Group #31897111 — subgroups

Subgroups — #31897111

Order 18176.

418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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×#17986395	C₂	1	1	yes	maximal, characteristic
2	#22589184	C₂	1	1	yes	maximal, characteristic
3	#22587098	C₂	1	1	yes	maximal, characteristic
4	#22587025	C₂	1	1	yes	maximal, characteristic
5	#22587013	C₂	1	1	yes	maximal, characteristic
6	#22586627	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1997	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556128	C₂²	1	1	yes	characteristic
9	#17986395	—	2	1	no	—
10	#17986395	—	2	1	no	—
11	#17986395	—	2	2	no	—
12	#17986052	C₂²	1	1	yes	characteristic
13	C₂×#14556059	C₄	1	4	yes	—
14	#17986023	C₂²	1	1	yes	characteristic
15	C₂×#14556046	—	2	2	no	—
16	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
17	#17985751	—	2	2	no	—
18	#17985746	—	2	2	no	—
19	#17985745	—	2	2	no	—
20	#17985721	—	2	1	no	—
21	#17985721	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
23	#423×C₇₁	C₂²	1	1	yes	characteristic
24	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
25	#343×C₇₁	—	2	2	no	—
26	C₂²×Dic₁₄₂	—	2	1	no	—
27	C₂×#11765849	—	2	1	no	—
28	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
29	#14556128	—	2	1	no	—
30	#14556128	—	2	1	no	—
31	#14556128	—	2	1	no	—
32	#14556128	—	2	1	no	—
33	C₂×C₄⋊Dic₇₁	—	2	1	no	—
34	C₂×C₄⋊Dic₇₁	C₂×C₄	1	2	yes	—
35	#14556059	—	2	4	no	—
36	#14556059	—	2	4	no	—
37	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
38	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
39	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
40	#14556046	—	4	4	no	—
41	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
42	C₄×C₇₁⋊C₈	—	2	1	no	—
43	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
44	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
45	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
46	C₂²×Q₈×C₇₁	—	2	1	no	—
47	C₂×M₁₆×C₇₁	—	2	1	no	—
48	C₂×M₁₆×C₇₁	D₄	1	2	yes	—
49	C₄⋊Q₈×C₇₁	—	2	1	no	—
50	C₄⋊Q₈×C₇₁	—	2	1	no	—
51	C₄⋊Q₈×C₇₁	—	2	1	no	—
52	C₄⋊Q₈×C₇₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
56	C₄⋊C₈×C₇₁	—	2	1	no	—
57	C₄⋊C₈×C₇₁	—	2	1	no	—
58	#97×C₇₁	—	2	1	no	—
59	C₄×C₈×C₇₁	—	2	1	no	—
60	C₂×Dic₁₄₂	—	4	1	no	—
61	C₂×Dic₁₄₂	—	4	1	no	—
62	C₂×Dic₁₄₂	—	4	2	no	—
63	C₂×Dic₁₄₂	—	4	2	no	—
64	C₂²×Dic₇₁	—	2	2	no	—
65	#11765849	—	4	2	no	—
66	C₂×C₇₁⋊C₈	—	2	4	no	—
67	C₂×C₇₁⋊C₈	—	2	2	no	—
68	C₂×C₇₁⋊C₈	—	4	1	no	—
69	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	2	yes	—
70	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	2	yes	—
71	C₄⋊Dic₇₁	—	2	2	no	—
72	C₄⋊Dic₇₁	—	2	2	no	—
73	C₄⋊Dic₇₁	—	4	1	no	—
74	C₄⋊Dic₇₁	—	4	1	no	—
75	C₂×Q₈×C₇₁	—	4	1	no	—
76	C₂×Q₈×C₇₁	—	4	1	no	—
77	C₂×Q₈×C₇₁	—	8	2	no	—
78	C₂²×C₄×C₇₁	—	2	2	no	—
