Subgroups — #34026995

Order 18688.

1018 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989626	C₂	1	2	yes	maximal
2	Q₈×C₄⋊#64408	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₄⋊#64408	C₂	1	1	yes	maximal, characteristic
4	#22626037	C₂	1	2	yes	maximal, complemented
5	#22625895	C₂	1	2	yes	maximal, complemented
6	#22625894	C₂	1	2	yes	maximal
7	#22625867	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625800	C₂	1	1	yes	maximal, characteristic, complemented
9	#22625799	C₂	1	1	yes	maximal, characteristic
10	#22625725	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×SD₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×#64408	C₂²	1	2	yes	—
13	C₂×D₄×#64408	C₂²	1	2	yes	—
14	C₂²×C₄⋊#64408	—	2	1	no	—
15	#17989626	—	2	8	no	—
16	C₂×#14556660	C₂²	1	2	yes	—
17	C₂×#14556660	C₂²	1	2	yes	—
18	#17989588	C₂²	1	1	yes	characteristic
19	C₂×#14556654	C₂²	1	2	yes	—
20	C₂×#14556653	C₂²	1	2	yes	—
21	C₂×#14556645	C₂²	1	2	yes	—
22	#17989538	—	2	2	no	—
23	#17989538	C₂²	1	2	yes	—
24	#17989538	C₂²	1	2	yes	—
25	#17989534	—	2	2	no	—
26	#17989533	—	2	1	no	—
27	#17989533	C₂²	1	1	yes	characteristic
28	#17989533	C₂²	1	1	yes	characteristic
29	#17989529	—	2	1	no	—
30	C₄×C₄⋊#64408	—	2	1	no	—
31	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
32	#17989460	C₂²	1	2	yes	—
33	#17989460	C₂²	1	2	yes	—
34	#17989452	C₂²	1	2	yes	—
35	C₂×SD₁₆×D₇₃	C₂²	1	1	yes	characteristic
36	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
38	#17988678	C₄	1	1	yes	characteristic, complemented
39	C₄×#11924017	C₄	1	1	yes	characteristic, complemented
40	SD₁₆×Dic₇₃	C₄	1	1	yes	characteristic, complemented
41	C₄×#11924015	C₄	1	1	yes	characteristic, complemented
42	#17988674	C₄	1	1	yes	characteristic, complemented
43	C₄×#11924016	C₄	1	1	yes	characteristic, complemented
44	#17988672	C₄	1	1	yes	characteristic, complemented
45	#106×D₇₃	C₂²	1	1	yes	characteristic
46	#103×D₇₃	C₂²	1	1	yes	characteristic
47	#102×D₇₃	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
49	C₄×SD₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
50	C₂³×#64408	—	2	2	no	—
51	C₂×#11924036	C₂³	1	2	yes	—
52	Q₈×#64408	—	2	4	no	—
53	Q₈×#64408	—	4	2	no	—
54	D₄×#64408	—	2	4	no	—
55	D₄×#64408	—	4	2	no	—
56	C₂×C₄⋊#64408	—	2	2	no	—
57	C₂×C₄⋊#64408	—	2	2	no	—
58	C₂×C₄⋊#64408	—	2	2	no	—
59	C₂×C₄⋊#64408	—	2	1	no	—
60	C₂×C₄⋊#64408	—	2	1	no	—
61	C₂×C₄⋊#64408	—	2	1	no	—
62	C₂×C₄⋊#64408	—	2	1	no	—
63	C₂×C₄⋊#64408	—	4	4	no	—
64	C₂×C₄⋊#64408	D₄	1	1	yes	characteristic
65	C₂×C₄⋊#64408	D₄	1	1	yes	characteristic
66	C₂×C₄⋊#64408	C₂³	1	2	yes	—
67	C₂×C₄⋊#64408	C₂³	1	2	yes	—
68	C₂×C₂²⋊#64408	—	2	2	no	—
69	C₂×C₄×#64408	—	2	2	no	—
70	C₂×C₄×#64408	C₂³	1	2	yes	—
