Group #25072474 — subgroups

Subgroups — C₂×#19133736 #25072474

Order 11008.

1010 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 219 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×#14583629	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583278	C₂	1	1	yes	maximal, characteristic
3	C₂×#14583195	C₂	1	2	yes	maximal
4	#19133736	C₂	1	8	yes	maximal, direct product factor
5	C₂×#14582629	C₂	1	2	yes	maximal
6	C₂×C₄₃×#333	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10621885	—	2	2	no	—
8	#14583629	—	2	4	no	—
9	#14583629	—	2	2	no	—
10	#14583629	C₂²	1	4	yes	—
11	C₂×#13063325	C₂²	1	1	yes	characteristic
12	C₂×#13063324	—	2	2	no	—
13	C₂×#13063323	—	2	2	no	—
14	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
15	C₂×#13063290	—	2	2	no	—
16	#14583278	—	2	2	no	—
17	#14583278	C₂²	1	4	yes	—
18	#14583195	—	2	4	no	—
19	#14583195	C₂²	1	8	yes	—
20	C₂×#13063259	—	2	2	no	—
21	C₂×#13063250	—	2	2	no	—
22	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	#14582629	C₂²	1	8	yes	—
24	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
26	C₄₃×#333	C₂²	1	4	yes	—
27	C₂²×Dic₈₆	—	2	2	no	—
28	C₂²×Dic₈₆	—	2	1	no	—
29	C₂²×Dic₈₆	D₄	1	2	yes	—
30	C₂×#10621885	—	2	8	no	—
31	C₂×#10621885	—	4	8	no	—
32	C₂²×C₄₃⋊C₈	—	2	1	no	—
33	#13063325	—	2	2	no	—
34	#13063325	—	2	1	no	—
35	#13063325	C₂³	1	2	yes	—
36	#13063324	—	2	8	no	—
37	#13063324	—	2	8	no	—
38	#13063323	—	2	8	no	—
39	#13063323	—	2	8	no	—
40	C₄×Dic₈₆	—	2	2	no	—
41	C₄×Dic₈₆	—	2	2	no	—
42	C₄×Dic₈₆	D₄	1	4	yes	—
43	C₄×Dic₈₆	C₂³	1	4	yes	—
44	#13063290	—	2	8	no	—
45	#13063290	—	2	8	no	—
46	C₂×C₄⋊Dic₄₃	—	2	2	no	—
47	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
48	C₂×Dic₄₃⋊C₄	—	2	4	no	—
49	C₂×Dic₄₃⋊C₄	—	2	2	no	—
50	C₂×C₄×Dic₄₃	—	2	2	no	—
51	C₂×C₄×Dic₄₃	—	2	2	no	—
52	#13063259	—	2	8	no	—
53	#13063250	—	2	8	no	—
54	C₄×C₄₃⋊C₈	—	2	1	no	—
55	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
57	C₂²×C₈×C₄₃	—	2	2	no	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
60	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₄₃	—	2	2	no	—
64	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
65	C₂×Q₈×C₄₃	—	2	2	no	—
66	C₂×Q₈×C₄₃	—	4	4	no	—
67	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
68	C₂²×C₄×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
71	C₂²×Dic₄₃	—	2	2	no	—
72	C₂²×Dic₄₃	—	2	2	no	—
73	C₂²×Dic₄₃	—	4	1	no	—
74	C₂×Dic₈₆	—	2	2	no	—
75	C₂×Dic₈₆	—	2	4	no	—
76	C₂×Dic₈₆	—	2	2	no	—
77	C₂×Dic₈₆	—	2	8	no	—
78	C₂×Dic₈₆	—	4	4	no	—
79	C₂×Dic₈₆	—	4	1	no	—
80	C₂×Dic₈₆	—	8	4	no	—
81	C₂×Dic₈₆	Q₁₆	1	8	yes	complemented
82	C₂×Dic₈₆	C₂×D₄	1	4	yes	—
83	C₂×C₈×C₄₃	—	2	4	no	—
84	C₂×C₈×C₄₃	—	4	4	no	—
85	C₄⋊C₄×C₄₃	—	2	4	no	—
86	C₄⋊C₄×C₄₃	—	2	4	no	—
87	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₄²×C₄₃	C₂×D₄	1	2	yes	—
