Group #23773181 — subgroups

Subgroups — #23773181

Order 10112.

388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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	#19099118	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#11929623	C₂	1	1	yes	maximal, characteristic
3	#19098869	C₂	1	2	yes	maximal, complemented
4	#19098861	C₂	1	2	yes	maximal, complemented
5	#19098859	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098853	C₂	1	1	yes	maximal, characteristic, complemented
7	#19098845	C₂	1	1	yes	maximal, characteristic, complemented
8	#19098600	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₈×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#19098556	C₂	1	2	yes	maximal
11	#474×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11929623	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₇₉	C₂²	1	2	yes	—
14	#14579161	C₂²	1	1	yes	characteristic
15	#14579152	C₂²	1	2	yes	—
16	#14579141	—	2	1	no	—
17	#14579137	—	2	1	no	—
18	Q₈×Dic₇₉	—	2	1	no	—
19	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
20	#14579126	—	2	1	no	—
21	#14579126	C₂²	1	1	yes	characteristic
22	D₄×Dic₇₉	C₂²	1	1	yes	characteristic
23	C₄×C₂²⋊D₇₉	—	2	1	no	—
24	(C₂²⋊D₇₉)⋊C₄	—	2	1	no	—
25	#14579119	C₂²	1	1	yes	characteristic
26	#14579119	C₂²	1	2	yes	—
27	#14579117	—	2	1	no	—
28	C₂×C₄×Dic₇₉	—	2	1	no	—
29	C₄²×D₇₉	C₂²	1	1	yes	characteristic
30	#14579095	C₂²	1	2	yes	—
31	#14579092	C₂²	1	2	yes	—
32	#14579092	C₂²	1	2	yes	—
33	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
34	Dic₇₉⋊C₈	C₂²	1	2	yes	—
35	#14579086	C₂²	1	2	yes	—
36	#14579084	C₂²	1	2	yes	—
37	#14579082	C₂²	1	2	yes	—
38	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
40	#107×C₇₉	C₂²	1	2	yes	—
41	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
42	#102×C₇₉	C₂²	1	2	yes	—
43	#11929623	—	2	2	no	—
44	#11929623	Q₈	1	4	yes	complemented
45	C₂×Dic₁₅₈	—	2	1	no	—
46	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
47	C₂×C₂²⋊D₇₉	—	2	1	no	—
48	C₂²×Dic₇₉	—	2	1	no	—
49	C₂²×Dic₇₉	—	2	1	no	—
50	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
51	C₂×C₄×D₇₉	D₄	1	1	yes	characteristic
52	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
53	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
54	C₈×D₇₉	—	2	4	no	—
55	C₄⋊Dic₇₉	—	2	2	no	—
56	C₄⋊Dic₇₉	—	2	1	no	—
57	C₄⋊Dic₇₉	C₂³	1	2	yes	—
58	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
59	Dic₇₉⋊C₄	—	2	1	no	—
60	Dic₇₉⋊C₄	—	2	2	no	—
61	Dic₇₉⋊C₄	—	2	1	no	—
62	C₂²⋊Dic₇₉	—	2	1	no	—
63	(C₂×D₇₉)⋊C₄	—	2	1	no	—
64	(C₂×D₇₉)⋊C₄	—	2	2	no	—
65	C₄×Dic₇₉	—	2	1	no	—
66	C₄×Dic₇₉	—	2	1	no	—
67	C₄×Dic₇₉	—	2	2	no	—
68	C₄×Dic₇₉	—	2	1	no	—
69	C₄×Dic₇₉	D₄	1	1	yes	characteristic
70	C₄×Dic₇₉	D₄	1	1	yes	characteristic
