Group #34187764 — subgroups

Subgroups — #34187764

Order 20224.

390 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19098966	C₂	1	1	yes	maximal, characteristic
2	#23763537	C₂	1	1	yes	maximal, characteristic
3	#23762084	C₂	1	1	yes	maximal, characteristic
4	#23762082	C₂	1	1	yes	maximal, characteristic
5	#23762081	C₂	1	1	yes	maximal, characteristic
6	#23761693	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1549	C₂	1	1	yes	maximal, characteristic
8	C₂×#14579161	C₂²	1	1	yes	characteristic
9	#19098966	—	2	1	no	—
10	#19098966	—	2	1	no	—
11	#19098966	C₄	1	4	yes	—
12	#19098616	C₂²	1	1	yes	characteristic
13	C₂×#14579094	—	2	2	no	—
14	#19098587	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
16	#19098327	—	2	2	no	—
17	#19098312	—	2	2	no	—
18	#19098311	—	2	2	no	—
19	#19098310	—	2	2	no	—
20	#19098285	—	2	1	no	—
21	#19098284	—	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	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
29	#14579161	—	2	1	no	—
30	#14579161	—	2	1	no	—
31	#14579161	—	2	1	no	—
32	#14579161	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊Dic₇₉	—	2	1	no	—
34	C₂×C₄⋊Dic₇₉	—	2	1	no	—
35	#14579094	—	2	4	no	—
36	#14579094	—	2	4	no	—
37	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
38	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
39	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
40	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
41	C₄×C₇₉⋊C₈	—	2	1	no	—
42	C₄×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
43	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
44	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₇₉	—	2	1	no	—
46	C₂×M₁₆×C₇₉	—	2	1	no	—
47	C₄⋊Q₈×C₇₉	—	2	1	no	—
48	C₄⋊Q₈×C₇₉	—	2	1	no	—
49	C₄⋊Q₈×C₇₉	—	2	1	no	—
50	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
53	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₇₉	—	2	1	no	—
55	C₄⋊C₈×C₇₉	—	2	1	no	—
56	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
57	C₂²⋊C₈×C₇₉	—	2	1	no	—
58	C₄×C₈×C₇₉	—	2	1	no	—
59	C₂×Dic₁₅₈	—	2	2	no	—
60	C₂×Dic₁₅₈	—	4	1	no	—
61	C₂×Dic₁₅₈	—	8	2	no	—
62	C₂²×Dic₇₉	—	4	1	no	—
63	#11929608	—	4	2	no	—
64	C₂×C₇₉⋊C₈	—	2	2	no	—
65	C₂×C₇₉⋊C₈	—	2	2	no	—
66	C₂×C₇₉⋊C₈	—	2	2	no	—
67	C₂×C₇₉⋊C₈	—	4	1	no	—
68	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
69	C₂×C₇₉⋊C₈	C₂²⋊C₄	1	2	yes	—
70	C₄⋊Dic₇₉	—	2	2	no	—
71	C₄⋊Dic₇₉	—	2	2	no	—
72	C₄⋊Dic₇₉	—	4	1	no	—
73	C₄⋊Dic₇₉	—	4	1	no	—
74	C₂×Q₈×C₇₉	—	2	2	no	—
75	C₂×Q₈×C₇₉	—	4	1	no	—
76	C₂×Q₈×C₇₉	—	8	2	no	—
77	C₂²×C₄×C₇₉	—	4	1	no	—
78	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
80	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
81	M₁₆×C₇₉	—	4	2	no	—
82	C₂×C₈×C₇₉	—	2	2	no	—
