Subgroups — C₃²×#3098 #11770147

Order 1152.

1194 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#537	C₂	1	1	yes	maximal, characteristic
2	C₃²×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#485	C₂	1	2	yes	maximal, complemented
4	C₃²×#484	C₂	1	2	yes	maximal, complemented
5	C₃²×#482	C₂	1	2	yes	maximal, complemented
6	C₃²×#480	C₂	1	2	yes	maximal, complemented
7	C₃²×#428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃²×#107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#417	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3098	C₃	1	4	yes	maximal, direct product factor
13	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₃²×C₂²⋊Q₈	—	2	1	no	—
18	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₃²×#121	—	2	1	no	—
20	C₃²×#121	—	2	2	no	—
21	C₃²×#121	C₂²	1	2	yes	—
22	C₃²×C₄×Q₈	—	2	1	no	—
23	C₃²×C₄×D₄	—	2	2	no	—
24	C₃²×C₄×D₄	—	2	1	no	—
25	C₃²×#117	C₂²	1	2	yes	—
26	C₃²×#117	C₂²	1	1	yes	characteristic
27	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃²×#107	C₂²	1	2	yes	—
31	C₃²×#107	C₂²	1	2	yes	—
32	C₃²×#107	C₂²	1	2	yes	—
33	C₃²×#106	C₂²	1	2	yes	—
34	C₃²×#103	C₂²	1	1	yes	characteristic
35	C₃²×#103	C₂²	1	2	yes	—
36	C₃²×#103	C₂²	1	1	yes	characteristic
37	C₃²×#102	C₂²	1	1	yes	characteristic
38	C₃²×#102	C₂²	1	2	yes	—
39	C₃²×#102	C₂²	1	1	yes	characteristic
40	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₃×#537	C₂×C₃	1	4	yes	—
43	C₃×#520	C₂×C₃	1	4	yes	complemented
44	C₃×#485	C₂×C₃	1	8	yes	complemented
45	C₃×#484	C₂×C₃	1	8	yes	complemented
46	C₃×#482	C₂×C₃	1	8	yes	complemented
47	C₃×#480	C₂×C₃	1	8	yes	complemented
48	C₃×#428	C₂×C₃	1	4	yes	complemented
49	C₂×C₃×#107	C₂×C₃	1	4	yes	complemented
50	C₃×#417	C₂×C₃	1	4	yes	complemented
51	C₃×#416	C₂×C₃	1	4	yes	complemented
52	C₃×#408	C₂×C₃	1	4	yes	complemented
53	C₃²×#41	—	2	2	no	—
54	C₃²×#41	—	2	2	no	—
55	C₃²×#41	—	2	2	no	—
56	C₃²×#41	—	2	2	no	—
57	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
58	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃²×D₄	—	2	1	no	—
60	C₂×C₃²×D₄	—	2	2	no	—
61	C₂×C₃²×D₄	D₄	1	2	yes	—
62	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
63	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃²×C₄	—	2	2	no	—
65	C₂²×C₃²×C₄	—	2	1	no	—
66	C₂²×C₃²×C₄	—	2	1	no	—
67	C₂²×C₃²×C₄	—	2	1	no	—
68	C₂²×C₃²×C₄	C₂³	1	2	yes	—
69	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
70	C₃²×M₁₆	—	2	2	no	—
71	C₂×C₃²×C₈	—	2	2	no	—
72	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃²×C₈	C₂³	1	2	yes	—
75	C₃²×C₄⋊C₄	—	2	2	no	—
76	C₃²×C₄⋊C₄	—	2	1	no	—
77	C₃²×C₄⋊C₄	—	2	1	no	—
78	C₃²×C₄⋊C₄	—	2	2	no	—
79	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
81	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
82	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₃²×C₂²⋊C₄	—	2	2	no	—
84	C₃²×C₂²⋊C₄	—	2	1	no	—
85	C₃²×C₂²⋊C₄	—	2	2	no	—
86	C₃²×C₂²⋊C₄	—	2	2	no	—
87	C₃²×C₄²	—	2	2	no	—
88	C₃²×C₄²	—	2	1	no	—
89	#3098	C₃²	1	1	yes	characteristic, direct product factor, Sylow
90	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
91	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
92	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
93	C₂²×C₃×C₈	C₂²×C₃	1	4	yes	—
94	C₃×C₂²⋊Q₈	—	2	4	no	—
95	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
96	C₃×#121	—	2	4	no	—
97	C₃×#121	—	2	8	no	—