71	#14556660	—	2	4	no	—
72	#14556660	—	4	2	no	—
73	#14556658	—	2	1	no	—
74	C₄⋊#10596833	—	2	1	no	—
75	#14556654	—	2	4	no	—
76	#14556653	—	2	4	no	—
77	#14556645	—	2	4	no	—
78	(C₂×#64408)⋊C₄	—	2	2	no	—
79	(C₂×#64408)⋊C₄	—	2	2	no	—
80	(C₂×#64408)⋊C₄	D₄	1	2	yes	—
81	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
82	C₂×D₄×D₇₃	C₂³	1	1	yes	characteristic
83	C₂²×C₄×D₇₃	—	2	1	no	—
84	C₂×#11924017	C₂×C₄	1	1	yes	characteristic
85	C₂×#11924016	C₂×C₄	1	1	yes	characteristic
86	C₂×#11924015	C₂×C₄	1	1	yes	characteristic
87	SD₁₆×D₇₃	D₄	1	4	yes	—
88	SD₁₆×D₇₃	Q₈	1	4	yes	—
89	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
90	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
91	Q₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
92	C₄×Dic₁₄₆	—	2	1	no	—
93	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic, complemented
94	#14556556	—	2	1	no	—
95	#14556556	C₂×C₄	1	1	yes	characteristic, complemented
96	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
97	D₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
98	#14556553	C₂×C₄	1	1	yes	characteristic
99	C₄×C₂²⋊D₇₃	—	2	1	no	—
100	#14556551	—	2	1	no	—
101	C₄⋊C₄×D₇₃	—	2	1	no	—
102	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
103	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
104	C₂²⋊C₄×D₇₃	—	2	1	no	—
105	C₄²×D₇₃	—	2	1	no	—
106	C₄²×D₇₃	C₂³	1	1	yes	characteristic
107	#14556523	C₂×C₄	1	1	yes	characteristic, complemented
108	#14556522	C₂×C₄	1	1	yes	characteristic, complemented
109	#14556522	C₂×C₄	1	1	yes	characteristic, complemented
110	#14556516	C₂×C₄	1	1	yes	characteristic, complemented
111	#14556515	C₂×C₄	1	1	yes	characteristic, complemented
112	#14556514	C₂×C₄	1	1	yes	characteristic, complemented
113	#14556513	C₂×C₄	1	1	yes	characteristic
114	#14556512	C₂×C₄	1	1	yes	characteristic
115	#14556511	C₂×C₄	1	1	yes	characteristic
116	C₄×#10596831	C₂×C₄	1	1	yes	characteristic, complemented
117	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
118	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
119	C₂×SD₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
120	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
121	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
122	#106×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
123	#103×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
124	#102×C₇₃	C₂×C₄	1	1	yes	characteristic
125	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂²×#64408	—	2	2	no	—
127	C₂²×#64408	—	2	2	no	—
128	C₂²×#64408	—	4	4	no	—
129	C₂²×#64408	—	4	4	no	—
130	C₂²×#64408	—	8	2	no	—
131	C₂²×#64408	C₂×D₄	1	2	yes	—
132	C₂²×#64408	C₂×D₄	1	2	yes	—
133	#11924036	—	2	2	no	—
