Subgroups — #41×C₄⋊#64408 #34030641

Order 18688.

3250 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×#64408	C₂	1	2	yes	maximal
2	#22626446	C₂	1	2	yes	maximal, complemented
3	Q₈×C₄⋊#64408	C₂	1	2	yes	maximal, complemented
4	#22626444	C₂	1	6	yes	maximal, complemented
5	D₄×C₄⋊#64408	C₂	1	6	yes	maximal, complemented
6	#22626391	C₂	1	6	yes	maximal, complemented
7	#22626380	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₄⋊#64408	C₂	1	3	yes	maximal, complemented
9	C₄×#41×D₇₃	C₂	1	1	yes	maximal, characteristic
10	#41×#64408	—	2	16	no	—
11	C₂×Q₈×#64408	C₂²	1	4	yes	—
12	C₂×D₄×#64408	C₂²	1	12	yes	—
13	C₂×#14556670	C₂²	1	6	yes	—
14	C₂²×C₄⋊#64408	C₂²	1	6	yes	—
15	C₂²×C₄×#64408	C₂²	1	6	yes	—
16	#17989538	C₂²	1	12	yes	—
17	#17989538	C₂²	1	12	yes	—
18	#17989534	C₂²	1	24	yes	—
19	#17989533	C₂²	1	6	yes	—
20	#17989531	C₂²	1	6	yes	—
21	#17989529	C₂²	1	6	yes	—
22	#17989529	C₂²	1	6	yes	—
23	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊#64408	C₂²	1	3	yes	—
25	C₄×C₄⋊#64408	C₂²	1	6	yes	—
26	C₄×C₄⋊#64408	C₂²	1	6	yes	—
27	C₄×C₄⋊#64408	C₂²	1	6	yes	—
28	C₄×C₄⋊#64408	C₂²	1	6	yes	—
29	C₂×(C₂×#64408)⋊C₄	C₂²	1	6	yes	—
30	C₂×#41×D₇₃	C₂²	1	1	yes	characteristic
31	#41×Dic₇₃	C₄	1	1	yes	characteristic, complemented
32	C₄×#11924029	C₄	1	1	yes	characteristic, complemented
33	C₄×#11924029	C₄	1	1	yes	characteristic, complemented
34	C₄×#11924028	C₄	1	3	yes	complemented
35	#17989055	C₄	1	3	yes	complemented
36	C₄×#11924027	C₄	1	3	yes	complemented
37	C₄×#11924027	C₄	1	3	yes	complemented
38	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
39	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
40	C₄×D₄×D₇₃	C₂²	1	3	yes	—
41	C₄×D₄×D₇₃	C₂²	1	3	yes	—
42	#117×D₇₃	C₂²	1	3	yes	—
43	C₂×C₄²×D₇₃	C₂²	1	3	yes	—
44	C₄×#41×C₇₃	C₄	1	1	yes	characteristic, complemented
45	C₂³×#64408	C₂³	1	12	yes	—
46	Q₈×#64408	—	2	16	no	—
47	D₄×#64408	—	2	48	no	—
48	#14556670	—	2	24	no	—
49	C₂×C₄⋊#64408	—	2	24	no	—
50	C₂×C₄⋊#64408	C₂³	1	6	yes	—
51	C₂×C₄⋊#64408	C₂³	1	12	yes	—
52	C₂×C₄⋊#64408	C₂³	1	12	yes	—
53	C₂×C₄⋊#64408	C₂³	1	12	yes	—
54	C₂×C₄⋊#64408	C₂³	1	2	yes	—
55	C₂×C₂²⋊#64408	C₂³	1	12	yes	—
56	C₂×C₄×#64408	—	2	24	no	—
57	C₂×C₄×#64408	C₂³	1	2	yes	—
58	C₂×C₄×#64408	C₂³	1	6	yes	—
59	C₂×C₄×#64408	C₂³	1	12	yes	—
60	(C₂×#64408)⋊C₄	C₂³	1	2	yes	—
61	(C₂×#64408)⋊C₄	C₂³	1	6	yes	—
62	(C₂×#64408)⋊C₄	C₂³	1	12	yes	—
63	(C₂×#64408)⋊C₄	C₂³	1	12	yes	—
64	C₂×#11924029	C₂×C₄	1	1	yes	characteristic
65	C₂×#11924028	C₂×C₄	1	3	yes	—
66	C₂×#11924027	C₂×C₄	1	3	yes	—
67	#41×D₇₃	D₄	1	8	yes	—
68	#41×D₇₃	Q₈	1	8	yes	—