89	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
90	#10621885	—	4	16	no	—
91	C₄⋊Dic₄₃	—	2	2	no	—
92	C₄⋊Dic₄₃	—	2	4	no	—
93	C₄⋊Dic₄₃	—	4	2	no	—
94	C₄⋊Dic₄₃	C₂×D₄	1	4	yes	—
95	Dic₄₃⋊C₄	—	2	16	no	—
96	Dic₄₃⋊C₄	—	2	4	no	—
97	Dic₄₃⋊C₄	—	2	4	no	—
98	C₄×Dic₄₃	—	2	8	no	—
99	C₄×Dic₄₃	—	2	4	no	—
100	C₄×Dic₄₃	—	2	4	no	—
101	C₂×C₄₃⋊C₈	—	2	4	no	—
102	C₂×C₄₃⋊C₈	—	2	2	no	—
103	C₂³×C₄₃	#120	1	1	yes	characteristic
104	Q₈×C₄₃	—	4	4	no	—
105	Q₈×C₄₃	—	8	2	no	—
106	C₂×C₄×C₄₃	—	2	2	no	—
107	C₂×C₄×C₄₃	—	2	4	no	—
108	C₂×C₄×C₄₃	—	4	4	no	—
109	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
110	C₂×C₄×C₄₃	#120	1	2	yes	—
111	C₂×C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
112	C₂×C₄×C₄₃	#137	1	4	yes	—
113	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
114	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
115	C₂×Dic₄₃	—	2	4	no	—
116	C₂×Dic₄₃	—	2	8	no	—
117	C₂×Dic₄₃	—	2	4	no	—
118	C₂×Dic₄₃	—	4	4	no	—
119	C₂×Dic₄₃	—	4	2	no	—
120	C₂×Dic₄₃	—	8	2	no	—
121	Dic₈₆	—	2	4	no	—
122	Dic₈₆	—	2	8	no	—
123	Dic₈₆	—	4	4	no	—
124	Dic₈₆	—	8	8	no	—
125	Dic₈₆	—	8	2	no	—
126	Dic₈₆	C₂×Q₁₆	1	8	yes	complemented
127	C₈×C₄₃	—	4	4	no	—
128	C₄₃⋊C₈	—	2	4	no	—
129	C₂×#1633	—	43	1	no	maximal, Sylow
130	C₂²×C₄₃	#451	1	4	yes	—
131	C₂²×C₄₃	#453	1	2	yes	—
132	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
133	C₄×C₄₃	—	2	1	no	—
134	C₄×C₄₃	—	2	1	no	—
135	C₄×C₄₃	—	4	4	no	—
136	C₄×C₄₃	#451	1	4	yes	—
137	C₄×C₄₃	C₂²×Q₁₆	1	2	yes	—
138	C₄×C₄₃	C₂×#137	1	2	yes	—
139	Dic₄₃	—	2	8	no	—
140	Dic₄₃	—	4	4	no	—
141	Dic₄₃	—	8	2	no	—
142	C₂×Q₈²	—	43	1	no	—
143	C₂×#494	—	43	1	no	—
144	C₂×#477	—	43	2	no	—
145	#1633	—	43	8	no	—
146	C₂×#333	D₄₃	1	1	yes	characteristic
147	C₂×Q₈⋊C₈	—	43	2	no	—
148	C₂×C₄₃	#1633	1	4	yes	complemented
149	C₂×C₄₃	C₂×#451	1	2	yes	—
150	C₂×C₄₃	C₂×#453	1	1	yes	characteristic
151	C₂²×Q₁₆	—	86	2	no	—
152	Q₈²	—	43	4	no	—
153	Q₈²	—	86	4	no	—
154	Q₈²	—	86	2	no	—
155	C₂×C₄⋊Q₈	—	43	1	no	—
156	C₂×C₄⋊Q₈	—	86	2	no	—
157	C₂×C₄⋊Q₈	—	86	2	no	—
158	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
159	C₂×C₄×Q₈	—	43	2	no	—
160	C₂×C₄×Q₈	—	86	2	no	—
161	#494	—	43	4	no	—
162	#494	—	86	2	no	—
163	#477	—	43	8	no	—
164	#477	—	86	4	no	—
165	C₂×#107	—	86	2	no	—
166	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
167	C₂×#103	—	86	2	no	—
168	C₂×C₄×C₈	—	43	1	no	—
169	#333	C₂×D₄₃	1	4	yes	—
170	Q₈⋊C₈	—	43	8	no	—
171	C₄₃	C₂×#1633	1	1	yes	characteristic, complemented, Sylow
172	C₂²×Q₈	—	43	2	no	—
173	C₂²×Q₈	—	86	2	no	—
174	C₂²×Q₈	—	86	1	no	—
175	C₂²×Q₈	D₁₇₂	1	2	yes	—
176	C₂×Q₁₆	—	86	8	no	—
177	C₂×Q₁₆	—	172	8	no	—
178	C₂²×C₈	—	2	2	no	—
179	C₂²×C₈	—	86	1	no	—
180	C₄⋊Q₈	—	2	2	no	—
181	C₄⋊Q₈	—	43	2	no	—
182	C₄⋊Q₈	—	86	8	no	—
183	C₄⋊Q₈	—	86	8	no	—
184	C₄⋊Q₈	—	86	8	no	—
185	C₄⋊Q₈	—	86	8	no	—
