Subgroups — #49167474

Order 37504.

520 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22627630	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#34036638	C₂	1	1	yes	maximal, characteristic
4	#34036203	C₂	1	1	yes	maximal, characteristic, complemented
5	#34036201	C₂	1	1	yes	maximal, characteristic, complemented
6	#34036199	C₂	1	1	yes	maximal, characteristic, complemented
7	#34036197	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×D₁₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊D₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊D₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#34036154	C₂	1	1	yes	maximal, characteristic, complemented
12	#34036094	C₂	1	1	yes	maximal, characteristic, complemented
13	#34036091	C₂	1	1	yes	maximal, characteristic, complemented
14	#34036083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₄×C₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#17989802	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₂₉₃	C₂²	1	1	yes	characteristic
18	#22627630	—	2	4	no	—
19	C₂×#17989786	C₂²	1	1	yes	characteristic, complemented
20	C₂×#17989785	C₂²	1	1	yes	characteristic
21	C₂×#17989785	C₂²	1	1	yes	characteristic
22	C₂×#17989785	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#14556873	C₂²	1	1	yes	characteristic
24	C₂×C₈×D₂₉₃	—	2	4	no	—
25	C₂×C₈×D₂₉₃	C₂²	1	1	yes	characteristic
26	C₂×C₈×D₂₉₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×D₂₉₃	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₂₉₃	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₂₉₃	C₂²	1	1	yes	characteristic, complemented
30	#22627609	C₄	1	1	yes	characteristic
31	#22627606	C₄	1	1	yes	characteristic
32	#22627602	C₄	1	1	yes	characteristic
33	#22627601	C₄	1	1	yes	characteristic
34	#22627597	C₄	1	1	yes	characteristic
35	#22627596	C₄	1	1	yes	characteristic
36	#22627594	C₄	1	1	yes	characteristic
37	#22627592	C₄	1	1	yes	characteristic
38	C₄×D₁₁₇₂	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₂₉₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₂₉₃	C₂²	1	1	yes	characteristic
41	#22627581	C₂²	1	1	yes	characteristic
42	C₄⋊#14556873	C₂²	1	1	yes	characteristic, complemented
43	#22627553	C₂²	1	1	yes	characteristic, complemented
44	#22627553	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊#14556873	C₂²	1	1	yes	characteristic
46	C₂²⋊#14556873	C₂²	1	1	yes	characteristic, complemented
47	#22627536	C₂²	1	1	yes	characteristic
48	#22627536	C₂²	1	1	yes	characteristic
49	#22627536	C₂²	1	1	yes	characteristic, complemented
50	#22627536	C₂²	1	1	yes	characteristic, complemented
51	#22627535	C₂²	1	1	yes	characteristic, complemented
