Group #34008111 — subgroups

Subgroups — #34008111

Order 18688.

512 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 138 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	#22625717	C₂	1	1	yes	maximal, characteristic
2	C₄×#14556658	C₂	1	1	yes	maximal, characteristic
3	#22624767	C₂	1	4	yes	maximal
4	C₄⋊Q₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556658	—	2	1	no	—
6	C₂×C₄⋊#10596833	C₂²	1	2	yes	—
7	C₂×#14556646	—	2	1	no	—
8	C₂×C₄×#10596833	C₂²	1	2	yes	—
9	#17989453	—	2	1	no	—
10	#17989453	—	2	1	no	—
11	C₂×Q₈×Dic₇₃	—	2	1	no	—
12	#17988494	—	2	1	no	—
13	#17988486	—	2	1	no	—
14	#17988486	C₄	1	2	yes	—
15	#17988457	C₄	1	1	yes	characteristic
16	C₄⋊C₄×Dic₇₃	—	2	1	no	—
17	C₄⋊C₄×Dic₇₃	C₂²	1	2	yes	—
18	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₇₃	C₄	1	1	yes	characteristic
20	C₂²×#10596833	—	2	2	no	—
21	C₂²×#10596833	—	2	2	no	—
22	#14556658	—	2	4	no	—
23	C₄⋊#10596833	—	2	2	no	—
24	C₄⋊#10596833	Q₈	1	4	yes	complemented
25	#14556646	—	4	2	no	—
26	C₄×#10596833	—	2	4	no	—
27	Q₈×Dic₇₃	—	4	2	no	—
28	Q₈×Dic₇₃	—	4	2	no	—
29	C₂×C₄⋊Dic₇₃	—	2	2	no	—
30	C₂×C₄⋊Dic₇₃	—	2	1	no	—
31	C₂×C₄⋊Dic₇₃	—	2	1	no	—
32	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
33	C₂×C₄×Dic₇₃	—	2	2	no	—
34	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
36	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
37	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
38	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
40	#14556498	—	2	2	no	—
41	#14556498	—	2	2	no	—
42	C₂²×Q₈×C₇₃	—	2	1	no	—
43	C₄⋊Q₈×C₇₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
45	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
47	C₂×#10596833	—	2	4	no	—
48	C₂×#10596833	—	2	4	no	—
49	C₂×#10596833	—	4	2	no	—
50	C₂×#10596833	—	4	2	no	—
51	C₂×#10596833	—	4	2	no	—
52	C₂×#10596833	—	4	2	no	—
53	C₂²×Dic₇₃	—	2	2	no	—
54	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
55	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
57	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
58	C₄⋊Dic₇₃	—	2	4	no	—
59	C₄⋊Dic₇₃	—	4	2	no	—
60	C₄⋊Dic₇₃	—	4	2	no	—
61	C₄⋊Dic₇₃	—	4	4	no	—
62	C₄×Dic₇₃	—	2	2	no	—
63	C₄×Dic₇₃	—	2	2	no	—
64	C₄×Dic₇₃	—	2	2	no	—
65	C₄×Dic₇₃	—	4	1	no	—
66	C₄×Dic₇₃	—	4	2	no	—
67	C₄×Dic₇₃	—	4	2	no	—
68	C₄×Dic₇₃	D₈	1	2	yes	—
69	C₄×Dic₇₃	SD₁₆	1	2	yes	—
70	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
71	C₄×Dic₇₃	#41	1	2	yes	—
72	C₂×Q₈×C₇₃	—	2	4	no	—
73	C₂×Q₈×C₇₃	—	4	2	no	—
74	C₂×Q₈×C₇₃	—	4	2	no	—
75	C₂²×C₄×C₇₃	—	2	2	no	—
76	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
79	C₄⋊C₄×C₇₃	—	2	4	no	—
80	C₄⋊C₄×C₇₃	—	2	2	no	—
81	C₄⋊C₄×C₇₃	M₁₆	1	4	yes	—
82	C₄²×C₇₃	—	2	2	no	—
83	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	Q₈×C₇₃	—	4	8	no	—
85	C₂×C₄×C₇₃	—	2	1	no	—