186	C₄⋊Q₈	—	86	1	no	—
187	C₄⋊Q₈	—	86	2	no	—
188	C₄⋊Q₈	D₁₇₂	1	2	yes	—
189	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
190	C₄×Q₈	—	43	4	no	—
191	C₄×Q₈	—	43	4	no	—
192	C₄×Q₈	—	86	8	no	—
193	C₄×Q₈	—	86	8	no	—
194	C₄×Q₈	—	86	2	no	—
195	C₄×Q₈	—	86	2	no	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	43	2	no	—
198	C₂×C₄⋊C₄	—	86	4	no	—
199	C₂×C₄⋊C₄	—	86	2	no	—
200	C₂×C₄⋊C₄	—	86	2	no	—
201	C₂×C₄²	—	86	2	no	—
202	C₂×C₄²	—	86	2	no	—
203	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
204	#107	—	86	8	no	—
205	C₄⋊C₈	—	2	2	no	—
206	C₄⋊C₈	C₂²×D₄₃	1	4	yes	—
207	#103	—	86	8	no	—
208	C₄×C₈	—	43	2	no	—
209	C₄×C₈	—	86	1	no	—
210	C₂×Q₈	—	2	2	no	—
211	C₂×Q₈	—	4	4	no	—
212	C₂×Q₈	—	43	8	no	—
213	C₂×Q₈	—	43	4	no	—
214	C₂×Q₈	—	86	8	no	—
215	C₂×Q₈	—	86	2	no	—
216	C₂×Q₈	—	86	4	no	—
217	C₂×Q₈	—	86	2	no	—
218	C₂×Q₈	—	344	4	no	—
219	C₂×Q₈	—	172	4	no	—
220	C₂×Q₈	—	172	1	no	—
221	C₂×Q₈	C₂×D₁₇₂	1	4	yes	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	86	2	no	—
224	C₂²×C₄	—	86	2	no	—
225	C₂²×C₄	—	172	1	no	—
226	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
227	C₂²×C₄	D₄×D₄₃	1	2	yes	—
228	Q₁₆	—	172	16	no	—
229	C₂×C₈	—	2	4	no	—
230	C₂×C₈	—	4	4	no	—
231	C₂×C₈	—	86	4	no	—
232	C₂×C₈	—	86	2	no	—
233	C₄⋊C₄	—	2	4	no	—
234	C₄⋊C₄	—	2	4	no	—
235	C₄⋊C₄	—	43	4	no	—
236	C₄⋊C₄	—	86	16	no	—
237	C₄⋊C₄	—	86	2	no	—
238	C₄⋊C₄	—	86	4	no	—
239	C₄⋊C₄	—	86	4	no	—
240	C₄⋊C₄	—	86	4	no	—
241	C₄⋊C₄	—	172	2	no	—
242	C₄²	—	86	8	no	—
243	C₄²	—	86	4	no	—
244	C₄²	—	86	4	no	—
245	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
246	C₄²	D₄×D₄₃	1	2	yes	—
247	C₄²	C₂³×D₄₃	1	1	yes	characteristic
248	C₂³	#13063295	1	1	yes	characteristic
249	Q₈	—	4	4	no	—
250	Q₈	—	8	2	no	—
251	Q₈	—	43	8	no	—
252	Q₈	—	86	8	no	—
253	Q₈	—	86	4	no	—
254	Q₈	—	344	2	no	—
255	Q₈	—	344	8	no	—
256	Q₈	—	172	4	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	4	4	no	—
260	C₂×C₄	—	86	8	no	—
261	C₂×C₄	—	86	4	no	—
262	C₂×C₄	—	86	4	no	—
263	C₂×C₄	—	344	2	no	—
264	C₂×C₄	—	172	2	no	—
265	C₂×C₄	—	172	4	no	—
266	C₂×C₄	#13063295	1	1	yes	characteristic
267	C₂×C₄	#13063295	1	2	yes	—
268	C₂×C₄	Q₁₆×D₄₃	1	4	yes	—
269	C₂×C₄	#13063354	1	4	yes	—
270	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
271	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
272	C₈	—	4	4	no	—
273	C₈	—	86	4	no	—
274	C₂²	#14583056	1	4	yes	—
275	C₂²	#14583069	1	2	yes	—
276	C₂²	C₂×#13063295	1	1	yes	characteristic
277	C₄	—	2	1	no	—
278	C₄	—	2	1	no	—
279	C₄	—	4	4	no	—
280	C₄	—	86	8	no	—
281	C₄	—	344	2	no	—
282	C₄	—	172	4	no	—
283	C₄	#14583056	1	4	yes	—
284	C₄	C₂×Q₁₆×D₄₃	1	2	yes	—
285	C₄	C₂×#13063354	1	2	yes	—
286	C₂	#19133736	1	4	yes	direct product factor
287	C₂	C₂×#14583056	1	2	yes	—
288	C₂	C₂×#14583069	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14583629