52	#22627534	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₂₉₃	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₈×C₂₉₃	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₂₉₃	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₂₉₃	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₂₉₃	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₂₉₃	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₂₉₃	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₈×C₂₉₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₂₉₃	C₂×C₄	1	1	yes	characteristic
62	#17989802	—	2	2	no	—
63	#17989802	—	2	2	no	—
64	C₂×Dic₅₈₆	C₂×C₄	1	1	yes	characteristic
65	C₂×D₁₁₇₂	C₂×C₄	1	1	yes	characteristic
66	C₂×D₁₁₇₂	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₂₉₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₂₉₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊D₂₉₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₂₉₃	C₂×C₄	1	1	yes	characteristic
71	C₂²×Dic₂₉₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₂₉₃	—	2	2	no	—
73	C₂×C₄×D₂₉₃	—	2	2	no	—
74	C₂×C₄×D₂₉₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₂₉₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₂₉₃	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₂₉₃	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₂₉₃	C₂³	1	1	yes	characteristic
79	#17989786	—	2	2	no	—
80	#17989785	—	2	2	no	—
81	#17989785	—	2	2	no	—
82	#17989785	—	2	2	no	—
83	C₂×#14556873	—	2	2	no	—
84	C₂×#14556873	C₂³	1	1	yes	characteristic
85	C₂×#14556873	C₂³	1	1	yes	characteristic
86	C₂×#14556873	C₂³	1	1	yes	characteristic
87	C₂×#14556873	C₂³	1	1	yes	characteristic
88	C₈×D₂₉₃	—	2	2	no	—
89	C₈×D₂₉₃	—	2	2	no	—
90	C₈×D₂₉₃	—	2	2	no	—
91	C₈×D₂₉₃	—	2	2	no	—
92	C₈×D₂₉₃	D₄	1	4	yes	complemented
93	C₄⋊Dic₂₉₃	C₂×C₄	1	1	yes	characteristic
94	#17989781	C₂×C₄	1	1	yes	characteristic
95	#17989781	C₂×C₄	1	1	yes	characteristic
96	#17989781	C₂×C₄	1	1	yes	characteristic
97	#17989781	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊Dic₂₉₃	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₂₉₃	C₂×C₄	1	1	yes	characteristic
100	#17989779	C₂×C₄	1	1	yes	characteristic
101	#17989779	C₂×C₄	1	1	yes	characteristic
102	#17989779	C₂×C₄	1	1	yes	characteristic
103	#17989779	C₂×C₄	1	1	yes	characteristic
104	#17989779	C₂×C₄	1	1	yes	characteristic
105	#17989779	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₂₉₃	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
110	C₂×C₈×C₂₉₃	—	2	2	no	—
111	C₂×C₈×C₂₉₃	—	2	2	no	—
112	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
119	C₄²×C₂₉₃	C₂³	1	1	yes	characteristic
120	C₂²×D₂₉₃	—	2	2	no	—
121	C₂²×D₂₉₃	—	2	2	no	—
122	C₂²×D₂₉₃	—	2	2	no	—
123	C₂²×D₂₉₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₂₉₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₂₉₃	C₂²×C₄	1	1	yes	characteristic
126	Dic₅₈₆	—	2	2	no	—
127	D₁₁₇₂	—	2	2	no	—
128	D₁₁₇₂	—	2	2	no	—
129	C₂²⋊D₂₉₃	—	2	2	no	—
130	C₂²⋊D₂₉₃	—	2	2	no	—
131	C₂²⋊D₂₉₃	—	2	2	no	—
132	C₂²⋊D₂₉₃	—	2	2	no	—
133	C₂×Dic₂₉₃	—	2	2	no	—
134	C₂×Dic₂₉₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×Dic₂₉₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×Dic₂₉₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×Dic₂₉₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₂₉₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×D₂₉₃	—	2	2	no	—