83	C₂×C₈×C₇₉	—	4	1	no	—
84	C₄⋊C₄×C₇₉	—	2	2	no	—
85	C₄⋊C₄×C₇₉	—	2	2	no	—
86	C₄⋊C₄×C₇₉	—	4	1	no	—
87	C₄⋊C₄×C₇₉	—	4	1	no	—
88	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
89	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
90	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
91	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
92	C₂³×C₇₉	#124	1	1	yes	characteristic
93	Q₈×C₇₉	—	8	2	no	—
94	Q₈×C₇₉	—	8	2	no	—
95	C₂×C₄×C₇₉	—	2	2	no	—
96	C₂×C₄×C₇₉	—	2	2	no	—
97	C₂×C₄×C₇₉	—	4	2	no	—
98	C₂×C₄×C₇₉	—	8	2	no	—
99	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
101	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
103	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
104	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
105	C₂×C₄×C₇₉	#137	1	2	yes	—
106	C₂×C₄×C₇₉	#137	1	2	yes	—
107	C₂×Dic₇₉	—	4	2	no	—
108	C₂×Dic₇₉	—	8	2	no	—
109	Dic₁₅₈	—	8	2	no	—
110	Dic₁₅₈	—	8	2	no	—
111	C₈×C₇₉	—	4	2	no	—
112	C₈×C₇₉	—	8	1	no	—
113	C₇₉⋊C₈	—	2	2	no	—
114	C₇₉⋊C₈	—	2	2	no	—
115	C₇₉⋊C₈	—	4	2	no	—
116	C₇₉⋊C₈	—	8	1	no	—
117	C₂²×C₇₉	—	2	1	no	—
118	C₂²×C₇₉	—	2	1	no	—
119	C₂²×C₇₉	#390	1	1	yes	characteristic
120	C₂²×C₇₉	#491	1	2	yes	—
121	C₄×C₇₉	—	2	1	no	—
122	C₄×C₇₉	—	2	1	no	—
123	C₄×C₇₉	—	8	2	no	—
124	C₄×C₇₉	#419	1	2	yes	—
125	C₄×C₇₉	#472	1	2	yes	—
126	C₄×C₇₉	#473	1	2	yes	—
127	C₄×C₇₉	#497	1	1	yes	characteristic
128	C₄×C₇₉	#497	1	1	yes	characteristic
129	Dic₇₉	—	8	2	no	—
130	#9778	—	79	1	no	maximal, Sylow
131	C₂×C₇₉	—	2	2	no	—
132	C₂×C₇₉	#1960	1	1	yes	characteristic
133	C₂×C₇₉	#1978	1	1	yes	characteristic
134	C₂×C₇₉	#1979	1	1	yes	characteristic
135	C₂×#500	—	79	1	no	—
136	#1837	—	79	1	no	—
137	#1549	—	79	1	no	—
138	#1549	D₇₉	1	1	yes	characteristic
139	#1548	—	79	1	no	—
140	#1548	—	79	1	no	—
141	#1452	—	79	1	no	—
142	C₇₉	#9778	1	1	yes	characteristic, complemented, Sylow
143	C₂×C₄⋊Q₈	—	79	1	no	—
144	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
145	#500	—	79	4	no	—
146	#500	—	158	1	no	—
147	#500	—	158	1	no	—
148	#431	—	79	1	no	—
149	#431	C₂×D₇₉	1	1	yes	characteristic
150	C₂×#107	—	158	2	no	—
151	#423	—	79	1	no	—
152	#423	C₂×D₇₉	1	1	yes	characteristic
153	C₂×C₄×C₈	—	79	1	no	—
154	#341	—	158	2	no	—
155	#333	—	158	2	no	—
156	#333	—	158	2	no	—
157	#332	—	2	2	no	—
158	#332	—	158	2	no	—
159	#322	—	158	1	no	—
160	#322	—	158	1	no	—
161	C₂²×Q₈	—	2	1	no	—
162	C₂²×Q₈	—	158	1	no	—
163	C₂×M₁₆	—	2	1	no	—
164	C₂×M₁₆	—	158	1	no	—
165	C₂²×C₈	—	79	2	no	—
166	C₄⋊Q₈	—	2	1	no	—
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	—	79	2	no	—
170	C₄⋊Q₈	—	158	1	no	—
171	C₄⋊Q₈	—	158	1	no	—
172	C₄⋊Q₈	—	158	1	no	—
173	C₄⋊Q₈	C₄×D₇₉	1	2	yes	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	158	1	no	—