134	#11924036	—	2	2	no	—
135	C₂×#10596833	—	2	2	no	—
136	C₄⋊#64408	—	2	2	no	—
137	C₄⋊#64408	—	2	2	no	—
138	C₄⋊#64408	—	2	2	no	—
139	C₄⋊#64408	—	2	2	no	—
140	C₄⋊#64408	—	2	2	no	—
141	C₄⋊#64408	—	2	2	no	—
142	C₄⋊#64408	—	4	4	no	—
143	C₄⋊#64408	—	4	4	no	—
144	C₄⋊#64408	—	4	2	no	—
145	C₄⋊#64408	—	4	2	no	—
146	C₄⋊#64408	—	8	1	no	—
147	C₄⋊#64408	—	8	1	no	—
148	C₄⋊#64408	—	8	2	no	—
149	C₂²⋊#64408	—	4	4	no	—
150	C₄×#64408	—	2	2	no	—
151	C₄×#64408	—	2	2	no	—
152	C₄×#64408	—	4	4	no	—
153	C₂³×D₇₃	—	2	1	no	—
154	C₂×Dic₁₄₆	—	2	1	no	—
155	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
156	Q₈×D₇₃	—	2	1	no	—
157	Q₈×D₇₃	—	2	1	no	—
158	Q₈×D₇₃	C₂×D₄	1	2	yes	—
159	Q₈×D₇₃	C₂×Q₈	1	2	yes	—
160	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₂²⋊D₇₃	—	2	1	no	—
162	D₄×D₇₃	—	2	1	no	—
163	D₄×D₇₃	—	2	1	no	—
164	D₄×D₇₃	C₂×D₄	1	2	yes	—
165	D₄×D₇₃	C₂×Q₈	1	2	yes	—
166	C₂²×Dic₇₃	—	2	1	no	—
167	C₂×C₄×D₇₃	—	2	1	no	—
168	C₂×C₄×D₇₃	—	2	1	no	—
169	C₂×C₄×D₇₃	—	2	1	no	—
170	C₂×C₄×D₇₃	—	2	1	no	—
171	C₂×C₄×D₇₃	—	2	1	no	—
172	C₂×C₄×D₇₃	—	4	2	no	—
173	C₂×C₄×D₇₃	—	4	2	no	—
174	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
177	#11924017	C₄⋊C₄	1	4	yes	complemented
178	#11924016	C₄⋊C₄	1	4	yes	complemented
179	#11924015	C₄⋊C₄	1	4	yes	complemented
180	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
181	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
182	C₈×D₇₃	—	2	1	no	—
183	C₈×D₇₃	—	2	1	no	—
184	C₈×D₇₃	C₂×D₄	1	2	yes	—
185	C₈×D₇₃	C₂×Q₈	1	2	yes	—
186	C₄⋊Dic₇₃	—	2	1	no	—
187	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
188	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
189	#11924007	—	2	1	no	—
190	#11924007	—	2	1	no	—
191	#11924007	—	2	1	no	—
192	#11924007	—	2	1	no	—
193	C₂²⋊Dic₇₃	—	2	1	no	—
194	#11924005	—	2	1	no	—
195	#11924005	—	2	1	no	—
196	C₄×Dic₇₃	—	2	1	no	—
197	C₄×Dic₇₃	—	2	1	no	—
198	C₄×Dic₇₃	—	2	1	no	—
199	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₇₃	#41	1	1	yes	characteristic
201	C₄×Dic₇₃	#41	1	1	yes	characteristic
202	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₇₃	—	2	1	no	—
205	SD₁₆×C₇₃	C₄⋊C₄	1	4	yes	complemented
206	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊C₄×C₇₃	—	2	1	no	—
209	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
211	C₂²⋊C₄×C₇₃	—	2	1	no	—
212	C₄²×C₇₃	—	2	1	no	—
213	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
214	C₂³×C₇₃	—	2	1	no	—
215	C₂²×D₇₃	—	2	1	no	—
216	C₂²×D₇₃	—	2	2	no	—
217	C₂²×D₇₃	—	2	2	no	—
218	C₂²×D₇₃	—	4	1	no	—
219	C₂²×D₇₃	—	4	1	no	—
220	C₂²×D₇₃	—	4	1	no	—
221	C₂²×D₇₃	—	4	1	no	—
222	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×#64408	—	2	2	no	—
224	C₂×#64408	—	2	2	no	—
225	C₂×#64408	—	2	2	no	—
