Subgroups — #85987

Order 384.

1124 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#5817	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	#5791	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	#5641	C₂	1	1	yes	maximal, characteristic, complemented
7	#5640	C₂	1	2	yes	maximal, complemented
8	#5639	C₂	1	1	yes	maximal, characteristic, complemented
9	#5638	C₂	1	2	yes	maximal, complemented
10	#5637	C₂	1	2	yes	maximal, complemented
11	#5636	C₂	1	2	yes	maximal, complemented
12	#5633	C₂	1	1	yes	maximal, characteristic, complemented
13	#5631	C₂	1	1	yes	maximal, characteristic, complemented
14	#5627	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	#5624	C₂	1	1	yes	maximal, characteristic, complemented
17	#5622	C₂	1	1	yes	maximal, characteristic, complemented
18	#5515	C₂	1	2	yes	maximal, complemented
19	#5513	C₂	1	1	yes	maximal, characteristic, complemented
20	#5507	C₂	1	1	yes	maximal, characteristic, complemented
21	#5504	C₂	1	2	yes	maximal, complemented
22	#5495	C₂	1	2	yes	maximal, complemented
23	#5490	C₂	1	2	yes	maximal, complemented
24	#3520	—	3	1	no	maximal, Sylow
25	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
27	C₂²×#67	C₂²	1	1	yes	characteristic
28	C₂×#239	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×#235	C₂²	1	2	yes	—
31	C₂×#235	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
33	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
40	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	#953	C₂²	1	2	yes	—
43	C₂×#217	C₂²	1	1	yes	characteristic
44	#947	C₂²	1	1	yes	characteristic, complemented
45	#947	C₂²	1	2	yes	complemented
46	#946	C₂²	1	2	yes	complemented
47	#946	C₂²	1	2	yes	complemented
48	#946	C₂²	1	1	yes	characteristic, complemented
49	#946	C₂²	1	1	yes	characteristic, complemented
50	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
51	Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
52	#944	C₂²	1	2	yes	complemented
53	#944	C₂²	1	1	yes	characteristic, complemented
54	#930	C₂²	1	2	yes	—
55	#930	C₂²	1	1	yes	characteristic
56	#930	C₂²	1	1	yes	characteristic, complemented
57	#929	C₂²	1	2	yes	—
58	#929	C₂²	1	2	yes	complemented
59	#929	C₂²	1	2	yes	complemented
60	C₄×#67	C₂²	1	1	yes	characteristic
61	C₄×#67	C₂²	1	2	yes	—
62	C₄×#67	C₂²	1	1	yes	characteristic
63	C₄×#67	C₂²	1	1	yes	characteristic
64	C₄×#67	C₂²	1	1	yes	characteristic
65	C₄×#67	C₂²	1	2	yes	—
66	C₄×#67	C₂²	1	1	yes	characteristic
67	C₄×#67	C₂²	1	1	yes	characteristic
68	C₄×#67	C₂²	1	1	yes	characteristic
69	C₄×#67	C₂²	1	1	yes	characteristic
70	C₄×#67	C₂²	1	2	yes	complemented
71	C₄×#67	C₂²	1	2	yes	complemented
72	C₂×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
