Subgroups — #14540280

Order 2176.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587635	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#63230	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₆₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763199	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763057	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763043	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763021	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763009	C₂	1	1	yes	maximal, characteristic, complemented
9	#11762959	C₂	1	1	yes	maximal, characteristic, complemented
10	#11762954	C₂	1	1	yes	maximal, characteristic, complemented
11	#11762948	C₂	1	1	yes	maximal, characteristic, complemented
12	#11762942	C₂	1	1	yes	maximal, characteristic, complemented
13	#11762907	C₂	1	1	yes	maximal, characteristic, complemented
14	#11762881	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#548	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₇	C₂²	1	1	yes	characteristic, complemented
17	C₂²×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
18	C₂×D₄×D₁₇	—	2	1	no	—
19	C₂²×D₆₈	C₂²	1	1	yes	characteristic
20	C₂²×D₆₈	C₂²	1	1	yes	characteristic
21	C₁₇×#124	—	2	1	no	—
22	C₁₇×#124	C₂²	1	1	yes	characteristic, complemented
23	C₁₇×C₂²⋊Q₈	—	2	1	no	—
24	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₁₇×#121	—	2	1	no	—
26	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
27	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
28	C₄×D₄×C₁₇	—	2	1	no	—
29	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
30	#10587635	—	2	4	no	—
31	C₂×#63230	—	2	4	no	—
32	C₂×#63230	C₂²	1	1	yes	characteristic
33	C₂×#63230	C₂²	1	1	yes	characteristic
34	C₂×#63230	C₂²	1	1	yes	characteristic, complemented
35	C₂×#63230	C₂²	1	1	yes	characteristic, complemented
36	C₂×#63230	C₂²	1	1	yes	characteristic, complemented
37	C₂×#63230	C₂²	1	1	yes	characteristic, complemented
38	C₂×#63228	C₂²	1	1	yes	characteristic
39	C₂×#63228	C₂²	1	1	yes	characteristic, complemented
40	C₂×#63228	C₂²	1	1	yes	characteristic, complemented
41	#10587616	C₂²	1	1	yes	characteristic
42	#10587616	C₂²	1	1	yes	characteristic
43	C₂×#63223	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#3622	C₂²	1	1	yes	characteristic, complemented
45	#10587581	—	2	1	no	—
46	#10587568	—	2	1	no	—
47	#10587568	—	2	1	no	—
48	#10587560	C₂²	1	1	yes	characteristic
49	C₄×D₆₈	C₂²	1	1	yes	characteristic
50	#10587506	C₂²	1	1	yes	characteristic, complemented
51	#10587506	C₂²	1	1	yes	characteristic, complemented
52	#10587503	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊#3622	C₂²	1	1	yes	characteristic, complemented
54	C₂²⋊#3622	C₂²	1	1	yes	characteristic, complemented
55	#10587480	C₂²	1	1	yes	characteristic
56	#10587480	C₂²	1	1	yes	characteristic, complemented
