Group #17958822 — subgroups

Subgroups — #17958822

Order 4352.

352 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 96 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	#14545143	C₂	1	1	yes	maximal, characteristic, complemented
2	#14545117	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈⋊#63216	C₂	1	2	yes	maximal, complemented
4	#14543735	C₂	1	2	yes	maximal, complemented
5	C₈×#63256	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587530	—	2	1	no	—
7	#11763730	—	2	1	no	—
8	#11763730	—	2	1	no	—
9	C₄⋊#63216	C₂²	1	2	yes	—
10	#11763704	—	2	1	no	—
11	C₄×#63216	C₂²	1	2	yes	—
12	C₄×#63256	C₄	1	1	yes	characteristic
13	Q₈×#3622	C₂²	1	1	yes	characteristic
14	C₈×D₆₈	—	2	1	no	—
15	C₈×D₆₈	C₄	1	1	yes	characteristic
16	#11762874	—	2	1	no	—
17	#11762874	C₂²	1	1	yes	characteristic
18	#11762861	—	2	1	no	—
19	#11762861	C₄	1	1	yes	characteristic
20	C₄×C₈×D₁₇	—	2	1	no	—
21	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
22	C₈×Q₈×C₁₇	C₄	1	1	yes	characteristic
23	C₂×#63256	C₈	1	1	yes	characteristic
24	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
25	Q₈×Dic₁₇	C₈	1	1	yes	characteristic
26	C₂×C₈×D₁₇	—	2	1	no	—
27	C₂×C₈×D₁₇	—	2	1	no	—
28	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
29	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
30	#10587579	—	2	1	no	—
31	#10587579	C₈	1	1	yes	characteristic
32	#10587578	—	2	1	no	—
33	#10587578	C₈	1	1	yes	characteristic
34	C₄×D₆₈	—	2	1	no	—
35	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
36	C₄²×D₁₇	—	2	1	no	—
37	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×#63216	—	2	2	no	—
39	C₂×#63216	—	2	2	no	—
40	#10587530	—	4	2	no	—
41	C₁₇×C₄⋊C₈	—	2	1	no	—
42	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₇	—	2	1	no	—
44	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
45	#10587491	—	2	1	no	—
46	#10587491	—	2	1	no	—
47	#10587491	—	2	1	no	—
48	C₈×Dic₁₇	—	2	1	no	—
49	C₈×Dic₁₇	D₄	1	1	yes	characteristic
50	C₈×Dic₁₇	D₄	1	1	yes	characteristic
51	C₄⋊#3622	—	2	1	no	—
52	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
53	C₄×#3622	—	2	1	no	—
54	C₄×#3622	C₂³	1	1	yes	characteristic
55	C₂×Q₈×C₁₇	C₂×C₈	1	1	yes	characteristic
56	#63256	—	2	2	no	—
57	#63256	—	2	2	no	—