73	#926	C₂²	1	1	yes	characteristic, complemented
74	#926	C₂²	1	2	yes	complemented
75	#924	C₂²	1	1	yes	characteristic
76	#924	C₂²	1	2	yes	complemented
77	#924	C₂²	1	1	yes	characteristic, complemented
78	C₂×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
79	C₂×C₄×Dic₃	C₂²	1	1	yes	characteristic
80	#898	C₂²	1	2	yes	complemented
81	#898	C₂²	1	2	yes	complemented
82	#898	C₂²	1	2	yes	complemented
83	#897	C₂²	1	1	yes	characteristic, complemented
84	#896	C₂²	1	2	yes	complemented
85	#896	C₂²	1	2	yes	complemented
86	#896	C₂²	1	2	yes	complemented
87	#895	C₂²	1	1	yes	characteristic, complemented
88	#894	C₂²	1	2	yes	complemented
89	#894	C₂²	1	2	yes	complemented
90	#894	C₂²	1	2	yes	complemented
91	#893	C₂²	1	2	yes	complemented
92	#893	C₂²	1	2	yes	complemented
93	#893	C₂²	1	1	yes	characteristic, complemented
94	#892	C₂²	1	2	yes	complemented
95	#892	C₂²	1	2	yes	complemented
96	#892	C₂²	1	1	yes	characteristic, complemented
97	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
98	D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
99	D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
100	#890	C₂²	1	1	yes	characteristic, complemented
101	#889	C₂²	1	2	yes	complemented
102	#889	C₂²	1	2	yes	complemented
103	#889	C₂²	1	2	yes	complemented
104	#888	C₂²	1	1	yes	characteristic, complemented
105	#887	C₂²	1	1	yes	characteristic, complemented
106	#887	C₂²	1	2	yes	complemented
107	#887	C₂²	1	2	yes	complemented
108	#886	C₂²	1	2	yes	—
109	#885	C₂²	1	2	yes	—
110	#885	C₂²	1	2	yes	complemented
111	#884	C₂²	1	2	yes	—
112	#884	C₂²	1	2	yes	—
113	#883	C₂²	1	2	yes	—
114	#883	C₂²	1	2	yes	complemented
115	#882	C₂²	1	2	yes	—
116	#67⋊C₄	C₂²	1	2	yes	—
117	#67⋊C₄	C₂²	1	2	yes	—
118	D₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	#879	C₂²	1	2	yes	complemented
120	#879	C₂²	1	2	yes	complemented
121	#878	C₂²	1	2	yes	—
122	#878	C₂²	1	2	yes	—
123	#877	C₂²	1	2	yes	—
124	#556	—	3	1	no	—
125	#554	—	3	2	no	—
126	#552	—	3	1	no	—
127	#552	—	3	1	no	—
128	#551	—	3	2	no	—
129	#551	—	3	2	no	—
130	D₄×Q₈	—	3	1	no	—
131	#548	—	3	1	no	—
132	#548	—	3	1	no	—
133	#547	—	3	1	no	—
134	#547	—	3	1	no	—
135	#546	—	3	2	no	—
136	#542	—	3	2	no	—
137	#539	—	3	2	no	—
138	#539	—	3	2	no	—
139	#533	—	3	1	no	—
140	#529	—	3	1	no	—
141	#525	—	3	1	no	—
142	#525	—	3	1	no	—
143	C₂×C₂²⋊Q₈	—	3	1	no	—
144	C₂×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
145	#520	—	3	2	no	—
146	C₂×C₄×D₄	—	3	1	no	—
147	C₂⁴×C₃	C₂³	1	1	yes	characteristic
148	C₂³×D₃	C₂³	1	1	yes	characteristic
149	C₂×C₃×Q₈	—	4	2	no	—
150	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃×Q₈	C₂³	1	2	yes	—
153	C₂²×C₃×C₄	—	4	2	no	—