69	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
70	C₂×D₄×D₇₃	C₂³	1	3	yes	—
71	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
72	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
73	C₂²×C₄×D₇₃	C₂³	1	3	yes	—
74	Q₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
75	Q₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
76	C₄×Dic₁₄₆	C₂×C₄	1	3	yes	complemented
77	C₄×Dic₁₄₆	C₂×C₄	1	3	yes	complemented
78	#14556556	C₂×C₄	1	3	yes	complemented
79	#14556556	C₂×C₄	1	3	yes	complemented
80	C₄×D₂₉₂	C₂×C₄	1	3	yes	complemented
81	C₄×D₂₉₂	C₂×C₄	1	3	yes	complemented
82	D₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
83	D₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
84	#14556553	C₂×C₄	1	3	yes	complemented
85	#14556553	C₂×C₄	1	3	yes	complemented
86	C₄×C₂²⋊D₇₃	C₂×C₄	1	6	yes	complemented
87	C₄×C₂²⋊D₇₃	C₂×C₄	1	6	yes	complemented
88	#14556551	C₂×C₄	1	6	yes	complemented
89	#14556551	C₂×C₄	1	6	yes	complemented
90	#14556550	C₂×C₄	1	3	yes	complemented
91	#14556549	C₂×C₄	1	3	yes	complemented
92	#14556549	C₂×C₄	1	3	yes	complemented
93	#14556548	C₂×C₄	1	6	yes	complemented
94	#14556547	C₂×C₄	1	6	yes	complemented
95	C₄⋊C₄×D₇₃	C₂³	1	3	yes	—
96	C₄⋊C₄×D₇₃	C₂³	1	3	yes	—
97	C₂²⋊C₄×D₇₃	C₂³	1	6	yes	—
98	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
99	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
100	C₂×C₄×Dic₇₃	C₂×C₄	1	3	yes	complemented
101	C₄²×D₇₃	C₂×C₄	1	3	yes	complemented
102	C₄²×D₇₃	C₂×C₄	1	3	yes	complemented
103	C₄²×D₇₃	C₂×C₄	1	3	yes	complemented
104	C₄²×D₇₃	C₂×C₄	1	3	yes	complemented
105	C₄²×D₇₃	C₂³	1	1	yes	characteristic
106	C₄²×D₇₃	C₂³	1	3	yes	—
107	C₄²×D₇₃	C₂³	1	3	yes	—
108	C₄²×D₇₃	C₂³	1	3	yes	—
109	C₂×#41×C₇₃	C₂×C₄	1	1	yes	characteristic
110	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
111	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
112	C₄×D₄×C₇₃	C₂×C₄	1	3	yes	complemented
113	C₄×D₄×C₇₃	C₂×C₄	1	3	yes	complemented
114	#117×C₇₃	C₂×C₄	1	3	yes	complemented
115	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	complemented
116	C₂²×#64408	—	2	24	no	—
117	C₂²×#64408	—	2	24	no	—
118	C₂²×#64408	—	4	12	no	—
119	C₂²×#64408	C₂⁴	1	12	yes	—
120	C₂²×#64408	C₂⁴	1	4	yes	—
121	C₄⋊#64408	—	2	24	no	—
122	C₄⋊#64408	—	2	24	no	—
123	C₄⋊#64408	—	2	12	no	—
124	C₄⋊#64408	—	4	12	no	—
125	C₄⋊#64408	#41	1	8	yes	direct product factor
126	C₂²⋊#64408	—	2	24	no	—
127	C₄×#64408	—	2	24	no	—
128	C₄×#64408	—	2	4	no	—
129	C₄×#64408	—	2	12	no	—
130	C₂³×D₇₃	C₂⁴	1	3	yes	—
131	#11924029	C₄⋊C₄	1	8	yes	complemented
132	#11924028	C₄⋊C₄	1	24	yes	complemented