58	C₂×D₆₈	—	2	1	no	—
59	C₂×D₆₈	C₂×C₈	1	1	yes	characteristic
60	C₂×C₄×D₁₇	—	2	1	no	—
61	C₂×C₄×D₁₇	—	2	1	no	—
62	C₂×C₄×D₁₇	—	2	1	no	—
63	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
65	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
66	C₂×C₈×C₁₇	—	2	1	no	—
67	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₄⋊C₄×C₁₇	—	2	1	no	—
70	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
71	C₄²×C₁₇	—	2	1	no	—
72	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
73	#63227	—	2	1	no	—
74	#63227	—	2	1	no	—
75	#63227	—	2	1	no	—
76	C₄⋊Dic₁₇	—	2	1	no	—
77	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
78	C₄×Dic₁₇	—	2	1	no	—
79	C₄×Dic₁₇	—	2	1	no	—
80	C₄×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
82	C₄×Dic₁₇	M₁₆	1	1	yes	characteristic
83	C₂×#3622	—	2	1	no	—
84	C₂×#3622	C₂×D₄	1	1	yes	characteristic
85	C₂×#3622	C₂×D₄	1	1	yes	characteristic
86	C₈×D₁₇	—	2	1	no	—
87	C₈×D₁₇	—	2	1	no	—
88	C₈×D₁₇	—	4	1	no	—
89	C₈×D₁₇	—	4	2	no	—
90	C₈×D₁₇	—	4	1	no	—
91	C₈×D₁₇	—	4	1	no	—
92	#63216	—	4	2	no	—
93	#63216	—	4	2	no	—
94	#11623	—	17	1	no	maximal, Sylow
95	C₂²×D₁₇	—	2	1	no	—
96	C₂²×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
97	Q₈×C₁₇	—	2	1	no	—
98	Q₈×C₁₇	M₃₂	1	2	yes	complemented
99	C₂×C₄×C₁₇	—	2	1	no	—
100	C₂×C₄×C₁₇	—	2	1	no	—
101	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
103	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
104	C₂×Dic₁₇	—	2	1	no	—
105	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
106	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
107	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
108	D₆₈	—	2	4	no	—
109	D₆₈	—	2	1	no	—
110	D₆₈	M₃₂	1	2	yes	complemented
111	C₄×D₁₇	—	2	4	no	—
112	C₄×D₁₇	—	2	1	no	—
113	C₄×D₁₇	—	2	1	no	—
114	C₄×D₁₇	—	2	1	no	—
115	C₄×D₁₇	—	2	1	no	—
116	C₄×D₁₇	—	2	2	no	—
117	C₄×D₁₇	—	4	1	no	—
118	C₄×D₁₇	—	4	1	no	—
119	C₄×D₁₇	—	4	2	no	—
120	C₈×C₁₇	—	2	1	no	—
121	C₈×C₁₇	—	2	1	no	—
122	C₈×C₁₇	—	4	1	no	—
123	#3622	—	2	1	no	—
124	#3622	—	4	1	no	—
125	#3622	AGL(1,ℤ/8)	1	1	yes	characteristic
126	#3622	#137	1	1	yes	characteristic
127	C₈×#41	—	17	1	no	—
128	#2162	—	17	1	no	—
129	#2150	—	17	1	no	—
130	Q₈⋊C₁₆	—	17	2	no	—
131	D₄⋊C₁₆	—	17	2	no	—