C₂

yes

maximal, characteristic

C₂×#14583278

C₂

yes

maximal, characteristic

C₂×#14583195

C₂

yes

maximal

#19133736

C₂

yes

maximal, direct product factor

C₂×#14582629

C₂

yes

maximal

C₂×C₄₃×#333

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

C₂×#13063325

C₂²

yes

characteristic

C₂×#13063324

—

C₂×#13063323

—

C₂×C₄×Dic₈₆

C₂²

yes

—

C₂×#13063290

—

#14583278

—

#14583278

C₂²

yes

—

#14583195

—

#14583195

C₂²

yes

—

C₂×#13063259

—

C₂×#13063250

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582629

C₂²

yes

—

C₂×C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₃

C₂²

yes

—

C₄₃×#333

C₂²

yes

—

C₂²×Dic₈₆

—

C₂²×Dic₈₆

—

C₂²×Dic₈₆

D₄

yes

—

C₂×#10621885

—

C₂×#10621885

—

C₂²×C₄₃⋊C₈

—

#13063325

—

#13063325

—

#13063325

C₂³

yes

—

—

—

—

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

C₄×Dic₈₆

D₄

yes

—

C₄×Dic₈₆

C₂³

yes

—

#13063290

—

#13063290

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

D₄

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

—

#13063259

—

#13063250

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

C₂³

yes

—

C₂²×Q₈×C₄₃

D₄

yes

—

C₂²×C₈×C₄₃

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

D₄

yes

—

C₄⋊Q₈×C₄₃

C₂³

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

C₂³

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

Q₁₆

yes

complemented

C₂×Dic₈₆

C₂×D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂⁴

yes

characteristic

#10621885

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×D₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

