Group #34176489 — subgroups

Subgroups — #34176489

Order 20224.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₄×#14579161	C₂	1	1	yes	maximal, characteristic
2	#23763253	C₂	1	1	yes	maximal, characteristic
3	#23761222	C₂	1	4	yes	maximal
4	C₇₉×#1839	C₂	1	1	yes	maximal, characteristic
5	C₂×#14579161	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₁₅₈	—	2	1	no	—
7	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
8	C₂×#14579072	—	2	1	no	—
9	#19098469	—	2	1	no	—
10	#19098461	—	2	1	no	—
11	#19098461	C₂²	1	2	yes	—
12	#19098433	C₄	1	1	yes	characteristic
13	C₄×C₄⋊Dic₇₉	—	2	1	no	—
14	C₄×C₄⋊Dic₇₉	C₄	1	2	yes	—
15	#19098318	C₂²	1	2	yes	—
16	C₄³×C₇₉	C₂²	1	1	yes	characteristic
17	#336×C₇₉	—	2	1	no	—
18	#336×C₇₉	—	2	1	no	—
19	#336×C₇₉	C₂²	1	2	yes	—
20	C₂²×Dic₁₅₈	—	2	1	no	—
21	C₂²×C₇₉⋊C₈	—	2	2	no	—
22	#14579161	—	2	4	no	—
23	C₄×Dic₁₅₈	—	4	2	no	—
24	C₄×Dic₁₅₈	—	4	2	no	—
25	C₂×C₄⋊Dic₇₉	—	2	1	no	—
26	C₂×C₄⋊Dic₇₉	—	2	1	no	—
27	C₂×C₄⋊Dic₇₉	—	2	1	no	—
28	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
29	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
30	C₂×Dic₇₉⋊C₄	—	2	2	no	—
31	C₂×C₄×Dic₇₉	—	2	2	no	—
32	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
33	#14579072	—	4	2	no	—
34	C₇₉⋊#95	—	2	2	no	—
35	C₇₉⋊#95	—	2	2	no	—
36	C₂²×C₈×C₇₉	—	2	2	no	—
37	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
44	C₂×Dic₁₅₈	—	2	4	no	—
45	C₂×Dic₁₅₈	—	4	2	no	—
46	C₂×Dic₁₅₈	—	4	2	no	—
47	C₂²×Dic₇₉	—	2	2	no	—
48	C₂²×Dic₇₉	—	2	2	no	—
49	C₂×C₇₉⋊C₈	—	2	4	no	—
50	C₂×C₇₉⋊C₈	—	4	2	no	—
51	C₂×C₇₉⋊C₈	—	4	2	no	—
52	C₄⋊Dic₇₉	—	2	4	no	—
53	C₄⋊Dic₇₉	—	2	2	no	—
54	C₄⋊Dic₇₉	—	4	2	no	—
55	C₄⋊Dic₇₉	—	4	2	no	—
56	C₄⋊Dic₇₉	—	4	2	no	—
57	C₄⋊Dic₇₉	M₁₆	1	4	yes	—
58	Dic₇₉⋊C₄	—	4	2	no	—
59	Dic₇₉⋊C₄	—	4	2	no	—
60	C₄×Dic₇₉	—	4	4	no	—
61	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₇₉	—	4	2	no	—
69	C₂×C₈×C₇₉	—	4	2	no	—
70	C₂×C₈×C₇₉	—	4	2	no	—
71	C₄²×C₇₉	—	2	2	no	—
72	C₄²×C₇₉	—	2	2	no	—
73	C₄²×C₇₉	—	2	2	no	—
74	C₄²×C₇₉	—	2	2	no	—
75	C₄²×C₇₉	—	4	1	no	—
76	C₄²×C₇₉	—	4	1	no	—
77	C₄²×C₇₉	D₈	1	2	yes	—
78	C₄²×C₇₉	SD₁₆	1	2	yes	—
79	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₇₉	—	2	1	no	—
81	C₂×C₄×C₇₉	—	2	1	no	—
82	C₂×C₄×C₇₉	—	2	1	no	—
83	C₂×C₄×C₇₉	—	2	1	no	—
84	C₂×C₄×C₇₉	—	2	1	no	—
85	C₂×C₄×C₇₉	—	2	1	no	—
86	C₂×C₄×C₇₉	—	2	1	no	—
87	C₂×C₄×C₇₉	—	2	1	no	—
88	C₂×C₄×C₇₉	—	2	1	no	—
89	C₂×C₄×C₇₉	—	2	1	no	—
90	C₂×C₄×C₇₉	—	2	1	no	—
91	C₂×C₄×C₇₉	—	2	1	no	—
92	C₂×C₄×C₇₉	—	2	1	no	—
93	C₂×C₄×C₇₉	—	2	1	no	—
94	C₂×C₄×C₇₉	#101	1	2	yes	—
95	C₂×C₄×C₇₉	#102	1	2	yes	—