71	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
72	C₂×Q₈×C₇₉	—	2	1	no	—
73	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₇₉	—	2	1	no	—
75	C₂×C₈×C₇₉	C₂³	1	2	yes	—
76	C₄⋊C₄×C₇₉	—	2	1	no	—
77	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
78	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
79	C₂²⋊C₄×C₇₉	—	2	1	no	—
80	C₄²×C₇₉	C₂³	1	1	yes	characteristic
81	C₂³×C₇₉	—	2	1	no	—
82	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₇₉	—	4	2	no	—
84	D₄×C₇₉	—	2	1	no	—
85	D₄×C₇₉	C₂×Q₈	1	2	yes	—
86	C₂×C₄×C₇₉	—	2	1	no	—
87	C₂×C₄×C₇₉	—	2	2	no	—
88	C₂×C₄×C₇₉	—	4	2	no	—
89	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
92	C₂²⋊D₇₉	—	2	4	no	—
93	C₂×Dic₇₉	—	2	1	no	—
94	C₂×Dic₇₉	—	2	4	no	—
95	C₂×Dic₇₉	—	2	1	no	—
96	C₂×Dic₇₉	—	2	2	no	—
97	C₂×Dic₇₉	—	4	2	no	—
98	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
99	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
100	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
101	C₄×D₇₉	—	2	2	no	—
102	C₄×D₇₉	—	4	1	no	—
103	C₄×D₇₉	C₂×Q₈	1	2	yes	—
104	C₄×D₇₉	#41	1	2	yes	—
105	Dic₁₅₈	—	2	1	no	—
106	Dic₁₅₈	—	4	2	no	—
107	Dic₁₅₈	C₂×Q₈	1	2	yes	—
108	C₈×C₇₉	—	2	2	no	—
109	C₇₉⋊C₈	—	2	2	no	—
110	C₂²×C₇₉	—	2	2	no	—
111	C₂²×C₇₉	—	4	1	no	—
112	C₂²×C₇₉	—	4	1	no	—
113	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
114	C₂×D₇₉	—	2	1	no	—
115	C₂×D₇₉	—	2	1	no	—
116	C₂×D₇₉	C₂²⋊Q₈	1	2	yes	—
117	C₄×C₇₉	—	2	1	no	—
118	C₄×C₇₉	—	4	1	no	—
119	C₄×C₇₉	—	4	2	no	—
120	C₄×C₇₉	#135	1	2	yes	—
121	C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
122	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
123	Dic₇₉	—	2	2	no	—
124	Dic₇₉	—	2	1	no	—
125	Dic₇₉	—	2	1	no	—
126	Dic₇₉	—	4	2	no	—
127	Dic₇₉	—	4	1	no	—
128	Dic₇₉	C₂²⋊Q₈	1	2	yes	—
129	C₂×C₇₉	—	4	2	no	—
130	C₂×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
131	C₂×C₇₉	C₂×#135	1	1	yes	characteristic
132	C₂×C₇₉	#575	1	1	yes	characteristic
133	D₇₉	—	2	2	no	—
134	#3076	—	79	1	no	maximal, Sylow
135	C₇₉	#3076	1	1	yes	characteristic, complemented, Sylow
136	#533	—	79	1	no	—
137	C₄×#41	—	79	1	no	—
138	#479	—	79	2	no	—
139	#478	—	79	2	no	—
140	#477	—	79	1	no	—
141	#476	—	79	1	no	—
142	#475	—	79	1	no	—
143	#474	D₇₉	1	1	yes	characteristic, complemented
144	#427	—	79	2	no	—
145	C₂×C₄⋊C₈	—	79	1	no	—
146	#416	—	79	2	no	—
147	C₂×#41	—	79	1	no	—
148	C₂²×C₈	—	79	2	no	—
149	C₄⋊Q₈	—	79	1	no	—
150	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
151	#125	—	79	2	no	—
152	C₂²⋊Q₈	—	158	1	no	—
153	C₂²⋊Q₈	—	158	1	no	—
154	C₄×Q₈	—	79	1	no	—
155	C₄×Q₈	—	79	1	no	—
156	C₄×Q₈	—	158	1	no	—
157	C₄×Q₈	—	158	1	no	—
158	C₄×D₄	—	79	1	no	—
159	C₄×D₄	—	158	1	no	—
160	C₄×D₄	—	158	1	no	—
161	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
162	#117	—	79	1	no	—
163	#117	—	79	2	no	—