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³	1	2	yes	—
158	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³	1	2	yes	—
160	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₂×#67	—	2	4	no	—
163	C₂×#67	C₂³	1	2	yes	—
164	C₂×#67	C₂³	1	1	yes	characteristic
165	C₂×#67	C₂³	1	1	yes	characteristic
166	C₂×#67	C₂³	1	1	yes	characteristic
167	C₂×#67	C₂³	1	2	yes	—
168	C₂×#67	C₂³	1	2	yes	—
169	C₂×#67	C₂³	1	1	yes	characteristic
170	C₂²×Dic₃	C₂³	1	1	yes	characteristic
171	C₂²×Dic₃	C₂³	1	1	yes	characteristic
172	C₂²×Dic₃	C₂³	1	1	yes	characteristic
173	#239	—	4	2	no	—
174	D₃×Q₈	—	4	2	no	—
175	#235	—	2	8	no	—
176	#235	—	4	2	no	—
177	C₂×D₁₂	C₂³	1	2	yes	—
178	C₂×D₁₂	C₂³	1	1	yes	characteristic
179	C₂×D₁₂	C₂³	1	2	yes	—
180	C₂×C₄×D₃	—	4	2	no	—
181	C₂×C₄×D₃	C₂³	1	2	yes	—
182	C₂×C₄×D₃	C₂³	1	2	yes	—
183	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₃	C₂³	1	2	yes	—
186	C₂×C₄×D₃	C₂³	1	2	yes	—
187	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₃	C₂³	1	2	yes	—
189	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
190	C₂×Dic₆	C₂³	1	2	yes	—
191	C₂×Dic₆	C₂³	1	1	yes	characteristic
192	C₂×Dic₆	C₂³	1	2	yes	—
193	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	#217	C₂³	1	2	yes	—
205	#217	C₂³	1	2	yes	—
206	#217	C₂³	1	1	yes	characteristic
207	#217	C₂³	1	1	yes	characteristic
208	#217	C₂³	1	2	yes	—
209	#217	C₂³	1	1	yes	characteristic
210	#217	C₂³	1	1	yes	characteristic
211	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
220	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
222	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
223	(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
224	(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₄⋊Dic₃	C₂³	1	2	yes	—
228	C₄⋊Dic₃	C₂³	1	2	yes	—
229	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₃	C₂³	1	1	yes	characteristic
231	Dic₃⋊C₄	C₂³	1	2	yes	—
232	Dic₃⋊C₄	C₂³	1	2	yes	—
233	Dic₃⋊C₄	C₂³	1	2	yes	—
234	Dic₃⋊C₄	C₂³	1	2	yes	—
235	Dic₃⋊C₄	C₂³	1	2	yes	—
236	Dic₃⋊C₄	C₂³	1	2	yes	—
237	Dic₃⋊C₄	C₂³	1	2	yes	—
238	Dic₃⋊C₄	C₂³	1	2	yes	—
239	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₃⋊C₄	C₂³	1	2	yes	—
241	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₃⋊C₄	C₂³	1	2	yes	—
244	Dic₃⋊C₄	C₂³	1	1	yes	characteristic
245	C₄×Dic₃	C₂³	1	2	yes	—
246	C₄×Dic₃	C₂³	1	2	yes	—
247	C₄×Dic₃	C₂³	1	2	yes	—
248	C₄×Dic₃	C₂³	1	2	yes	—
249	C₄×Dic₃	C₂³	1	1	yes	characteristic
250	C₄×Dic₃	C₂³	1	2	yes	—
251	C₄×Dic₃	C₂³	1	1	yes	characteristic
252	C₄×Dic₃	C₂³	1	1	yes	characteristic
253	C₄×Dic₃	C₂³	1	1	yes	characteristic
254	C₂×#41	—	3	1	no	—
255	C₂×#41	—	3	2	no	—
256	C₂×#41	—	3	1	no	—
257	C₂²×Q₈	—	3	1	no	—
