Subgroups — #16836224

Order 3712.

502 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×#11745346	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#90800	C₂	1	1	yes	maximal, characteristic, complemented
3	#14272198	C₂	1	1	yes	maximal, characteristic, complemented
4	#14272196	C₂	1	1	yes	maximal, characteristic, complemented
5	#14272195	C₂	1	1	yes	maximal, characteristic, complemented
6	#14272194	C₂	1	1	yes	maximal, characteristic, complemented
7	#14272194	C₂	1	1	yes	maximal, characteristic, complemented
8	#14272192	C₂	1	1	yes	maximal, characteristic, complemented
9	#14272190	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#6599	C₂	1	1	yes	maximal, characteristic, complemented
11	#14272169	C₂	1	1	yes	maximal, characteristic, complemented
12	#14272136	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂²⋊#6599	C₂	1	1	yes	maximal, characteristic, complemented
14	#14272127	C₂	1	1	yes	maximal, characteristic, complemented
15	#14271669	C₂	1	1	yes	maximal, characteristic
16	C₂³×Dic₂₉	C₂²	1	1	yes	characteristic
17	C₂×#90807	C₂²	1	1	yes	characteristic
18	C₂×#90800	—	2	4	no	—
19	C₂×#90800	C₂²	1	1	yes	characteristic
20	C₂×#90800	C₂²	1	1	yes	characteristic
21	C₂×#90800	C₂²	1	1	yes	characteristic
22	C₂×#90800	C₂²	1	1	yes	characteristic
23	C₂×#90800	C₂²	1	1	yes	characteristic, complemented
24	C₂²×#6599	C₂²	1	1	yes	characteristic
25	C₂²×#6599	C₂²	1	1	yes	characteristic
26	C₂²×#6599	C₂²	1	1	yes	characteristic
27	C₂²×#6599	C₂²	1	1	yes	characteristic
28	C₂²×#6599	C₂²	1	1	yes	characteristic, complemented
29	#11745346	—	2	4	no	—
30	C₂×#90796	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₂₉×#120	C₄	1	1	yes	characteristic
33	#11745315	C₄	1	1	yes	characteristic
34	#11745301	C₄	1	1	yes	characteristic
35	#11745301	C₄	1	1	yes	characteristic
36	#11745297	C₄	1	1	yes	characteristic
37	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
38	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
39	#11745248	C₄	1	1	yes	characteristic
40	#11745243	C₂²	1	1	yes	characteristic
41	#11745243	C₂²	1	1	yes	characteristic
42	#11745240	C₄	1	1	yes	characteristic
43	#11745240	C₄	1	1	yes	characteristic
44	#11745239	C₂²	1	1	yes	characteristic
45	C₂²⋊#6599	C₂²	1	1	yes	characteristic
46	C₂²⋊#6599	C₂²	1	1	yes	characteristic
47	C₂²⋊#6599	C₂²	1	1	yes	characteristic
48	C₂²⋊#6599	C₂²	1	1	yes	characteristic
49	C₂²⋊#6599	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#6599	C₂²	1	1	yes	characteristic, complemented
51	#11745220	C₂²	1	1	yes	characteristic, complemented
52	#11745220	C₂²	1	1	yes	characteristic, complemented
53	#11745219	C₂²	1	1	yes	characteristic, complemented
54	#11745219	C₂²	1	1	yes	characteristic, complemented