96	C₂×C₄×C₇₉	#102	1	2	yes	—
97	C₂×C₄×C₇₉	#104	1	2	yes	—
98	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
99	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
100	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₇₉	#137	1	2	yes	—
102	C₂×Dic₇₉	—	2	4	no	—
103	C₂×Dic₇₉	—	4	2	no	—
104	C₂×Dic₇₉	—	4	2	no	—
105	C₂×Dic₇₉	—	4	2	no	—
106	C₂×Dic₇₉	—	4	2	no	—
107	C₂×Dic₇₉	—	4	2	no	—
108	Dic₁₅₈	—	4	8	no	—
109	C₈×C₇₉	—	8	2	no	—
110	C₇₉⋊C₈	—	4	4	no	—
111	C₂²×C₇₉	#407	1	1	yes	characteristic
112	C₂²×C₇₉	#410	1	1	yes	characteristic
113	C₂²×C₇₉	C₂×#101	1	1	yes	characteristic
114	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
115	C₂²×C₇₉	#419	1	1	yes	characteristic
116	C₂²×C₇₉	C₂×#104	1	1	yes	characteristic
117	C₂²×C₇₉	#421	1	1	yes	characteristic
118	C₄×C₇₉	—	2	2	no	—
119	C₄×C₇₉	—	2	2	no	—
120	C₄×C₇₉	—	2	2	no	—
121	C₄×C₇₉	—	2	2	no	—
122	C₄×C₇₉	—	2	1	no	—
123	C₄×C₇₉	—	2	1	no	—
124	C₄×C₇₉	—	2	2	no	—
125	C₄×C₇₉	—	2	2	no	—
126	Dic₇₉	—	4	4	no	—
127	Dic₇₉	—	8	2	no	—
128	#7625	—	79	1	no	maximal, Sylow
129	C₂×C₇₉	#1467	1	1	yes	characteristic
130	C₂×C₇₉	#1486	1	1	yes	characteristic
131	C₂×C₇₉	#1491	1	1	yes	characteristic
132	C₂×C₇₉	#1502	1	1	yes	characteristic
133	C₂×C₇₉	#1515	1	1	yes	characteristic
134	C₂×C₇₉	#1531	1	1	yes	characteristic
135	C₂×C₇₉	#1546	1	1	yes	characteristic
136	C₄×C₄⋊Q₈	—	79	1	no	—
137	#1839	D₇₉	1	1	yes	characteristic
138	#1767	—	79	1	no	—
139	#1271	—	79	4	no	—
140	C₇₉	#7625	1	1	yes	characteristic, complemented, Sylow
141	C₂×C₄⋊Q₈	—	79	1	no	—
142	C₂×C₄×Q₈	—	158	1	no	—
143	C₂×C₄⋊C₈	—	158	1	no	—
144	C₂×#97	—	158	1	no	—
145	#391	—	158	1	no	—
146	#389	—	79	2	no	—
147	#389	—	158	1	no	—
148	#384	—	79	1	no	—
149	C₄×C₄⋊C₄	—	79	2	no	—
150	C₄×C₄⋊C₄	—	158	1	no	—
151	C₄³	C₂×D₇₉	1	1	yes	characteristic
152	#336	—	2	1	no	—
153	#336	—	2	1	no	—
154	#336	—	79	2	no	—
155	#336	C₂×D₇₉	1	2	yes	—
156	C₂²×Q₈	—	158	1	no	—
157	C₂²×C₈	—	2	2	no	—
158	C₂²×C₈	—	158	2	no	—
159	C₄⋊Q₈	—	158	4	no	—
160	C₄×Q₈	—	316	2	no	—
161	C₄×Q₈	—	316	2	no	—
162	C₂×C₄⋊C₄	—	79	2	no	—
163	C₂×C₄⋊C₄	—	79	2	no	—
164	C₂×C₄⋊C₄	—	158	1	no	—
165	C₂×C₄⋊C₄	—	158	1	no	—
166	C₂×C₄⋊C₄	—	158	2	no	—
167	C₂×C₄⋊C₄	—	158	1	no	—
168	C₂×C₄²	—	158	2	no	—
169	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
170	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
171	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
172	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
173	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
174	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
