylow
135	C₂×C₇₉	—	2	2	no	—
136	C₂×C₇₉	#1966	1	1	yes	characteristic
137	C₂×C₇₉	#1968	1	1	yes	characteristic
138	C₂×C₇₉	#1977	1	1	yes	characteristic
139	C₂×#498	—	79	1	no	—
140	#1997	—	79	1	no	—
141	#1966	—	79	1	no	—
142	#1566	—	79	1	no	—
143	#1549	—	79	1	no	—
144	#1546	D₇₉	1	1	yes	characteristic
145	C₈×M₁₆	—	79	1	no	—
146	C₇₉	#9794	1	1	yes	characteristic, complemented, Sylow
147	C₂×C₄⋊Q₈	—	79	1	no	—
148	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
149	#498	—	158	1	no	—
150	#498	—	158	1	no	—
151	#498	—	158	2	no	—
152	#431	C₂×D₇₉	1	1	yes	characteristic
153	C₂×#106	—	79	4	no	—
154	#423	—	79	1	no	—
155	#423	C₂×D₇₉	1	1	yes	characteristic
156	C₂×#101	—	158	2	no	—
157	C₄×M₁₆	—	79	1	no	—
158	C₂×C₄×C₈	—	79	1	no	—
159	#343	—	158	2	no	—
160	#334	—	158	2	no	—
161	#332	—	2	2	no	—
162	#332	—	158	2	no	—
163	#322	—	158	1	no	—
164	C₈²	—	158	1	no	—
165	C₂²×Q₈	—	2	1	no	—
166	C₂²×Q₈	—	158	1	no	—
167	C₂×M₁₆	—	2	1	no	—
168	C₂×M₁₆	—	79	2	no	—
169	C₂×M₁₆	—	158	1	no	—
170	C₂²×C₈	—	79	2	no	—
171	C₄⋊Q₈	—	2	1	no	—
172	C₄⋊Q₈	—	2	1	no	—
173	C₄⋊Q₈	—	2	1	no	—
174	C₄⋊Q₈	—	2	1	no	—
175	C₄⋊Q₈	—	158	1	no	—
176	C₄⋊Q₈	—	158	1	no	—
177	C₄⋊Q₈	—	158	1	no	—
178	C₄⋊Q₈	—	158	1	no	—
179	C₂×C₄⋊C₄	—	2	1	no	—
180	C₂×C₄⋊C₄	—	79	2	no	—
181	C₂×C₄⋊C₄	—	158	1	no	—
182	C₂×C₄⋊C₄	C₄×D₇₉	1	2	yes	—
183	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
184	#106	—	158	4	no	—
185	#106	—	158	4	no	—
186	C₄⋊C₈	—	2	1	no	—
187	C₄⋊C₈	—	2	1	no	—
188	C₄⋊C₈	—	158	1	no	—
189	C₄⋊C₈	—	158	1	no	—
190	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
191	#101	—	316	4	no	—
192	C₂²⋊C₈	—	2	1	no	—
193	#97	—	158	1	no	—
194	C₄×C₈	—	2	1	no	—
195	C₄×C₈	—	79	1	no	—
196	C₄×C₈	—	79	1	no	—
197	C₄×C₈	—	79	2	no	—
198	C₄×C₈	—	158	1	no	—
199	C₂×Q₈	—	4	1	no	—
200	C₂×Q₈	—	4	1	no	—
201	C₂×Q₈	—	4	2	no	—
202	C₂×Q₈	—	4	2	no	—
203	C₂×Q₈	—	316	1	no	—
204	C₂×Q₈	—	316	1	no	—
205	C₂×Q₈	—	632	2	no	—
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	158	2	no	—
208	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
209	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
210	C₂²×C₄	#11929623	1	1	yes	characteristic
211	M₁₆	—	4	2	no	—
212	M₁₆	—	316	2	no	—
213	M₁₆	—	79	4	no	—
214	M₁₆	—	158	2	no	—
215	C₂×C₈	—	2	2	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	316	1	no	—
218	C₂×C₈	—	79	2	no	—
219	C₂×C₈	—	79	2	no	—
220	C₂×C₈	—	158	4	no	—
221	C₂×C₈	—	158	2	no	—
222	C₄⋊C₄	—	2	2	no	—
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	4	1	no	—
225	C₄⋊C₄	—	4	1	no	—
226	C₄⋊C₄	—	316	1	no	—
227	C₄⋊C₄	—	316	1	no	—
228	C₄⋊C₄	—	158	2	no	—
229	C₄⋊C₄	—	158	2	no	—
230	C₄²	D₄×D₇₉	1	1	yes	characteristic
231	C₄²	D₄×D₇₉	1	1	yes	characteristic
232	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
233	C₄²	#11929624	1	1	yes	characteristic
234	C₂³	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
235	Q₈	—	8	1	no	—
236	Q₈	—	8	1	no	—
237	Q₈	—	8	2	no	—
238	Q₈	—	632	2	no	—
239	Q₈	—	632	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	4	4	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	316	2	no	—
245	C₂×C₄	—	632	2	no	—
246	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
247	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
248	C₂×C₄	#14579133	1	1	yes	characteristic
249	C₂×C₄	#14579134	1	1	yes	characteristic
250	C₂×C₄	#14579147	1	1	yes	characteristic
251	C₂×C₄	#14579157	1	1	yes	characteristic
252	C₂×C₄	SD₁₆×D₇₉	1	2	yes	—
253	C₂×C₄	#14579180	1	2	yes	—
254	C₈	—	4	2	no	—
255	C₈	—	8	1	no	—
256	C₈	—	79	4	no	—
257	C₈	—	632	1	no	—
258	C₈	—	158	4	no	—
259	C₈	—	158	2	no	—
260	C₂²	—	2	1	no	—
261	C₂²	—	2	1	no	—
262	C₂²	#19098463	1	1	yes	characteristic
263	C₂²	#19098654	1	2	yes	—
264	C₄	—	2	1	no	—
265	C₄	—	2	1	no	—
266	C₄	—	8	2	no	—
267	C₄	—	632	2	no	—
268	C₄	#101×D₇₉	1	2	yes	—
269	C₄	#19098791	1	2	yes	—
270	C₄	#19098828	1	2	yes	—
271	C₄	#19098934	1	1	yes	characteristic
272	C₄	#19098946	1	1	yes	characteristic
273	C₂	—	2	2	no	—
274	C₂	#23764242	1	1	yes	characteristic
275	C₂	#23764255	1	1	yes	characteristic
276	C₂	#23764302	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098959