177	C₂×C₄⋊C₄	—	158	1	no	—
178	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
179	#107	—	158	4	no	—
180	#107	—	158	4	no	—
181	C₄⋊C₈	—	2	1	no	—
182	C₄⋊C₈	—	2	1	no	—
183	C₄⋊C₈	—	79	2	no	—
184	C₄⋊C₈	—	158	1	no	—
185	C₄⋊C₈	—	158	1	no	—
186	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
187	C₂²⋊C₈	—	2	1	no	—
188	C₂²⋊C₈	—	158	1	no	—
189	C₄×C₈	—	2	1	no	—
190	C₄×C₈	—	79	2	no	—
191	C₄×C₈	—	79	1	no	—
192	C₄×C₈	—	79	1	no	—
193	C₄×C₈	—	158	1	no	—
194	C₂×Q₈	—	2	2	no	—
195	C₂×Q₈	—	4	1	no	—
196	C₂×Q₈	—	8	2	no	—
197	C₂×Q₈	—	316	1	no	—
198	C₂×Q₈	—	632	2	no	—
199	C₂×Q₈	—	158	2	no	—
200	C₂²×C₄	—	4	1	no	—
201	C₂²×C₄	—	316	1	no	—
202	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
203	C₂²×C₄	#11929623	1	1	yes	characteristic
204	C₂²×C₄	#11929624	1	1	yes	characteristic
205	M₁₆	—	4	2	no	—
206	M₁₆	—	316	2	no	—
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	—	4	1	no	—
209	C₂×C₈	—	316	1	no	—
210	C₂×C₈	—	79	2	no	—
211	C₂×C₈	—	79	2	no	—
212	C₂×C₈	—	158	2	no	—
213	C₂×C₈	—	158	2	no	—
214	C₂×C₈	—	158	2	no	—
215	C₄⋊C₄	—	2	2	no	—
216	C₄⋊C₄	—	2	2	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄⋊C₄	—	4	1	no	—
219	C₄⋊C₄	—	316	1	no	—
220	C₄⋊C₄	—	316	1	no	—
221	C₄⋊C₄	—	158	2	no	—
222	C₄⋊C₄	—	158	2	no	—
223	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
224	C₄²	D₄×D₇₉	1	1	yes	characteristic
225	C₄²	D₄×D₇₉	1	1	yes	characteristic
226	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
227	C₂³	#14579147	1	1	yes	characteristic
228	Q₈	—	8	2	no	—
229	Q₈	—	8	2	no	—
230	Q₈	—	632	2	no	—
231	Q₈	—	632	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	—	316	2	no	—
237	C₂×C₄	—	632	2	no	—
238	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
239	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
240	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
241	C₂×C₄	#14579133	1	1	yes	characteristic
242	C₂×C₄	#14579134	1	1	yes	characteristic
243	C₂×C₄	#14579157	1	1	yes	characteristic
244	C₂×C₄	#14579190	1	2	yes	—
245	C₂×C₄	#14579193	1	2	yes	—
246	C₈	—	4	2	no	—
247	C₈	—	8	1	no	—
248	C₈	—	316	2	no	—
249	C₈	—	632	1	no	—
250	C₈	—	158	2	no	—
251	C₈	—	158	2	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	#19098463	1	1	yes	characteristic
255	C₂²	#19098930	1	2	yes	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	8	2	no	—
259	C₄	—	632	2	no	—
260	C₄	#19098570	1	2	yes	—
261	C₄	#19098831	1	2	yes	—
262	C₄	#19098837	1	2	yes	—
263	C₄	#19098954	1	1	yes	characteristic
264	C₄	#19098956	1	1	yes	characteristic
265	C₂	—	2	2	no	—
266	C₂	#23764218	1	1	yes	characteristic
267	C₂	#23764309	1	1	yes	characteristic
268	C₂	#23764312	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098966