175	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
176	C₄⋊C₈	—	158	4	no	—
177	#97	—	316	2	no	—
178	#95	—	158	2	no	—
179	#95	—	158	2	no	—
180	C₂×Q₈	—	316	2	no	—
181	C₂×Q₈	—	316	2	no	—
182	C₂×Q₈	—	158	4	no	—
183	C₂²×C₄	—	158	2	no	—
184	C₂²×C₄	—	158	2	no	—
185	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
186	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
187	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
188	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
190	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
191	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	316	2	no	—
196	C₂×C₈	—	316	2	no	—
197	C₂×C₈	—	158	4	no	—
198	C₄⋊C₄	—	316	2	no	—
199	C₄⋊C₄	—	316	2	no	—
200	C₄⋊C₄	—	316	2	no	—
201	C₄⋊C₄	—	316	2	no	—
202	C₄⋊C₄	—	316	2	no	—
203	C₄⋊C₄	—	79	4	no	—
204	C₄⋊C₄	—	158	4	no	—
205	C₄⋊C₄	—	158	2	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	2	2	no	—
208	C₄²	—	2	2	no	—
209	C₄²	—	2	2	no	—
210	C₄²	—	4	1	no	—
211	C₄²	—	4	1	no	—
212	C₄²	—	316	4	no	—
213	C₄²	D₆₃₂	1	2	yes	—
214	C₄²	#11929613	1	2	yes	—
215	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
216	Q₈	—	316	8	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	316	2	no	—
232	C₂×C₄	—	316	2	no	—
233	C₂×C₄	—	316	2	no	—
234	C₂×C₄	—	316	2	no	—
235	C₂×C₄	—	316	2	no	—
236	C₂×C₄	—	158	4	no	—
237	C₂×C₄	#14579079	1	2	yes	—
238	C₂×C₄	#14579083	1	2	yes	—
239	C₂×C₄	#14579083	1	2	yes	—
240	C₂×C₄	#14579087	1	2	yes	—
241	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
242	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
243	C₂×C₄	C₂×#11929613	1	1	yes	characteristic
244	C₂×C₄	#14579191	1	2	yes	—
245	C₈	—	8	2	no	—
246	C₈	—	316	4	no	—
247	C₂²	#19098526	1	1	yes	characteristic
248	C₂²	#19098536	1	1	yes	characteristic
249	C₂²	C₂×#14579079	1	1	yes	characteristic
250	C₂²	C₂×#14579083	1	1	yes	characteristic
251	C₂²	#19098571	1	1	yes	characteristic
252	C₂²	C₂×#14579087	1	1	yes	characteristic
253	C₂²	#19098581	1	1	yes	characteristic
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	2	2	no	—
257	C₄	—	2	2	no	—
258	C₄	—	2	2	no	—
259	C₄	—	2	2	no	—
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	316	4	no	—
263	C₄	—	632	2	no	—
264	C₂	#23761743	1	1	yes	characteristic
265	C₂	#23761826	1	1	yes	characteristic
266	C₂	#23761846	1	1	yes	characteristic
267	C₂	#23761896	1	1	yes	characteristic
268	C₂	#23761950	1	1	yes	characteristic
269	C₂	#23762016	1	1	yes	characteristic
270	C₂	#23762071	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#14579161