86	C₂×C₄×C₇₃	—	2	1	no	—
87	C₂×C₄×C₇₃	—	2	1	no	—
88	C₂×C₄×C₇₃	—	2	1	no	—
89	C₂×C₄×C₇₃	—	2	4	no	—
90	C₂×C₄×C₇₃	—	4	2	no	—
91	C₂×C₄×C₇₃	—	4	2	no	—
92	C₂×C₄×C₇₃	#102	1	2	yes	—
93	C₂×C₄×C₇₃	#104	1	2	yes	—
94	C₂×C₄×C₇₃	C₄×Q₈	1	2	yes	—
95	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
96	C₂×C₄×C₇₃	#131	1	2	yes	—
97	C₂×Dic₇₃	—	2	1	no	—
98	C₂×Dic₇₃	—	2	1	no	—
99	C₂×Dic₇₃	—	2	1	no	—
100	C₂×Dic₇₃	—	2	1	no	—
101	C₂×Dic₇₃	—	2	1	no	—
102	C₂×Dic₇₃	—	2	1	no	—
103	C₂×Dic₇₃	—	2	1	no	—
104	C₂×Dic₇₃	—	4	2	no	—
105	C₂×Dic₇₃	—	4	2	no	—
106	C₂×Dic₇₃	—	4	2	no	—
107	C₂×Dic₇₃	#102	1	2	yes	—
108	C₂×Dic₇₃	C₂²⋊Q₈	1	2	yes	—
109	C₂×Dic₇₃	#124	1	1	yes	characteristic
110	C₂×Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
111	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
112	C₂×Dic₇₃	C₂×SD₁₆	1	1	yes	characteristic
113	C₂×Dic₇₃	#137	1	2	yes	—
114	#10596833	—	4	4	no	—
115	#10596833	—	4	4	no	—
116	C₂²×C₇₃	#391	1	1	yes	characteristic
117	C₂²×C₇₃	#407	1	1	yes	characteristic
118	C₂²×C₇₃	#408	1	1	yes	characteristic
119	C₂²×C₇₃	C₂×#102	1	1	yes	characteristic
120	C₂²×C₇₃	#419	1	1	yes	characteristic
121	C₂²×C₇₃	C₂×#104	1	1	yes	characteristic
122	C₂²×C₇₃	#421	1	1	yes	characteristic
123	C₄×C₇₃	—	2	2	no	—
124	C₄×C₇₃	—	2	2	no	—
125	C₄×C₇₃	—	4	4	no	—
126	C₄×C₇₃	#446	1	4	yes	—
127	Dic₇₃	—	2	1	no	—
128	Dic₇₃	—	2	1	no	—
129	Dic₇₃	—	2	2	no	—
130	Dic₇₃	—	4	1	no	—
131	Dic₇₃	—	8	2	no	—
132	Dic₇₃	#474	1	2	yes	—
133	Dic₇₃	#475	1	2	yes	—
134	#9869	—	73	1	no	maximal, Sylow
135	C₂×C₇₃	#1486	1	1	yes	characteristic
136	C₂×C₇₃	#1491	1	1	yes	characteristic
137	C₂×C₇₃	#1492	1	1	yes	characteristic
138	C₂×C₇₃	#1497	1	1	yes	characteristic
139	C₂×C₇₃	#1985	1	1	yes	characteristic
140	C₂×C₇₃	#1986	1	1	yes	characteristic
141	C₂×C₇₃	#1988	1	1	yes	characteristic
142	C₄×C₄⋊Q₈	—	73	1	no	—
143	#1767	—	73	1	no	—
144	C₄×C₄⋊C₈	—	73	1	no	—
145	#1279	—	73	4	no	—
146	C₇₃	#9869	1	1	yes	characteristic, complemented, Sylow
147	C₂×C₄⋊Q₈	#64408	1	1	yes	characteristic
148	C₂×C₄×Q₈	—	146	1	no	—
149	C₂×C₄⋊C₈	—	73	2	no	—
150	C₂×C₄⋊C₈	—	146	1	no	—
151	C₂×#97	—	146	1	no	—
152	C₂×C₄×C₈	—	73	2	no	—
153	#391	—	146	1	no	—
154	#389	—	73	2	no	—
155	#389	—	146	1	no	—
156	#384	—	73	1	no	—
157	C₄×C₄⋊C₄	—	73	2	no	—
158	C₄×C₄⋊C₄	—	146	1	no	—
159	C₄³	—	73	1	no	—
160	#336	—	146	1	no	—
161	#336	—	146	1	no	—
162	C₂²×Q₈	—	2	1	no	—
163	C₂²×C₈	—	146	2	no	—
164	C₂²×C₈	—	146	2	no	—
165	C₄⋊Q₈	—	2	4	no	—
166	C₄×Q₈	—	292	2	no	—
167	C₄×Q₈	—	292	2	no	—
168	C₂×C₄⋊C₄	—	2	1	no	—
169	C₂×C₄⋊C₄	—	73	2	no	—
170	C₂×C₄⋊C₄	—	146	2	no	—
171	C₂×C₄⋊C₄	—	146	1	no	—
172	C₂×C₄⋊C₄	—	146	1	no	—
173	C₂×C₄⋊C₄	C₂×#64408	1	2	yes	—
174	C₂×C₄²	—	73	1	no	—
175	C₂×C₄²	—	73	1	no	—
176	C₂×C₄²	—	73	1	no	—
177	C₂×C₄²	—	73	1	no	—
178	C₂×C₄²	—	73	1	no	—
179	C₂×C₄²	—	73	1	no	—