132	C₂²×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
133	C₂×D₁₇	—	2	1	no	—
134	C₂×D₁₇	—	2	2	no	—
135	C₂×D₁₇	—	2	1	no	—
136	C₂×D₁₇	—	2	1	no	—
137	C₂×D₁₇	—	4	1	no	—
138	C₂×D₁₇	—	4	1	no	—
139	C₄×C₁₇	—	2	2	no	—
140	C₄×C₁₇	—	2	1	no	—
141	C₄×C₁₇	—	4	1	no	—
142	C₄×C₁₇	#417	1	1	yes	characteristic
143	C₄×C₁₇	#421	1	1	yes	characteristic
144	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
145	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
146	Dic₁₇	—	2	1	no	—
147	Dic₁₇	—	2	1	no	—
148	Dic₁₇	—	4	1	no	—
149	Dic₁₇	#350	1	2	yes	—
150	C₄×#41	—	17	1	no	—
151	C₂×M₃₂	—	34	1	no	—
152	C₈×Q₈	—	17	1	no	—
153	C₈×Q₈	#595	1	1	yes	characteristic
154	C₈×D₄	—	17	1	no	—
155	C₈×D₄	—	17	1	no	—
156	C₈×D₄	—	34	1	no	—
157	C₈×D₄	—	34	1	no	—
158	#431	—	17	1	no	—
159	#431	—	34	1	no	—
160	C₂×C₄×C₈	—	17	1	no	—
161	C₂×C₄×C₈	—	34	1	no	—
162	C₄⋊C₁₆	—	17	2	no	—
163	C₄⋊C₁₆	—	34	1	no	—
164	C₄⋊C₁₆	—	34	1	no	—
165	C₂²⋊C₁₆	—	34	1	no	—
166	C₄×C₁₆	—	17	2	no	—
167	C₂×C₁₇	#1477	1	1	yes	characteristic
168	C₂×C₁₇	#2112	1	1	yes	characteristic
169	C₂×C₁₇	C₂×#350	1	1	yes	characteristic
170	D₁₇	—	4	1	no	—
171	D₁₇	—	4	2	no	—
172	C₂×#41	—	17	1	no	—
173	C₂²×C₈	—	17	1	no	—
174	C₂²×C₈	—	17	1	no	—
175	C₂²×C₈	—	34	1	no	—
176	C₂²×C₈	—	34	1	no	—
177	C₄×Q₈	—	17	1	no	—
178	C₄×Q₈	C₂×#595	1	1	yes	characteristic
179	C₄×D₄	—	17	1	no	—
180	C₄×D₄	—	17	1	no	—
181	C₄×D₄	—	34	1	no	—
182	C₄×D₄	—	34	1	no	—
183	#117	—	17	1	no	—
184	#117	—	34	1	no	—
185	C₂×C₄²	—	17	1	no	—
186	C₂×C₄²	—	34	1	no	—
187	M₃₂	—	68	2	no	—
188	C₂×C₁₆	—	34	2	no	—
189	C₂×C₁₆	—	34	2	no	—
190	C₄⋊C₈	—	2	1	no	—
191	C₄⋊C₈	—	17	1	no	—
192	C₄⋊C₈	—	34	1	no	—
193	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
194	C₂²⋊C₈	—	34	1	no	—
195	C₂²⋊C₈	—	34	1	no	—
196	C₂²⋊C₈	—	34	1	no	—
197	C₄×C₈	—	2	1	no	—
198	C₄×C₈	—	17	1	no	—
199	C₄×C₈	—	17	1	no	—
200	C₄×C₈	—	17	1	no	—
201	C₄×C₈	—	34	1	no	—
202	C₄×C₈	—	34	1	no	—
203	C₄×C₈	C₂×#595	1	1	yes	characteristic
204	C₁₇	#11623	1	1	yes	characteristic, complemented, Sylow
205	#41	—	34	2	no	—
206	#41	—	34	2	no	—
207	C₂×Q₈	#63242	1	1	yes	characteristic
208	C₂×D₄	—	17	1	no	—
209	C₂×D₄	—	34	1	no	—
210	C₂²×C₄	—	17	1	no	—
211	C₂²×C₄	—	17	1	no	—
212	C₂²×C₄	—	17	1	no	—
213	C₂²×C₄	—	34	1	no	—