C₂

yes

maximal, characteristic

#23763537

C₂

yes

maximal, characteristic

#23762084

C₂

yes

maximal, characteristic

#23762082

C₂

yes

maximal, characteristic

#23762081

C₂

yes

maximal, characteristic

#23761693

C₂

yes

maximal, characteristic

C₇₉×#1549

C₂

yes

maximal, characteristic

C₂×#14579161

C₂²

yes

—

—

C₄

yes

—

#19098616

C₂²

yes

characteristic

C₂×#14579094

—

#19098587

C₂²

yes

characteristic

C₂×C₄×C₇₉⋊C₈

C₂²

yes

—

—

—

—

—

—

C₂×C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#431×C₇₉

C₂²

yes

characteristic

#423×C₇₉

C₂²

yes

characteristic

#332×C₇₉

—

C₂²×Dic₁₅₈

—

C₂×#11929608

—

C₂²×C₇₉⋊C₈

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

#14579094

—

#14579094

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

C₂×C₄

yes

—

C₄×C₇₉⋊C₈

D₄

yes

characteristic

C₄×C₇₉⋊C₈

D₄

yes

characteristic

C₂²×Q₈×C₇₉

—

C₂×M₁₆×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

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

—

C₂×C₇₉⋊C₈

—

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

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

C₂²×C₄×C₇₉

yes

C₂²×C₄×C₇₉

yes

M₁₆×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

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₂³×C₇₉

#124

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

100

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

101

C₂×C₄×C₇₉

C₄×D₄

yes

characteristic

102

C₂×C₄×C₇₉

#121

yes

characteristic

103

C₂×C₄×C₇₉

#121

yes

characteristic

104

C₂×C₄×C₇₉

#127

yes

characteristic

105

C₂×C₄×C₇₉

#137

yes

—

106

C₂×C₄×C₇₉

#137

yes

—

107

C₂×Dic₇₉

—

108

C₂×Dic₇₉

—

109

Dic₁₅₈

—

110

Dic₁₅₈

—

111

C₈×C₇₉

—

112

C₈×C₇₉

—

113

C₇₉⋊C₈

—

114

C₇₉⋊C₈

—

115

C₇₉⋊C₈

—

116

C₇₉⋊C₈

—

117

C₂²×C₇₉

—

118

C₂²×C₇₉

—

119

C₂²×C₇₉

#390

yes

characteristic

120

C₂²×C₇₉

#491

yes

—

121

C₄×C₇₉

—

122

C₄×C₇₉

—

123

C₄×C₇₉

—

124

C₄×C₇₉

#419

yes

—

125

C₄×C₇₉

#472

yes

—

126

C₄×C₇₉

#473

yes

—

127

C₄×C₇₉

#497

yes

characteristic

128

C₄×C₇₉

#497

yes

characteristic

129

Dic₇₉

—

130

#9778

—

maximal, Sylow

131

C₂×C₇₉

—

132

C₂×C₇₉

#1960

yes

characteristic

133

C₂×C₇₉

#1978

yes

characteristic

134

C₂×C₇₉

#1979

yes

characteristic

135

C₂×#500

—

136

#1837

—

137

#1549

—

138

#1549

D₇₉

yes

characteristic

139

#1548

—

140

#1548

—

141

#1452

—

142

C₇₉

#9778

yes

characteristic, complemented, Sylow

143

C₂×C₄⋊Q₈

—

144

C₂×C₄⋊Q₈

C₂×D₇₉

yes

characteristic

145

#500

—

146

#500

—

158

—

147

#500

—

158

—

148

#431

—

149

#431

C₂×D₇₉

yes

characteristic

150

C₂×#107

—

158

—

151

#423

—

152

#423

C₂×D₇₉

yes

characteristic

153

C₂×C₄×C₈

—

154

#341

—

158

—

155

#333

—

158

—

156

#333

—

158

—

157

#332

—

158

#332

—

158

—

159

#322

—

158

—

160

#322

—

158

—

161

C₂²×Q₈

—

162

C₂²×Q₈

—

158

—

163

C₂×M₁₆

—

164

C₂×M₁₆

—

158

—

165

C₂²×C₈

—

166

C₄⋊Q₈

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

158

—

171

C₄⋊Q₈

—

158

—

172

C₄⋊Q₈