164	#117	—	158	1	no	—
165	C₂×C₄²	—	79	1	no	—
166	C₂×C₄²	—	158	1	no	—
167	#107	—	79	2	no	—
168	#107	C₂×D₇₉	1	2	yes	—
169	#106	—	79	2	no	—
170	#106	—	79	2	no	—
171	C₄⋊C₈	—	79	2	no	—
172	C₄⋊C₈	—	79	1	no	—
173	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
174	#103	—	79	2	no	—
175	#103	—	79	2	no	—
176	#102	—	79	2	no	—
177	#102	C₂×D₇₉	1	2	yes	—
178	#41	—	79	4	no	—
179	#41	—	158	2	no	—
180	C₂×Q₈	—	2	1	no	—
181	C₂×Q₈	—	79	1	no	—
182	C₂×Q₈	—	158	1	no	—
183	C₂×D₄	—	158	1	no	—
184	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	79	1	no	—
187	C₂²×C₄	—	79	1	no	—
188	C₂²×C₄	—	79	1	no	—
189	C₂²×C₄	—	158	1	no	—
190	C₂²×C₄	—	158	1	no	—
191	C₂×C₈	—	79	2	no	—
192	C₂×C₈	—	158	4	no	—
193	C₂×C₈	C₂²×D₇₉	1	2	yes	—
194	C₄⋊C₄	—	2	1	no	—
195	C₄⋊C₄	—	79	2	no	—
196	C₄⋊C₄	—	79	1	no	—
197	C₄⋊C₄	—	158	1	no	—
198	C₄⋊C₄	—	158	2	no	—
199	C₄⋊C₄	—	158	2	no	—
200	C₄⋊C₄	—	158	1	no	—
201	C₄⋊C₄	—	158	1	no	—
202	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
203	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
204	C₂²⋊C₄	—	2	1	no	—
205	C₂²⋊C₄	—	158	1	no	—
206	C₂²⋊C₄	—	158	2	no	—
207	C₂²⋊C₄	—	158	1	no	—
208	C₄²	—	79	1	no	—
209	C₄²	—	79	1	no	—
210	C₄²	—	79	1	no	—
211	C₄²	—	158	1	no	—
212	C₄²	—	158	1	no	—
213	C₄²	—	158	2	no	—
214	C₄²	—	158	1	no	—
215	C₄²	C₂²×D₇₉	1	1	yes	characteristic
216	C₂³	—	2	1	no	—
217	C₂³	—	79	1	no	—
218	Q₈	—	4	2	no	—
219	Q₈	—	316	2	no	—
220	Q₈	—	79	2	no	—
221	Q₈	—	158	1	no	—
222	D₄	—	2	1	no	—
223	D₄	—	158	4	no	—
224	D₄	Q₈×D₇₉	1	2	yes	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	316	1	no	—
229	C₂×C₄	—	316	2	no	—
230	C₂×C₄	—	79	1	no	—
231	C₂×C₄	—	79	2	no	—
232	C₂×C₄	—	79	2	no	—
233	C₂×C₄	—	79	1	no	—
234	C₂×C₄	—	79	1	no	—
235	C₂×C₄	—	158	1	no	—
236	C₂×C₄	—	158	2	no	—
237	C₂×C₄	—	158	4	no	—
238	C₂×C₄	—	158	1	no	—
239	C₂×C₄	—	158	2	no	—
240	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
241	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
242	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
243	C₈	—	2	2	no	—
244	C₈	—	158	2	no	—
245	C₂²	—	2	2	no	—
246	C₂²	—	4	1	no	—
247	C₂²	—	4	1	no	—
248	C₂²	—	79	2	no	—
249	C₂²	—	158	1	no	—
250	C₂²	—	158	1	no	—
251	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
252	C₄	—	2	1	no	—
253	C₄	—	4	1	no	—
254	C₄	—	4	2	no	—
255	C₄	—	316	1	no	—
256	C₄	—	316	2	no	—
257	C₄	—	79	2	no	—
258	C₄	—	158	2	no	—
259	C₄	—	158	1	no	—
260	C₄	—	158	1	no	—
261	C₄	#14579180	1	2	yes	—
262	C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
263	C₄	#41×D₇₉	1	1	yes	characteristic
264	C₂	—	4	2	no	—
265	C₂	—	158	2	no	—
266	C₂	C₂²⋊Q₈×D₇₉	1	1	yes	characteristic
267	C₂	C₂×#14579180	1	1	yes	characteristic
268	C₂	#19099362	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099118