98	C₃×#121	C₂²×C₃	1	8	yes	—
99	C₃×C₄×Q₈	—	2	4	no	—
100	C₃×C₄×D₄	—	2	8	no	—
101	C₃×C₄×D₄	—	2	4	no	—
102	C₃×#117	C₂²×C₃	1	4	yes	—
103	C₃×#117	C₂²×C₃	1	8	yes	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
106	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
107	C₃×#107	C₂²×C₃	1	8	yes	—
108	C₃×#107	C₂²×C₃	1	8	yes	—
109	C₃×#107	C₂²×C₃	1	8	yes	—
110	C₃×#106	C₂²×C₃	1	8	yes	—
111	C₃×#103	C₂²×C₃	1	4	yes	—
112	C₃×#103	C₂²×C₃	1	4	yes	—
113	C₃×#103	C₂²×C₃	1	8	yes	—
114	C₃×#102	C₂²×C₃	1	4	yes	—
115	C₃×#102	C₂²×C₃	1	4	yes	—
116	C₃×#102	C₂²×C₃	1	8	yes	—
117	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	—
118	C₃×C₂²⋊C₈	C₂²×C₃	1	8	yes	—
119	C₂³×C₃²	—	2	1	no	—
120	C₂³×C₃²	C₂×D₄	1	2	yes	—
121	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
122	C₃²×Q₈	—	2	2	no	—
123	C₃²×Q₈	—	2	1	no	—
124	C₃²×Q₈	—	2	1	no	—
125	C₃²×D₄	—	2	4	no	—
126	C₃²×D₄	—	2	2	no	—
127	C₃²×D₄	—	2	1	no	—
128	C₃²×D₄	—	2	1	no	—
129	C₃²×D₄	—	4	2	no	—
130	C₃²×D₄	—	8	2	no	—
131	C₂×C₃²×C₄	—	2	2	no	—
132	C₂×C₃²×C₄	—	2	2	no	—
133	C₂×C₃²×C₄	—	2	1	no	—
134	C₂×C₃²×C₄	—	2	2	no	—
135	C₂×C₃²×C₄	—	2	1	no	—
136	C₂×C₃²×C₄	—	2	2	no	—
137	C₂×C₃²×C₄	—	2	1	no	—
138	C₂×C₃²×C₄	—	4	2	no	—
139	C₂×C₃²×C₄	—	8	1	no	—
140	C₂×C₃²×C₄	—	8	2	no	—
141	C₂×C₃²×C₄	—	8	1	no	—
142	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
143	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃²×C₄	#41	1	2	yes	—
145	C₂×C₃²×C₄	#41	1	2	yes	—
146	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
147	C₃²×C₈	—	2	1	no	—
148	C₃²×C₈	—	2	1	no	—
149	C₃²×C₈	—	2	2	no	—
150	#537	C₂×C₃²	1	1	yes	characteristic
151	#520	C₂×C₃²	1	1	yes	characteristic, complemented
152	#485	C₂×C₃²	1	2	yes	complemented
153	#484	C₂×C₃²	1	2	yes	complemented
154	#482	C₂×C₃²	1	2	yes	complemented
155	#480	C₂×C₃²	1	2	yes	complemented
156	#428	C₂×C₃²	1	1	yes	characteristic, complemented
157	C₂×#107	C₂×C₃²	1	1	yes	characteristic, complemented
158	#417	C₂×C₃²	1	1	yes	characteristic, complemented
159	#416	C₂×C₃²	1	1	yes	characteristic, complemented
160	#408	C₂×C₃²	1	1	yes	characteristic, complemented
161	C₃×#41	—	2	8	no	—
162	C₃×#41	—	2	8	no	—
163	C₃×#41	—	2	8	no	—
164	C₃×#41	—	2	8	no	—
165	C₂×C₃×Q₈	C₃×D₄	1	4	yes	—
166	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
167	C₂×C₃×D₄	—	2	4	no	—
168	C₂×C₃×D₄	—	2	8	no	—
169	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
170	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
171	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
172	C₂²×C₃×C₄	—	2	8	no	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	2	4	no	—
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
177	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
178	C₃×M₁₆	—	2	8	no	—
179	C₂×C₃×C₈	—	2	8	no	—
180	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
181	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
182	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
183	C₃×C₄⋊C₄	—	2	8	no	—
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	—	2	4	no	—
186	C₃×C₄⋊C₄	—	2	8	no	—
187	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
188	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
189	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
190	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
191	C₃×C₂²⋊C₄	—	2	8	no	—
192	C₃×C₂²⋊C₄	—	2	4	no	—