180	C₂×C₄²	—	146	2	no	—
181	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
182	C₄⋊C₈	—	73	4	no	—
183	C₄⋊C₈	—	146	2	no	—
184	C₄⋊C₈	—	146	4	no	—
185	#97	—	292	2	no	—
186	C₄×C₈	—	146	4	no	—
187	#95	—	146	2	no	—
188	#95	—	146	2	no	—
189	C₂×Q₈	—	2	4	no	—
190	C₂×Q₈	—	4	2	no	—
191	C₂×Q₈	—	4	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	73	1	no	—
194	C₂²×C₄	—	73	1	no	—
195	C₂²×C₄	—	73	1	no	—
196	C₂²×C₄	—	73	1	no	—
197	C₂²×C₄	—	146	2	no	—
198	C₂²×C₄	C₂²⋊#64408	1	1	yes	characteristic
199	C₂²×C₄	C₂²⋊#64408	1	1	yes	characteristic
200	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
201	C₂×C₈	—	292	2	no	—
202	C₂×C₈	—	292	2	no	—
203	C₂×C₈	—	292	2	no	—
204	C₂×C₈	—	292	2	no	—
205	C₂×C₈	—	146	4	no	—
206	C₂×C₈	—	146	4	no	—
207	C₄⋊C₄	—	2	4	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	292	4	no	—
210	C₄⋊C₄	—	292	2	no	—
211	C₄⋊C₄	—	292	2	no	—
212	C₄⋊C₄	—	146	4	no	—
213	C₄⋊C₄	#11924037	1	4	yes	—
214	C₄²	—	2	2	no	—
215	C₄²	—	292	1	no	—
216	C₄²	—	292	2	no	—
217	C₄²	—	292	2	no	—
218	C₄²	—	73	2	no	—
219	C₄²	—	73	2	no	—
220	C₄²	—	73	2	no	—
221	C₄²	—	73	2	no	—
222	C₄²	—	146	2	no	—
223	C₄²	—	146	2	no	—
224	C₄²	—	146	2	no	—
225	C₂³	C₂×C₂²⋊#64408	1	1	yes	characteristic
226	Q₈	—	4	8	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	—	2	4	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	292	2	no	—
235	C₂×C₄	—	292	2	no	—
236	C₂×C₄	—	292	2	no	—
237	C₂×C₄	—	73	2	no	—
238	C₂×C₄	—	73	1	no	—
239	C₂×C₄	—	73	1	no	—
240	C₂×C₄	—	73	2	no	—
241	C₂×C₄	—	73	1	no	—
242	C₂×C₄	—	73	1	no	—
243	C₂×C₄	—	73	2	no	—
244	C₂×C₄	—	146	1	no	—
245	C₂×C₄	—	146	1	no	—
246	C₂×C₄	—	146	1	no	—
247	C₂×C₄	—	146	1	no	—
248	C₂×C₄	—	146	1	no	—
249	C₂×C₄	—	146	1	no	—
250	C₂×C₄	—	146	1	no	—
251	C₂×C₄	#14556653	1	2	yes	—
252	C₂×C₄	#14556656	1	2	yes	—
253	C₂×C₄	Q₈×#64408	1	2	yes	—
254	C₂×C₄	C₂×#11924037	1	2	yes	—
255	C₂×C₄	#14556679	1	2	yes	—
256	C₈	—	292	4	no	—
257	C₈	—	292	4	no	—
258	C₂²	(C₂×#64408)⋊Q₈	1	1	yes	characteristic
259	C₂²	#17989557	1	1	yes	characteristic
260	C₂²	#17989562	1	1	yes	characteristic
261	C₂²	C₂×#14556653	1	1	yes	characteristic
262	C₂²	#17989580	1	1	yes	characteristic
263	C₂²	C₂×#14556656	1	1	yes	characteristic
264	C₂²	#17989585	1	1	yes	characteristic
265	C₄	—	2	2	no	—
266	C₄	—	2	2	no	—
267	C₄	—	4	4	no	—
268	C₄	—	292	1	no	—
269	C₄	—	584	2	no	—
270	C₄	—	73	2	no	—
271	C₄	—	73	2	no	—
272	C₄	—	146	1	no	—
273	C₄	—	146	1	no	—
274	C₄	—	146	2	no	—
275	C₄	#17989638	1	4	yes	—
276	C₂	#22625256	1	1	yes	characteristic
277	C₂	#22625273	1	1	yes	characteristic
278	C₂	#22625278	1	1	yes	characteristic
279	C₂	#22625295	1	1	yes	characteristic
280	C₂	#22626105	1	1	yes	characteristic
281	C₂	#22626106	1	1	yes	characteristic
282	C₂	#22626110	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22625717