55	#11745218	C₂²	1	1	yes	characteristic, complemented
56	#11745218	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊#6599	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊#6599	C₂²	1	1	yes	characteristic, complemented
59	C₄×#6599	C₂²	1	1	yes	characteristic, complemented
60	C₄×#6599	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
62	C₂×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
63	C₂×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
64	C₂×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₂₉	—	2	2	no	—
70	C₂²×Dic₂₉	—	2	2	no	—
71	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
72	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
73	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
74	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
75	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
76	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
77	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
78	#90807	—	2	2	no	—
79	#90807	—	2	2	no	—
80	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
81	C₂×Dic₅₈	C₂×C₄	1	1	yes	characteristic
82	#90800	—	2	2	no	—
83	#90800	—	2	2	no	—
84	#90800	—	2	2	no	—
85	#90800	—	2	2	no	—
86	#90800	D₄	1	4	yes	complemented
87	C₂×#6599	—	2	2	no	—
88	C₂×#6599	—	2	2	no	—
89	C₂×#6599	—	2	2	no	—
90	C₂×#6599	—	2	2	no	—
91	C₂×#6599	—	2	2	no	—
92	C₂×#6599	C₂³	1	1	yes	characteristic
93	C₂×#6599	C₂³	1	1	yes	characteristic
94	C₂×#6599	C₂³	1	1	yes	characteristic
95	C₂×#6599	C₂³	1	1	yes	characteristic
96	C₂×#6599	C₂³	1	1	yes	characteristic
97	C₂×#6599	C₂³	1	1	yes	characteristic
98	C₂×#6599	C₂³	1	1	yes	characteristic
99	C₂×#6599	C₂³	1	1	yes	characteristic
100	#90796	—	2	2	no	—
101	D₂₉⋊C₈	—	2	2	no	—
102	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
108	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
109	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
110	#90781	C₂×C₄	1	1	yes	characteristic
111	#90781	C₂×C₄	1	1	yes	characteristic
112	C₄⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
113	C₄⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
114	#90779	C₂×C₄	1	1	yes	characteristic
115	#90779	C₂×C₄	1	1	yes	characteristic
116	#90779	C₂×C₄	1	1	yes	characteristic
117	#90779	C₂×C₄	1	1	yes	characteristic
118	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
119	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
120	C₂³×C₂₉	—	2	2	no	—
121	C₂³×C₂₉	—	2	2	no	—
122	C₂³×C₂₉	—	4	1	no	—
123	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
124	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
125	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
126	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₂₉	—	2	2	no	—