C₂

yes

maximal, characteristic

#23763253

C₂

yes

maximal, characteristic

#23761222

C₂

yes

maximal

C₇₉×#1839

C₂

yes

maximal, characteristic

C₂×#14579161

C₄

yes

characteristic

C₂×C₄×Dic₁₅₈

—

C₂×C₄⋊(C₇₉⋊C₈)

—

—

—

—

C₂²

yes

—

#19098433

C₄

yes

characteristic

C₄×C₄⋊Dic₇₉

—

C₄×C₄⋊Dic₇₉

C₄

yes

—

#19098318

C₂²

yes

—

C₄³×C₇₉

C₂²

yes

characteristic

#336×C₇₉

—

#336×C₇₉

—

#336×C₇₉

C₂²

yes

—

C₂²×Dic₁₅₈

—

C₂²×C₇₉⋊C₈

—

#14579161

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂×C₄

yes

—

C₂×C₄⋊Dic₇₉

C₂×C₄

yes

—

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

C₄⋊(C₇₉⋊C₈)

—

#14579072

—

C₇₉⋊#95

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

—

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

M₁₆

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

D₈

yes

—

C₄²×C₇₉

SD₁₆

yes

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

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×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#101

yes

—

C₂×C₄×C₇₉

#102

yes

—

C₂×C₄×C₇₉

#102

yes

—

C₂×C₄×C₇₉

#104

yes

—

C₂×C₄×C₇₉

C₂×M₁₆

yes

—

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

100

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

101

C₂×C₄×C₇₉

#137

yes

—

102

C₂×Dic₇₉

—

103

C₂×Dic₇₉

—

104

C₂×Dic₇₉

—

105

C₂×Dic₇₉

—

106

C₂×Dic₇₉

—

107

C₂×Dic₇₉

—

108

Dic₁₅₈

—

109

C₈×C₇₉

—

110

C₇₉⋊C₈

—

111

C₂²×C₇₉

#407

yes

characteristic

112

C₂²×C₇₉

#410

yes

characteristic

113

C₂²×C₇₉

C₂×#101

yes

characteristic

114

C₂²×C₇₉

C₂×#102

yes

characteristic

115

C₂²×C₇₉

#419

yes

characteristic

116

C₂²×C₇₉

C₂×#104

yes

characteristic

117

C₂²×C₇₉

#421

yes

characteristic

118

C₄×C₇₉

—

119

C₄×C₇₉

—

120

C₄×C₇₉

—

121

C₄×C₇₉

—

122

C₄×C₇₉

—

123

C₄×C₇₉

—

124

C₄×C₇₉

—

125

C₄×C₇₉

—

126

Dic₇₉

—

127

Dic₇₉

—

128

#7625

—

maximal, Sylow

129

C₂×C₇₉

#1467

yes

characteristic

130

C₂×C₇₉

#1486

yes

characteristic

131

C₂×C₇₉

#1491

yes

characteristic

132

C₂×C₇₉

#1502

yes

characteristic

133

C₂×C₇₉

#1515

yes

characteristic

134

C₂×C₇₉

#1531

yes

characteristic

135

C₂×C₇₉

#1546

yes

characteristic

136

C₄×C₄⋊Q₈

—

137

#1839

D₇₉

yes

characteristic

138

#1767

—

139

#1271

—

140

C₇₉

#7625

yes

characteristic, complemented, Sylow

141

C₂×C₄⋊Q₈

—

142

C₂×C₄×Q₈

—

158

—

143

C₂×C₄⋊C₈

—

158

—

144

C₂×#97

—

158

—

145

#391

—

158

—

146

#389

—

147

#389

—

158

—

148

#384

—

149

C₄×C₄⋊C₄

—

150

C₄×C₄⋊C₄

—

158

—

151

C₄³

C₂×D₇₉

yes

characteristic

152

#336

—

153

#336

—

154

#336

—

155

#336

C₂×D₇₉

yes

—

156

C₂²×Q₈

—

158

—

157

C₂²×C₈

—

158

C₂²×C₈

—

158

—

159

C₄⋊Q₈

—

158

—

160

C₄×Q₈

—

316

—

161

C₄×Q₈

—

316

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

158

—

165

C₂×C₄⋊C₄

—

158

—

166

C₂×C₄⋊C₄

—

158

—

167

C₂×C₄⋊C₄

—

158

—

168

C₂×C₄²

—

158

—

169

C₂×C₄²

C₄×D₇₉

yes

characteristic

170

C₂×C₄²

C₄×D₇₉

yes

characteristic

171

C₂×C₄²

D₃₁₆

yes

characteristic

172

C₂×C₄²

D₃₁₆

yes

characteristic

173

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