C₂

yes

maximal, characteristic, complemented

C₄×#11929623

C₂

yes

maximal, characteristic

#19098869

C₂

yes

maximal, complemented

#19098861

C₂

yes

maximal, complemented

#19098859

C₂

yes

maximal, characteristic, complemented

#19098853

C₂

yes

maximal, characteristic, complemented

#19098845

C₂

yes

maximal, characteristic, complemented

#19098600

C₂

yes

maximal, complemented

C₄⋊C₈×D₇₉

C₂

yes

maximal, characteristic, complemented

#19098556

C₂

yes

maximal

#474×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929623

C₂²

yes

characteristic

C₂×C₈×D₇₉

C₂²

yes

—

#14579161

C₂²

yes

characteristic

#14579152

C₂²

yes

—

#14579141

—

#14579137

—

Q₈×Dic₇₉

—

C₄×Dic₁₅₈

C₂²

yes

characteristic

#14579126

—

#14579126

C₂²

yes

characteristic

D₄×Dic₇₉

C₂²

yes

characteristic

C₄×C₂²⋊D₇₉

—

(C₂²⋊D₇₉)⋊C₄

—

#14579119

C₂²

yes

characteristic

#14579119

C₂²

yes

—

#14579117

—

C₂×C₄×Dic₇₉

—

C₄²×D₇₉

C₂²

yes

characteristic

#14579095

C₂²

yes

—

#14579092

C₂²

yes

—

#14579092

C₂²

yes

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

Dic₇₉⋊C₈

C₂²

yes

—

#14579086

C₂²

yes

—

#14579084

C₂²

yes

—

#14579082

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

—

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#102×C₇₉

C₂²

yes

—

#11929623

—

#11929623

Q₈

yes

complemented

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

C₂³

yes

characteristic

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

D₄

yes

characteristic

C₂×C₄×D₇₉

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

C₂³

yes

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂³

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

D₄

yes

characteristic

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

—

C₂×D₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

C₂³

yes

characteristic

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

characteristic

100

C₂×Dic₇₉

C₂×D₄

yes

characteristic

101

C₄×D₇₉

—

102

C₄×D₇₉

—

103

C₄×D₇₉

C₂×Q₈

yes

—

104

C₄×D₇₉

#41

yes

—

105

Dic₁₅₈

—

106

Dic₁₅₈

—

107

Dic₁₅₈

C₂×Q₈

yes

—

108

C₈×C₇₉

—

109

C₇₉⋊C₈

—

110

C₂²×C₇₉

—

111

C₂²×C₇₉

—

112

C₂²×C₇₉

—

113

C₂²×C₇₉

C₂²×D₄

yes

characteristic

114

C₂×D₇₉

—

115

C₂×D₇₉

—

116

C₂×D₇₉

C₂²⋊Q₈

yes

—

117

C₄×C₇₉

—

118

C₄×C₇₉

—

119

C₄×C₇₉

—

120

C₄×C₇₉

#135

yes

—

121

C₄×C₇₉

C₂²×Q₈

yes

characteristic

122

C₄×C₇₉

C₂×#41

yes

characteristic

123

Dic₇₉

—

124

Dic₇₉

—

125

Dic₇₉

—

126

Dic₇₉

—

127

Dic₇₉

—

128

Dic₇₉

C₂²⋊Q₈

yes

—

129

C₂×C₇₉

—

130

C₂×C₇₉

C₂×C₂²⋊Q₈

yes

characteristic

131

C₂×C₇₉

C₂×#135

yes

characteristic

132

C₂×C₇₉

#575

yes

characteristic

133

D₇₉

—

134

#3076

—

maximal, Sylow

135

C₇₉

#3076

yes

characteristic, complemented, Sylow

136

#533

—

137

C₄×#41

—

138

#479

—

139

#478

—

140

#477

—

141

#476

—

142

#475

—

143

#474

D₇₉

yes

characteristic, complemented

144

#427

—

145

C₂×C₄⋊C₈

—

146

#416

—

147

C₂×#41

—

148

C₂²×C₈

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

151

#125

—

152

C₂²⋊Q₈

—

158

—

153

C₂²⋊Q₈

—

158

—

154

C₄×Q₈

—

155

C₄×Q₈

—

156

C₄×Q₈

—

158

—

157

C₄×Q₈

—

158

—

158

C₄×D₄

—

159

C₄×D₄

—

158

—

160

C₄×D₄

—

158

—

161

C₄×D₄

C₂×D₇₉

yes