100

C₄×Dic₄₃

—

101

C₂×C₄₃⋊C₈

—

102

C₂×C₄₃⋊C₈

—

103

C₂³×C₄₃

#120

yes

characteristic

104

Q₈×C₄₃

—

105

Q₈×C₄₃

—

106

C₂×C₄×C₄₃

—

107

C₂×C₄×C₄₃

—

108

C₂×C₄×C₄₃

—

109

C₂×C₄×C₄₃

#120

yes

characteristic

110

C₂×C₄×C₄₃

#120

yes

—

111

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

112

C₂×C₄×C₄₃

#137

yes

—

113

C₂×C₄×C₄₃

C₂²×D₄

yes

—

114

C₂×C₄×C₄₃

C₂²×D₄

yes

characteristic

115

C₂×Dic₄₃

—

116

C₂×Dic₄₃

—

117

C₂×Dic₄₃

—

118

C₂×Dic₄₃

—

119

C₂×Dic₄₃

—

120

C₂×Dic₄₃

—

121

Dic₈₆

—

122

Dic₈₆

—

123

Dic₈₆

—

124

Dic₈₆

—

125

Dic₈₆

—

126

Dic₈₆

C₂×Q₁₆

yes

complemented

127

C₈×C₄₃

—

128

C₄₃⋊C₈

—

129

C₂×#1633

—

maximal, Sylow

130

C₂²×C₄₃

#451

yes

—

131

C₂²×C₄₃

#453

yes

—

132

C₂²×C₄₃

C₂×#120

yes

characteristic

133

C₄×C₄₃

—

134

C₄×C₄₃

—

135

C₄×C₄₃

—

136

C₄×C₄₃

#451

yes

—

137

C₄×C₄₃

C₂²×Q₁₆

yes

—

138

C₄×C₄₃

C₂×#137

yes

—

139

Dic₄₃

—

140

Dic₄₃

—

141

Dic₄₃

—

142

C₂×Q₈²

—

143

C₂×#494

—

144

C₂×#477

—

145

#1633

—

146

C₂×#333

D₄₃

yes

characteristic

147

C₂×Q₈⋊C₈

—

148

C₂×C₄₃

#1633

yes

complemented

149

C₂×C₄₃

C₂×#451

yes

—

150

C₂×C₄₃

C₂×#453

yes

characteristic

151

C₂²×Q₁₆

—

152

Q₈²

—

153

Q₈²

—

154

Q₈²

—

155

C₂×C₄⋊Q₈

—

156

C₂×C₄⋊Q₈

—

157

C₂×C₄⋊Q₈

—

158

C₂×C₄⋊Q₈

C₂×D₄₃

yes

characteristic

159

C₂×C₄×Q₈

—

160

C₂×C₄×Q₈

—

161

#494

—

162

#494

—

163

#477

—

164

#477

—

165

C₂×#107

—

166

C₂×C₄⋊C₈

C₂×D₄₃

yes

—

167

C₂×#103

—

168

C₂×C₄×C₈

—

169

#333

C₂×D₄₃

yes

—

170

Q₈⋊C₈

—

171

C₄₃

C₂×#1633

yes

characteristic, complemented, Sylow

172

C₂²×Q₈

—

173

C₂²×Q₈

—

174

C₂²×Q₈

—

175

C₂²×Q₈

D₁₇₂

yes

—

176

C₂×Q₁₆

—

177

C₂×Q₁₆

—

172

—

178

C₂²×C₈

—

179

C₂²×C₈

—

180

C₄⋊Q₈

—

181

C₄⋊Q₈

—

182

C₄⋊Q₈

—

183

C₄⋊Q₈

—

184

C₄⋊Q₈

—

185

C₄⋊Q₈

—

186

C₄⋊Q₈

—

187

C₄⋊Q₈

—

188

C₄⋊Q₈

D₁₇₂

yes

—

189

C₄⋊Q₈

C₂²×D₄₃

yes

—

190

C₄×Q₈

—

191

C₄×Q₈

—

192

C₄×Q₈

—

193

C₄×Q₈

—

194

C₄×Q₈

—

195

C₄×Q₈

—

196

C₂×C₄⋊C₄

—

197

C₂×C₄⋊C₄

—

198

C₂×C₄⋊C₄

—

199

C₂×C₄⋊C₄

—

200

C₂×C₄⋊C₄

—

201

C₂×C₄²

—

202

C₂×C₄²

—

203

C₂×C₄²

C₂²×D₄₃

yes

characteristic

204

#107

—

205

C₄⋊C₈

—

206

C₄⋊C₈

C₂²×D₄₃

yes

—

207

#103

—

208

C₄×C₈

—

209

C₄×C₈

—

210

C₂×Q₈

—

211

C₂×Q₈

—

212

C₂×Q₈

—

213

C₂×Q₈

—

214

C₂×Q₈

—

215

C₂×Q₈

—

216

C₂×Q₈

—

217

C₂×Q₈

—

218

C₂×Q₈

—

344

—

219

C₂×Q₈

—

172

—

220

C₂×Q₈

—

172