57	#10587480	C₂²	1	1	yes	characteristic, complemented
58	#10587478	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊#3622	C₂²	1	1	yes	characteristic, complemented
60	#10587474	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₇	—	2	1	no	—
62	C₂³×D₁₇	—	2	1	no	—
63	#41×C₁₇	—	2	2	no	—
64	#41×C₁₇	—	4	1	no	—
65	C₂×Q₈×C₁₇	—	2	1	no	—
66	C₂×Q₈×C₁₇	—	2	2	no	—
67	C₂×Q₈×C₁₇	—	4	1	no	—
68	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
69	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
70	C₂×D₄×C₁₇	—	2	1	no	—
71	C₂×D₄×C₁₇	—	2	1	no	—
72	C₂×D₄×C₁₇	D₄	1	1	yes	characteristic
73	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	—	2	1	no	—
75	C₂²×C₄×C₁₇	—	2	1	no	—
76	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊D₁₇	—	2	1	no	—
79	C₂×C₂²⋊D₁₇	—	2	1	no	—
80	D₄×D₁₇	—	4	4	no	—
81	C₂×D₆₈	—	2	2	no	—
82	C₂×D₆₈	—	2	2	no	—
83	C₂×D₆₈	—	2	1	no	—
84	C₂×D₆₈	—	2	1	no	—
85	C₂×D₆₈	—	2	1	no	—
86	C₂×D₆₈	—	2	1	no	—
87	C₂×D₆₈	—	4	1	no	—
88	C₂×D₆₈	—	4	1	no	—
89	C₂×D₆₈	C₂³	1	1	yes	characteristic
90	C₂×D₆₈	C₂³	1	1	yes	characteristic
91	C₂×D₆₈	C₂³	1	1	yes	characteristic
92	C₂×C₄×D₁₇	—	2	1	no	—
93	C₄⋊C₄×C₁₇	—	2	1	no	—
94	C₄⋊C₄×C₁₇	—	2	1	no	—
95	C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
96	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
97	C₂²⋊C₄×C₁₇	—	2	1	no	—
98	C₂²⋊C₄×C₁₇	—	2	1	no	—
99	C₂²⋊C₄×C₁₇	—	2	1	no	—
100	C₂²⋊C₄×C₁₇	—	2	1	no	—
101	C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
102	C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
103	C₄²×C₁₇	—	2	1	no	—
104	C₄²×C₁₇	C₂³	1	1	yes	characteristic
105	#63230	—	2	2	no	—
106	#63230	—	2	2	no	—
107	#63230	—	2	2	no	—
108	#63230	—	2	2	no	—
109	#63230	—	4	1	no	—
110	#63230	D₄	1	4	yes	complemented
111	#63228	—	2	2	no	—
112	#63228	—	2	2	no	—
113	#63228	—	4	1	no	—
114	#63227	—	2	1	no	—
115	#63227	—	2	1	no	—
116	#63227	—	2	1	no	—
117	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
118	#63223	—	2	2	no	—
119	C₂×#3622	—	2	2	no	—
120	C₂×#3622	C₂³	1	1	yes	characteristic
121	C₂×#3622	C₂³	1	1	yes	characteristic
122	C₂×#3622	C₂³	1	1	yes	characteristic
123	C₂×#3622	C₂³	1	1	yes	characteristic
124	C₂³×C₁₇	—	2	1	no	—
125	C₂³×C₁₇	C₂×D₄	1	1	yes	characteristic
126	C₂³×C₁₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₁₇	—	2	1	no	—
128	C₂²×D₁₇	—	2	1	no	—
129	C₂²×D₁₇	—	2	1	no	—
130	C₂²×D₁₇	—	4	2	no	—
131	C₂²×D₁₇	—	4	2	no	—
132	C₂²×D₁₇	—	4	2	no	—
133	C₂²×D₁₇	—	4	2	no	—
134	C₂²×D₁₇	—	8	1	no	—
135	C₂²×D₁₇	—	8	1	no	—
136	Q₈×C₁₇	—	2	1	no	—
137	Q₈×C₁₇	—	2	1	no	—
138	Q₈×C₁₇	—	2	1	no	—
139	Q₈×C₁₇	—	4	2	no	—
140	Q₈×C₁₇	C₂×D₄	1	2	yes	complemented
141	D₄×C₁₇	—	2	2	no	—
142	D₄×C₁₇	—	2	1	no	—
143	D₄×C₁₇	—	2	1	no	—
144	D₄×C₁₇	—	4	2	no	—
145	D₄×C₁₇	—	4	2	no	—
146	C₂×C₄×C₁₇	—	2	1	no	—
147	C₂×C₄×C₁₇	—	2	1	no	—
148	C₂×C₄×C₁₇	—	2	1	no	—
149	C₂×C₄×C₁₇	—	2	1	no	—
150	C₂×C₄×C₁₇	—	2	1	no	—