214	C₂²×C₄	—	34	1	no	—
215	C₂²×C₄	—	34	1	no	—
216	C₂×C₈	—	2	1	no	—
217	C₂×C₈	—	17	1	no	—
218	C₂×C₈	—	17	1	no	—
219	C₂×C₈	—	34	1	no	—
220	C₂×C₈	—	34	1	no	—
221	C₂×C₈	—	34	1	no	—
222	C₂×C₈	—	68	1	no	—
223	C₂×C₈	—	68	2	no	—
224	C₂×C₈	—	68	1	no	—
225	C₂×C₈	—	68	1	no	—
226	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
227	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
228	C₄⋊C₄	—	2	1	no	—
229	C₄⋊C₄	—	17	1	no	—
230	C₄⋊C₄	—	34	1	no	—
231	C₄⋊C₄	#63242	1	1	yes	characteristic
232	C₂²⋊C₄	—	34	1	no	—
233	C₂²⋊C₄	—	34	1	no	—
234	C₂²⋊C₄	—	34	1	no	—
235	C₄²	—	2	1	no	—
236	C₄²	—	17	1	no	—
237	C₄²	—	17	1	no	—
238	C₄²	—	17	1	no	—
239	C₄²	—	34	1	no	—
240	C₄²	—	34	1	no	—
241	C₄²	C₂²×#595	1	1	yes	characteristic
242	C₁₆	—	68	2	no	—
243	C₁₆	—	68	2	no	—
244	C₂³	—	17	1	no	—
245	C₂³	—	34	1	no	—
246	Q₈	—	2	1	no	—
247	Q₈	#10587530	1	2	yes	complemented
248	D₄	—	17	2	no	—
249	D₄	—	34	4	no	—
250	D₄	—	34	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	17	1	no	—
254	C₂×C₄	—	17	1	no	—
255	C₂×C₄	—	17	1	no	—
256	C₂×C₄	—	34	2	no	—
257	C₂×C₄	—	34	4	no	—
258	C₂×C₄	—	34	1	no	—
259	C₂×C₄	—	34	1	no	—
260	C₂×C₄	—	34	1	no	—
261	C₂×C₄	—	34	1	no	—
262	C₂×C₄	—	34	1	no	—
263	C₂×C₄	—	68	2	no	—
264	C₂×C₄	—	68	1	no	—
265	C₂×C₄	—	68	1	no	—
266	C₂×C₄	C₂×#63242	1	1	yes	characteristic
267	C₂×C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
268	C₂×C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
269	C₈	—	2	1	no	—
270	C₈	—	2	1	no	—
271	C₈	—	4	1	no	—
272	C₈	—	17	1	no	—
273	C₈	—	17	1	no	—
274	C₈	—	34	1	no	—
275	C₈	—	68	1	no	—
276	C₂²	—	34	2	no	—
277	C₂²	—	34	1	no	—
278	C₂²	—	34	1	no	—
279	C₂²	—	34	1	no	—
280	C₂²	—	68	1	no	—
281	C₂²	—	68	1	no	—
282	C₂²	#11763777	1	1	yes	characteristic
283	C₄	—	2	2	no	—
284	C₄	—	2	1	no	—
285	C₄	—	4	1	no	—
286	C₄	—	17	2	no	—
287	C₄	—	34	1	no	—
288	C₄	—	34	1	no	—
289	C₄	—	68	1	no	—
290	C₄	#11763800	1	1	yes	characteristic
291	C₄	#11763808	1	1	yes	characteristic
292	C₄	#11763865	1	1	yes	characteristic
293	C₄	C₂×#10587530	1	1	yes	characteristic
294	C₂	—	68	1	no	—
295	C₂	—	68	2	no	—
296	C₂	#14544082	1	1	yes	characteristic
297	C₂	#14545012	1	1	yes	characteristic
298	C₂	#14545024	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14545143