258	C₂²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
259	C₂²×D₄	—	3	1	no	—
260	C₂³×C₄	—	3	1	no	—
261	C₂³×C₄	C₂×D₃	1	1	yes	characteristic
262	C₄⋊Q₈	—	3	1	no	—
263	C₄⋊Q₈	—	3	2	no	—
264	C₄⋊Q₈	—	3	1	no	—
265	#126	—	3	2	no	—
266	#126	—	3	2	no	—
267	#126	—	3	2	no	—
268	#126	—	3	2	no	—
269	#126	—	3	2	no	—
270	#125	—	3	1	no	—
271	#125	—	3	2	no	—
272	#125	—	3	2	no	—
273	#125	—	3	2	no	—
274	#124	—	3	1	no	—
275	#124	—	3	2	no	—
276	#124	—	3	2	no	—
277	#124	—	3	2	no	—
278	#123	—	3	2	no	—
279	#123	—	3	2	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	#123	—	3	2	no	—
283	#123	—	3	2	no	—
284	#123	—	3	2	no	—
285	#123	—	3	2	no	—
286	#123	—	3	2	no	—
287	C₂²⋊Q₈	—	3	1	no	—
288	C₂²⋊Q₈	—	3	1	no	—
289	C₂²⋊Q₈	—	3	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	1	no	—
296	C₂²⋊Q₈	—	3	2	no	—
297	C₂²⋊Q₈	—	3	2	no	—
298	C₂²⋊Q₈	—	3	2	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
301	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
302	C₂²⋊Q₈	C₂×D₃	1	2	yes	—
303	C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
304	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
305	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
306	#121	—	3	1	no	—
307	#121	—	3	1	no	—
308	#121	—	3	2	no	—
309	#121	—	3	1	no	—
310	#121	—	3	2	no	—
311	#121	—	3	2	no	—
312	#120	—	3	2	no	—
313	#120	—	3	2	no	—
314	C₄×Q₈	—	3	1	no	—
315	C₄×Q₈	—	3	1	no	—
316	C₄×Q₈	—	3	2	no	—
317	C₄×Q₈	—	3	2	no	—
318	C₄×Q₈	—	3	1	no	—
319	C₄×D₄	—	3	1	no	—
320	C₄×D₄	—	3	1	no	—
321	C₄×D₄	—	3	1	no	—
322	C₄×D₄	—	3	1	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	1	no	—
325	C₄×D₄	—	3	1	no	—
326	C₄×D₄	—	3	1	no	—
327	C₄×D₄	—	3	2	no	—
328	C₄×D₄	—	3	2	no	—
329	C₄×D₄	—	3	2	no	—
330	C₄×D₄	—	3	2	no	—
331	C₄×D₄	—	3	2	no	—
332	C₄×D₄	—	3	2	no	—
333	C₄×D₄	—	3	1	no	—
334	C₄×D₄	—	3	2	no	—
335	C₄×D₄	—	3	2	no	—
336	#117	—	3	2	no	—
337	#117	—	3	1	no	—
338	#117	—	3	2	no	—
339	#117	—	3	2	no	—
340	#117	—	3	1	no	—
341	#117	—	3	2	no	—
342	C₂×C₄⋊C₄	—	3	1	no	—
343	C₂×C₄⋊C₄	—	3	2	no	—
344	C₂×C₄⋊C₄	—	3	2	no	—
345	C₂×C₄⋊C₄	—	3	1	no	—
346	C₂×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
347	C₂×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
348	C₂×C₂²⋊C₄	—	3	1	no	—
349	C₂×C₂²⋊C₄	—	3	1	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂×C₂²⋊C₄	C₂×D₃	1	2	yes	—
352	C₂×C₄²	—	3	1	no	—
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	—	2	2	no	—
355	C₂³×C₃	—	4	1	no	—
356	C₂³×C₃	C₂⁴	1	1	yes	characteristic
357	C₂³×C₃	C₂⁴	1	1	yes	characteristic
358	C₂³×C₃	C₂⁴	1	1	yes	characteristic
359	C₂²×D₃	—	2	2	no	—
360	C₂²×D₃	—	2	2	no	—
361	C₂²×D₃	—	4	1	no	—
362	C₂²×D₃	C₂⁴	1	1	yes	characteristic
363	C₂²×D₃	C₂⁴	1	2	yes	—
364	C₂²×D₃	C₂⁴	1	1	yes	characteristic