226	C₂×#64408	—	2	2	no	—
227	C₂×#64408	—	2	2	no	—
228	C₂×#64408	—	2	2	no	—
229	C₂×#64408	—	4	2	no	—
230	C₂×#64408	—	4	2	no	—
231	C₂×#64408	—	4	2	no	—
232	C₂×#64408	—	4	2	no	—
233	C₂×#64408	—	4	2	no	—
234	C₂×#64408	—	4	2	no	—
235	C₂×#64408	—	8	8	no	—
236	Q₈×C₇₃	—	2	1	no	—
237	Q₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	complemented
238	D₄×C₇₃	—	2	1	no	—
239	D₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
240	C₂×C₄×C₇₃	—	2	1	no	—
241	C₂×C₄×C₇₃	—	2	1	no	—
242	C₂×C₄×C₇₃	—	2	1	no	—
243	C₂×C₄×C₇₃	—	4	2	no	—
244	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
247	C₂²⋊D₇₃	—	2	2	no	—
248	C₂²⋊D₇₃	—	2	2	no	—
249	C₂×Dic₇₃	—	2	1	no	—
250	C₂×Dic₇₃	—	2	1	no	—
251	C₂×Dic₇₃	—	2	1	no	—
252	C₂×Dic₇₃	—	4	2	no	—
253	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
254	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
255	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
256	D₂₉₂	—	2	1	no	—
257	D₂₉₂	C₂×C₄⋊C₄	1	2	yes	—
258	C₄×D₇₃	—	2	2	no	—
259	C₄×D₇₃	—	2	2	no	—
260	C₄×D₇₃	—	2	1	no	—
261	C₄×D₇₃	—	2	1	no	—
262	C₄×D₇₃	—	4	1	no	—
263	C₄×D₇₃	—	4	1	no	—
264	C₄×D₇₃	—	4	1	no	—
265	C₄×D₇₃	—	4	1	no	—
266	C₄×D₇₃	—	4	2	no	—
267	C₄×D₇₃	—	4	2	no	—
268	C₄×D₇₃	AGL(1,ℤ/8)	1	2	yes	—
269	C₄×D₇₃	#137	1	2	yes	—
270	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
271	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
272	C₄×D₇₃	H(5,𝔽₂)	1	1	yes	characteristic
273	C₄×D₇₃	2₋¹⁺⁴	1	1	yes	characteristic
274	Dic₁₄₆	—	2	1	no	—
275	Dic₁₄₆	—	2	2	no	—
276	Dic₁₄₆	—	2	2	no	—
277	Dic₁₄₆	C₂×C₄⋊C₄	1	2	yes	complemented
278	#10596833	—	4	2	no	—
279	C₈×C₇₃	—	2	1	no	—
280	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	complemented
281	#10596831	—	2	1	no	—
282	#10596831	C₂×C₄⋊C₄	1	2	yes	complemented
283	C₂²×C₇₃	—	2	2	no	—
284	C₂²×C₇₃	—	4	1	no	—
285	C₂²×C₇₃	—	4	1	no	—
286	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂×D₇₃	—	2	2	no	—
288	C₂×D₇₃	—	4	1	no	—
289	C₂×D₇₃	—	4	1	no	—
290	C₂×D₇₃	—	4	2	no	—
291	C₂×D₇₃	—	4	2	no	—
292	C₂×D₇₃	—	4	2	no	—
293	C₂×D₇₃	—	4	2	no	—
294	C₂×D₇₃	D₄²	1	1	yes	characteristic
295	C₂×D₇₃	D₄×Q₈	1	1	yes	characteristic
296	C₂×D₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₂×D₇₃	C₂×#137	1	1	yes	characteristic
298	C₂×D₇₃	#576	1	1	yes	characteristic
299	C₂×D₇₃	#578	1	1	yes	characteristic
300	#64408	—	4	2	no	—
301	#64408	—	4	2	no	—
302	#64408	—	8	2	no	—
303	#64408	—	8	2	no	—
304	C₄×C₇₃	—	2	2	no	—
305	C₄×C₇₃	—	2	1	no	—
306	C₄×C₇₃	—	4	1	no	—
307	C₄×C₇₃	—	4	1	no	—
308	C₄×C₇₃	#440	1	2	yes	complemented
309	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
310	C₄×C₇₃	#520	1	1	yes	characteristic
311	Dic₇₃	—	2	2	no	—
312	Dic₇₃	—	2	1	no	—