79	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
82	M₁₆×C₇₁	—	2	2	no	—
83	M₁₆×C₇₁	—	2	2	no	—
84	M₁₆×C₇₁	—	4	2	no	—
85	C₂×C₈×C₇₁	—	2	2	no	—
86	C₂×C₈×C₇₁	—	4	1	no	—
87	C₄⋊C₄×C₇₁	—	2	2	no	—
88	C₄⋊C₄×C₇₁	—	2	2	no	—
89	C₄⋊C₄×C₇₁	—	4	1	no	—
90	C₄⋊C₄×C₇₁	—	4	1	no	—
91	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
92	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
93	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
94	C₄²×C₇₁	#41	1	1	yes	characteristic
95	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
96	Q₈×C₇₁	—	8	2	no	—
97	Q₈×C₇₁	—	8	2	no	—
98	C₂×C₄×C₇₁	—	2	2	no	—
99	C₂×C₄×C₇₁	—	2	2	no	—
100	C₂×C₄×C₇₁	—	4	2	no	—
101	C₂×C₄×C₇₁	—	8	2	no	—
102	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
105	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
106	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
107	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
108	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	2	yes	—
109	C₂×C₄×C₇₁	#137	1	2	yes	—
110	C₂×Dic₇₁	—	4	2	no	—
111	C₂×Dic₇₁	—	4	4	no	—
112	Dic₁₄₂	—	8	2	no	—
113	Dic₁₄₂	—	8	1	no	—
114	Dic₁₄₂	—	8	1	no	—
115	C₈×C₇₁	—	4	2	no	—
116	C₈×C₇₁	—	8	1	no	—
117	C₇₁⋊C₈	—	2	2	no	—
118	C₇₁⋊C₈	—	4	2	no	—
119	C₇₁⋊C₈	—	8	1	no	—
120	C₇₁⋊C₈	#101	1	4	yes	complemented
121	C₂²×C₇₁	—	2	1	no	—
122	C₂²×C₇₁	—	2	1	no	—
123	C₂²×C₇₁	#390	1	1	yes	characteristic
124	C₂²×C₇₁	#440	1	2	yes	—
125	C₄×C₇₁	—	2	1	no	—
126	C₄×C₇₁	—	2	1	no	—
127	C₄×C₇₁	—	8	2	no	—
128	C₄×C₇₁	C₂×#101	1	2	yes	—
129	C₄×C₇₁	#468	1	2	yes	—
130	C₄×C₇₁	#471	1	2	yes	—
131	C₄×C₇₁	#496	1	1	yes	characteristic
132	C₄×C₇₁	#497	1	1	yes	characteristic
133	Dic₇₁	—	8	2	no	—
134	#9806	—	71	1	no	maximal, Sylow
135	C₂×C₇₁	—	2	2	no	—
136	C₂×C₇₁	#1966	1	1	yes	characteristic
137	C₂×C₇₁	#1973	1	1	yes	characteristic
138	C₂×C₇₁	#1977	1	1	yes	characteristic
139	C₂×#498	—	71	1	no	—
140	#1997	D₇₁	1	1	yes	characteristic
141	#1966	—	71	1	no	—
142	#1567	—	71	1	no	—
143	#1549	—	71	1	no	—
144	#1546	—	71	1	no	—
145	#1451	—	71	1	no	—
146	C₇₁	#9806	1	1	yes	characteristic, complemented, Sylow
147	C₂×C₄⋊Q₈	—	71	1	no	—
148	C₂×C₄⋊Q₈	C₂×D₇₁	1	1	yes	characteristic
149	#498	—	142	1	no	—
150	#498	—	142	1	no	—
151	#498	—	142	2	no	—
152	#431	—	71	1	no	—
153	C₂×#106	—	71	4	no	—
154	#423	—	71	1	no	—
155	#423	C₂×D₇₁	1	1	yes	characteristic
156	C₂×#101	—	142	2	no	—
157	C₄×M₁₆	C₂×D₇₁	1	1	yes	characteristic
158	C₂×C₄×C₈	—	71	1	no	—
159	#343	—	2	2	no	—
160	#335	—	142	2	no	—
161	#332	—	142	2	no	—
162	#332	—	142	2	no	—
163	#322	—	142	1	no	—
164	#322	—	142	1	no	—
165	C₂²×Q₈	—	2	1	no	—
166	C₂²×Q₈	—	142	1	no	—
167	C₂×M₁₆	—	2	1	no	—
168	C₂×M₁₆	—	142	1	no	—
169	C₂×M₁₆	C₂²⋊D₇₁	1	2	yes	—
170	C₂²×C₈	—	71	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	—	142	1	no	—