140	C₄×D₂₉₃	—	2	1	no	—
141	C₄×D₂₉₃	—	2	1	no	—
142	C₄×D₂₉₃	—	2	1	no	—
143	C₄×D₂₉₃	—	2	1	no	—
144	C₄×D₂₉₃	—	2	2	no	—
145	C₄×D₂₉₃	C₂×D₄	1	2	yes	—
146	C₄×D₂₉₃	#41	1	2	yes	—
147	#14556873	—	2	1	no	—
148	#14556873	—	2	1	no	—
149	#14556873	—	2	1	no	—
150	#14556873	C₂×D₄	1	2	yes	—
151	C₂³×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
152	C₂³×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
153	D₄×C₂₉₃	—	2	2	no	—
154	C₂×C₄×C₂₉₃	—	2	1	no	—
155	C₂×C₄×C₂₉₃	—	2	1	no	—
156	C₂×C₄×C₂₉₃	—	2	1	no	—
157	C₂×C₄×C₂₉₃	—	2	1	no	—
158	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×C₂₉₃	C₂⁴	1	1	yes	characteristic
163	C₈×C₂₉₃	—	2	1	no	—
164	C₈×C₂₉₃	—	2	1	no	—
165	C₈×C₂₉₃	—	2	1	no	—
166	C₈×C₂₉₃	C₂×D₄	1	2	yes	—
167	C₂²×C₂₉₃	—	2	1	no	—
168	C₂²×C₂₉₃	—	2	1	no	—
169	C₂²×C₂₉₃	—	2	1	no	—
170	C₂²×C₂₉₃	—	2	1	no	—
171	C₂²×C₂₉₃	—	2	1	no	—
172	C₂²×C₂₉₃	#131	1	2	yes	complemented
173	C₂²×C₂₉₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₂₉₃	—	2	8	no	—
175	C₂×D₂₉₃	—	2	1	no	—
176	C₂×D₂₉₃	—	2	1	no	—
177	C₂×D₂₉₃	—	2	1	no	—
178	C₂×D₂₉₃	—	2	1	no	—
179	C₂×D₂₉₃	—	2	1	no	—
180	C₂×D₂₉₃	—	2	1	no	—
181	C₂×D₂₉₃	—	2	1	no	—
182	C₂×D₂₉₃	C₄×D₄	1	2	yes	—
183	C₂×D₂₉₃	#131	1	2	yes	complemented
184	C₄×C₂₉₃	—	2	1	no	—
185	C₄×C₂₉₃	—	2	1	no	—
186	C₄×C₂₉₃	—	2	1	no	—
187	C₄×C₂₉₃	—	2	1	no	—
188	C₄×C₂₉₃	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₂₉₃	C₂×#41	1	1	yes	characteristic
190	Dic₂₉₃	—	2	1	no	—
191	Dic₂₉₃	—	2	1	no	—
192	Dic₂₉₃	—	2	1	no	—
193	Dic₂₉₃	—	2	1	no	—
194	Dic₂₉₃	C₄×D₄	1	2	yes	—
195	C₂×C₂₉₃	—	2	2	no	—
196	C₂×C₂₉₃	—	4	1	no	—
197	C₂×C₂₉₃	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×C₂₉₃	C₂×#131	1	1	yes	characteristic
199	C₂×C₂₉₃	C₂×#131	1	1	yes	characteristic
200	D₂₉₃	—	2	2	no	—
201	D₂₉₃	—	2	2	no	—
202	D₂₉₃	—	4	1	no	—
203	C₂₉₃	#2929	1	1	yes	characteristic, complemented, Sylow
204	#2929	—	293	1	no	maximal, Sylow
205	C₂×#131	—	293	1	no	—
206	C₂³×C₈	—	293	1	no	—
207	#525	—	293	1	no	—
208	#435	—	293	1	no	—
209	#435	—	293	1	no	—
210	#435	—	293	1	no	—
211	#435	—	293	1	no	—
212	C₈×D₄	—	293	1	no	—
213	C₈×D₄	—	293	1	no	—
214	C₈×D₄	—	293	1	no	—
215	C₈×D₄	D₂₉₃	1	1	yes	characteristic, complemented
216	#424	—	293	1	no	—
217	#408	—	293	1	no	—
218	#407	—	293	1	no	—
219	#405	—	293	1	no	—
220	C₂×#41	—	293	1	no	—
221	C₂³×C₄	—	293	1	no	—
222	#131	—	586	4	no	—
223	C₂×M₁₆	—	293	1	no	—
224	C₂×M₁₆	—	293	1	no	—
225	C₂×M₁₆	—	293	1	no	—
226	C₂×M₁₆	—	293	1	no	—
227	C₂²×C₈	—	293	1	no	—
228	C₂²×C₈	—	293	1	no	—
229	C₂²×C₈	—	293	1	no	—
230	C₂²×C₈	—	293	1	no	—
231	C₂²×C₈	—	293	1	no	—
232	C₂²×C₈	—	293	1	no	—
233	C₂²×C₈	—	586	4	no	—
234	C₂²×C₈	C₂×D₂₉₃	1	1	yes	characteristic
235	C₂²×C₈	C₂×D₂₉₃	1	1	yes	characteristic, complemented
236	#123	—	293	1	no	—
237	#123	—	293	1	no	—
238	C₂²⋊Q₈	—	293	1	no	—
239	C₂²⋊Q₈	—	293	1	no	—