133	#11924027	C₄⋊C₄	1	24	yes	complemented
134	C₂×Dic₁₄₆	C₂²×C₄	1	3	yes	—
135	Q₈×D₇₃	C₂×D₄	1	4	yes	—
136	Q₈×D₇₃	C₂×Q₈	1	4	yes	—
137	C₂×D₂₉₂	C₂²×C₄	1	3	yes	—
138	C₂×C₂²⋊D₇₃	C₂²×C₄	1	6	yes	—
139	D₄×D₇₃	C₂×D₄	1	12	yes	—
140	D₄×D₇₃	C₂×Q₈	1	12	yes	—
141	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
142	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
143	C₂²×Dic₇₃	C₂²×C₄	1	3	yes	—
144	C₂×C₄×D₇₃	—	2	12	no	—
145	C₂×C₄×D₇₃	—	4	6	no	—
146	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
147	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
148	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
149	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
150	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
151	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
152	C₂×C₄×D₇₃	C₂×D₄	1	12	yes	—
153	C₂×C₄×D₇₃	C₂×Q₈	1	12	yes	—
154	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
156	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
157	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×D₇₃	C₂⁴	1	3	yes	—
159	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
160	C₄⋊Dic₇₃	C₂²×C₄	1	3	yes	—
161	C₄⋊Dic₇₃	C₂²×C₄	1	3	yes	—
162	#11924007	C₂²×C₄	1	6	yes	—
163	#11924007	C₂²×C₄	1	6	yes	—
164	C₂²⋊Dic₇₃	C₂²×C₄	1	6	yes	—
165	#11924005	C₂²×C₄	1	6	yes	—
166	#11924005	C₂²×C₄	1	6	yes	—
167	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
171	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
172	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
173	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
174	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
175	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
176	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
177	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
178	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
179	#41×C₇₃	C₄⋊C₄	1	8	yes	complemented
180	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
181	C₂×D₄×C₇₃	C₂²×C₄	1	3	yes	—
182	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
183	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
184	C₂²×C₄×C₇₃	C₂²×C₄	1	3	yes	—
185	C₄⋊C₄×C₇₃	C₂²×C₄	1	3	yes	—
186	C₄⋊C₄×C₇₃	C₂²×C₄	1	3	yes	—
187	C₂²⋊C₄×C₇₃	C₂²×C₄	1	6	yes	—
188	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
189	C₄²×C₇₃	C₂²×C₄	1	3	yes	—
190	C₄²×C₇₃	C₂²×C₄	1	3	yes	—
191	C₄²×C₇₃	C₂²×C₄	1	3	yes	—
192	C₂³×C₇₃	C₂³×C₄	1	3	yes	—
193	C₂²×D₇₃	—	2	6	no	—
194	C₂²×D₇₃	—	2	6	no	—
195	C₂²×D₇₃	C₂³×C₄	1	3	yes	—
196	C₂²×D₇₃	C₂²×D₄	1	6	yes	—