176	C₄⋊Q₈	—	142	1	no	—
177	C₄⋊Q₈	—	142	1	no	—
178	C₄⋊Q₈	—	142	1	no	—
179	C₂×C₄⋊C₄	—	2	1	no	—
180	C₂×C₄⋊C₄	—	71	2	no	—
181	C₂×C₄⋊C₄	—	142	1	no	—
182	C₂×C₄⋊C₄	C₄×D₇₁	1	2	yes	—
183	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
184	#106	—	142	4	no	—
185	#106	—	142	4	no	—
186	C₄⋊C₈	—	2	1	no	—
187	C₄⋊C₈	—	2	1	no	—
188	C₄⋊C₈	—	71	2	no	—
189	C₄⋊C₈	—	142	1	no	—
190	C₄⋊C₈	—	142	1	no	—
191	#101	—	284	4	no	—
192	C₂²⋊C₈	—	142	1	no	—
193	#97	—	2	1	no	—
194	C₄×C₈	—	2	1	no	—
195	C₄×C₈	—	71	1	no	—
196	C₄×C₈	—	71	1	no	—
197	C₄×C₈	—	71	2	no	—
198	C₄×C₈	—	142	1	no	—
199	C₂×Q₈	—	4	1	no	—
200	C₂×Q₈	—	4	1	no	—
201	C₂×Q₈	—	8	2	no	—
202	C₂×Q₈	—	284	1	no	—
203	C₂×Q₈	—	284	1	no	—
204	C₂×Q₈	—	284	2	no	—
205	C₂×Q₈	—	284	2	no	—
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	142	2	no	—
208	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
209	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
210	C₂²×C₄	#11765865	1	1	yes	characteristic
211	M₁₆	—	2	2	no	—
212	M₁₆	—	2	2	no	—
213	M₁₆	—	4	2	no	—
214	M₁₆	—	284	2	no	—
215	C₂×C₈	—	2	2	no	—
216	C₂×C₈	—	4	1	no	—
217	C₂×C₈	—	284	1	no	—
218	C₂×C₈	—	71	2	no	—
219	C₂×C₈	—	71	2	no	—
220	C₂×C₈	—	142	2	no	—
221	C₂×C₈	—	142	4	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	—	284	1	no	—
227	C₄⋊C₄	—	284	1	no	—
228	C₄⋊C₄	—	142	2	no	—
229	C₄⋊C₄	—	142	2	no	—
230	C₄²	D₄×D₇₁	1	1	yes	characteristic
231	C₄²	D₄×D₇₁	1	1	yes	characteristic
232	C₄²	D₄×D₇₁	1	1	yes	characteristic
233	C₄²	#11765864	1	1	yes	characteristic
234	C₂³	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
235	Q₈	—	8	2	no	—
236	Q₈	—	8	2	no	—
237	Q₈	—	568	1	no	—
238	Q₈	—	568	1	no	—
239	Q₈	—	568	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	—	8	2	no	—
244	C₂×C₄	—	284	4	no	—
245	C₂×C₄	—	284	2	no	—
246	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
247	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
248	C₂×C₄	#14556100	1	1	yes	characteristic
249	C₂×C₄	#14556101	1	1	yes	characteristic
250	C₂×C₄	#14556114	1	1	yes	characteristic
251	C₂×C₄	#14556124	1	1	yes	characteristic
252	C₂×C₄	#14556153	1	2	yes	—
253	C₂×C₄	#14556159	1	2	yes	—
254	C₈	—	4	2	no	—
255	C₈	—	8	1	no	—
256	C₈	—	284	2	no	—
257	C₈	—	568	1	no	—
258	C₈	—	71	4	no	—
259	C₈	—	142	2	no	—
260	C₂²	—	2	1	no	—
261	C₂²	—	2	1	no	—
262	C₂²	#17985899	1	1	yes	characteristic
263	C₂²	#17986097	1	2	yes	—
264	C₄	—	2	1	no	—
265	C₄	—	2	1	no	—
266	C₄	—	8	2	no	—
267	C₄	—	568	2	no	—
268	C₄	#101×D₇₁	1	2	yes	—
269	C₄	#17986247	1	2	yes	—
270	C₄	#17986261	1	2	yes	—
271	C₄	#17986389	1	1	yes	characteristic
272	C₄	#17986391	1	1	yes	characteristic
273	C₂	—	2	2	no	—
274	C₂	#22589182	1	1	yes	characteristic
275	C₂	#22589224	1	1	yes	characteristic
276	C₂	#22589240	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17986395