365	C₃×Q₈	—	2	2	no	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	—	4	2	no	—
368	C₂×C₃×C₄	—	2	4	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	4	1	no	—
373	C₂×C₃×C₄	—	4	1	no	—
374	C₂×C₃×C₄	—	4	1	no	—
375	C₂×C₃×C₄	—	4	2	no	—
376	C₂×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂×C₃×C₄	C₂⁴	1	2	yes	—
381	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	#67	—	2	4	no	—
385	#67	—	2	2	no	—
386	#67	—	2	4	no	—
387	#67	—	2	2	no	—
388	#67	—	2	2	no	—
389	#67	—	4	2	no	—
390	#67	#41	1	4	yes	complemented
391	C₂×Dic₃	—	2	2	no	—
392	C₂×Dic₃	—	2	2	no	—
393	C₂×Dic₃	—	4	1	no	—
394	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₃	C₂⁴	1	2	yes	—
396	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₃	C₂⁴	1	2	yes	—
399	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₃	C₂⁴	1	2	yes	—
401	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₃	C₂⁴	1	1	yes	characteristic
403	D₁₂	—	2	4	no	—
404	D₁₂	—	2	2	no	—
405	D₁₂	—	4	2	no	—
406	C₄×D₃	—	2	4	no	—
407	C₄×D₃	—	2	2	no	—
408	C₄×D₃	—	2	2	no	—
409	C₄×D₃	—	2	4	no	—
410	C₄×D₃	—	4	1	no	—
411	C₄×D₃	—	4	1	no	—
412	C₄×D₃	—	4	2	no	—
413	C₄×D₃	—	4	2	no	—
414	C₄×D₃	—	4	2	no	—
415	Dic₆	—	2	2	no	—
416	Dic₆	—	2	4	no	—
417	Dic₆	—	4	2	no	—
418	C₂⁴	—	3	1	no	—
419	C₂⁴	C₂²×D₃	1	1	yes	characteristic
420	#41	—	6	8	no	—
421	#41	—	12	2	no	—
422	#41	—	12	2	no	—
423	C₂×Q₈	—	3	2	no	—
424	C₂×Q₈	—	3	1	no	—
425	C₂×Q₈	—	3	2	no	—
426	C₂×Q₈	—	4	2	no	—
427	C₂×Q₈	—	12	2	no	—
428	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
429	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
430	C₂×Q₈	C₂²×D₃	1	2	yes	—
431	C₂×D₄	—	3	1	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	3	1	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	1	no	—
437	C₂×D₄	—	3	2	no	—
438	C₂×D₄	—	3	2	no	—
439	C₂×D₄	—	3	1	no	—
440	C₂×D₄	—	3	2	no	—
441	C₂×D₄	—	6	4	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	1	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	2	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	1	no	—
448	C₂²×C₄	—	3	1	no	—
449	C₂²×C₄	—	3	2	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	3	2	no	—
452	C₂²×C₄	—	3	2	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	12	2	no	—
456	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₃	1	2	yes	—
458	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
459	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
460	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
461	C₂²×C₄	C₂²×D₃	1	2	yes	—
462	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
463	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	2	no	—
466	C₄⋊C₄	—	3	1	no	—