240	#121	—	293	1	no	—
241	#121	—	293	1	no	—
242	#120	—	293	1	no	—
243	#120	—	293	1	no	—
244	C₄×D₄	—	293	1	no	—
245	C₄×D₄	—	293	1	no	—
246	C₄×D₄	—	293	1	no	—
247	C₄×D₄	C₂×D₂₉₃	1	1	yes	characteristic
248	#117	—	293	1	no	—
249	C₄⋊C₈	—	293	1	no	—
250	C₄⋊C₈	—	293	1	no	—
251	C₄⋊C₈	—	293	1	no	—
252	C₄⋊C₈	C₂×D₂₉₃	1	1	yes	characteristic, complemented
253	C₂²⋊C₈	—	293	1	no	—
254	C₂²⋊C₈	—	293	1	no	—
255	C₂²⋊C₈	—	293	1	no	—
256	C₂²⋊C₈	—	293	1	no	—
257	C₂²⋊C₈	—	293	1	no	—
258	C₂²⋊C₈	—	293	1	no	—
259	C₂²⋊C₈	C₂×D₂₉₃	1	1	yes	characteristic
260	C₂²⋊C₈	C₂×D₂₉₃	1	1	yes	characteristic, complemented
261	#97	—	293	1	no	—
262	#97	—	293	1	no	—
263	C₄×C₈	—	293	1	no	—
264	C₄×C₈	C₂×D₂₉₃	1	1	yes	characteristic, complemented
265	C₂⁴	—	293	1	no	—
266	#41	—	586	2	no	—
267	#41	—	586	2	no	—
268	C₂×Q₈	—	293	1	no	—
269	C₂×D₄	—	293	1	no	—
270	C₂×D₄	—	293	1	no	—
271	C₂×D₄	—	293	1	no	—
272	C₂×D₄	—	293	1	no	—
273	C₂×D₄	—	293	1	no	—
274	C₂×D₄	—	293	1	no	—
275	C₂×D₄	C₄×D₂₉₃	1	1	yes	characteristic
276	C₂²×C₄	—	293	1	no	—
277	C₂²×C₄	—	293	1	no	—
278	C₂²×C₄	—	293	1	no	—
279	C₂²×C₄	—	293	1	no	—
280	C₂²×C₄	—	293	1	no	—
281	C₂²×C₄	—	293	1	no	—
282	C₂²×C₄	—	586	2	no	—
283	C₂²×C₄	—	586	2	no	—
284	C₂²×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₂₉₃	1	1	yes	characteristic
286	M₁₆	—	586	2	no	—
287	M₁₆	—	586	2	no	—
288	M₁₆	—	586	2	no	—
289	M₁₆	—	586	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	293	1	no	—
293	C₂×C₈	—	293	4	no	—
294	C₂×C₈	—	293	1	no	—
295	C₂×C₈	—	293	1	no	—
296	C₂×C₈	—	293	1	no	—
297	C₂×C₈	—	586	2	no	—
298	C₂×C₈	—	586	2	no	—
299	C₂×C₈	—	586	2	no	—
300	C₂×C₈	—	586	2	no	—
301	C₂×C₈	—	586	2	no	—
302	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
306	C₄⋊C₄	—	293	1	no	—
307	C₄⋊C₄	—	293	1	no	—
308	C₄⋊C₄	—	293	1	no	—
309	C₄⋊C₄	—	293	1	no	—
310	C₄⋊C₄	—	293	1	no	—
311	C₄⋊C₄	C₄×D₂₉₃	1	1	yes	characteristic
312	C₂²⋊C₄	—	293	1	no	—
313	C₂²⋊C₄	—	293	1	no	—
314	C₂²⋊C₄	—	293	1	no	—
315	C₂²⋊C₄	—	293	1	no	—
316	C₂²⋊C₄	—	293	1	no	—
317	C₂²⋊C₄	—	293	1	no	—
318	C₂²⋊C₄	—	293	1	no	—
319	C₂²⋊C₄	—	293	1	no	—
320	C₂²⋊C₄	C₄×D₂₉₃	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₂₉₃	1	1	yes	characteristic
322	C₄²	—	293	1	no	—
323	C₄²	C₂²×D₂₉₃	1	1	yes	characteristic
324	C₂³	—	293	1	no	—
325	C₂³	—	293	1	no	—
326	C₂³	—	293	1	no	—
327	C₂³	—	586	2	no	—
328	C₂³	—	586	2	no	—
329	C₂³	—	586	2	no	—
330	C₂³	C₂×C₄×D₂₉₃	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₂₉₃	1	1	yes	characteristic
332	Q₈	—	586	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	586	2	no	—
335	D₄	—	586	2	no	—
336	D₄	—	586	2	no	—
337	D₄	—	586	2	no	—
338	D₄	—	586	2	no	—
339	D₄	—	586	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	293	1	no	—
345	C₂×C₄	—	293	2	no	—
346	C₂×C₄	—	293	2	no	—
347	C₂×C₄	—	293	1	no	—
348	C₂×C₄	—	293	1	no	—
349	C₂×C₄	—	293	1	no	—
350	C₂×C₄	—	293	1	no	—
351	C₂×C₄	—	586	2	no	—
352	C₂×C₄	—	586	2	no	—
353	C₂×C₄	—	586	2	no	—
354	C₂×C₄	—	586	1	no	—