C₂

yes

maximal, characteristic, complemented

#14545117

C₂

yes

maximal, characteristic, complemented

Q₈⋊#63216

C₂

yes

maximal, complemented

#14543735

C₂

yes

maximal, complemented

C₈×#63256

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#11763704

—

C₄×#63216

C₂²

yes

—

C₄×#63256

C₄

yes

characteristic

Q₈×#3622

C₂²

yes

characteristic

C₈×D₆₈

—

C₈×D₆₈

C₄

yes

characteristic

#11762874

—

#11762874

C₂²

yes

characteristic

#11762861

—

#11762861

C₄

yes

characteristic

C₄×C₈×D₁₇

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

C₈×Q₈×C₁₇

C₄

yes

characteristic

C₂×#63256

C₈

yes

characteristic

C₄×Q₈×C₁₇

C₂×C₄

yes

characteristic

Q₈×Dic₁₇

C₈

yes

characteristic

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

D₄

yes

characteristic

C₂×C₈×D₁₇

D₄

yes

characteristic

#10587579

—

#10587579

C₈

yes

characteristic

#10587578

—

#10587578

C₈

yes

characteristic

C₄×D₆₈

—

C₄×D₆₈

C₂×C₄

yes

characteristic

C₄²×D₁₇

—

C₄²×D₁₇

C₂×C₄

yes

—

—

—

C₁₇×C₄⋊C₈

—

C₁₇×C₄⋊C₈

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

—

—

C₈×Dic₁₇

—

C₈×Dic₁₇

D₄

yes

characteristic

C₈×Dic₁₇

D₄

yes

characteristic

C₄⋊#3622

—

C₄⋊#3622

C₂×C₄

yes

characteristic

C₄×#3622

—

C₄×#3622

C₂³

yes

characteristic

C₂×Q₈×C₁₇

C₂×C₈

yes

characteristic

#63256

—

#63256

—

C₂×D₆₈

—

C₂×D₆₈

C₂×C₈

yes

characteristic

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₈

yes

characteristic

C₂×C₄×D₁₇

M₁₆

yes

characteristic

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

C₂×C₈

yes

characteristic

C₄²×C₁₇

—

C₄²×C₁₇

C₂²×C₄

yes

—

—

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

C₂²⋊C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

M₁₆

yes

characteristic

C₂×#3622

—

C₂×#3622

C₂×D₄

yes

characteristic

C₂×#3622

C₂×D₄

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

—

—

—

—

C₂²×D₁₇

—

C₂²×D₁₇

C₂²⋊C₈

yes

characteristic

Q₈×C₁₇

—

Q₈×C₁₇

M₃₂

yes

complemented

C₂×C₄×C₁₇

—

100

C₂×C₄×C₁₇

—

101

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

102

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

103

C₂×C₄×C₁₇

C₂×M₁₆

yes

characteristic

104

C₂×Dic₁₇

—

105

C₂×Dic₁₇

C₂²⋊C₈

yes

characteristic

106

C₂×Dic₁₇

C₂²⋊C₈

yes

characteristic

107

C₂×Dic₁₇

C₂²⋊C₈

yes

characteristic

108

D₆₈

—

109

D₆₈

—

110

D₆₈

M₃₂

yes

complemented

111

C₄×D₁₇

—

112

C₄×D₁₇

—

113

C₄×D₁₇

—

114

C₄×D₁₇

—

115

C₄×D₁₇

—

116

C₄×D₁₇

—

117

C₄×D₁₇

—

118

C₄×D₁₇

—

119

C₄×D₁₇

—

120

C₈×C₁₇

—

121

C₈×C₁₇

—

122

C₈×C₁₇

—

123

#3622

—

124

#3622

—

125

yes

126

yes

127

C₈×#41

—

128

#2162

—

129

#2150

—

130

Q₈⋊C₁₆

—

131

D₄⋊C₁₆

—

132

C₂²×C₁₇

C₂×C₂²⋊C₈

yes

characteristic

133

C₂×D₁₇

—

134

C₂×D₁₇

—

135

C₂×D₁₇

—

136

C₂×D₁₇

—

137

C₂×D₁₇

—

138

C₂×D₁₇

—

139

C₄×C₁₇

—

140

C₄×C₁₇

—

141

C₄×C₁₇

—

142

C₄×C₁₇

#417

yes

characteristic

143

C₄×C₁₇

#421

yes

characteristic

144

C₄×C₁₇

C₂×M₃₂

yes

characteristic

145

C₄×C₁₇

C₂×M₃₂

yes

characteristic

146

Dic₁₇

—

147

Dic₁₇

—

148

Dic₁₇

—

149

Dic₁₇

#350

yes

—

150

C₄×#41

—

151

C₂×M₃₂

—

152

C₈×Q₈

—

153

C₈×Q₈

#595

yes

characteristic

154

C₈×D₄

—

155

C₈×D₄

—

156

C₈×D₄

—

157

C₈×D₄

—

158

#431

—

159

#431

—

160

C₂×C₄×C₈

—

161

C₂×C₄×C₈

—

162

C₄⋊C₁₆

—

163

C₄⋊C₁₆

—

164

C₄⋊C₁₆

—

165

C₂²⋊C₁₆

—

166

C₄×C₁₆

—

167

C₂×C₁₇

#1477

yes

characteristic

168