151	C₂×C₄×C₁₇	—	2	1	no	—
152	C₂×C₄×C₁₇	—	2	1	no	—
153	C₂×C₄×C₁₇	—	4	2	no	—
154	C₂×C₄×C₁₇	—	4	2	no	—
155	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
160	C₂²⋊D₁₇	—	4	2	no	—
161	C₂²⋊D₁₇	—	4	2	no	—
162	C₂×Dic₁₇	—	2	1	no	—
163	D₆₈	—	2	1	no	—
164	D₆₈	—	2	1	no	—
165	D₆₈	—	2	1	no	—
166	D₆₈	—	2	1	no	—
167	D₆₈	—	2	1	no	—
168	D₆₈	—	4	2	no	—
169	D₆₈	—	4	2	no	—
170	D₆₈	—	4	2	no	—
171	D₆₈	—	8	1	no	—
172	D₆₈	C₂×D₄	1	2	yes	—
173	C₄×D₁₇	—	4	2	no	—
174	#3622	—	2	1	no	—
175	#3622	—	2	1	no	—
176	#3622	—	2	1	no	—
177	#3622	C₂×D₄	1	2	yes	complemented
178	#3265	—	17	1	no	maximal, Sylow
179	C₂²×C₁₇	—	2	1	no	—
180	C₂²×C₁₇	—	2	1	no	—
181	C₂²×C₁₇	—	2	1	no	—
182	C₂²×C₁₇	—	2	1	no	—
183	C₂²×C₁₇	—	2	1	no	—
184	C₂²×C₁₇	—	4	1	no	—
185	C₂²×C₁₇	—	4	1	no	—
186	C₂²×C₁₇	—	4	1	no	—
187	C₂²×C₁₇	AGL(1,ℤ/8)	1	2	yes	complemented
188	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×D₁₇	—	2	2	no	—
190	C₂×D₁₇	—	4	1	no	—
191	C₂×D₁₇	—	4	1	no	—
192	C₂×D₁₇	—	4	1	no	—
193	C₂×D₁₇	—	4	1	no	—
194	C₂×D₁₇	—	4	1	no	—
195	C₂×D₁₇	—	4	1	no	—
196	C₂×D₁₇	—	4	1	no	—
197	C₂×D₁₇	—	4	1	no	—
198	C₂×D₁₇	—	8	4	no	—
199	C₂×D₁₇	—	8	4	no	—
200	C₄×C₁₇	—	2	1	no	—
201	C₄×C₁₇	—	2	1	no	—
202	C₄×C₁₇	—	2	2	no	—
203	C₄×C₁₇	—	2	1	no	—
204	C₄×C₁₇	—	2	1	no	—
205	C₄×C₁₇	—	4	1	no	—
206	C₄×C₁₇	—	4	1	no	—
207	C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
208	C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
209	Dic₁₇	—	4	1	no	—
210	C₂×AGL(1,ℤ/8)	—	17	1	no	—
211	C₂²×SD₁₆	—	17	1	no	—
212	#548	D₁₇	1	1	yes	characteristic, complemented
213	D₄²	—	17	1	no	—
214	#496	—	17	1	no	—
215	#468	—	17	1	no	—
216	#466	—	17	1	no	—
217	#463	—	17	1	no	—
218	#460	—	17	1	no	—
219	#450	—	17	1	no	—
220	#449	—	17	1	no	—
221	#448	—	17	1	no	—
222	#447	—	17	1	no	—
223	#440	—	17	1	no	—
224	#435	—	17	1	no	—
225	C₂×C₁₇	—	2	2	no	—
226	C₂×C₁₇	—	4	1	no	—
227	C₂×C₁₇	—	8	1	no	—
228	C₂×C₁₇	D₄²	1	1	yes	characteristic
229	C₂×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂×C₁₇	#577	1	1	yes	characteristic
231	D₁₇	—	4	2	no	—
232	D₁₇	—	8	1	no	—
233	D₁₇	—	8	1	no	—
234	C₂×#41	C₂×D₁₇	1	1	yes	characteristic, complemented
235	C₂²×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
236	C₂²×D₄	—	17	1	no	—
237	C₂²×D₄	—	17	1	no	—
238	C₂²×D₄	—	34	1	no	—
239	AGL(1,ℤ/8)	—	34	4	no	—
240	C₂×SD₁₆	—	17	1	no	—
241	C₂×SD₁₆	—	17	1	no	—
242	C₂×SD₁₆	—	17	1	no	—
243	C₂×SD₁₆	—	17	1	no	—
244	C₂×SD₁₆	—	17	1	no	—
245	C₂×SD₁₆	—	17	1	no	—
246	C₂×SD₁₆	—	34	4	no	—
247	C₂×D₈	—	17	1	no	—
248	C₂×D₈	—	17	1	no	—
249	C₂×D₈	—	17	1	no	—
250	C₂×M₁₆	—	17	1	no	—
251	C₂²×C₈	—	17	1	no	—
252	#127	—	17	1	no	—
253	#124	—	2	1	no	—
254	#124	C₂×D₁₇	1	1	yes	characteristic, complemented
255	C₂²⋊Q₈	—	2	1	no	—
256	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
257	#121	—	2	1	no	—
258	#121	—	17	1	no	—
259	#121	—	17	1	no	—
260	#121	—	34	1	no	—
261	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