313	Dic₇₃	—	4	1	no	—
314	Dic₇₃	—	4	1	no	—
315	Dic₇₃	#440	1	2	yes	complemented
316	Dic₇₃	#547	1	1	yes	characteristic
317	Dic₇₃	#554	1	1	yes	characteristic
318	#22671	—	73	1	no	maximal, Sylow
319	C₂×C₇₃	—	4	2	no	—
320	C₂×C₇₃	D₄×C₄⋊C₄	1	1	yes	characteristic
321	C₂×C₇₃	C₂×#440	1	1	yes	characteristic
322	C₂×C₇₃	#2951	1	1	yes	characteristic
323	D₇₃	—	4	2	no	—
324	D₇₃	#3274	1	1	yes	characteristic
325	D₇₃	#3276	1	1	yes	characteristic
326	D₇₃	#3385	1	1	yes	characteristic
327	D₇₃	#3386	1	1	yes	characteristic
328	C₂×#440	—	73	2	no	—
329	C₂×C₄×SD₁₆	—	73	1	no	—
330	Q₈×C₄⋊C₄	—	73	1	no	—
331	D₄×C₄⋊C₄	—	73	1	no	—
332	#1944	—	73	2	no	—
333	#1863	—	73	2	no	—
334	#1862	—	73	2	no	—
335	#1845	—	73	1	no	—
336	#1803	—	73	1	no	—
337	#1802	—	73	1	no	—
338	#1770	—	73	1	no	—
339	C₇₃	#22671	1	1	yes	characteristic, complemented, Sylow
340	C₂²×SD₁₆	—	73	1	no	—
341	C₂×C₄×Q₈	—	73	2	no	—
342	C₂×C₄×Q₈	—	73	1	no	—
343	C₂×C₄×D₄	—	73	2	no	—
344	C₂×C₄×D₄	—	73	1	no	—
345	C₂²×C₄⋊C₄	—	146	1	no	—
346	#440	—	146	8	no	—
347	C₄×SD₁₆	—	73	1	no	—
348	C₄×SD₁₆	—	73	1	no	—
349	C₄×SD₁₆	—	73	1	no	—
350	C₄×SD₁₆	—	73	1	no	—
351	C₄×SD₁₆	—	73	1	no	—
352	C₄×SD₁₆	—	73	1	no	—
353	C₄×SD₁₆	—	73	1	no	—
354	C₄×SD₁₆	#64408	1	1	yes	characteristic, complemented
355	C₂×#107	—	73	2	no	—
356	C₂×#107	—	73	2	no	—
357	C₂×#106	—	73	1	no	—
358	C₂×C₄⋊C₈	—	73	1	no	—
359	C₂×#103	—	73	1	no	—
360	C₂×#103	—	73	2	no	—
361	C₂×#102	—	73	1	no	—
362	C₂×#102	—	73	2	no	—
363	C₂×#97	—	73	2	no	—
364	C₂×C₄×C₈	—	73	1	no	—
365	#389	—	73	2	no	—
366	#389	—	73	2	no	—
367	#389	—	146	2	no	—
368	#385	—	146	2	no	—
369	#384	—	73	1	no	—
370	#384	—	73	1	no	—
371	#384	—	146	1	no	—
372	#380	—	146	1	no	—
373	C₄×C₄⋊C₄	—	73	1	no	—
374	C₄×C₄⋊C₄	—	146	1	no	—
375	#340	—	73	2	no	—
376	#340	—	73	2	no	—
377	#336	—	73	2	no	—
378	C₂²×Q₈	—	73	1	no	—
379	C₂²×D₄	—	73	1	no	—
380	C₂³×C₄	—	146	1	no	—
381	C₂³×C₄	—	146	2	no	—
382	C₂×SD₁₆	—	73	1	no	—
383	C₂×SD₁₆	—	73	1	no	—
384	C₂×SD₁₆	—	73	4	no	—
385	C₂×SD₁₆	—	73	4	no	—
386	C₂×SD₁₆	—	73	1	no	—
387	C₂×SD₁₆	C₂×#64408	1	1	yes	characteristic
388	C₂²×C₈	—	73	1	no	—
389	C₂²×C₈	—	73	1	no	—
390	C₂²×C₈	—	73	2	no	—
391	C₄×Q₈	—	292	2	no	—
392	C₄×Q₈	—	73	1	no	—
393	C₄×Q₈	—	73	1	no	—
394	C₄×Q₈	—	73	1	no	—
395	C₄×Q₈	—	146	1	no	—
396	C₄×Q₈	—	146	4	no	—
397	C₄×Q₈	—	146	1	no	—
398	C₄×Q₈	C₂×#64408	1	1	yes	characteristic, complemented
399	C₄×D₄	—	292	2	no	—
400	C₄×D₄	—	73	1	no	—
401	C₄×D₄	—	73	1	no	—
402	C₄×D₄	—	73	1	no	—
403	C₄×D₄	—	146	1	no	—
404	C₄×D₄	—	146	1	no	—
405	C₄×D₄	—	146	4	no	—
406	C₄×D₄	C₂×#64408	1	1	yes	characteristic
407	C₂×C₄⋊C₄	—	292	4	no	—
408	C₂×C₄⋊C₄	—	73	1	no	—
409	C₂×C₄⋊C₄	—	73	1	no	—
410	C₂×C₄⋊C₄	—	73	1	no	—
411	C₂×C₄⋊C₄	—	73	1	no	—