197	C₂²×D₇₃	C₂²×Q₈	1	6	yes	—
198	C₂²×D₇₃	C₂⁵	1	1	yes	characteristic
199	C₂×#64408	—	2	4	no	—
200	C₂×#64408	—	2	4	no	—
201	C₂×#64408	—	2	12	no	—
202	C₂×#64408	—	2	12	no	—
203	C₂×#64408	—	2	12	no	—
204	C₂×#64408	—	4	48	no	—
205	C₂×#64408	C₂×#41	1	8	yes	—
206	Q₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	complemented
207	D₄×C₇₃	C₂×C₄⋊C₄	1	12	yes	complemented
208	C₂×C₄×C₇₃	—	2	6	no	—
209	C₂×C₄×C₇₃	—	4	3	no	—
210	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	12	yes	complemented
211	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₇₃	C₂³×C₄	1	3	yes	—
213	C₂×C₄×C₇₃	C₂³×C₄	1	3	yes	—
214	C₂×C₄×C₇₃	C₂³×C₄	1	3	yes	—
215	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
217	C₂²⋊D₇₃	C₂×C₄⋊C₄	1	24	yes	complemented
218	C₂×Dic₇₃	—	2	6	no	—
219	C₂×Dic₇₃	—	4	3	no	—
220	C₂×Dic₇₃	C₂×C₄⋊C₄	1	12	yes	complemented
221	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
222	C₂×Dic₇₃	C₂³×C₄	1	3	yes	—
223	C₂×Dic₇₃	C₂³×C₄	1	3	yes	—
224	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×Dic₇₃	C₂³×C₄	1	3	yes	—
226	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
227	D₂₉₂	C₂×C₄⋊C₄	1	12	yes	complemented
228	C₄×D₇₃	—	2	6	no	—
229	C₄×D₇₃	—	2	2	no	—
230	C₄×D₇₃	—	2	6	no	—
231	C₄×D₇₃	—	2	6	no	—
232	C₄×D₇₃	—	2	6	no	—
233	C₄×D₇₃	—	4	3	no	—
234	C₄×D₇₃	—	4	3	no	—
235	C₄×D₇₃	C₂×C₄⋊C₄	1	12	yes	complemented
236	C₄×D₇₃	C₂×C₄⋊C₄	1	12	yes	complemented
237	C₄×D₇₃	C₂²×D₄	1	2	yes	—
238	C₄×D₇₃	C₂²×D₄	1	6	yes	—
239	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
240	C₄×D₇₃	C₂²×Q₈	1	6	yes	—
241	C₄×D₇₃	C₂×#41	1	4	yes	—
242	Dic₁₄₆	C₂×C₄⋊C₄	1	12	yes	complemented
243	C₂²×C₇₃	—	2	3	no	—
244	C₂²×C₇₃	—	2	3	no	—
245	C₂²×C₇₃	C₂²×C₄⋊C₄	1	6	yes	—
246	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
247	C₂×D₇₃	—	2	3	no	—
248	C₂×D₇₃	—	2	3	no	—
249	C₂×D₇₃	—	2	12	no	—
250	C₂×D₇₃	—	2	12	no	—
251	C₂×D₇₃	C₂²×C₄⋊C₄	1	6	yes	—
252	C₂×D₇₃	C₂³×D₄	1	1	yes	characteristic
253	C₂×D₇₃	C₂³×Q₈	1	1	yes	characteristic
254	C₂×D₇₃	C₂²×#41	1	2	yes	—
255	C₂×D₇₃	#585	1	2	yes	—
256	#64408	—	2	8	no	—
257	#64408	—	4	12	no	—
258	C₄×C₇₃	—	2	3	no	—
259	C₄×C₇₃	—	2	1	no	—
260	C₄×C₇₃	—	2	3	no	—
261	C₄×C₇₃	C₂²×C₄⋊C₄	1	6	yes	—
262	C₄×C₇₃	C₂²×C₄⋊C₄	1	2	yes	—
263	C₄×C₇₃	C₄×#41	1	2	yes	complemented
264	Dic₇₃	—	2	3	no	—
265	Dic₇₃	—	2	1	no	—
266	Dic₇₃	—	2	3	no	—
267	Dic₇₃	C₂²×C₄⋊C₄	1	6	yes	—
268	Dic₇₃	C₂²×C₄⋊C₄	1	2	yes	—
269	Dic₇₃	C₄×#41	1	2	yes	complemented
270	C₄⋊C₄×#41	—	73	1	no	maximal, Sylow
271	C₂×C₇₃	—	2	6	no	—
272	C₂×C₇₃	C₂³×C₄⋊C₄	1	1	yes	characteristic
273	C₂×C₇₃	C₂×C₄×#41	1	1	yes	characteristic
