Group #34008122 — subgroups

Subgroups — #34008122

Order 18688.

490 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 140 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	#22625846	C₂	1	1	yes	maximal, characteristic
2	#22625645	C₂	1	1	yes	maximal, characteristic
3	#22624767	C₂	1	4	yes	maximal
4	#22612498	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊#10596833	C₂²	1	2	yes	—
6	C₂×C₄×#10596833	C₂²	1	2	yes	—
7	#17989453	—	2	1	no	—
8	#17989453	—	2	1	no	—
9	#17989453	—	2	1	no	—
10	#17989453	—	2	1	no	—
11	C₂×#14556591	C₄	1	1	yes	characteristic
12	C₂×#14556556	—	2	1	no	—
13	#17988492	—	2	1	no	—
14	#17988483	—	2	1	no	—
15	#17988483	C₄	1	2	yes	—
16	C₄⋊C₄×Dic₇₃	—	2	1	no	—
17	C₄⋊C₄×Dic₇₃	C₂²	1	2	yes	—
18	C₄²×Dic₇₃	C₂²	1	1	yes	characteristic
19	#384×C₇₃	C₄	1	1	yes	characteristic
20	C₂²×#10596833	—	2	2	no	—
21	C₂²×#10596833	—	2	2	no	—
22	C₄⋊#10596833	—	2	4	no	—
23	C₄×#10596833	—	2	2	no	—
24	C₄×#10596833	Q₈	1	4	yes	complemented
25	C₂²×Dic₁₄₆	—	2	1	no	—
26	#14556591	—	2	2	no	—
27	#14556591	C₈	1	4	yes	complemented
28	#14556556	—	4	4	no	—
29	C₂×C₄⋊Dic₇₃	—	2	1	no	—
30	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
31	C₂×#11924007	—	2	2	no	—
32	C₂×C₄×Dic₇₃	—	2	2	no	—
33	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×Dic₇₃	D₄	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	C₂³	1	1	yes	characteristic
39	#14556498	—	2	2	no	—
40	#14556498	—	2	2	no	—
41	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
42	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
43	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂×#10596833	—	2	4	no	—
46	C₂×#10596833	—	4	2	no	—
47	C₂×#10596833	—	4	2	no	—
48	C₂×#10596833	—	4	2	no	—
49	C₂×#10596833	—	4	2	no	—
50	C₂×#10596833	—	4	2	no	—
51	C₂×Dic₁₄₆	—	2	4	no	—
52	C₂×Dic₁₄₆	—	4	2	no	—
53	C₂×Dic₁₄₆	—	4	2	no	—
54	C₂²×Dic₇₃	—	2	2	no	—
55	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
59	C₄⋊Dic₇₃	—	2	4	no	—
60	C₄⋊Dic₇₃	—	2	2	no	—
61	C₄⋊Dic₇₃	C₂×C₈	1	4	yes	—
62	#11924007	—	4	4	no	—
63	C₄×Dic₇₃	—	2	2	no	—
64	C₄×Dic₇₃	—	2	2	no	—
65	C₄×Dic₇₃	—	2	2	no	—
66	C₄×Dic₇₃	—	4	1	no	—
67	C₄×Dic₇₃	—	4	1	no	—
68	C₄×Dic₇₃	—	4	4	no	—
69	C₄×Dic₇₃	C₂×Q₈	1	2	yes	—
70	C₄×Dic₇₃	#41	1	2	yes	—
71	C₂²×C₄×C₇₃	—	2	2	no	—
72	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
75	C₄⋊C₄×C₇₃	—	2	4	no	—
76	C₄⋊C₄×C₇₃	—	4	2	no	—
77	C₄⋊C₄×C₇₃	—	4	2	no	—
78	C₄²×C₇₃	C₂×C₈	1	2	yes	—
79	C₄²×C₇₃	M₁₆	1	2	yes	—
80	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₇₃	—	2	1	no	—
82	C₂×C₄×C₇₃	—	2	1	no	—
83	C₂×C₄×C₇₃	—	2	1	no	—
84	C₂×C₄×C₇₃	—	2	1	no	—
85	C₂×C₄×C₇₃	—	4	2	no	—
86	C₂×C₄×C₇₃	—	4	2	no	—
87	C₂×C₄×C₇₃	—	4	2	no	—