193	C₃×C₂²⋊C₄	—	2	8	no	—
194	C₃×C₂²⋊C₄	—	2	8	no	—
195	C₃×C₄²	—	2	8	no	—
196	C₃×C₄²	—	2	4	no	—
197	C₂²×C₃²	—	2	1	no	—
198	C₂²×C₃²	—	2	1	no	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	—	2	2	no	—
201	C₂²×C₃²	—	2	2	no	—
202	C₂²×C₃²	—	4	1	no	—
203	C₂²×C₃²	—	4	1	no	—
204	C₂²×C₃²	—	4	1	no	—
205	C₂²×C₃²	#123	1	2	yes	—
206	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
207	C₃²×C₄	—	2	2	no	—
208	C₃²×C₄	—	4	1	no	—
209	C₃²×C₄	—	4	2	no	—
210	C₃²×C₄	—	4	1	no	—
211	C₃²×C₄	—	4	2	no	—
212	C₃²×C₄	—	4	1	no	—
213	C₃²×C₄	#123	1	2	yes	—
214	C₃²×C₄	C₂×#41	1	1	yes	characteristic
215	C₃²×C₄	C₂×#41	1	1	yes	characteristic
216	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
217	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
218	C₂×M₁₆	C₂²×C₃²	1	1	yes	characteristic
219	C₂²×C₈	C₂²×C₃²	1	1	yes	characteristic
220	C₂²⋊Q₈	—	2	1	no	—
221	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
222	#121	—	2	1	no	—
223	#121	—	2	2	no	—
224	#121	C₂²×C₃²	1	2	yes	—
225	C₄×Q₈	—	2	1	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	1	no	—
228	#117	C₂²×C₃²	1	1	yes	characteristic
229	#117	C₂²×C₃²	1	2	yes	—
230	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
232	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
233	#107	C₂²×C₃²	1	2	yes	—
234	#107	C₂²×C₃²	1	2	yes	—
235	#107	C₂²×C₃²	1	2	yes	—
236	#106	C₂²×C₃²	1	2	yes	—
237	#103	C₂²×C₃²	1	1	yes	characteristic
238	#103	C₂²×C₃²	1	1	yes	characteristic
239	#103	C₂²×C₃²	1	2	yes	—
240	#102	C₂²×C₃²	1	1	yes	characteristic
241	#102	C₂²×C₃²	1	1	yes	characteristic
242	#102	C₂²×C₃²	1	2	yes	—
243	C₂²⋊C₈	C₂²×C₃²	1	2	yes	—
244	C₂²⋊C₈	C₂²×C₃²	1	2	yes	—
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
247	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
248	C₃×Q₈	—	2	8	no	—
249	C₃×Q₈	—	2	4	no	—
250	C₃×Q₈	—	2	4	no	—
251	C₃×D₄	—	2	16	no	—
252	C₃×D₄	—	2	8	no	—
253	C₃×D₄	—	2	4	no	—
254	C₃×D₄	—	2	4	no	—
255	C₃×D₄	—	4	8	no	—
256	C₃×D₄	—	8	8	no	—
257	C₂×C₃×C₄	—	2	8	no	—
258	C₂×C₃×C₄	—	2	8	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	8	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	8	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	4	8	no	—
265	C₂×C₃×C₄	—	8	4	no	—
266	C₂×C₃×C₄	—	8	8	no	—
267	C₂×C₃×C₄	—	8	4	no	—
268	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
269	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
270	C₂×C₃×C₄	C₃×#41	1	8	yes	—
271	C₂×C₃×C₄	C₃×#41	1	8	yes	—
272	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
273	C₃×C₈	—	2	4	no	—
274	C₃×C₈	—	2	4	no	—
275	C₃×C₈	—	2	8	no	—
276	C₂×C₃²	—	2	2	no	—
277	C₂×C₃²	—	4	2	no	—
278	C₂×C₃²	—	8	1	no	—
279	C₂×C₃²	C₂×#123	1	1	yes	characteristic
280	C₂×C₃²	#576	1	1	yes	characteristic
281	C₂×C₃²	#578	1	1	yes	characteristic
282	#41	—	2	2	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	C₂×Q₈	C₃²×D₄	1	1	yes	characteristic
287	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	C₃²×D₄	1	2	yes	—
291	C₂×D₄	C₃²×D₄	1	1	yes	characteristic
292	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	C₂³×C₃²	1	2	yes	—
298	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
299	M₁₆	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	C₂³×C₃²	1	2	yes	—
302	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
303	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