C₂

yes

maximal, characteristic

#23764388

C₂

yes

maximal, characteristic

#23764245

C₂

yes

maximal, characteristic

#23762155

C₂

yes

maximal, characteristic

#23762084

C₂

yes

maximal, characteristic

#23761681

C₂

yes

maximal, characteristic

C₇₉×#1546

C₂

yes

maximal, characteristic

C₂×#14579161

C₂²

yes

—

—

—

C₄

yes

—

#19098587

C₂²

yes

characteristic

C₂×#14579080

—

C₄×#11929608

C₂²

yes

characteristic

C₂×C₄×C₇₉⋊C₈

C₂²

yes

—

—

—

—

C₈×C₇₉⋊C₈

—

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#431×C₇₉

C₂²

yes

characteristic

#423×C₇₉

C₂²

yes

characteristic

#332×C₇₉

—

C₂²×Dic₁₅₈

—

C₂×#11929608

—

C₂×#11929608

D₄

yes

—

C₂²×C₇₉⋊C₈

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂×C₄

yes

—

#14579092

—

#14579092

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

#14579080

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

D₄

yes

characteristic

C₄×C₇₉⋊C₈

D₄

yes

characteristic

C₄×C₇₉⋊C₈

D₄

yes

—

C₂²×Q₈×C₇₉

—

C₂×M₁₆×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂×C₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