88	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
89	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
90	C₂×C₄×C₇₃	C₄×Q₈	1	2	yes	—
91	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
92	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₃	#131	1	2	yes	—
94	C₂×Dic₇₃	—	2	1	no	—
95	C₂×Dic₇₃	—	2	1	no	—
96	C₂×Dic₇₃	—	2	4	no	—
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	—	4	2	no	—
104	C₂×Dic₇₃	—	4	2	no	—
105	C₂×Dic₇₃	C₂²⋊Q₈	1	2	yes	—
106	C₂×Dic₇₃	#124	1	1	yes	characteristic
107	C₂×Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
108	C₂×Dic₇₃	AGL(1,ℤ/8)	1	2	yes	—
109	C₂×Dic₇₃	#137	1	2	yes	—
110	Dic₁₄₆	—	4	8	no	—
111	#10596833	—	4	4	no	—
112	#10596833	—	8	2	no	—
113	C₂²×C₇₃	#391	1	1	yes	characteristic
114	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
115	C₂²×C₇₃	#408	1	1	yes	characteristic
116	C₂²×C₇₃	#418	1	1	yes	characteristic
117	C₂²×C₇₃	#419	1	1	yes	characteristic
118	C₂²×C₇₃	#421	1	1	yes	characteristic
119	C₂²×C₇₃	#421	1	1	yes	characteristic
120	C₄×C₇₃	—	2	2	no	—
121	C₄×C₇₃	—	2	2	no	—
122	C₄×C₇₃	—	8	2	no	—
123	C₄×C₇₃	C₈×Q₈	1	2	yes	—
124	C₄×C₇₃	#446	1	2	yes	—
125	Dic₇₃	—	2	2	no	—
126	Dic₇₃	—	4	4	no	—
127	Dic₇₃	—	4	1	no	—
128	Dic₇₃	—	4	1	no	—
129	Dic₇₃	#489	1	2	yes	—
130	Dic₇₃	#501	1	2	yes	—
131	#9873	—	73	1	no	maximal, Sylow
132	C₂×C₇₃	#1478	1	1	yes	characteristic
133	C₂×C₇₃	#1479	1	1	yes	characteristic
134	C₂×C₇₃	#1496	1	1	yes	characteristic
135	C₂×C₇₃	#1497	1	1	yes	characteristic
136	C₂×C₇₃	#1984	1	1	yes	characteristic
137	C₂×C₇₃	#1993	1	1	yes	characteristic
138	C₂×C₇₃	#1995	1	1	yes	characteristic
139	C₄×C₄⋊Q₈	—	73	1	no	—
140	#1831	—	73	1	no	—
141	#1744	—	73	1	no	—
142	#1279	—	73	4	no	—
143	C₇₃	#9873	1	1	yes	characteristic, complemented, Sylow
144	C₂×C₄⋊Q₈	—	73	1	no	—
145	C₂×C₄×Q₈	—	146	1	no	—
146	C₂×C₄⋊C₈	—	73	2	no	—
147	C₂×C₄×C₈	—	73	2	no	—
148	#391	—	146	1	no	—
149	#389	—	73	2	no	—
150	#389	—	146	1	no	—
151	#384	#64408	1	1	yes	characteristic
152	C₄×C₄⋊C₄	—	73	2	no	—
153	C₄×C₄⋊C₄	—	146	1	no	—
154	C₄³	—	73	1	no	—
155	#336	—	146	1	no	—
156	#336	—	146	1	no	—
157	#336	—	146	1	no	—
158	#336	—	146	1	no	—
159	C₂²×Q₈	—	146	1	no	—
160	C₂²×C₈	—	146	2	no	—
161	C₂²×C₈	—	146	2	no	—
162	C₄⋊Q₈	—	73	4	no	—
163	C₄⋊Q₈	—	146	2	no	—
164	C₄×Q₈	—	292	4	no	—
165	C₂×C₄⋊C₄	—	2	1	no	—
166	C₂×C₄⋊C₄	—	2	1	no	—
167	C₂×C₄⋊C₄	—	73	2	no	—
168	C₂×C₄⋊C₄	—	146	2	no	—
169	C₂×C₄⋊C₄	—	146	1	no	—
170	C₂×C₄⋊C₄	C₂×#64408	1	2	yes	—
171	C₂×C₄²	—	73	1	no	—
172	C₂×C₄²	—	73	1	no	—
173	C₂×C₄²	—	73	1	no	—
174	C₂×C₄²	—	73	1	no	—
175	C₂×C₄²	—	73	1	no	—
176	C₂×C₄²	—	73	1	no	—
177	C₂×C₄²	—	146	2	no	—
178	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
179	C₄⋊C₈	—	146	4	no	—