274	C₂×C₇₃	#3428	1	1	yes	characteristic
275	D₇₃	—	2	6	no	—
276	D₇₃	D₄×#41	1	2	yes	—
277	D₇₃	Q₈×#41	1	2	yes	—
278	C₂×C₄×#41	—	73	1	no	—
279	C₂×C₄×#41	—	73	2	no	—
280	#2351	—	73	2	no	—
281	Q₈×C₄⋊C₄	—	73	2	no	—
282	#2349	—	73	6	no	—
283	D₄×C₄⋊C₄	—	73	6	no	—
284	#2296	—	73	6	no	—
285	#2285	—	73	3	no	—
286	C₂×C₄×C₄⋊C₄	—	73	3	no	—
287	C₇₃	C₄⋊C₄×#41	1	1	yes	characteristic, complemented, Sylow
288	C₂²×#41	—	73	1	no	—
289	C₄×#41	—	73	1	no	—
290	C₄×#41	—	73	1	no	—
291	C₄×#41	—	73	1	no	—
292	C₄×#41	—	73	3	no	—
293	C₄×#41	—	73	3	no	—
294	C₄×#41	—	73	3	no	—
295	C₄×#41	—	73	3	no	—
296	C₄×#41	—	146	16	no	—
297	C₄×#41	#64408	1	1	yes	characteristic, complemented
298	C₂×C₄×Q₈	—	73	1	no	—
299	C₂×C₄×Q₈	—	73	1	no	—
300	C₂×C₄×Q₈	—	73	4	no	—
301	C₂×C₄×D₄	—	73	3	no	—
302	C₂×C₄×D₄	—	73	3	no	—
303	C₂×C₄×D₄	—	73	12	no	—
304	C₂×#117	—	73	3	no	—
305	C₂×#117	—	73	6	no	—
306	C₂²×C₄⋊C₄	—	73	6	no	—
307	C₂²×C₄²	—	73	3	no	—
308	C₂²×C₄²	—	73	6	no	—
309	#389	—	73	12	no	—
310	#389	—	73	12	no	—
311	#385	—	73	24	no	—
312	#384	—	73	6	no	—
313	#382	—	73	6	no	—
314	#380	—	73	6	no	—
315	#380	—	73	6	no	—
316	C₄×C₄⋊C₄	—	73	6	no	—
317	C₄×C₄⋊C₄	—	73	6	no	—
318	C₄×C₄⋊C₄	—	73	1	no	—
319	C₄×C₄⋊C₄	—	73	3	no	—
320	C₄×C₄⋊C₄	—	73	6	no	—
321	C₄×C₄⋊C₄	—	73	6	no	—
322	C₂×#95	—	73	6	no	—
323	C₂×#41	—	73	8	no	—
324	C₂×#41	—	73	8	no	—
325	C₂×#41	—	73	1	no	—
326	C₂×#41	—	73	3	no	—
327	C₂×#41	—	73	3	no	—
328	C₂×#41	C₂×#64408	1	1	yes	characteristic
329	C₂²×Q₈	—	73	1	no	—
330	C₂²×D₄	—	73	3	no	—
331	C₂³×C₄	—	73	3	no	—
332	C₂³×C₄	—	73	12	no	—
333	C₂³×C₄	—	73	3	no	—
334	C₂³×C₄	—	73	3	no	—
335	C₄×Q₈	—	73	1	no	—
336	C₄×Q₈	—	73	1	no	—
337	C₄×Q₈	—	73	3	no	—
338	C₄×Q₈	—	73	3	no	—
339	C₄×Q₈	—	73	3	no	—
340	C₄×Q₈	—	73	3	no	—
341	C₄×Q₈	—	146	16	no	—
342	C₄×Q₈	C₂×#64408	1	1	yes	characteristic, complemented
343	C₄×Q₈	C₂×#64408	1	1	yes	characteristic, complemented
344	C₄×D₄	—	73	3	no	—
345	C₄×D₄	—	73	3	no	—
346	C₄×D₄	—	73	6	no	—
347	C₄×D₄	—	73	6	no	—
348	C₄×D₄	—	73	3	no	—
349	C₄×D₄	—	73	3	no	—
350	C₄×D₄	—	73	6	no	—
351	C₄×D₄	—	73	6	no	—
352	C₄×D₄	—	73	3	no	—
353	C₄×D₄	—	73	3	no	—
354	C₄×D₄	—	146	48	no	—
355	C₄×D₄	C₂×#64408	1	3	yes	complemented
356	C₄×D₄	C₂×#64408	1	3	yes	complemented
357	#117	—	73	3	no	—
358	#117	—	73	3	no	—
359	#117	—	73	3	no	—
360	#117	—	73	6	no	—
361	#117	—	73	6	no	—
362	#117	—	146	24	no	—
363	#117	C₂×#64408	1	3	yes	complemented
364	C₂×C₄⋊C₄	—	73	12	no	—
365	C₂×C₄⋊C₄	—	73	2	no	—
366	C₂×C₄⋊C₄	—	73	3	no	—
367	C₂×C₄⋊C₄	—	73	3	no	—
368	C₂×C₄⋊C₄	—	73	6	no	—
369	C₂×C₄⋊C₄	—	73	12	no	—
370	C₂×C₄⋊C₄	—	73	12	no	—
371	C₂×C₄⋊C₄	—	146	24	no	—