355	C₂×C₄	—	586	1	no	—
356	C₂×C₄	—	586	1	no	—
357	C₂×C₄	—	586	1	no	—
358	C₂×C₄	C₂×C₄×D₂₉₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₂₉₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₂₉₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₂₉₃	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₂₉₃	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	293	2	no	—
367	C₈	—	586	1	no	—
368	C₈	—	586	1	no	—
369	C₈	—	586	1	no	—
370	C₈	D₄×D₂₉₃	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	293	2	no	—
377	C₂²	—	293	2	no	—
378	C₂²	—	586	8	no	—
379	C₂²	—	586	1	no	—
380	C₂²	—	586	1	no	—
381	C₂²	—	586	1	no	—
382	C₂²	—	586	1	no	—
383	C₂²	—	586	1	no	—
384	C₂²	—	586	1	no	—
385	C₂²	—	586	1	no	—
386	C₂²	#22627630	1	2	yes	complemented
387	C₂²	C₂²×C₄×D₂₉₃	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	293	2	no	—
393	C₄	—	586	1	no	—
394	C₄	—	586	1	no	—
395	C₄	—	586	1	no	—
396	C₄	—	586	1	no	—
397	C₄	C₂×D₄×D₂₉₃	1	1	yes	characteristic
398	C₄	#41×D₂₉₃	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	586	2	no	—
402	C₂	—	586	2	no	—
403	C₂	—	1172	1	no	—
404	C₂	C₄×D₄×D₂₉₃	1	1	yes	characteristic
405	C₂	#131×D₂₉₃	1	1	yes	characteristic
406	C₂	C₂×#22627630	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₂₉₃
commutator, socle	C₂²×C₂₉₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₉₃
Fitting	C₈×D₄×C₂₉₃	C₂
prime radical	#34036638	C₂
cosocle	C₂×C₄×C₂₉₃	C₂⁴
hypercenter	C₈×D₄	D₂₉₃
hypocenter	C₂₉₃	#2929
LCS	G ▷ C₂²×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#22627630	C₂	semidirect
2. C₂²×C₈×D₂₉₃	C₂	semidirect
4. #34036203	C₂	semidirect
5. #34036201	C₂	semidirect
6. #34036199	C₂	semidirect
7. #34036197	C₂	semidirect
8. C₈×D₁₁₇₂	C₂	semidirect
9. C₈×C₂²⋊D₂₉₃	C₂	semidirect
10. C₈×C₂²⋊D₂₉₃	C₂	semidirect
11. #34036154	C₂	semidirect
12. #34036094	C₂	semidirect
13. #34036091	C₂	semidirect
14. #34036083	C₂	semidirect
15. C₈×D₄×C₂₉₃	C₂	semidirect
19. C₂×#17989786	C₂²	semidirect
22. C₂×#17989785	C₂²	semidirect
29. C₂×C₈×D₂₉₃	C₂²	semidirect
42. C₄⋊#14556873	C₂²	semidirect
43. #22627553	C₂²	semidirect
44. #22627553	C₂²	semidirect
46. C₂²⋊#14556873	C₂²	semidirect
49. #22627536	C₂²	semidirect
50. #22627536	C₂²	semidirect
51. #22627535	C₂²	semidirect
52. #22627534	C₂²	semidirect
53. C₈×Dic₂₉₃	C₂²	semidirect
55. C₂²×C₈×C₂₉₃	C₂²	semidirect
57. C₄⋊C₈×C₂₉₃	C₂²	semidirect
59. C₂²⋊C₈×C₂₉₃	C₂²	semidirect
60. C₄×C₈×C₂₉₃	C₂²	semidirect
92. C₈×D₂₉₃	D₄	semidirect
172. C₂²×C₂₉₃	#131	semidirect
183. C₂×D₂₉₃	#131	semidirect
203. C₂₉₃	#2929	semidirect
215. C₈×D₄	D₂₉₃	semidirect
235. C₂²×C₈	C₂×D₂₉₃	semidirect
252. C₄⋊C₈	C₂×D₂₉₃	semidirect
260. C₂²⋊C₈	C₂×D₂₉₃	semidirect
264. C₄×C₈	C₂×D₂₉₃	semidirect
386. C₂²	#22627630	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22627630	2
C₂²×C₈×D₂₉₃	2
#34036638	2
#34036203	2
#34036201	2
#34036199	2
#34036197	2
C₈×D₁₁₇₂	2
C₈×C₂²⋊D₂₉₃	2
#34036154	2
#34036094	2
#34036091	2
#34036083	2
C₈×D₄×C₂₉₃	2
#2929	293