—

221

C₂×Q₈

C₂×D₁₇₂

yes

—

222

C₂²×C₄

—

223

C₂²×C₄

—

224

C₂²×C₄

—

225

C₂²×C₄

—

172

—

226

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

227

C₂²×C₄

D₄×D₄₃

yes

—

228

Q₁₆

—

172

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₄⋊C₄

—

239

C₄⋊C₄

—

240

C₄⋊C₄

—

241

C₄⋊C₄

—

172

—

242

C₄²

—

243

C₄²

—

244

C₄²

—

245

C₄²

C₂×D₁₇₂

yes

characteristic

246

C₄²

D₄×D₄₃

yes

—

247

C₄²

C₂³×D₄₃

yes

characteristic

248

C₂³

#13063295

yes

characteristic

249

Q₈

—

250

Q₈

—

251

Q₈

—

252

Q₈

—

253

Q₈

—

254

Q₈

—

344

—

255

Q₈

—

344

—

256

Q₈

—

172

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

344

—

264

C₂×C₄

—

172

—

265

C₂×C₄

—

172

—

266

C₂×C₄

#13063295

yes

characteristic

267

C₂×C₄

#13063295

yes

—

268

C₂×C₄

Q₁₆×D₄₃

yes

—

269

C₂×C₄

#13063354

yes

—

270

C₂×C₄

C₂×D₄×D₄₃

yes

—

271

C₂×C₄

C₂²×D₁₇₂

yes

characteristic

272

C₈

—

273

C₈

—

274

C₂²

#14583056

yes

—

275

C₂²

#14583069

yes

—

276

C₂²

C₂×#13063295

yes

characteristic

277

C₄

—

278

C₄

—

279

C₄

—

280

C₄

—

281

C₄

—

344

—

282

C₄

—

172

—

283

C₄

#14583056

yes

—

284

C₄

C₂×Q₁₆×D₄₃

yes

—

285

C₄

C₂×#13063354

yes

—

286

C₂

#19133736

yes

direct product factor

287

C₂

C₂×#14583056

yes

—

288

C₂

C₂×#14583069

yes

characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#333	C₂
socle, prime radical	C₂³×C₄₃	#120
hypercenter	C₂×#333	D₄₃
hypocenter	C₄₃	C₂×#1633
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

subgroup

G/H

center

C₂³

#13063295

commutator, cosocle

C₄²×C₄₃

C₂⁴

Frattini

C₄²

C₂³×D₄₃

Fitting

C₂×C₄₃×#333

C₂

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

N	H ≅ G/N	type
4. #19133736	C₂	direct (N × H)
81. C₂×Dic₈₆	Q₁₆	semidirect
126. Dic₈₆	C₂×Q₁₆	semidirect
148. C₂×C₄₃	#1633	semidirect
171. C₄₃	C₂×#1633	semidirect
286. C₂	#19133736	direct (N × H)

H ≅ G/N

type

4. #19133736

C₂

direct (N × H)

81. C₂×Dic₈₆

Q₁₆

semidirect

126. Dic₈₆

C₂×Q₁₆

semidirect

148. C₂×C₄₃

#1633

semidirect

171. C₄₃

C₂×#1633

semidirect

286. C₂

#19133736

direct (N × H)

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

subgroup	index
C₂×#14583629	2
C₂×#14583278	2
C₂×#14583195	2
#19133736	2
C₂×#14582629	2
C₂×C₄₃×#333	2
C₂×#1633	43

subgroup

index

C₂×C₄₃×#333

Subgroups — C₂×#19133736 #25072474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#19133736 #25072474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19133736 #25072474