372	C₂×C₂²⋊C₄	—	73	6	no	—
373	C₂×C₂²⋊C₄	—	73	12	no	—
374	C₂×C₄²	—	73	3	no	—
375	C₂×C₄²	—	73	3	no	—
376	C₂×C₄²	—	73	3	no	—
377	C₂×C₄²	—	73	3	no	—
378	C₂×C₄²	—	73	3	no	—
379	C₂×C₄²	—	73	3	no	—
380	C₂×C₄²	—	73	3	no	—
381	C₂×C₄²	—	73	3	no	—
382	C₂×C₄²	—	73	3	no	—
383	C₂×C₄²	—	73	3	no	—
384	C₂×C₄²	—	73	1	no	—
385	C₂×C₄²	—	73	6	no	—
386	C₂×C₄²	—	73	12	no	—
387	C₂×C₄²	—	73	2	no	—
388	C₂×C₄²	—	146	24	no	—
389	C₂×C₄²	C₂×#64408	1	3	yes	complemented
390	#95	—	73	2	no	—
391	#95	—	73	6	no	—
392	#95	—	73	12	no	—
393	#95	—	73	12	no	—
394	C₂⁴	—	73	3	no	—
395	#41	—	73	8	no	—
396	#41	—	73	24	no	—
397	#41	—	73	24	no	—
398	#41	C₄⋊#64408	1	8	yes	direct product factor
399	C₂×Q₈	—	73	4	no	—
400	C₂×Q₈	—	73	4	no	—
401	C₂×Q₈	—	73	3	no	—
402	C₂×Q₈	C₂²×#64408	1	1	yes	characteristic
403	C₂×D₄	—	73	6	no	—
404	C₂×D₄	—	73	12	no	—
405	C₂×D₄	—	73	12	no	—
406	C₂×D₄	—	73	3	no	—
407	C₂×D₄	C₂²×#64408	1	3	yes	—
408	C₂²×C₄	—	292	6	no	—
409	C₂²×C₄	—	292	12	no	—
410	C₂²×C₄	—	73	3	no	—
411	C₂²×C₄	—	73	3	no	—
412	C₂²×C₄	—	73	3	no	—
413	C₂²×C₄	—	73	3	no	—
414	C₂²×C₄	—	73	3	no	—
415	C₂²×C₄	—	73	3	no	—
416	C₂²×C₄	—	73	1	no	—
417	C₂²×C₄	—	73	3	no	—
418	C₂²×C₄	—	73	1	no	—
419	C₂²×C₄	—	73	12	no	—
420	C₂²×C₄	—	73	12	no	—
421	C₂²×C₄	—	73	4	no	—
422	C₂²×C₄	—	73	3	no	—
423	C₂²×C₄	—	73	3	no	—
424	C₂²×C₄	—	73	3	no	—
425	C₂²×C₄	—	73	1	no	—
426	C₂²×C₄	—	73	3	no	—
427	C₂²×C₄	—	73	3	no	—
428	C₂²×C₄	—	73	12	no	—
429	C₂²×C₄	—	146	12	no	—
430	C₂²×C₄	—	146	24	no	—
431	C₂²×C₄	—	146	24	no	—
432	C₂²×C₄	C₂²×#64408	1	3	yes	—
433	C₂²×C₄	C₂²×#64408	1	3	yes	—
434	C₂²×C₄	C₂²×#64408	1	3	yes	—
435	C₄⋊C₄	—	292	12	no	—
436	C₄⋊C₄	—	73	8	no	—
437	C₄⋊C₄	—	73	6	no	—
438	C₄⋊C₄	—	73	6	no	—
439	C₄⋊C₄	—	73	3	no	—
440	C₄⋊C₄	—	73	3	no	—
441	C₄⋊C₄	—	146	12	no	—
442	C₄⋊C₄	—	146	24	no	—
443	C₄⋊C₄	—	146	24	no	—
444	C₄⋊C₄	C₂²×#64408	1	3	yes	—
445	C₄⋊C₄	C₂²×#64408	1	3	yes	—
446	C₂²⋊C₄	—	73	6	no	—
447	C₂²⋊C₄	—	73	6	no	—
448	C₂²⋊C₄	—	73	6	no	—
449	C₂²⋊C₄	—	146	24	no	—
450	C₂²⋊C₄	C₂²×#64408	1	6	yes	—
451	C₄²	—	73	1	no	—
452	C₄²	—	73	1	no	—
453	C₄²	—	73	3	no	—
454	C₄²	—	73	3	no	—
455	C₄²	—	73	3	no	—
456	C₄²	—	73	3	no	—
457	C₄²	—	73	3	no	—
458	C₄²	—	73	3	no	—
459	C₄²	—	73	3	no	—
460	C₄²	—	73	3	no	—
461	C₄²	—	73	1	no	—
462	C₄²	—	73	3	no	—
463	C₄²	—	146	4	no	—
464	C₄²	—	146	12	no	—
465	C₄²	—	146	24	no	—
466	C₄²	C₂²×#64408	1	3	yes	—
467	C₄²	C₂²×#64408	1	3	yes	—
468	C₄²	C₂²×#64408	1	1	yes	characteristic
469	C₄²	C₂²×#64408	1	3	yes	—
470	C₂³	—	73	1	no	—
471	C₂³	—	73	6	no	—
472	C₂³	—	73	6	no	—
473	C₂³	—	73	3	no	—
474	C₂³	—	146	6	no	—
475	C₂³	—	146	6	no	—