C₂

yes

maximal, characteristic

#22589184

C₂

yes

maximal, characteristic

#22587098

C₂

yes

maximal, characteristic

#22587025

C₂

yes

maximal, characteristic

#22587013

C₂

yes

maximal, characteristic

#22586627

C₂

yes

maximal, characteristic

C₇₁×#1997

C₂

yes

maximal, characteristic

C₂×#14556128

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₂×#14556059

C₄

yes

—

#17986023

C₂²

yes

characteristic

C₂×#14556046

—

C₂×C₄×C₇₁⋊C₈

C₂²

yes

—

—

—

—

—

C₂×C₄⋊Q₈×C₇₁

C₂²

yes

characteristic

#423×C₇₁

C₂²

yes

characteristic

C₄×M₁₆×C₇₁

C₂²

yes

characteristic

#343×C₇₁

—

C₂²×Dic₁₄₂

—

C₂×#11765849

—

C₂²×C₇₁⋊C₈

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₇₁

—

C₂×C₄⋊Dic₇₁

C₂×C₄

yes

—

#14556059

—

#14556059

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

D₄

yes

—

#14556046

—

C₂²⋊(C₇₁⋊C₈)

—

C₄×C₇₁⋊C₈

—

C₄×C₇₁⋊C₈

D₄

yes

characteristic

C₄×C₇₁⋊C₈

D₄

yes

characteristic

C₄×C₇₁⋊C₈

D₄

yes

—

C₂²×Q₈×C₇₁

—

C₂×M₁₆×C₇₁

—

C₂×M₁₆×C₇₁

D₄

yes

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₄⋊Q₈×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

C₂×C₄⋊C₄×C₇₁

C₂×C₄

yes

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

#97×C₇₁

—

C₄×C₈×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

—

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

#41

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

#41

yes

characteristic

C₂³×C₇₁

C₄×D₄

yes

characteristic

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

100

C₂×C₄×C₇₁

—

101

C₂×C₄×C₇₁

—

102

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

103

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

104

C₂×C₄×C₇₁

#121

yes

characteristic

105

C₂×C₄×C₇₁

#121

yes

characteristic

106

C₂×C₄×C₇₁

#124

yes

characteristic

107

C₂×C₄×C₇₁

#127

yes

characteristic

108

C₂×C₄×C₇₁

AGL(1,ℤ/8)