309	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
310	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
311	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	1	no	—
318	C₂²×C₃	—	2	4	no	—
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	2	8	no	—
321	C₂²×C₃	—	2	8	no	—
322	C₂²×C₃	—	2	8	no	—
323	C₂²×C₃	—	4	4	no	—
324	C₂²×C₃	—	4	4	no	—
325	C₂²×C₃	—	4	4	no	—
326	C₂²×C₃	C₃×#123	1	8	yes	—
327	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
328	C₃×C₄	—	2	8	no	—
329	C₃×C₄	—	4	8	no	—
330	C₃×C₄	—	4	4	no	—
331	C₃×C₄	—	4	8	no	—
332	C₃×C₄	—	4	4	no	—
333	C₃×C₄	—	4	4	no	—
334	C₃×C₄	C₃×#123	1	8	yes	—
335	C₃×C₄	C₂×C₃×#41	1	4	yes	—
336	C₃×C₄	C₂×C₃×#41	1	4	yes	—
337	C₃²	#3098	1	1	yes	characteristic, direct product factor, Sylow
338	C₂³	—	2	1	no	—
339	C₂³	C₂×C₃²×D₄	1	2	yes	—
340	C₂³	C₂×C₃²×D₄	1	1	yes	characteristic
341	Q₈	—	2	2	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	D₄	—	2	4	no	—
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	8	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	1	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	1	no	—
361	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
362	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
363	C₂×C₄	C₃²×#41	1	2	yes	—
364	C₂×C₄	C₃²×#41	1	2	yes	—
365	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	2	no	—
369	C₂×C₃	—	2	8	no	—
370	C₂×C₃	—	4	8	no	—
371	C₂×C₃	—	8	4	no	—
372	C₂×C₃	C₂×C₃×#123	1	4	yes	—
373	C₂×C₃	C₃×#576	1	4	yes	—
374	C₂×C₃	C₃×#578	1	4	yes	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	C₃²×#123	1	2	yes	—
384	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	C₃²×#123	1	2	yes	—
392	C₄	C₂×C₃²×#41	1	1	yes	characteristic
393	C₄	C₂×C₃²×#41	1	1	yes	characteristic
394	C₃	C₃×#3098	1	4	yes	direct product factor
395	C₂	—	2	2	no	—
396	C₂	—	4	2	no	—
397	C₂	—	8	1	no	—
398	C₂	C₂×C₃²×#123	1	1	yes	characteristic
399	C₂	C₃²×#576	1	1	yes	characteristic
400	C₂	C₃²×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
prime radical	C₃²×#537	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×#520	C₂	semidirect
3. C₃²×#485	C₂	semidirect
4. C₃²×#484	C₂	semidirect
5. C₃²×#482	C₂	semidirect
6. C₃²×#480	C₂	semidirect
7. C₃²×#428	C₂	semidirect
8. C₂×C₃²×#107	C₂	semidirect
9. C₃²×#417	C₂	semidirect
10. C₃²×#416	C₂	semidirect
11. C₃²×#408	C₂	semidirect
12. C₃×#3098	C₃	direct (N × H)
43. C₃×#520	C₂×C₃	semidirect
44. C₃×#485	C₂×C₃	semidirect
45. C₃×#484	C₂×C₃	semidirect
46. C₃×#482	C₂×C₃	semidirect
47. C₃×#480	C₂×C₃	semidirect
48. C₃×#428	C₂×C₃	semidirect
49. C₂×C₃×#107	C₂×C₃	semidirect
50. C₃×#417	C₂×C₃	semidirect
51. C₃×#416	C₂×C₃	semidirect
52. C₃×#408	C₂×C₃	semidirect
89. #3098	C₃²	direct (N × H)
151. #520	C₂×C₃²	semidirect
152. #485	C₂×C₃²	semidirect
153. #484	C₂×C₃²	semidirect
154. #482	C₂×C₃²	semidirect
155. #480	C₂×C₃²	semidirect
156. #428	C₂×C₃²	semidirect
157. C₂×#107	C₂×C₃²	semidirect
158. #417	C₂×C₃²	semidirect
159. #416	C₂×C₃²	semidirect
160. #408	C₂×C₃²	semidirect
337. C₃²	#3098	direct (N × H)
394. C₃	C₃×#3098	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#537	2
C₃²×#520	2
C₃²×#485	2
C₃²×#484	2
C₃²×#482	2
C₃²×#480	2
C₃²×#428	2
C₂×C₃²×#107	2
C₃²×#417	2
C₃²×#416	2
C₃²×#408	2
C₃×#3098	3

Subgroups — C32×#3098 #11770147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3098 #11770147