C₂×C₁₇

#2112

yes

characteristic

169

C₂×C₁₇

C₂×#350

yes

characteristic

170

D₁₇

—

171

D₁₇

—

172

C₂×#41

—

173

C₂²×C₈

—

174

C₂²×C₈

—

175

C₂²×C₈

—

176

C₂²×C₈

—

177

C₄×Q₈

—

178

C₄×Q₈

C₂×#595

yes

characteristic

179

C₄×D₄

—

180

C₄×D₄

—

181

C₄×D₄

—

182

C₄×D₄

—

183

#117

—

184

#117

—

185

C₂×C₄²

—

186

C₂×C₄²

—

187

M₃₂

—

188

C₂×C₁₆

—

189

C₂×C₁₆

—

190

C₄⋊C₈

—

191

C₄⋊C₈

—

192

C₄⋊C₈

—

193

C₄⋊C₈

C₂×#595

yes

characteristic

194

C₂²⋊C₈

—

195

C₂²⋊C₈

—

196

C₂²⋊C₈

—

197

C₄×C₈

—

198

C₄×C₈

—

199

C₄×C₈

—

200

C₄×C₈

—

201

C₄×C₈

—

202

C₄×C₈

—

203

C₄×C₈

C₂×#595

yes

characteristic

204

C₁₇

#11623

yes

characteristic, complemented, Sylow

205

#41

—

206

#41

—

207

C₂×Q₈

#63242

yes

characteristic

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂²×C₄

—

211

C₂²×C₄

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

—

219

C₂×C₈

—

220

C₂×C₈

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

C₂²⋊#595

yes

characteristic

227

C₂×C₈

C₂²⋊#595

yes

characteristic

228

C₄⋊C₄

—

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

#63242

yes

characteristic

232

C₂²⋊C₄

—

233

C₂²⋊C₄

—

234

C₂²⋊C₄

—

235

C₄²

—

236

C₄²

—

237

C₄²

—

238

C₄²

—

239

C₄²

—

240

C₄²

—

241

C₄²

C₂²×#595

yes

characteristic

242

C₁₆

—

243

C₁₆

—

244

C₂³

—

245

C₂³

—

246

Q₈

—

247

Q₈

#10587530

yes

complemented

248

D₄

—

249

D₄

—

250

D₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

C₂×#63242

yes

characteristic

267

C₂×C₄

D₁₇⋊M₁₆

yes

characteristic

268

C₂×C₄

C₂×C₂²⋊#595

yes

characteristic

269

C₈

—

270

C₈

—

271

C₈

—

272

C₈

—

273

C₈

—

274

C₈

—

275

C₈

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

—

281

C₂²

—

282

C₂²

#11763777

yes

characteristic

283

C₄

—

284

C₄

—

285

C₄

—

286

C₄

—

287

C₄

—

288

C₄

—

289

C₄

—

290

C₄

#11763800

yes

characteristic

291

C₄

#11763808

yes

characteristic

292

C₄

#11763865

yes

characteristic

293

C₄

C₂×#10587530

yes

characteristic

294

C₂

—

295

C₂

—

296

C₂

#14544082

yes

characteristic

297

C₂

#14545012

yes

characteristic

298

C₂

#14545024

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₂²×C₈
Frattini	C₄²	C₂²×#595
Fitting	C₈×Q₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₂²⋊C₈
prime radical	C₂×#63256	C₈
cosocle	C₄×#3622	C₂³
hypercenter	C₈×Q₈	#595
hypocenter	C₁₇	#11623
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₈

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊#595

commutator

C₂×C₄×C₁₇

C₂²×C₈

Frattini

C₄²

C₂²×#595

Fitting

C₈×Q₈×C₁₇

C₄

socle

C₂²×C₁₇

C₂×C₂²⋊C₈

C₈

C₂³

C₈×Q₈

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₈

N	H ≅ G/N	type
1. #14545143	C₂	semidirect
2. #14545117	C₂	semidirect
3. Q₈⋊#63216	C₂	semidirect
4. #14543735	C₂	semidirect
98. Q₈×C₁₇	M₃₂	semidirect
110. D₆₈	M₃₂	semidirect
204. C₁₇	#11623	semidirect
247. Q₈	#10587530	semidirect

H ≅ G/N

type

1. #14545143

C₂

semidirect

2. #14545117

C₂

semidirect

3. Q₈⋊#63216

C₂

semidirect

4. #14543735

C₂

semidirect

98. Q₈×C₁₇

M₃₂

semidirect

110. D₆₈

M₃₂

semidirect

204. C₁₇

#11623

semidirect

247. Q₈

#10587530

semidirect

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

subgroup	index
#14545143	2
#14545117	2
Q₈⋊#63216	2
#14543735	2
C₈×#63256	2
#11623	17

subgroup

index

Subgroups — #17958822

Conjugacy classes of subgroups

Complements

Maximal subgroups