yes

—

109

C₂×C₄×C₇₁

#137

yes

—

110

C₂×Dic₇₁

—

111

C₂×Dic₇₁

—

112

Dic₁₄₂

—

113

Dic₁₄₂

—

114

Dic₁₄₂

—

115

C₈×C₇₁

—

116

C₈×C₇₁

—

117

C₇₁⋊C₈

—

118

C₇₁⋊C₈

—

119

C₇₁⋊C₈

—

120

C₇₁⋊C₈

#101

yes

complemented

121

C₂²×C₇₁

—

122

C₂²×C₇₁

—

123

C₂²×C₇₁

#390

yes

characteristic

124

C₂²×C₇₁

#440

yes

—

125

C₄×C₇₁

—

126

C₄×C₇₁

—

127

C₄×C₇₁

—

128

C₄×C₇₁

C₂×#101

yes

—

129

C₄×C₇₁

#468

yes

—

130

C₄×C₇₁

#471

yes

—

131

C₄×C₇₁

#496

yes

characteristic

132

C₄×C₇₁

#497

yes

characteristic

133

Dic₇₁

—

134

#9806

—

maximal, Sylow

135

C₂×C₇₁

—

136

C₂×C₇₁

#1966

yes

characteristic

137

C₂×C₇₁

#1973

yes

characteristic

138

C₂×C₇₁

#1977

yes

characteristic

139

C₂×#498

—

140

#1997

D₇₁

yes

characteristic

141

#1966

—

142

#1567

—

143

#1549

—

144

#1546

—

145

#1451

—

146

C₇₁

#9806

yes

characteristic, complemented, Sylow

147

C₂×C₄⋊Q₈

—

148

C₂×C₄⋊Q₈

C₂×D₇₁

yes

characteristic

149

#498

—

142

—

150

#498

—

142

—

151

#498

—

142

—

152

#431

—

153

C₂×#106

—

154

#423

—

155

#423

C₂×D₇₁

yes

characteristic

156

C₂×#101

—

142

—

157

C₄×M₁₆

C₂×D₇₁

yes

characteristic

158

C₂×C₄×C₈

—

159

#343

—

160

#335

—

142

—

161

#332

—

142

—

162

#332

—

142

—

163

#322

—

142

—

164

#322

—

142

—

165

C₂²×Q₈

—

166

C₂²×Q₈

—

142

—

167

C₂×M₁₆

—

168

C₂×M₁₆

—

142

—

169

C₂×M₁₆

C₂²⋊D₇₁

yes

—

170

C₂²×C₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

174

C₄⋊Q₈

—

175

C₄⋊Q₈

—

142

—

176

C₄⋊Q₈

—

142

—

177

C₄⋊Q₈

—

142

—

178

C₄⋊Q₈

—

142

—

179

C₂×C₄⋊C₄

—

180

C₂×C₄⋊C₄

—

181

C₂×C₄⋊C₄

—

142

—

182

C₂×C₄⋊C₄

C₄×D₇₁

yes

—

183

C₂×C₄²

C₂²×D₇₁

yes

characteristic

184

#106

—

142

—

185

#106

—

142

—

186

C₄⋊C₈

—

187

C₄⋊C₈

—

188

C₄⋊C₈

—

189

C₄⋊C₈

—

142

—

190

C₄⋊C₈

—

142

—

191

#101

—

284

—

192

C₂²⋊C₈

—

142

—

193

#97

—

194

C₄×C₈

—

195

C₄×C₈

—

196

C₄×C₈

—

197

C₄×C₈

—

198

C₄×C₈

—

142

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂×Q₈

—

202

C₂×Q₈

—

284

—

203

C₂×Q₈

—

284

—

204

C₂×Q₈

—

284

—

205

C₂×Q₈

—

284

—

206

C₂²×C₄

—

207

C₂²×C₄

—

142

—

208

C₂²×C₄

C₂×C₄×D₇₁

yes

characteristic

209

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

210

C₂²×C₄

#11765865

yes

characteristic

211

M₁₆

—

212

M₁₆

—

213

M₁₆

—

214

M₁₆

—

284

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

284

—

218

C₂×C₈

—

219

C₂×C₈

—

220

C₂×C₈

—

142

—

221

C₂×C₈

—

142

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

284

—

227

C₄⋊C₄

—

284

—

228

C₄⋊C₄

—

142

—

229

C₄⋊C₄

—

142

—

230

C₄²

D₄×D₇₁

yes

characteristic

231

C₄²

D₄×D₇₁

yes

characteristic

232

C₄²

D₄×D₇₁

yes

characteristic

233

C₄²

#11765864

yes

characteristic

234

C₂³

C₄×C₂²⋊D₇₁

yes

characteristic

235

Q₈

—

236

Q₈

—

237

Q₈

—

568

—

238

Q₈

—

568

—

239

Q₈

—

568

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

284

—

245

C₂×C₄

—

284

—

246

C₂×C₄

C₂²⋊C₄×D₇₁

yes

characteristic

247

C₂×C₄

(C₂²⋊D₇₁)⋊C₄

yes

characteristic

248

C₂×C₄

#14556100

yes

characteristic

249

C₂×C₄

#14556101

yes

characteristic

250

C₂×C₄

#14556114

yes

characteristic

251

C₂×C₄

#14556124

yes

characteristic

252

C₂×C₄

#14556153

yes

—

253

C₂×C₄

#14556159

yes

—

254

C₈

—

255

C₈

—

256

C₈

—

284

—

257

C₈

—

568

—

258

C₈

—

259

C₈

—

142

—

260

C₂²

—

261

C₂²

—

262

C₂²

#17985899

yes

characteristic

263

C₂²

#17986097

yes

—

264

C₄

—

265

C₄

—

266

C₄

—

267

C₄

—

568

—

268

C₄

#101×D₇₁

yes

—

269

C₄

#17986247

yes

—

270

C₄

#17986261

yes

—

271

C₄

#17986389

yes

characteristic

272

C₄

#17986391

yes

characteristic

273

C₂

—

274

C₂

#22589182

yes

characteristic

275

C₂

#22589224

yes

characteristic

276

C₂

#22589240

yes

characteristic

	subgroup	G/H
center	C₂²	#17985899
commutator	C₂²×C₄×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1997	C₂
socle	C₂²×C₇₁	#390
prime radical	C₂³×C₇₁	C₄×D₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1997	D₇₁
hypocenter	C₇₁	#9806
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1997

subgroup

G/H

center

C₂²

#17985899

commutator

C₂²×C₄×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1997

C₂

socle

C₂²×C₇₁

#390

prime radical

C₂³×C₇₁

C₄×D₄

cosocle

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1997

N	H ≅ G/N	type
120. C₇₁⋊C₈	#101	semidirect
146. C₇₁	#9806	semidirect

H ≅ G/N

type

120. C₇₁⋊C₈

#101

semidirect

146. C₇₁

#9806

semidirect

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

subgroup	index
C₂×#17986395	2
#22589184	2
#22587098	2
#22587025	2
#22587013	2
#22586627	2
C₇₁×#1997	2
#9806	71

subgroup

index

C₇₁×#1997

Subgroups — #31897111

Conjugacy classes of subgroups

Complements

Maximal subgroups