476	C₂³	C₂³×#64408	1	3	yes	—
477	Q₈	—	73	12	no	—
478	Q₈	C₂×C₄⋊#64408	1	4	yes	complemented
479	D₄	—	73	24	no	—
480	D₄	—	73	12	no	—
481	D₄	C₂×C₄⋊#64408	1	12	yes	complemented
482	C₂×C₄	—	2	6	no	—
483	C₂×C₄	—	4	3	no	—
484	C₂×C₄	—	292	3	no	—
485	C₂×C₄	—	292	3	no	—
486	C₂×C₄	—	292	48	no	—
487	C₂×C₄	—	292	3	no	—
488	C₂×C₄	—	73	12	no	—
489	C₂×C₄	—	73	1	no	—
490	C₂×C₄	—	73	1	no	—
491	C₂×C₄	—	73	3	no	—
492	C₂×C₄	—	73	2	no	—
493	C₂×C₄	—	73	6	no	—
494	C₂×C₄	—	73	2	no	—
495	C₂×C₄	—	73	6	no	—
496	C₂×C₄	—	73	12	no	—
497	C₂×C₄	—	73	12	no	—
498	C₂×C₄	—	73	4	no	—
499	C₂×C₄	—	73	8	no	—
500	C₂×C₄	—	73	1	no	—
501	C₂×C₄	—	73	3	no	—
502	C₂×C₄	—	73	3	no	—
503	C₂×C₄	—	146	6	no	—
504	C₂×C₄	—	146	6	no	—
505	C₂×C₄	—	146	6	no	—
506	C₂×C₄	—	146	2	no	—
507	C₂×C₄	—	146	12	no	—
508	C₂×C₄	—	146	12	no	—
509	C₂×C₄	—	146	12	no	—
510	C₂×C₄	—	146	6	no	—
511	C₂×C₄	—	146	4	no	—
512	C₂×C₄	—	146	4	no	—
513	C₂×C₄	—	146	6	no	—
514	C₂×C₄	C₂×C₄⋊#64408	1	12	yes	complemented
515	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
516	C₂×C₄	C₂³×#64408	1	3	yes	—
517	C₂×C₄	C₂³×#64408	1	3	yes	—
518	C₂×C₄	C₂³×#64408	1	3	yes	—
519	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
520	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
521	C₂²	—	2	3	no	—
522	C₂²	—	2	3	no	—
523	C₂²	—	73	1	no	—
524	C₂²	—	73	1	no	—
525	C₂²	—	73	2	no	—
526	C₂²	—	73	2	no	—
527	C₂²	—	73	6	no	—
528	C₂²	—	146	12	no	—
529	C₂²	—	146	12	no	—
530	C₂²	—	146	3	no	—
531	C₂²	—	146	3	no	—
532	C₂²	C₂²×C₄⋊#64408	1	6	yes	—
533	C₂²	C₂⁴×#64408	1	1	yes	characteristic
534	C₄	—	2	3	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	3	no	—
537	C₄	—	292	12	no	—
538	C₄	—	73	2	no	—
539	C₄	—	73	6	no	—
540	C₄	—	73	2	no	—
541	C₄	—	146	8	no	—
542	C₄	—	146	3	no	—
543	C₄	—	146	1	no	—
544	C₄	—	146	3	no	—
545	C₄	C₂²×C₄⋊#64408	1	2	yes	—
546	C₄	C₂²×C₄⋊#64408	1	6	yes	—
547	C₄	#41×#64408	1	2	yes	complemented
548	C₂	—	2	6	no	—
549	C₂	—	73	2	no	—
550	C₂	—	73	2	no	—
551	C₂	—	146	6	no	—
552	C₂	C₂³×C₄⋊#64408	1	1	yes	characteristic
553	C₂	C₂×#41×#64408	1	1	yes	characteristic
554	C₂	#22626911	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂⁴×C₄
Frattini	C₂²	C₂⁴×#64408
Fitting	C₄×#41×C₇₃	C₄
prime radical	C₂×#41×D₇₃	C₂²
cosocle	C₂²×D₇₃	C₂⁵
hypercenter	C₄×#41	#64408
hypocenter	C₇₃	C₄⋊C₄×#41
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
2. #22626446	C₂	semidirect
3. Q₈×C₄⋊#64408	C₂	semidirect
4. #22626444	C₂	semidirect
5. D₄×C₄⋊#64408	C₂	semidirect
6. #22626391	C₂	semidirect
7. #22626380	C₂	semidirect
8. C₂×C₄×C₄⋊#64408	C₂	semidirect