262	#120	—	34	1	no	—
263	#120	—	34	1	no	—
264	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	17	1	no	—
267	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
268	#107	—	17	1	no	—
269	C₄⋊C₈	—	17	1	no	—
270	#103	—	17	1	no	—
271	#103	—	17	1	no	—
272	#102	—	17	1	no	—
273	#102	—	17	1	no	—
274	#102	—	17	1	no	—
275	#102	—	17	1	no	—
276	C₂²⋊C₈	—	17	1	no	—
277	C₂²⋊C₈	—	17	1	no	—
278	#97	—	17	1	no	—
279	C₁₇	#3265	1	1	yes	characteristic, complemented, Sylow
280	C₂⁴	—	34	1	no	—
281	C₂⁴	—	34	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
288	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	17	1	no	—
292	C₂×D₄	—	17	1	no	—
293	C₂×D₄	—	17	1	no	—
294	C₂×D₄	—	34	2	no	—
295	C₂×D₄	—	34	2	no	—
296	C₂×D₄	—	34	1	no	—
297	C₂×D₄	—	34	1	no	—
298	C₂×D₄	—	34	1	no	—
299	C₂×D₄	—	34	1	no	—
300	C₂×D₄	—	34	1	no	—
301	C₂×D₄	—	34	1	no	—
302	C₂×D₄	—	68	1	no	—
303	C₂×D₄	—	68	1	no	—
304	C₂×D₄	—	68	4	no	—
305	C₂×D₄	C₂²⋊D₁₇	1	1	yes	characteristic
306	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	34	1	no	—
310	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
311	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
312	SD₁₆	—	17	4	no	—
313	SD₁₆	—	34	2	no	—
314	SD₁₆	—	34	2	no	—
315	SD₁₆	—	34	2	no	—
316	SD₁₆	—	34	2	no	—
317	SD₁₆	—	68	1	no	—
318	D₈	—	34	2	no	—
319	D₈	—	34	2	no	—
320	D₈	—	68	1	no	—
321	M₁₆	—	34	2	no	—
322	C₂×C₈	—	17	1	no	—
323	C₂×C₈	—	17	1	no	—
324	C₂×C₈	—	17	1	no	—
325	C₂×C₈	—	17	1	no	—
326	C₂×C₈	—	34	2	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	17	1	no	—
330	C₄⋊C₄	C₂²⋊D₁₇	1	1	yes	characteristic
331	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	34	1	no	—
337	C₂²⋊C₄	—	34	1	no	—
338	C₂²⋊C₄	—	34	1	no	—
339	C₂²⋊C₄	C₂²⋊D₁₇	1	1	yes	characteristic
340	C₂²⋊C₄	C₂²⋊D₁₇	1	1	yes	characteristic
341	C₄²	—	2	1	no	—
342	C₄²	C₂²×D₁₇	1	1	yes	characteristic
343	C₂³	—	2	1	no	—
344	C₂³	—	34	1	no	—
345	C₂³	—	34	1	no	—
346	C₂³	—	34	1	no	—
347	C₂³	—	68	2	no	—
348	C₂³	—	68	2	no	—
349	C₂³	—	68	2	no	—
350	C₂³	—	68	2	no	—
351	C₂³	—	136	1	no	—
352	C₂³	—	136	1	no	—
353	C₂³	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
354	C₂³	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	4	2	no	—
359	Q₈	D₄×D₁₇	1	2	yes	complemented
360	D₄	—	2	2	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	17	2	no	—
366	D₄	—	34	1	no	—
367	D₄	—	34	1	no	—
368	D₄	—	34	1	no	—
369	D₄	—	34	1	no	—
370	D₄	—	34	1	no	—
371	D₄	—	68	2	no	—
372	D₄	—	68	2	no	—
373	D₄	—	68	2	no	—
374	D₄	—	68	2	no	—
375	D₄	—	68	2	no	—
376	D₄	—	136	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	34	1	no	—
387	C₂×C₄	—	68	2	no	—
388	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
389	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
390	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
393	C₈	—	17	2	no	—
394	C₈	—	34	1	no	—