180	C₄×C₈	—	73	4	no	—
181	C₄×C₈	—	146	2	no	—
182	#95	—	146	2	no	—
183	#95	—	146	2	no	—
184	C₂×Q₈	—	292	2	no	—
185	C₂×Q₈	—	292	2	no	—
186	C₂×Q₈	—	146	4	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	73	1	no	—
189	C₂²×C₄	—	73	1	no	—
190	C₂²×C₄	—	73	1	no	—
191	C₂²×C₄	—	73	1	no	—
192	C₂²×C₄	—	146	2	no	—
193	C₂²×C₄	C₂²⋊#64408	1	1	yes	characteristic
194	C₂²×C₄	C₂²⋊#64408	1	1	yes	characteristic
195	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
196	C₂×C₈	—	292	2	no	—
197	C₂×C₈	—	292	2	no	—
198	C₂×C₈	—	292	2	no	—
199	C₂×C₈	—	292	2	no	—
200	C₂×C₈	—	292	2	no	—
201	C₂×C₈	—	146	4	no	—
202	C₄⋊C₄	—	2	4	no	—
203	C₄⋊C₄	—	4	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	292	4	no	—
206	C₄⋊C₄	—	73	4	no	—
207	C₄⋊C₄	—	146	2	no	—
208	C₄⋊C₄	—	146	4	no	—
209	C₄²	—	292	1	no	—
210	C₄²	—	292	1	no	—
211	C₄²	—	292	4	no	—
212	C₄²	—	73	2	no	—
213	C₄²	—	73	2	no	—
214	C₄²	—	146	2	no	—
215	C₄²	—	146	2	no	—
216	C₄²	—	146	2	no	—
217	C₄²	#11924036	1	2	yes	—
218	C₄²	#11924038	1	2	yes	—
219	C₂³	C₂×C₂²⋊#64408	1	1	yes	characteristic
220	Q₈	—	292	8	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	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	292	2	no	—
229	C₂×C₄	—	292	2	no	—
230	C₂×C₄	—	73	1	no	—
231	C₂×C₄	—	73	1	no	—
232	C₂×C₄	—	73	2	no	—
233	C₂×C₄	—	73	2	no	—
234	C₂×C₄	—	73	2	no	—
235	C₂×C₄	—	146	4	no	—
236	C₂×C₄	—	146	1	no	—
237	C₂×C₄	—	146	1	no	—
238	C₂×C₄	—	146	1	no	—
239	C₂×C₄	—	146	1	no	—
240	C₂×C₄	—	146	1	no	—
241	C₂×C₄	—	146	1	no	—
242	C₂×C₄	—	146	1	no	—
243	C₂×C₄	—	146	1	no	—
244	C₂×C₄	#14556648	1	2	yes	—
245	C₂×C₄	#14556648	1	2	yes	—
246	C₂×C₄	Q₈×#64408	1	2	yes	—
247	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
248	C₂×C₄	C₂×#11924038	1	1	yes	characteristic
249	C₂×C₄	#14556678	1	2	yes	—
250	C₈	—	292	4	no	—
251	C₈	—	584	2	no	—
252	C₂²	(C₂×#64408)⋊Q₈	1	1	yes	characteristic
253	C₂²	C₂×#14556648	1	1	yes	characteristic
254	C₂²	#17989561	1	1	yes	characteristic
255	C₂²	#17989579	1	1	yes	characteristic
256	C₂²	#17989580	1	1	yes	characteristic
257	C₂²	#17989585	1	1	yes	characteristic
258	C₂²	#17989586	1	1	yes	characteristic
259	C₄	—	2	2	no	—
260	C₄	—	2	2	no	—
261	C₄	—	8	2	no	—
262	C₄	—	292	1	no	—
263	C₄	—	292	1	no	—
264	C₄	—	292	4	no	—
265	C₄	—	73	2	no	—
266	C₄	—	73	2	no	—
267	C₄	—	146	2	no	—
268	C₄	#17989636	1	2	yes	—
269	C₄	#17989637	1	2	yes	—
270	C₂	#22625232	1	1	yes	characteristic
271	C₂	#22625235	1	1	yes	characteristic
272	C₂	#22625291	1	1	yes	characteristic
273	C₂	#22625294	1	1	yes	characteristic
274	C₂	#22626101	1	1	yes	characteristic
275	C₂	#22626115	1	1	yes	characteristic
276	C₂	#22626119	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22625846