174

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

175

C₂×C₄²

C₂²×D₇₉

yes

characteristic

176

C₄⋊C₈

—

158

—

177

#97

—

316

—

178

#95

—

158

—

179

#95

—

158

—

180

C₂×Q₈

—

316

—

181

C₂×Q₈

—

316

—

182

C₂×Q₈

—

158

—

183

C₂²×C₄

—

158

—

184

C₂²×C₄

—

158

—

185

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

186

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

187

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

188

C₂²×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

189

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

190

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

191

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

316

—

196

C₂×C₈

—

316

—

197

C₂×C₈

—

158

—

198

C₄⋊C₄

—

316

—

199

C₄⋊C₄

—

316

—

200

C₄⋊C₄

—

316

—

201

C₄⋊C₄

—

316

—

202

C₄⋊C₄

—

316

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

158

—

205

C₄⋊C₄

—

158

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

316

—

213

C₄²

D₆₃₂

yes

—

214

C₄²

#11929613

yes

—

215

C₂³

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

216

Q₈

—

316

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

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

—

230

C₂×C₄

—

231

C₂×C₄

—

316

—

232

C₂×C₄

—

316

—

233

C₂×C₄

—

316

—

234

C₂×C₄

—

316

—

235

C₂×C₄

—

316

—

236

C₂×C₄

—

158

—

237

C₂×C₄

#14579079

yes

—

238

C₂×C₄

#14579083

yes

—

239

C₂×C₄

#14579083

yes

—

240

C₂×C₄

#14579087

yes

—

241

C₂×C₄

M₁₆×D₇₉

yes

—

242

C₂×C₄

C₂×D₆₃₂

yes

characteristic

243

C₂×C₄

C₂×#11929613

yes

characteristic

244

C₂×C₄

#14579191

yes

—

245

C₈

—

246

C₈

—

316

—

247

C₂²

#19098526

yes

characteristic

248

C₂²

#19098536

yes

characteristic

249

C₂²

C₂×#14579079

yes

characteristic

250

C₂²

C₂×#14579083

yes

characteristic

251

C₂²

#19098571

yes

characteristic

252

C₂²

C₂×#14579087

yes

characteristic

253

C₂²

#19098581

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

316

—

263

C₄

—

632

—

264

C₂

#23761743

yes

characteristic

265

C₂

#23761826

yes

characteristic

266

C₂

#23761846

yes

characteristic

267

C₂

#23761896

yes

characteristic

268

C₂

#23761950

yes

characteristic

269

C₂

#23762016

yes

characteristic

270

C₂

#23762071

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₇₉)⋊C₄
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1839	C₂
socle, prime radical	C₂³×C₇₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1839	D₇₉
hypocenter	C₇₉	#7625
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

subgroup

G/H

center

C₂³

C₂×(C₂×D₇₉)⋊C₄

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1839

C₂

socle, prime radical

C₂³×C₇₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

N	H ≅ G/N	type
140. C₇₉	#7625	semidirect

H ≅ G/N

type

140. C₇₉

#7625

semidirect

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

subgroup	index
C₄×#14579161	2
#23763253	2
#23761222	2
C₇₉×#1839	2
#7625	79

subgroup

index

C₇₉×#1839

Subgroups — #34176489

Conjugacy classes of subgroups

Complements

Maximal subgroups