129	D₄×C₂₉	—	2	2	no	—
130	D₄×C₂₉	—	4	1	no	—
131	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²⋊D₂₉	—	2	2	no	—
135	C₂²⋊D₂₉	—	2	2	no	—
136	C₂²⋊D₂₉	—	2	2	no	—
137	C₂²⋊D₂₉	—	4	1	no	—
138	C₂×Dic₂₉	—	2	2	no	—
139	C₂×Dic₂₉	—	2	2	no	—
140	C₂×Dic₂₉	—	2	2	no	—
141	C₂×Dic₂₉	—	2	1	no	—
142	C₂×Dic₂₉	—	2	1	no	—
143	C₂×Dic₂₉	—	2	1	no	—
144	C₂×Dic₂₉	—	2	1	no	—
145	C₂×Dic₂₉	—	2	1	no	—
146	C₂×Dic₂₉	—	2	1	no	—
147	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×Dic₂₉	C₂×D₄	1	2	yes	—
154	C₂×Dic₂₉	#41	1	2	yes	—
155	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
156	C₄×D₂₉	—	2	1	no	—
157	C₄×D₂₉	—	2	1	no	—
158	Dic₅₈	—	2	2	no	—
159	#6599	—	2	1	no	—
160	#6599	—	2	1	no	—
161	#6599	—	2	1	no	—
162	#6599	—	2	1	no	—
163	#6599	—	2	1	no	—
164	#6599	—	2	1	no	—
165	#6599	C₂×D₄	1	2	yes	—
166	#6599	C₂×D₄	1	2	yes	—
167	#2933	—	29	1	no	maximal, Sylow
168	C₂²×C₂₉	—	2	1	no	—
169	C₂²×C₂₉	—	2	1	no	—
170	C₂²×C₂₉	—	2	1	no	—
171	C₂²×C₂₉	—	2	1	no	—
172	C₂²×C₂₉	—	2	1	no	—
173	C₂²×C₂₉	—	2	1	no	—
174	C₂²×C₂₉	—	2	1	no	—
175	C₂²×C₂₉	—	2	1	no	—
176	C₂²×C₂₉	—	2	1	no	—
177	C₂²×C₂₉	—	2	1	no	—
178	C₂²×C₂₉	—	4	4	no	—
179	C₂²×C₂₉	C₄×D₄	1	2	yes	—
180	C₂²×C₂₉	#131	1	2	yes	complemented
181	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
182	C₂×D₂₉	—	2	1	no	—
183	C₂×D₂₉	—	2	1	no	—
184	C₂×D₂₉	—	2	1	no	—
185	C₄×C₂₉	—	2	1	no	—
186	C₄×C₂₉	—	2	1	no	—
187	C₄×C₂₉	—	2	1	no	—
188	Dic₂₉	—	2	1	no	—
189	Dic₂₉	—	2	1	no	—
190	Dic₂₉	—	2	1	no	—
191	Dic₂₉	—	2	1	no	—
192	Dic₂₉	—	2	1	no	—
193	Dic₂₉	C₄×D₄	1	2	yes	—
194	Dic₂₉	C₂²×D₄	1	1	yes	characteristic
195	Dic₂₉	C₂×#41	1	1	yes	characteristic
196	C₂×#131	—	29	1	no	—
197	C₂²×M₁₆	—	29	1	no	—
198	#525	—	29	1	no	—
199	#436	—	29	1	no	—
200	#436	—	29	1	no	—
201	#435	—	29	1	no	—
202	#435	—	29	1	no	—
203	#435	—	29	1	no	—
204	#435	—	29	1	no	—
205	C₈×D₄	—	29	1	no	—
206	C₈×D₄	—	29	1	no	—
207	#424	—	29	1	no	—
208	#408	—	29	1	no	—
209	C₂×C₂²⋊C₈	—	29	1	no	—
210	#405	—	29	1	no	—
211	C₂×C₂₉	—	2	2	no	—
212	C₂×C₂₉	—	2	2	no	—
213	C₂×C₂₉	—	4	1	no	—
214	C₂×C₂₉	—	4	1	no	—
215	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
216	C₂×C₂₉	C₂×#131	1	1	yes	characteristic
217	C₂×C₂₉	#568	1	1	yes	characteristic
218	D₂₉	—	4	1	no	—
219	C₂×#41	—	29	1	no	—
220	C₂³×C₄	—	29	1	no	—
221	#131	—	58	4	no	—
222	C₂×M₁₆	—	29	1	no	—
223	C₂×M₁₆	—	29	1	no	—
224	C₂×M₁₆	—	29	1	no	—
225	C₂×M₁₆	—	29	1	no	—
226	C₂×M₁₆	—	29	1	no	—
227	C₂×M₁₆	—	29	1	no	—
228	C₂×M₁₆	—	58	4	no	—
229	C₂²×C₈	—	29	1	no	—
230	C₂²×C₈	—	29	1	no	—
231	C₂²×C₈	—	29	1	no	—
232	C₂²×C₈	—	29	1	no	—
233	C₂²×C₈	—	29	1	no	—
234	C₂²×C₈	—	29	1	no	—
235	#123	—	29	1	no	—
236	#123	—	29	1	no	—
237	C₂²⋊Q₈	—	29	1	no	—
238	C₂²⋊Q₈	—	29	1	no	—
239	#121	—	29	1	no	—
240	#121	—	29	1	no	—
241	#120	—	29	1	no	—