31. #41×Dic₇₃	C₄	semidirect
32. C₄×#11924029	C₄	semidirect
33. C₄×#11924029	C₄	semidirect
34. C₄×#11924028	C₄	semidirect
35. #17989055	C₄	semidirect
36. C₄×#11924027	C₄	semidirect
37. C₄×#11924027	C₄	semidirect
44. C₄×#41×C₇₃	C₄	semidirect
74. Q₈×Dic₇₃	C₂×C₄	semidirect
75. Q₈×Dic₇₃	C₂×C₄	semidirect
76. C₄×Dic₁₄₆	C₂×C₄	semidirect
77. C₄×Dic₁₄₆	C₂×C₄	semidirect
78. #14556556	C₂×C₄	semidirect
79. #14556556	C₂×C₄	semidirect
80. C₄×D₂₉₂	C₂×C₄	semidirect
81. C₄×D₂₉₂	C₂×C₄	semidirect
82. D₄×Dic₇₃	C₂×C₄	semidirect
83. D₄×Dic₇₃	C₂×C₄	semidirect
84. #14556553	C₂×C₄	semidirect
85. #14556553	C₂×C₄	semidirect
86. C₄×C₂²⋊D₇₃	C₂×C₄	semidirect
87. C₄×C₂²⋊D₇₃	C₂×C₄	semidirect
88. #14556551	C₂×C₄	semidirect
89. #14556551	C₂×C₄	semidirect
90. #14556550	C₂×C₄	semidirect
91. #14556549	C₂×C₄	semidirect
92. #14556549	C₂×C₄	semidirect
93. #14556548	C₂×C₄	semidirect
94. #14556547	C₂×C₄	semidirect
98. C₂×C₄×Dic₇₃	C₂×C₄	semidirect
99. C₂×C₄×Dic₇₃	C₂×C₄	semidirect
100. C₂×C₄×Dic₇₃	C₂×C₄	semidirect
101. C₄²×D₇₃	C₂×C₄	semidirect
102. C₄²×D₇₃	C₂×C₄	semidirect
103. C₄²×D₇₃	C₂×C₄	semidirect
104. C₄²×D₇₃	C₂×C₄	semidirect
110. C₄×Q₈×C₇₃	C₂×C₄	semidirect
111. C₄×Q₈×C₇₃	C₂×C₄	semidirect
112. C₄×D₄×C₇₃	C₂×C₄	semidirect
113. C₄×D₄×C₇₃	C₂×C₄	semidirect
114. #117×C₇₃	C₂×C₄	semidirect
115. C₂×C₄²×C₇₃	C₂×C₄	semidirect
125. C₄⋊#64408	#41	direct (N × H)
131. #11924029	C₄⋊C₄	semidirect
132. #11924028	C₄⋊C₄	semidirect
133. #11924027	C₄⋊C₄	semidirect
179. #41×C₇₃	C₄⋊C₄	semidirect
206. Q₈×C₇₃	C₂×C₄⋊C₄	semidirect
207. D₄×C₇₃	C₂×C₄⋊C₄	semidirect
210. C₂×C₄×C₇₃	C₂×C₄⋊C₄	semidirect
217. C₂²⋊D₇₃	C₂×C₄⋊C₄	semidirect
220. C₂×Dic₇₃	C₂×C₄⋊C₄	semidirect
227. D₂₉₂	C₂×C₄⋊C₄	semidirect
235. C₄×D₇₃	C₂×C₄⋊C₄	semidirect
236. C₄×D₇₃	C₂×C₄⋊C₄	semidirect
242. Dic₁₄₆	C₂×C₄⋊C₄	semidirect
263. C₄×C₇₃	C₄×#41	semidirect
269. Dic₇₃	C₄×#41	semidirect
287. C₇₃	C₄⋊C₄×#41	semidirect
297. C₄×#41	#64408	semidirect
342. C₄×Q₈	C₂×#64408	semidirect
343. C₄×Q₈	C₂×#64408	semidirect
355. C₄×D₄	C₂×#64408	semidirect
356. C₄×D₄	C₂×#64408	semidirect
363. #117	C₂×#64408	semidirect
389. C₂×C₄²	C₂×#64408	semidirect
398. #41	C₄⋊#64408	direct (N × H)
478. Q₈	C₂×C₄⋊#64408	semidirect
481. D₄	C₂×C₄⋊#64408	semidirect
514. C₂×C₄	C₂×C₄⋊#64408	semidirect
547. C₄	#41×#64408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×#64408	2
#22626446	2
Q₈×C₄⋊#64408	2
#22626444	2
D₄×C₄⋊#64408	2
#22626391	2
#22626380	2
C₂×C₄×C₄⋊#64408	2
C₄×#41×D₇₃	2
C₄⋊C₄×#41	73

Subgroups — #41×C4⋊#64408 #34030641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×C₄⋊#64408 #34030641