467	C₄⋊C₄	—	3	1	no	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	3	1	no	—
470	C₄⋊C₄	—	3	2	no	—
471	C₄⋊C₄	—	3	2	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	2	no	—
474	C₄⋊C₄	—	3	2	no	—
475	C₄⋊C₄	—	3	1	no	—
476	C₄⋊C₄	—	3	2	no	—
477	C₄⋊C₄	—	3	2	no	—
478	C₄⋊C₄	—	3	2	no	—
479	C₄⋊C₄	—	3	2	no	—
480	C₄⋊C₄	—	3	2	no	—
481	C₄⋊C₄	—	3	2	no	—
482	C₄⋊C₄	—	3	2	no	—
483	C₄⋊C₄	—	3	2	no	—
484	C₄⋊C₄	C₂²×D₃	1	2	yes	—
485	C₄⋊C₄	C₂²×D₃	1	2	yes	—
486	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₃	1	2	yes	—
489	C₄⋊C₄	C₂²×D₃	1	2	yes	—
490	C₄⋊C₄	C₂²×D₃	1	2	yes	—
491	C₂²⋊C₄	—	3	1	no	—
492	C₂²⋊C₄	—	3	2	no	—
493	C₂²⋊C₄	—	3	1	no	—
494	C₂²⋊C₄	—	3	1	no	—
495	C₂²⋊C₄	—	3	1	no	—
496	C₂²⋊C₄	—	3	2	no	—
497	C₂²⋊C₄	—	3	2	no	—
498	C₂²⋊C₄	—	3	1	no	—
499	C₂²⋊C₄	—	3	1	no	—
500	C₂²⋊C₄	—	3	1	no	—
501	C₂²⋊C₄	—	3	1	no	—
502	C₂²⋊C₄	—	3	2	no	—
503	C₂²⋊C₄	—	3	2	no	—
504	C₂²⋊C₄	—	3	2	no	—
505	C₂²⋊C₄	—	3	2	no	—
506	C₂²⋊C₄	—	3	2	no	—
507	C₂²⋊C₄	—	3	2	no	—
508	C₂²⋊C₄	—	3	2	no	—
509	C₂²⋊C₄	—	3	2	no	—
510	C₂²⋊C₄	—	3	2	no	—
511	C₂²⋊C₄	—	3	2	no	—
512	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
513	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
514	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
516	C₄²	—	3	1	no	—
517	C₄²	—	3	1	no	—
518	C₄²	—	3	1	no	—
519	C₄²	—	3	1	no	—
520	C₄²	—	3	2	no	—
521	C₄²	—	3	2	no	—
522	C₄²	—	3	2	no	—
523	C₄²	—	3	2	no	—
524	C₄²	—	3	2	no	—
525	C₂²×C₃	—	2	1	no	—
526	C₂²×C₃	—	2	1	no	—
527	C₂²×C₃	—	2	1	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	1	no	—
530	C₂²×C₃	—	2	1	no	—
531	C₂²×C₃	—	2	1	no	—
532	C₂²×C₃	—	4	4	no	—
533	C₂²×C₃	C₂×#41	1	2	yes	—
534	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
535	C₂²×C₃	C₂⁵	1	1	yes	characteristic
536	C₂×D₃	—	2	1	no	—
537	C₂×D₃	—	2	1	no	—
538	C₂×D₃	—	2	2	no	—
539	C₂×D₃	—	2	1	no	—
540	C₂×D₃	—	2	1	no	—
541	C₂×D₃	—	2	2	no	—
542	C₂×D₃	—	2	2	no	—
543	C₂×D₃	—	2	1	no	—
544	C₂×D₃	—	4	4	no	—
545	C₂×D₃	C₂×#41	1	2	yes	—
546	C₃×C₄	—	2	2	no	—
547	C₃×C₄	—	2	2	no	—
548	C₃×C₄	—	2	2	no	—
549	C₃×C₄	—	2	1	no	—
550	C₃×C₄	—	2	1	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	1	no	—
553	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
554	Dic₃	—	2	2	no	—
555	Dic₃	—	2	1	no	—
556	Dic₃	—	2	2	no	—
557	Dic₃	—	2	1	no	—
558	Dic₃	—	2	1	no	—
559	Dic₃	—	2	1	no	—
560	Dic₃	—	2	1	no	—
561	Dic₃	—	2	2	no	—
562	Dic₃	C₂×#41	1	2	yes	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	3	1	no	—
566	C₂³	—	3	1	no	—
567	C₂³	—	3	2	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	6	2	no	—
570	C₂³	—	6	2	no	—
571	C₂³	—	12	1	no	—
572	C₂³	C₂³×D₃	1	1	yes	characteristic
573	C₂³	C₂³×D₃	1	1	yes	characteristic
574	C₂³	C₂³×D₃	1	1	yes	characteristic