D₄

yes

—

C₂²⋊C₈×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

#11929608

—

#11929608

—

#11929608

SD₁₆

yes

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₇₉⋊C₈

C₂²⋊C₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

#41

yes

characteristic

C₂³×C₇₉

C₄×D₄

yes

characteristic

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

C₂×C₂²⋊C₄

yes

characteristic

104

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

105

C₂×C₄×C₇₉

#121

yes

characteristic

106

C₂×C₄×C₇₉

#121

yes

characteristic

107

C₂×C₄×C₇₉

#124

yes

characteristic

108

C₂×C₄×C₇₉

#127

yes

characteristic

109

C₂×C₄×C₇₉

C₂×SD₁₆

yes

—

110

C₂×C₄×C₇₉

#135

yes

—

111

C₂×Dic₇₉

—

112

C₂×Dic₇₉

—

113

Dic₁₅₈

—

114

Dic₁₅₈

—

115

C₈×C₇₉

—

116

C₈×C₇₉

—

117

C₇₉⋊C₈

—

118

C₇₉⋊C₈

—

119

C₇₉⋊C₈

—

120

C₇₉⋊C₈

#101

yes

complemented

121

C₂²×C₇₉

—

122

C₂²×C₇₉

—

123

C₂²×C₇₉

#390

yes

characteristic

124

C₂²×C₇₉

C₄×SD₁₆

yes

—

125

C₄×C₇₉

—

126

C₄×C₇₉

—

127

C₄×C₇₉

—

128

C₄×C₇₉

C₂×#101

yes

—

129

C₄×C₇₉

#465

yes

—

130

C₄×C₇₉

#471

yes

—

131

C₄×C₇₉

#492

yes

characteristic

132

C₄×C₇₉

#495

yes

characteristic

133

Dic₇₉

—

134

#9794

—

maximal, Sylow

135

C₂×C₇₉

—

136

C₂×C₇₉

#1966

yes

characteristic

137

C₂×C₇₉

#1968

yes

characteristic

138

C₂×C₇₉

#1977

yes

characteristic

139

C₂×#498

—

140

#1997

—

141

#1966

—

142

#1566

—

143

#1549

—

144

#1546

D₇₉

yes

characteristic

145

C₈×M₁₆

—

146

C₇₉

#9794

yes

characteristic, complemented, Sylow

147

C₂×C₄⋊Q₈

—

148

C₂×C₄⋊Q₈

C₂×D₇₉

yes

characteristic

149

#498

—

158

—

150

#498

—

158

—

151

#498

—

158

—

152

#431

C₂×D₇₉

yes

characteristic

153

C₂×#106

—

154

#423

—

155

#423

C₂×D₇₉

yes

characteristic

156

C₂×#101

—

158

—

157

C₄×M₁₆

—

158

C₂×C₄×C₈

—

159

#343

—

158

—

160

#334

—

158

—

161

#332

—

162

#332

—

158

—

163

#322

—

158

—

164

C₈²

—

158

—

165

C₂²×Q₈

—

166

C₂²×Q₈

—

158

—

167

C₂×M₁₆

—

168

C₂×M₁₆

—

169

C₂×M₁₆

—

158

—

170

C₂²×C₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

158

—

176

C₄⋊Q₈

—

158

—

177

C₄⋊Q₈

—

158

—

178

C₄⋊Q₈

—

158

—

179

C₂×C₄⋊C₄

—

180

C₂×C₄⋊C₄

—

181

C₂×C₄⋊C₄

—

158

—

182

C₂×C₄⋊C₄

C₄×D₇₉

yes

—

183

C₂×C₄²

C₂²×D₇₉

yes

characteristic

184

#106

—

158

—

185

#106

—

158

—

186

C₄⋊C₈

—

187

C₄⋊C₈

—

188

C₄⋊C₈

—

158

—

189

C₄⋊C₈

—

158

—

190

C₄⋊C₈

C₂²⋊D₇₉

yes

—

191

#101

—

316

—

192

C₂²⋊C₈

—

193

#97

—

158

—

194

C₄×C₈

—

195

C₄×C₈

—

196

C₄×C₈

—

197

C₄×C₈

—

198

C₄×C₈

—

158

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

203

C₂×Q₈

—

316

—

204

C₂×Q₈