characteristic

162

#117

—

163

#117

—

164

#117

—

158

—

165

C₂×C₄²

—

166

C₂×C₄²

—

158

—

167

#107

—

168

#107

C₂×D₇₉

yes

—

169

#106

—

170

#106

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

C₂×D₇₉

yes

characteristic

174

#103

—

175

#103

—

176

#102

—

177

#102

C₂×D₇₉

yes

—

178

#41

—

179

#41

—

158

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

158

—

183

C₂×D₄

—

158

—

184

C₂×D₄

C₂²×D₇₉

yes

characteristic

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

158

—

190

C₂²×C₄

—

158

—

191

C₂×C₈

—

192

C₂×C₈

—

158

—

193

C₂×C₈

C₂²×D₇₉

yes

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

158

—

198

C₄⋊C₄

—

158

—

199

C₄⋊C₄

—

158

—

200

C₄⋊C₄

—

158

—

201

C₄⋊C₄

—

158

—

202

C₄⋊C₄

C₂²×D₇₉

yes

—

203

C₄⋊C₄

C₂²×D₇₉

yes

characteristic

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

158

—

206

C₂²⋊C₄

—

158

—

207

C₂²⋊C₄

—

158

—

208

C₄²

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

158

—

212

C₄²

—

158

—

213

C₄²

—

158

—

214

C₄²

—

158

—

215

C₄²

C₂²×D₇₉

yes

characteristic

216

C₂³

—

217

C₂³

—

218

Q₈

—

219

Q₈

—

316

—

220

Q₈

—

221

Q₈

—

158

—

222

D₄

—

223

D₄

—

158

—

224

D₄

Q₈×D₇₉

yes

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

316

—

229

C₂×C₄

—

316

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

158

—

236

C₂×C₄

—

158

—

237

C₂×C₄

—

158

—

238

C₂×C₄

—

158

—

239

C₂×C₄

—

158

—

240

C₂×C₄

D₄×D₇₉

yes

characteristic

241

C₂×C₄

D₄×D₇₉

yes

characteristic

242

C₂×C₄

C₂³×D₇₉

yes

characteristic

243

C₈

—

244

C₈

—

158

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

158

—

250

C₂²

—

158

—

251

C₂²

C₂×D₄×D₇₉

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

316

—

256

C₄

—

316

—

257

C₄

—

258

C₄

—

158

—

259

C₄

—

158

—

260

C₄

—

158

—

261

C₄

#14579180

yes

—

262

C₄

C₂×Q₈×D₇₉

yes

characteristic

263

C₄

#41×D₇₉

yes

characteristic

264

C₂

—

265

C₂

—

158

—

266

C₂

C₂²⋊Q₈×D₇₉

yes

characteristic

267

C₂

C₂×#14579180

yes

characteristic

268

C₂

#19099362

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#474×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂×#11929623	C₂²
hypercenter	#474	D₇₉
hypocenter	C₇₉	#3076
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #474

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#474×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

C₂²

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #474

N	H ≅ G/N	type
1. #19099118	C₂	semidirect
3. #19098869	C₂	semidirect
4. #19098861	C₂	semidirect
5. #19098859	C₂	semidirect
6. #19098853	C₂	semidirect
7. #19098845	C₂	semidirect
8. #19098600	C₂	semidirect
9. C₄⋊C₈×D₇₉	C₂	semidirect
11. #474×C₇₉	C₂	semidirect
44. #11929623	Q₈	semidirect
135. C₇₉	#3076	semidirect
143. #474	D₇₉	semidirect

H ≅ G/N

type

1. #19099118

C₂

semidirect

3. #19098869

C₂

semidirect

4. #19098861

C₂

semidirect

5. #19098859

C₂

semidirect

6. #19098853

C₂

semidirect

7. #19098845

C₂

semidirect

8. #19098600

C₂

semidirect

9. C₄⋊C₈×D₇₉

C₂

semidirect

11. #474×C₇₉

C₂

semidirect

44. #11929623

Q₈

semidirect

135. C₇₉

#3076

semidirect

143. #474

D₇₉

semidirect

Subgroups — #23773181

Conjugacy classes of subgroups

Complements