395	C₈	—	34	1	no	—
396	C₈	—	34	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	34	2	no	—
406	C₂²	—	68	1	no	—
407	C₂²	—	68	1	no	—
408	C₂²	—	68	1	no	—
409	C₂²	—	68	1	no	—
410	C₂²	—	68	1	no	—
411	C₂²	—	68	1	no	—
412	C₂²	—	68	1	no	—
413	C₂²	—	68	1	no	—
414	C₂²	—	136	4	no	—
415	C₂²	—	136	4	no	—
416	C₂²	#10587635	1	2	yes	complemented
417	C₂²	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	68	1	no	—
426	C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
427	C₄	#10587691	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	4	1	no	—
430	C₂	—	8	1	no	—
431	C₂	—	68	2	no	—
432	C₂	—	136	1	no	—
433	C₂	—	136	1	no	—
434	C₂	D₄×C₂²⋊D₁₇	1	1	yes	characteristic
435	C₂	C₂×#10587635	1	1	yes	characteristic
436	C₂	#11763617	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₇
commutator, cosocle	C₂×C₄×C₁₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₇
Fitting	C₁₇×#548	C₂
socle	C₂²×C₁₇	C₂²×D₄
hypercenter	#548	D₁₇
hypocenter	C₁₇	#3265
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #548

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#10587635	C₂	semidirect
2. C₂²×#63230	C₂	semidirect
3. D₄×D₆₈	C₂	semidirect
4. #11763199	C₂	semidirect
5. #11763057	C₂	semidirect
6. #11763043	C₂	semidirect
7. #11763021	C₂	semidirect
8. #11763009	C₂	semidirect
9. #11762959	C₂	semidirect
10. #11762954	C₂	semidirect
11. #11762948	C₂	semidirect
12. #11762942	C₂	semidirect
13. #11762907	C₂	semidirect
14. #11762881	C₂	semidirect
15. C₁₇×#548	C₂	semidirect
16. C₂×#41×C₁₇	C₂²	semidirect
17. C₂²×Q₈×C₁₇	C₂²	semidirect
22. C₁₇×#124	C₂²	semidirect
24. C₁₇×C₂²⋊Q₈	C₂²	semidirect
26. C₁₇×#121	C₂²	semidirect
27. C₄×Q₈×C₁₇	C₂²	semidirect
34. C₂×#63230	C₂²	semidirect
35. C₂×#63230	C₂²	semidirect
36. C₂×#63230	C₂²	semidirect
37. C₂×#63230	C₂²	semidirect
39. C₂×#63228	C₂²	semidirect
40. C₂×#63228	C₂²	semidirect
43. C₂×#63223	C₂²	semidirect
44. C₂²×#3622	C₂²	semidirect
50. #10587506	C₂²	semidirect
51. #10587506	C₂²	semidirect
52. #10587503	C₂²	semidirect
53. C₂²⋊#3622	C₂²	semidirect
54. C₂²⋊#3622	C₂²	semidirect
56. #10587480	C₂²	semidirect
57. #10587480	C₂²	semidirect
58. #10587478	C₂²	semidirect
59. C₄⋊#3622	C₂²	semidirect
60. #10587474	C₂²	semidirect
110. #63230	D₄	semidirect
140. Q₈×C₁₇	C₂×D₄	semidirect
177. #3622	C₂×D₄	semidirect
187. C₂²×C₁₇	AGL(1,ℤ/8)	semidirect
212. #548	D₁₇	semidirect
234. C₂×#41	C₂×D₁₇	semidirect
235. C₂²×Q₈	C₂×D₁₇	semidirect
254. #124	C₂×D₁₇	semidirect
256. C₂²⋊Q₈	C₂×D₁₇	semidirect
261. #121	C₂×D₁₇	semidirect
264. C₄×Q₈	C₂×D₁₇	semidirect
279. C₁₇	#3265	semidirect
359. Q₈	D₄×D₁₇	semidirect
416. C₂²	#10587635	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587635	2
C₂²×#63230	2
D₄×D₆₈	2
#11763199	2
#11763057	2
#11763043	2
#11763021	2
#11763009	2
#11762959	2
#11762954	2
#11762948	2
#11762942	2
#11762907	2
#11762881	2
C₁₇×#548	2
#3265	17