—

316

—

205

C₂×Q₈

—

632

—

206

C₂²×C₄

—

207

C₂²×C₄

—

158

—

208

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

209

C₂²×C₄

D₄×D₇₉

yes

characteristic

210

C₂²×C₄

#11929623

yes

characteristic

211

M₁₆

—

212

M₁₆

—

316

—

213

M₁₆

—

214

M₁₆

—

158

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

316

—

218

C₂×C₈

—

219

C₂×C₈

—

220

C₂×C₈

—

158

—

221

C₂×C₈

—

158

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

316

—

227

C₄⋊C₄

—

316

—

228

C₄⋊C₄

—

158

—

229

C₄⋊C₄

—

158

—

230

C₄²

D₄×D₇₉

yes

characteristic

231

C₄²

D₄×D₇₉

yes

characteristic

232

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

233

C₄²

#11929624

yes

characteristic

234

C₂³

(C₂²⋊D₇₉)⋊C₄

yes

characteristic

235

Q₈

—

236

Q₈

—

237

Q₈

—

238

Q₈

—

632

—

239

Q₈

—

632

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

316

—

245

C₂×C₄

—

632

—

246

C₂×C₄

C₂²⋊C₄×D₇₉

yes

characteristic

247

C₂×C₄

C₄×C₂²⋊D₇₉

yes

characteristic

248

C₂×C₄

#14579133

yes

characteristic

249

C₂×C₄

#14579134

yes

characteristic

250

C₂×C₄

#14579147

yes

characteristic

251

C₂×C₄

#14579157

yes

characteristic

252

C₂×C₄

SD₁₆×D₇₉

yes

—

253

C₂×C₄

#14579180

yes

—

254

C₈

—

255

C₈

—

256

C₈

—

257

C₈

—

632

—

258

C₈

—

158

—

259

C₈

—

158

—

260

C₂²

—

261

C₂²

—

262

C₂²

#19098463

yes

characteristic

263

C₂²

#19098654

yes

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

—

632

—

268

C₄

#101×D₇₉

yes

—

269

C₄

#19098791

yes

—

270

C₄

#19098828

yes

—

271

C₄

#19098934

yes

characteristic

272

C₄

#19098946

yes

characteristic

273

C₂

—

274

C₂

#23764242

yes

characteristic

275

C₂

#23764255

yes

characteristic

276

C₂

#23764302

yes

characteristic

	subgroup	G/H
center	C₂²	#19098463
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1546	C₂
socle	C₂²×C₇₉	#390
prime radical	C₂³×C₇₉	C₄×D₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1546	D₇₉
hypocenter	C₇₉	#9794
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

subgroup

G/H

center

C₂²

#19098463

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1546

C₂

socle

C₂²×C₇₉

#390

prime radical

C₂³×C₇₉

C₄×D₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1546

N	H ≅ G/N	type
120. C₇₉⋊C₈	#101	semidirect
146. C₇₉	#9794	semidirect

H ≅ G/N

type

120. C₇₉⋊C₈

#101

semidirect

146. C₇₉

#9794

semidirect

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

subgroup	index
C₂×#19098959	2
#23764388	2
#23764245	2
#23762155	2
#23762084	2
#23761681	2
C₇₉×#1546	2
#9794	79

subgroup

index

C₇₉×#1546

Subgroups — #34187850

Conjugacy classes of subgroups

Complements

Maximal subgroups