C₂

yes

maximal, characteristic

#22625645

C₂

yes

maximal, characteristic

#22624767

C₂

yes

maximal

#22612498

C₂

yes

maximal, characteristic

C₂×C₄⋊#10596833

C₂²

yes

—

C₂×C₄×#10596833

C₂²

yes

—

—

—

—

—

C₄

yes

—

—

—

C₄

yes

—

C₄⋊C₄×Dic₇₃

—

C₄⋊C₄×Dic₇₃

C₂²

yes

—

C₄²×Dic₇₃

C₂²

yes

characteristic

#384×C₇₃

C₄

yes

—

—

—

—

Q₈

yes

complemented

C₂²×Dic₁₄₆

—

#14556591

—

#14556591

C₈

yes

complemented

#14556556

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₂×C₄

yes

—

C₂×#11924007

—

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

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

C₂×C₄

yes

—

—

—

—

—

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

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

C₂×C₈

yes

—

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×Q₈

yes

—

C₄×Dic₇₃

#41

yes

—

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

—

C₄²×C₇₃

C₂×C₈

yes

—

C₄²×C₇₃

M₁₆

yes

—

C₂³×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₈

yes

—

C₂×C₄×C₇₃

C₂²⋊C₈

yes

—

C₂×C₄×C₇₃

C₄×Q₈

yes

—

C₂×C₄×C₇₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₃

#131

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

100

C₂×Dic₇₃

—

101

C₂×Dic₇₃

—

102

C₂×Dic₇₃

—

103

C₂×Dic₇₃

—

104

C₂×Dic₇₃

—

105

C₂×Dic₇₃

C₂²⋊Q₈

yes

—

106

C₂×Dic₇₃

#124

yes

characteristic

107

C₂×Dic₇₃

C₄⋊Q₈

yes

characteristic

108

C₂×Dic₇₃

AGL(1,ℤ/8)