412	C₂×C₄⋊C₄	—	73	2	no	—
413	C₂×C₄⋊C₄	—	73	2	no	—
414	C₂×C₄⋊C₄	—	146	1	no	—
415	C₂×C₄⋊C₄	—	146	1	no	—
416	C₂×C₄⋊C₄	—	146	2	no	—
417	C₂×C₄⋊C₄	—	146	2	no	—
418	C₂×C₄⋊C₄	—	146	1	no	—
419	C₂×C₄⋊C₄	—	146	1	no	—
420	C₂×C₄⋊C₄	—	146	1	no	—
421	C₂×C₄⋊C₄	—	146	2	no	—
422	C₂×C₂²⋊C₄	—	146	1	no	—
423	C₂×C₂²⋊C₄	—	146	2	no	—
424	C₂×C₄²	—	73	1	no	—
425	C₂×C₄²	—	73	2	no	—
426	C₂×C₄²	—	146	1	no	—
427	C₂×C₄²	—	146	2	no	—
428	#107	—	292	2	no	—
429	#107	—	146	4	no	—
430	#106	—	73	1	no	—
431	#106	—	73	1	no	—
432	#106	—	73	1	no	—
433	#106	C₂×#64408	1	1	yes	characteristic, complemented
434	C₄⋊C₈	—	146	1	no	—
435	C₄⋊C₈	—	146	1	no	—
436	#103	—	73	1	no	—
437	#103	—	73	1	no	—
438	#103	—	73	1	no	—
439	#103	—	146	4	no	—
440	#103	C₂×#64408	1	1	yes	characteristic, complemented
441	#102	—	73	1	no	—
442	#102	—	73	1	no	—
443	#102	—	73	1	no	—
444	#102	—	146	4	no	—
445	#102	C₂×#64408	1	1	yes	characteristic
446	#97	—	146	4	no	—
447	C₄×C₈	—	73	1	no	—
448	C₄×C₈	—	73	1	no	—
449	C₄×C₈	—	73	1	no	—
450	C₄×C₈	C₂×#64408	1	1	yes	characteristic, complemented
451	#95	—	73	2	no	—
452	#95	—	146	2	no	—
453	#95	—	146	2	no	—
454	C₂⁴	—	146	1	no	—
455	C₂×Q₈	—	73	2	no	—
456	C₂×Q₈	—	73	2	no	—
457	C₂×Q₈	—	73	1	no	—
458	C₂×Q₈	—	146	1	no	—
459	C₂×Q₈	—	146	1	no	—
460	C₂×Q₈	—	146	1	no	—
461	C₂×Q₈	C₂²×#64408	1	1	yes	characteristic
462	C₂×D₄	—	73	2	no	—
463	C₂×D₄	—	73	2	no	—
464	C₂×D₄	—	73	1	no	—
465	C₂×D₄	—	146	1	no	—
466	C₂×D₄	—	146	1	no	—
467	C₂×D₄	—	146	1	no	—
468	C₂×D₄	C₂²×#64408	1	1	yes	characteristic
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	292	2	no	—
471	C₂²×C₄	—	292	2	no	—
472	C₂²×C₄	—	292	4	no	—
473	C₂²×C₄	—	292	4	no	—
474	C₂²×C₄	—	584	2	no	—
475	C₂²×C₄	—	73	1	no	—
476	C₂²×C₄	—	73	1	no	—
477	C₂²×C₄	—	73	1	no	—
478	C₂²×C₄	—	73	2	no	—
479	C₂²×C₄	—	73	2	no	—
480	C₂²×C₄	—	146	1	no	—
481	C₂²×C₄	—	146	1	no	—
482	C₂²×C₄	—	146	1	no	—
483	C₂²×C₄	—	146	1	no	—
484	C₂²×C₄	—	146	2	no	—
485	C₂²×C₄	—	146	2	no	—
486	C₂²×C₄	—	146	1	no	—
487	C₂²×C₄	—	146	1	no	—
488	SD₁₆	—	73	4	no	—
489	SD₁₆	—	73	4	no	—
490	SD₁₆	—	73	4	no	—
491	SD₁₆	C₄⋊#64408	1	4	yes	complemented
492	C₂×C₈	—	73	1	no	—
493	C₂×C₈	—	73	2	no	—
494	C₂×C₈	—	73	2	no	—
495	C₂×C₈	—	73	1	no	—
496	C₂×C₈	—	146	1	no	—
497	C₂×C₈	—	146	1	no	—
498	C₂×C₈	—	146	2	no	—
499	C₂×C₈	—	146	2	no	—
500	C₂×C₈	—	146	2	no	—
501	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
502	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	292	2	no	—
505	C₄⋊C₄	—	292	2	no	—
506	C₄⋊C₄	—	292	4	no	—
507	C₄⋊C₄	—	292	4	no	—
508	C₄⋊C₄	—	584	2	no	—
509	C₄⋊C₄	—	584	1	no	—
510	C₄⋊C₄	—	584	1	no	—
511	C₄⋊C₄	—	73	1	no	—
512	C₄⋊C₄	—	73	1	no	—
513	C₄⋊C₄	—	146	1	no	—
514	C₄⋊C₄	—	146	1	no	—
515	C₄⋊C₄	—	146	1	no	—