C₂

yes

maximal, characteristic

C₄×#14556658

C₂

yes

maximal, characteristic

#22624767

C₂

yes

maximal

C₄⋊Q₈×Dic₇₃

C₂

yes

maximal, characteristic

C₂×#14556658

—

C₂×C₄⋊#10596833

C₂²

yes

—

C₂×#14556646

—

C₂×C₄×#10596833

C₂²

yes

—

#17989453

—

#17989453

—

C₂×Q₈×Dic₇₃

—

#17988494

—

#17988486

—

#17988486

C₄

yes

—

#17988457

C₄

yes

characteristic

C₄⋊C₄×Dic₇₃

—

C₄⋊C₄×Dic₇₃

C₂²

yes

—

C₄²×Dic₇₃

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₇₃

C₄

yes

—

—

—

—

Q₈

yes

complemented

#14556646

—

C₄×#10596833

—

Q₈×Dic₇₃

—

Q₈×Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₇₃

D₄

yes

characteristic

C₂×C₄×Dic₇₃

D₄

yes

characteristic

C₂×C₄×Dic₇₃

D₄

yes

characteristic

C₂×C₄×Dic₇₃

D₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂³

yes

characteristic

#14556498

—

#14556498

—

C₂²×Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

—

—

—

—

—

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂²×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂²×Dic₇₃