yes

—

109

C₂×Dic₇₃

#137

yes

—

110

Dic₁₄₆

—

111

#10596833

—

112

#10596833

—

113

C₂²×C₇₃

#391

yes

characteristic

114

C₂²×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

115

C₂²×C₇₃

#408

yes

characteristic

116

C₂²×C₇₃

#418

yes

characteristic

117

C₂²×C₇₃

#419

yes

characteristic

118

C₂²×C₇₃

#421

yes

characteristic

119

C₂²×C₇₃

#421

yes

characteristic

120

C₄×C₇₃

—

121

C₄×C₇₃

—

122

C₄×C₇₃

—

123

C₄×C₇₃

C₈×Q₈

yes

—

124

C₄×C₇₃

#446

yes

—

125

Dic₇₃

—

126

Dic₇₃

—

127

Dic₇₃

—

128

Dic₇₃

—

129

Dic₇₃

#489

yes

—

130

Dic₇₃

#501

yes

—

131

#9873

—

maximal, Sylow

132

C₂×C₇₃

#1478

yes

characteristic

133

C₂×C₇₃

#1479

yes

characteristic

134

C₂×C₇₃

#1496

yes

characteristic

135

C₂×C₇₃

#1497

yes

characteristic

136

C₂×C₇₃

#1984

yes

characteristic

137

C₂×C₇₃

#1993

yes

characteristic

138

C₂×C₇₃

#1995

yes

characteristic

139

C₄×C₄⋊Q₈

—

140

#1831

—

141

#1744

—

142

#1279

—

143

C₇₃

#9873

yes

characteristic, complemented, Sylow

144

C₂×C₄⋊Q₈

—

145

C₂×C₄×Q₈

—

146

—

146

C₂×C₄⋊C₈

—

147

C₂×C₄×C₈

—

148

#391

—

146

—

149

#389

—

150

#389

—

146

—

151

#384

#64408

yes

characteristic

152

C₄×C₄⋊C₄

—

153

C₄×C₄⋊C₄

—

146

—

154

C₄³

—

155

#336

—

146

—

156

#336

—

146

—

157

#336

—

146

—

158

#336

—

146

—

159

C₂²×Q₈

—

146

—

160

C₂²×C₈

—

146

—

161

C₂²×C₈

—

146

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

—

146

—

164

C₄×Q₈

—

292

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

146

—

169

C₂×C₄⋊C₄

—

146

—

170

C₂×C₄⋊C₄

C₂×#64408

yes

—

171

C₂×C₄²

—

172

C₂×C₄²

—

173

C₂×C₄²

—

174

C₂×C₄²

—

175

C₂×C₄²

—

176

C₂×C₄²

—

177

C₂×C₄²

—

146

—

178

C₂×C₄²

C₂×#64408

yes

characteristic

179

C₄⋊C₈

—

146

—

180

C₄×C₈

—

181

C₄×C₈

—

146

—

182

#95

—

146

—

183

#95

—

146

—

184

C₂×Q₈

—

292

—

185

C₂×Q₈

—

292

—

186

C₂×Q₈

—

146

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

146

—

193

C₂²×C₄

C₂²⋊#64408

yes

characteristic

194

C₂²×C₄

C₂²⋊#64408

yes

characteristic

195

C₂²×C₄

C₂²×#64408

yes

characteristic

196

C₂×C₈

—

292

—

197

C₂×C₈

—

292

—

198

C₂×C₈

—

292

—

199

C₂×C₈

—

292

—

200

C₂×C₈

—

292

—

201

C₂×C₈

—

146

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

292

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

146

—

208

C₄⋊C₄

—

146

—

209

C₄²

—

292

—

210

C₄²

—

292

—

211

C₄²

—

292

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

146

—

215

C₄²

—

146

—

216

C₄²

—

146

—

217

C₄²

#11924036

yes

—

218

C₄²

#11924038

yes

—

219

C₂³

C₂×C₂²⋊#64408

yes

characteristic

220

Q₈

—

292

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

292

—

229

C₂×C₄

—

292

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

146

—

236

C₂×C₄

—

146

—

237

C₂×C₄

—

146

—

238

C₂×C₄

—

146

—

239

C₂×C₄

—

146

—

240

C₂×C₄

—

146

—

241

C₂×C₄

—

146

—

242

C₂×C₄

—

146

—

243

C₂×C₄

—

146

—

244

C₂×C₄

#14556648

yes

—

245

C₂×C₄

#14556648

yes

—

246

C₂×C₄

Q₈×#64408

yes

—

247

C₂×C₄

C₂×#11924036

yes

characteristic

248

C₂×C₄

C₂×#11924038

yes

characteristic

249

C₂×C₄

#14556678

yes

—

250

C₈

—

292

—

251

C₈

—

584

—

252

C₂²

(C₂×#64408)⋊Q₈

yes

characteristic

253

C₂²

C₂×#14556648

yes

characteristic

254

C₂²

#17989561

yes

characteristic

255

C₂²

#17989579

yes

characteristic

256

C₂²

#17989580

yes

characteristic

257

C₂²

#17989585

yes

characteristic

258

C₂²

#17989586

yes

characteristic

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

292

—

263

C₄

—

292

—

264

C₄

—

292

—

265

C₄

—

266

C₄

—

267

C₄

—

146

—

268

C₄

#17989636

yes

—

269

C₄

#17989637

yes

—

270

C₂

#22625232

yes

characteristic

271

C₂

#22625235

yes

characteristic

272

C₂

#22625291

yes

characteristic

273

C₂

#22625294

yes

characteristic

274

C₂

#22626101

yes

characteristic

275

C₂

#22626115

yes

characteristic

276

C₂

#22626119

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₈
Frattini	C₂²×C₄	C₂²×#64408
Fitting	#384×C₇₃	C₄
socle, prime radical	C₂³×C₇₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄×Dic₇₃	C₂³
hypercenter	#384	#64408
hypocenter	C₇₃	#9873
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₈

Frattini

C₂²×C₄

C₂²×#64408

Fitting

#384×C₇₃

C₄

socle, prime radical

C₂³×C₇₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄×Dic₇₃

C₂³

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
24. C₄×#10596833	Q₈	semidirect
27. #14556591	C₈	semidirect
143. C₇₃	#9873	semidirect

H ≅ G/N

type

24. C₄×#10596833

Q₈

semidirect

27. #14556591

C₈

semidirect

143. C₇₃

#9873

semidirect

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

subgroup	index
#22625846	2
#22625645	2
#22624767	2
#22612498	2
#9873	73

subgroup

index

Subgroups — #34008122

Conjugacy classes of subgroups

Complements

Maximal subgroups