516	C₄⋊C₄	—	146	1	no	—
517	C₄⋊C₄	—	146	2	no	—
518	C₄⋊C₄	—	146	2	no	—
519	C₄⋊C₄	—	146	2	no	—
520	C₄⋊C₄	—	146	2	no	—
521	C₄⋊C₄	—	146	2	no	—
522	C₄⋊C₄	—	146	2	no	—
523	C₄⋊C₄	—	146	1	no	—
524	C₄⋊C₄	C₂²×#64408	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×#64408	1	1	yes	characteristic
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	292	4	no	—
528	C₂²⋊C₄	—	146	1	no	—
529	C₂²⋊C₄	—	146	1	no	—
530	C₂²⋊C₄	—	146	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	292	4	no	—
533	C₄²	—	73	1	no	—
534	C₄²	—	73	1	no	—
535	C₄²	—	73	1	no	—
536	C₄²	—	146	1	no	—
537	C₄²	—	146	1	no	—
538	C₄²	—	146	2	no	—
539	C₄²	—	146	2	no	—
540	C₄²	—	146	1	no	—
541	C₄²	C₂²×#64408	1	1	yes	characteristic
542	C₂³	—	2	1	no	—
543	C₂³	—	292	1	no	—
544	C₂³	—	292	1	no	—
545	C₂³	—	292	1	no	—
546	C₂³	—	292	1	no	—
547	C₂³	—	73	1	no	—
548	C₂³	—	146	2	no	—
549	C₂³	—	146	2	no	—
550	C₂³	—	146	1	no	—
551	Q₈	—	2	1	no	—
552	Q₈	—	73	2	no	—
553	Q₈	—	146	2	no	—
554	Q₈	—	146	2	no	—
555	Q₈	—	146	1	no	—
556	Q₈	C₂×C₄⋊#64408	1	2	yes	complemented
557	D₄	—	2	1	no	—
558	D₄	—	73	2	no	—
559	D₄	—	146	2	no	—
560	D₄	—	146	2	no	—
561	D₄	—	146	1	no	—
562	D₄	C₂×C₄⋊#64408	1	2	yes	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	292	1	no	—
568	C₂×C₄	—	292	1	no	—
569	C₂×C₄	—	292	1	no	—
570	C₂×C₄	—	292	1	no	—
571	C₂×C₄	—	292	2	no	—
572	C₂×C₄	—	292	2	no	—
573	C₂×C₄	—	292	2	no	—
574	C₂×C₄	—	292	2	no	—
575	C₂×C₄	—	292	2	no	—
576	C₂×C₄	—	292	2	no	—
577	C₂×C₄	—	292	2	no	—
578	C₂×C₄	—	292	2	no	—
579	C₂×C₄	—	292	2	no	—
580	C₂×C₄	—	584	8	no	—
581	C₂×C₄	—	73	1	no	—
582	C₂×C₄	—	73	1	no	—
583	C₂×C₄	—	73	1	no	—
584	C₂×C₄	—	73	1	no	—
585	C₂×C₄	—	73	1	no	—
586	C₂×C₄	—	73	1	no	—
587	C₂×C₄	—	73	2	no	—
588	C₂×C₄	—	73	2	no	—
589	C₂×C₄	—	73	1	no	—
590	C₂×C₄	—	146	2	no	—
591	C₂×C₄	—	146	1	no	—
592	C₂×C₄	—	146	1	no	—
593	C₂×C₄	—	146	2	no	—
594	C₂×C₄	—	146	2	no	—
595	C₂×C₄	—	146	2	no	—
596	C₂×C₄	—	146	2	no	—
597	C₂×C₄	—	146	2	no	—
598	C₂×C₄	—	146	2	no	—
599	C₂×C₄	—	146	2	no	—
600	C₂×C₄	—	146	1	no	—
601	C₂×C₄	—	146	1	no	—
602	C₂×C₄	—	146	1	no	—
603	C₂×C₄	D₄×#64408	1	1	yes	characteristic
604	C₂×C₄	D₄×#64408	1	1	yes	characteristic
605	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
606	C₈	—	2	1	no	—
607	C₈	—	292	2	no	—
608	C₈	—	73	2	no	—
609	C₈	—	146	1	no	—
610	C₈	C₂×C₄⋊#64408	1	2	yes	complemented
611	C₂²	—	2	2	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	292	2	no	—
615	C₂²	—	292	2	no	—
616	C₂²	—	292	2	no	—
617	C₂²	—	292	2	no	—
618	C₂²	—	292	1	no	—
619	C₂²	—	292	1	no	—
620	C₂²	—	73	1	no	—
621	C₂²	—	73	1	no	—
622	C₂²	—	73	1	no	—
623	C₂²	—	73	1	no	—
624	C₂²	—	73	1	no	—
625	C₂²	—	73	1	no	—
626	C₂²	—	146	2	no	—
627	C₂²	C₂×D₄×#64408	1	1	yes	characteristic