—

158

—

173

C₄⋊Q₈

C₄×D₇₉

yes

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

158

—

177

C₂×C₄⋊C₄

—

158

—

178

C₂×C₄²

C₂²×D₇₉

yes

characteristic

179

#107

—

158

—

180

#107

—

158

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

158

—

185

C₄⋊C₈

—

158

—

186

C₄⋊C₈

C₂²⋊D₇₉

yes

—

187

C₂²⋊C₈

—

188

C₂²⋊C₈

—

158

—

189

C₄×C₈

—

190

C₄×C₈

—

191

C₄×C₈

—

192

C₄×C₈

—

193

C₄×C₈

—

158

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

316

—

198

C₂×Q₈

—

632

—

199

C₂×Q₈

—

158

—

200

C₂²×C₄

—

201

C₂²×C₄

—

316

—

202

C₂²×C₄

D₄×D₇₉

yes

characteristic

203

C₂²×C₄

#11929623

yes

characteristic

204

C₂²×C₄

#11929624

yes

characteristic

205

M₁₆

—

206

M₁₆

—

316

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

316

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

158

—

213

C₂×C₈

—

158

—

214

C₂×C₈

—

158

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

316

—

220

C₄⋊C₄

—

316

—

221

C₄⋊C₄

—

158

—

222

C₄⋊C₄

—

158

—

223

C₄²

C₂×C₄×D₇₉

yes

characteristic

224

C₄²

D₄×D₇₉

yes

characteristic

225

C₄²

D₄×D₇₉

yes

characteristic

226

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

227

C₂³

#14579147

yes

characteristic

228

Q₈

—

229

Q₈

—

230

Q₈

—

632

—

231

Q₈

—

632

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

316

—

237

C₂×C₄

—

632

—

238

C₂×C₄

C₂²⋊C₄×D₇₉

yes

characteristic

239

C₂×C₄

(C₂²⋊D₇₉)⋊C₄

yes

characteristic

240

C₂×C₄

C₄×C₂²⋊D₇₉

yes

characteristic

241

C₂×C₄

#14579133

yes

characteristic

242

C₂×C₄

#14579134

yes

characteristic

243

C₂×C₄

#14579157

yes

characteristic

244

C₂×C₄

#14579190

yes

—

245

C₂×C₄

#14579193

yes

—

246

C₈

—

247

C₈

—

248

C₈

—

316

—

249

C₈

—

632

—

250

C₈

—

158

—

251

C₈

—

158

—

252

C₂²

—

253

C₂²

—

254

C₂²

#19098463

yes

characteristic

255

C₂²

#19098930

yes

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

632

—

260

C₄

#19098570

yes

—

261

C₄

#19098831

yes

—

262

C₄

#19098837

yes

—

263

C₄

#19098954

yes

characteristic

264

C₄

#19098956

yes

characteristic

265

C₂

—

266

C₂

#23764218

yes

characteristic

267

C₂

#23764309

yes

characteristic

268

C₂

#23764312

yes

characteristic

	subgroup	G/H
center	C₂²	#19098463
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1549	C₂
socle	C₂²×C₇₉	#390
prime radical	C₂³×C₇₉	#124
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1549	D₇₉
hypocenter	C₇₉	#9778
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1549

subgroup

G/H

center

C₂²

#19098463

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1549

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1549

N	H ≅ G/N	type
142. C₇₉	#9778	semidirect

H ≅ G/N

type

142. C₇₉

#9778

semidirect

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

subgroup	index
C₂×#19098966	2
#23763537	2
#23762084	2
#23762082	2
#23762081	2
#23761693	2
C₇₉×#1549	2
#9778	79

subgroup

index

C₇₉×#1549

Subgroups — #34187764

Conjugacy classes of subgroups

Complements

Maximal subgroups