242	#120	#1181	1	1	yes	characteristic
243	C₄×D₄	—	29	1	no	—
244	C₄×D₄	—	29	1	no	—
245	C₄×D₄	—	29	1	no	—
246	C₄×D₄	—	29	1	no	—
247	#117	—	29	1	no	—
248	C₄⋊C₈	—	29	1	no	—
249	C₄⋊C₈	—	29	1	no	—
250	C₄⋊C₈	—	29	1	no	—
251	C₄⋊C₈	—	29	1	no	—
252	C₂²⋊C₈	—	29	1	no	—
253	C₂²⋊C₈	—	29	1	no	—
254	C₂²⋊C₈	—	29	1	no	—
255	C₂²⋊C₈	—	29	1	no	—
256	C₂²⋊C₈	—	29	1	no	—
257	C₂²⋊C₈	—	29	1	no	—
258	C₂²⋊C₈	—	29	1	no	—
259	C₂²⋊C₈	—	29	1	no	—
260	#97	—	29	1	no	—
261	#97	—	29	1	no	—
262	C₄×C₈	—	29	1	no	—
263	C₄×C₈	—	29	1	no	—
264	C₂₉	#2933	1	1	yes	characteristic, complemented, Sylow
265	C₂⁴	C₂×#1181	1	1	yes	characteristic
266	#41	—	58	2	no	—
267	#41	—	58	2	no	—
268	C₂×Q₈	—	29	1	no	—
269	C₂×D₄	—	29	1	no	—
270	C₂×D₄	—	29	1	no	—
271	C₂×D₄	—	29	1	no	—
272	C₂×D₄	—	29	1	no	—
273	C₂×D₄	C₂×#1181	1	1	yes	characteristic
274	C₂×D₄	C₂×#1181	1	1	yes	characteristic
275	C₂×D₄	C₂×#1181	1	1	yes	characteristic
276	C₂²×C₄	—	29	1	no	—
277	C₂²×C₄	—	29	1	no	—
278	C₂²×C₄	—	29	1	no	—
279	C₂²×C₄	—	29	1	no	—
280	C₂²×C₄	—	29	1	no	—
281	C₂²×C₄	—	29	1	no	—
282	C₂²×C₄	—	29	1	no	—
283	C₂²×C₄	—	29	1	no	—
284	C₂²×C₄	—	58	2	no	—
285	C₂²×C₄	—	58	2	no	—
286	M₁₆	—	29	4	no	—
287	M₁₆	—	58	2	no	—
288	M₁₆	—	58	2	no	—
289	M₁₆	—	58	2	no	—
290	M₁₆	—	58	2	no	—
291	M₁₆	—	58	2	no	—
292	C₂×C₈	—	29	1	no	—
293	C₂×C₈	—	29	1	no	—
294	C₂×C₈	—	29	1	no	—
295	C₂×C₈	—	29	1	no	—
296	C₂×C₈	—	29	1	no	—
297	C₂×C₈	—	29	1	no	—
298	C₂×C₈	—	29	1	no	—
299	C₂×C₈	—	29	1	no	—
300	C₂×C₈	—	58	2	no	—
301	C₂×C₈	—	58	2	no	—
302	C₂×C₈	—	58	2	no	—
303	C₂×C₈	—	58	2	no	—
304	C₂×C₈	—	58	2	no	—
305	C₂×C₈	—	58	2	no	—
306	C₄⋊C₄	—	29	1	no	—
307	C₄⋊C₄	—	29	1	no	—
308	C₄⋊C₄	—	29	1	no	—
309	C₄⋊C₄	—	29	1	no	—
310	C₄⋊C₄	—	29	1	no	—
311	C₄⋊C₄	—	29	1	no	—
312	C₂²⋊C₄	—	29	1	no	—
313	C₂²⋊C₄	—	29	1	no	—
314	C₂²⋊C₄	—	29	1	no	—
315	C₂²⋊C₄	—	29	1	no	—
316	C₂²⋊C₄	—	29	1	no	—
317	C₂²⋊C₄	—	29	1	no	—
318	C₂²⋊C₄	—	29	1	no	—
319	C₂²⋊C₄	C₂×#1181	1	1	yes	characteristic
320	C₂²⋊C₄	C₂×#1181	1	1	yes	characteristic
321	C₂²⋊C₄	C₂×#1181	1	1	yes	characteristic
322	C₄²	—	29	1	no	—
323	C₄²	—	29	1	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	29	1	no	—
328	C₂³	C₂²×#1181	1	1	yes	characteristic
329	C₂³	C₂²×#1181	1	1	yes	characteristic
330	C₂³	C₂²×#1181	1	1	yes	characteristic
331	C₂³	C₂²×#1181	1	1	yes	characteristic
332	Q₈	—	58	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	4	1	no	—
336	D₄	—	58	2	no	—
337	D₄	—	58	2	no	—
338	D₄	—	58	2	no	—
339	D₄	—	116	1	no	—
340	C₂×C₄	—	29	2	no	—
341	C₂×C₄	—	29	2	no	—
342	C₂×C₄	—	29	1	no	—
343	C₂×C₄	—	29	1	no	—
344	C₂×C₄	—	29	1	no	—
345	C₂×C₄	—	29	1	no	—
346	C₂×C₄	—	29	1	no	—
347	C₂×C₄	—	29	1	no	—
348	C₂×C₄	—	29	1	no	—
349	C₂×C₄	—	58	1	no	—
350	C₂×C₄	—	58	1	no	—
351	C₂×C₄	—	58	1	no	—
352	C₂×C₄	—	58	1	no	—