C₂×D₄

yes

characteristic

C₂²×Dic₇₃

C₂×D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₈

yes

—

C₄×Dic₇₃

SD₁₆

yes

—

C₄×Dic₇₃

C₂×Q₈

yes

—

C₄×Dic₇₃

#41

yes

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

M₁₆

yes

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#102

yes

—

C₂×C₄×C₇₃

#104

yes

—

C₂×C₄×C₇₃

C₄×Q₈

yes

—

C₂×C₄×C₇₃

C₂×M₁₆

yes

—

C₂×C₄×C₇₃

#131

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

100

C₂×Dic₇₃

—

101

C₂×Dic₇₃

—

102

C₂×Dic₇₃

—

103

C₂×Dic₇₃

—

104

C₂×Dic₇₃

—

105

C₂×Dic₇₃

—

106

C₂×Dic₇₃

—

107

C₂×Dic₇₃

#102

yes

—

108

C₂×Dic₇₃

C₂²⋊Q₈

yes

—

109

C₂×Dic₇₃

#124

yes

characteristic

110

C₂×Dic₇₃

C₄⋊Q₈

yes

characteristic

111

C₂×Dic₇₃

C₂×D₈

yes

characteristic

112

C₂×Dic₇₃

C₂×SD₁₆

yes

characteristic

113

C₂×Dic₇₃

#137

yes

—

114

#10596833

—

115

#10596833

—

116

C₂²×C₇₃

#391

yes

characteristic

117

C₂²×C₇₃

#407

yes

characteristic

118

C₂²×C₇₃

#408

yes

characteristic

119

C₂²×C₇₃

C₂×#102

yes

characteristic

120

C₂²×C₇₃

#419

yes

characteristic

121

C₂²×C₇₃

C₂×#104

yes

characteristic

122

C₂²×C₇₃

#421

yes

characteristic

123

C₄×C₇₃

—

124

C₄×C₇₃

—

125

C₄×C₇₃

—

126

C₄×C₇₃

#446

yes

—

127

Dic₇₃

—

128

Dic₇₃

—

129

Dic₇₃

—

130

Dic₇₃

—

131

Dic₇₃

—

132

Dic₇₃

#474

yes

—

133

Dic₇₃

#475

yes

—

134

#9869

—

maximal, Sylow

135

C₂×C₇₃

#1486

yes

characteristic

136

C₂×C₇₃

#1491

yes

characteristic

137

C₂×C₇₃

#1492

yes

characteristic

138

C₂×C₇₃

#1497

yes

characteristic

139

C₂×C₇₃

#1985

yes

characteristic

140

C₂×C₇₃

#1986

yes

characteristic

141

C₂×C₇₃

#1988

yes

characteristic

142

C₄×C₄⋊Q₈

—

143

#1767

—

144

C₄×C₄⋊C₈

—

145

#1279

—

146

C₇₃

#9869

yes

characteristic, complemented, Sylow

147

C₂×C₄⋊Q₈

#64408

yes

characteristic

148

C₂×C₄×Q₈

—

146

—

149

C₂×C₄⋊C₈

—

150

C₂×C₄⋊C₈

—

146

—

151

C₂×#97

—

146

—

152

C₂×C₄×C₈

—

153

#391

—

146

—

154

#389

—

155

#389

—

146

—

156

#384

—

157

C₄×C₄⋊C₄

—

158

C₄×C₄⋊C₄

—

146

—

159

C₄³

—

160

#336

—

146

—

161

#336

—

146

—

162

C₂²×Q₈

—

163

C₂²×C₈

—

146

—

164

C₂²×C₈

—

146

—

165

C₄⋊Q₈

—

166

C₄×Q₈

—

292

—

167

C₄×Q₈

—

292

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

146

—

171

C₂×C₄⋊C₄

—

146

—

172

C₂×C₄⋊C₄

—

146

—

173

C₂×C₄⋊C₄

C₂×#64408

yes

—

174

C₂×C₄²

—

175

C₂×C₄²

—

176

C₂×C₄²

—

177

C₂×C₄²

—

178

C₂×C₄²

—

179

C₂×C₄²

—

180

C₂×C₄²

—

146

—

181

C₂×C₄²

C₂×#64408

yes

characteristic

182

C₄⋊C₈

—

183

C₄⋊C₈

—

146

—

184

C₄⋊C₈

—

146

—

185

#97

—

292

—

186

C₄×C₈

—

146

—

187

#95

—

146

—

188

#95

—

146

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×Q₈

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

146

—

198

C₂²×C₄

C₂²⋊#64408

yes

characteristic