628	C₄	—	2	1	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	292	2	no	—
633	C₄	—	292	2	no	—
634	C₄	—	292	1	no	—
635	C₄	—	292	1	no	—
636	C₄	—	584	2	no	—
637	C₄	—	584	2	no	—
638	C₄	—	73	2	no	—
639	C₄	—	73	1	no	—
640	C₄	—	73	1	no	—
641	C₄	—	146	1	no	—
642	C₄	—	146	2	no	—
643	C₄	#17989626	1	2	yes	complemented
644	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
645	C₄	#17989656	1	1	yes	characteristic
646	C₂	—	4	2	no	—
647	C₂	—	292	2	no	—
648	C₂	—	73	1	no	—
649	C₂	—	73	1	no	—
650	C₂	—	73	1	no	—
651	C₂	—	73	1	no	—
652	C₂	D₄×C₄⋊#64408	1	1	yes	characteristic
653	C₂	C₂×#17989626	1	1	yes	characteristic
654	C₂	#22626693	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₄×SD₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×D₄×D₇₃	C₂³
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₄×SD₁₆	#64408
hypocenter	C₇₃	#22671
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×C₄⋊#64408	C₂	semidirect
4. #22626037	C₂	semidirect
5. #22625895	C₂	semidirect
7. #22625867	C₂	semidirect
8. #22625800	C₂	semidirect
10. #22625725	C₂	semidirect
38. #17988678	C₄	semidirect
39. C₄×#11924017	C₄	semidirect
40. SD₁₆×Dic₇₃	C₄	semidirect
41. C₄×#11924015	C₄	semidirect
42. #17988674	C₄	semidirect
43. C₄×#11924016	C₄	semidirect
44. #17988672	C₄	semidirect
49. C₄×SD₁₆×C₇₃	C₄	semidirect
91. Q₈×Dic₇₃	C₂×C₄	semidirect
93. C₄×Dic₁₄₆	C₂×C₄	semidirect
95. #14556556	C₂×C₄	semidirect
107. #14556523	C₂×C₄	semidirect
108. #14556522	C₂×C₄	semidirect
109. #14556522	C₂×C₄	semidirect
110. #14556516	C₂×C₄	semidirect
111. #14556515	C₂×C₄	semidirect
112. #14556514	C₂×C₄	semidirect
116. C₄×#10596831	C₂×C₄	semidirect
117. C₈×Dic₇₃	C₂×C₄	semidirect
118. C₈×Dic₇₃	C₂×C₄	semidirect
120. C₄×Q₈×C₇₃	C₂×C₄	semidirect
122. #106×C₇₃	C₂×C₄	semidirect
123. #103×C₇₃	C₂×C₄	semidirect
125. C₄×C₈×C₇₃	C₂×C₄	semidirect
177. #11924017	C₄⋊C₄	semidirect
178. #11924016	C₄⋊C₄	semidirect
179. #11924015	C₄⋊C₄	semidirect
205. SD₁₆×C₇₃	C₄⋊C₄	semidirect
237. Q₈×C₇₃	C₂×C₄⋊C₄	semidirect
277. Dic₁₄₆	C₂×C₄⋊C₄	semidirect
280. C₈×C₇₃	C₂×C₄⋊C₄	semidirect
282. #10596831	C₂×C₄⋊C₄	semidirect
308. C₄×C₇₃	#440	semidirect
315. Dic₇₃	#440	semidirect
339. C₇₃	#22671	semidirect
354. C₄×SD₁₆	#64408	semidirect
398. C₄×Q₈	C₂×#64408	semidirect
433. #106	C₂×#64408	semidirect
440. #103	C₂×#64408	semidirect
450. C₄×C₈	C₂×#64408	semidirect
491. SD₁₆	C₄⋊#64408	semidirect
556. Q₈	C₂×C₄⋊#64408	semidirect
610. C₈	C₂×C₄⋊#64408	semidirect
643. C₄	#17989626	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989626	2
Q₈×C₄⋊#64408	2
D₄×C₄⋊#64408	2
#22626037	2
#22625895	2
#22625894	2
#22625867	2
#22625800	2
#22625799	2
#22625725	2
C₄×SD₁₆×D₇₃	2
#22671	73