353	C₂×C₄	—	58	1	no	—
354	C₂×C₄	—	58	1	no	—
355	C₂×C₄	—	58	1	no	—
356	C₂×C₄	—	58	2	no	—
357	C₂×C₄	—	58	2	no	—
358	C₂×C₄	—	58	1	no	—
359	C₂×C₄	—	58	2	no	—
360	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
361	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
362	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
363	C₈	—	29	2	no	—
364	C₈	—	29	2	no	—
365	C₈	—	58	1	no	—
366	C₈	—	58	1	no	—
367	C₈	—	58	1	no	—
368	C₈	—	58	1	no	—
369	C₈	—	58	1	no	—
370	C₈	—	58	1	no	—
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	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	58	1	no	—
383	C₂²	—	58	1	no	—
384	C₂²	—	58	1	no	—
385	C₂²	#11745346	1	2	yes	complemented
386	C₂²	D₄×#1181	1	2	yes	—
387	C₂²	C₂³×#1181	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	29	1	no	—
392	C₄	—	29	1	no	—
393	C₄	—	29	2	no	—
394	C₄	—	58	1	no	—
395	C₄	—	58	1	no	—
396	C₄	—	58	1	no	—
397	C₄	—	58	1	no	—
398	C₄	—	58	1	no	—
399	C₂	—	2	2	no	—
400	C₂	—	2	2	no	—
401	C₂	—	4	1	no	—
402	C₂	—	4	1	no	—
403	C₂	—	116	1	no	—
404	C₂	C₂×D₄×#1181	1	1	yes	characteristic
405	C₂	C₂×#11745346	1	1	yes	characteristic
406	C₂	#14272241	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#1181
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×#120	C₄
prime radical	#14271669	C₂
cosocle	C₂×Dic₂₉	C₂⁴
hypercenter	#120	#1181
hypocenter	C₂₉	#2933
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #120

Complements

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

N	H ≅ G/N	type
1. C₂×#11745346	C₂	semidirect
2. C₂²×#90800	C₂	semidirect
3. #14272198	C₂	semidirect
4. #14272196	C₂	semidirect
5. #14272195	C₂	semidirect
6. #14272194	C₂	semidirect
7. #14272194	C₂	semidirect
8. #14272192	C₂	semidirect
9. #14272190	C₂	semidirect
10. D₄×#6599	C₂	semidirect
11. #14272169	C₂	semidirect
12. #14272136	C₂	semidirect
13. C₂×C₂²⋊#6599	C₂	semidirect
14. #14272127	C₂	semidirect
23. C₂×#90800	C₂²	semidirect
28. C₂²×#6599	C₂²	semidirect
30. C₂×#90796	C₂²	semidirect
31. C₂×D₂₉⋊C₈	C₂²	semidirect
49. C₂²⋊#6599	C₂²	semidirect
50. C₂²⋊#6599	C₂²	semidirect
51. #11745220	C₂²	semidirect
52. #11745220	C₂²	semidirect
53. #11745219	C₂²	semidirect
54. #11745219	C₂²	semidirect
55. #11745218	C₂²	semidirect
56. #11745218	C₂²	semidirect
57. C₄⋊#6599	C₂²	semidirect
58. C₄⋊#6599	C₂²	semidirect
59. C₄×#6599	C₂²	semidirect
60. C₄×#6599	C₂²	semidirect
86. #90800	D₄	semidirect
180. C₂²×C₂₉	#131	semidirect
264. C₂₉	#2933	semidirect
385. C₂²	#11745346	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745346	2
C₂²×#90800	2
#14272198	2
#14272196	2
#14272195	2
#14272194	2
#14272192	2
#14272190	2
D₄×#6599	2
#14272169	2
#14272136	2
C₂×C₂²⋊#6599	2
#14272127	2
#14271669	2
#2933	29