199

C₂²×C₄

C₂²⋊#64408

yes

characteristic

200

C₂²×C₄

C₂²×#64408

yes

characteristic

201

C₂×C₈

—

292

—

202

C₂×C₈

—

292

—

203

C₂×C₈

—

292

—

204

C₂×C₈

—

292

—

205

C₂×C₈

—

146

—

206

C₂×C₈

—

146

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

292

—

210

C₄⋊C₄

—

292

—

211

C₄⋊C₄

—

292

—

212

C₄⋊C₄

—

146

—

213

C₄⋊C₄

#11924037

yes

—

214

C₄²

—

215

C₄²

—

292

—

216

C₄²

—

292

—

217

C₄²

—

292

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₄²

—

222

C₄²

—

146

—

223

C₄²

—

146

—

224

C₄²

—

146

—

225

C₂³

C₂×C₂²⋊#64408

yes

characteristic

226

Q₈

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

292

—

235

C₂×C₄

—

292

—

236

C₂×C₄

—

292

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

146

—

245

C₂×C₄

—

146

—

246

C₂×C₄

—

146

—

247

C₂×C₄

—

146

—

248

C₂×C₄

—

146

—

249

C₂×C₄

—

146

—

250

C₂×C₄

—

146

—

251

C₂×C₄

#14556653

yes

—

252

C₂×C₄

#14556656

yes

—

253

C₂×C₄

Q₈×#64408

yes

—

254

C₂×C₄

C₂×#11924037

yes

—

255

C₂×C₄

#14556679

yes

—

256

C₈

—

292

—

257

C₈

—

292

—

258

C₂²

(C₂×#64408)⋊Q₈

yes

characteristic

259

C₂²

#17989557

yes

characteristic

260

C₂²

#17989562

yes

characteristic

261

C₂²

C₂×#14556653

yes

characteristic

262

C₂²

#17989580

yes

characteristic

263

C₂²

C₂×#14556656

yes

characteristic

264

C₂²

#17989585

yes

characteristic

265

C₄

—

266

C₄

—

267

C₄

—

268

C₄

—

292

—

269

C₄

—

584

—

270

C₄

—

271

C₄

—

272

C₄

—

146

—

273

C₄

—

146

—

274

C₄

—

146

—

275

C₄

#17989638

yes

—

276

C₂

#22625256

yes

characteristic

277

C₂

#22625273

yes

characteristic

278

C₂

#22625278

yes

characteristic

279

C₂

#22625295

yes

characteristic

280

C₂

#22626105

yes

characteristic

281

C₂

#22626106

yes

characteristic

282

C₂

#22626110

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊#64408
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×#64408
Fitting	C₂×C₄⋊Q₈×C₇₃	C₄
socle, prime radical	C₂³×C₇₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄×Dic₇₃	C₂³
hypercenter	C₂×C₄⋊Q₈	#64408
hypocenter	C₇₃	#9869
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊#64408

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×#64408

Fitting

C₂×C₄⋊Q₈×C₇₃

C₄

socle, prime radical

C₂³×C₇₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄×Dic₇₃

C₂³

C₂×C₄⋊Q₈

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
24. C₄⋊#10596833	Q₈	semidirect
146. C₇₃	#9869	semidirect

H ≅ G/N

type

24. C₄⋊#10596833

Q₈

semidirect

146. C₇₃

#9869

semidirect

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

subgroup	index
#22625717	2
C₄×#14556658	2
#22624767	2
C₄⋊Q₈×Dic₇₃	2
#9869	73

subgroup

index

C₄⋊Q₈×Dic₇₃

Subgroups — #34008111

Conjugacy classes of subgroups

Complements

Maximal subgroups