575	Q₈	—	2	2	no	—
576	Q₈	—	2	2	no	—
577	Q₈	—	4	2	no	—
578	Q₈	—	6	4	no	—
579	Q₈	—	6	2	no	—
580	Q₈	—	12	2	no	—
581	D₄	—	3	4	no	—
582	D₄	—	6	4	no	—
583	D₄	—	6	2	no	—
584	D₄	—	6	2	no	—
585	D₄	—	6	4	no	—
586	D₄	—	6	2	no	—
587	D₄	—	6	4	no	—
588	D₄	—	6	2	no	—
589	D₄	—	12	2	no	—
590	D₄	—	12	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	3	1	no	—
596	C₂×C₄	—	3	1	no	—
597	C₂×C₄	—	3	2	no	—
598	C₂×C₄	—	3	1	no	—
599	C₂×C₄	—	3	2	no	—
600	C₂×C₄	—	3	1	no	—
601	C₂×C₄	—	3	1	no	—
602	C₂×C₄	—	3	2	no	—
603	C₂×C₄	—	3	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	6	4	no	—
609	C₂×C₄	—	6	4	no	—
610	C₂×C₄	—	6	2	no	—
611	C₂×C₄	—	6	2	no	—
612	C₂×C₄	—	6	2	no	—
613	C₂×C₄	—	6	2	no	—
614	C₂×C₄	—	12	1	no	—
615	C₂×C₄	—	12	1	no	—
616	C₂×C₄	—	12	2	no	—
617	C₂×C₄	—	12	2	no	—
618	C₂×C₄	—	12	2	no	—
619	C₂×C₄	—	12	1	no	—
620	C₂×C₄	C₂³×D₃	1	2	yes	—
621	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₃	1	2	yes	—
624	C₂×C₄	C₂³×D₃	1	2	yes	—
625	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₃	1	2	yes	—
627	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
628	C₂×C₃	—	2	2	no	—
629	C₂×C₃	—	2	2	no	—
630	C₂×C₃	—	4	1	no	—
631	C₂×C₃	C₂²×#41	1	1	yes	characteristic
632	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
633	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
634	D₃	—	2	2	no	—
635	D₃	—	4	2	no	—
636	D₃	—	4	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	3	2	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	6	1	no	—
647	C₂²	—	6	1	no	—
648	C₂²	—	6	1	no	—
649	C₂²	—	6	2	no	—
650	C₂²	—	6	2	no	—
651	C₂²	—	6	1	no	—
652	C₂²	—	6	2	no	—
653	C₂²	—	6	1	no	—
654	C₂²	—	12	4	no	—
655	C₂²	#1007	1	2	yes	—
656	C₂²	D₃×#41	1	2	yes	—
657	C₂²	C₂⁴×D₃	1	1	yes	characteristic
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	3	2	no	—
666	C₄	—	6	1	no	—
667	C₄	—	6	1	no	—
668	C₄	—	6	2	no	—
669	C₄	—	6	1	no	—
670	C₄	—	6	1	no	—
671	C₄	—	6	2	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	2	no	—
674	C₄	#1004	1	2	yes	—
675	C₃	#3520	1	1	yes	characteristic, complemented, Sylow
676	C₂	—	2	2	no	—
677	C₂	—	2	2	no	—
678	C₂	—	4	1	no	—
679	C₂	—	6	2	no	—
680	C₂	—	12	1	no	—
681	C₂	—	12	2	no	—
682	C₂	C₂×#1004	1	1	yes	characteristic
683	C₂	C₂×#1007	1	1	yes	characteristic
684	C₂	C₂×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₂×C₃×C₂²⋊Q₈	C₂
hypercenter	C₂×C₂²⋊Q₈	D₃
hypocenter	C₃	#3520
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂²⋊Q₈	C₂	semidirect
2. #5817	C₂	semidirect
3. Q₈×#67	C₂	semidirect
4. #5791	C₂	semidirect
5. C₂×C₄×#67	C₂	semidirect
6. #5641	C₂	semidirect
7. #5640	C₂	semidirect
8. #5639	C₂	semidirect
9. #5638	C₂	semidirect
10. #5637	C₂	semidirect
11. #5636	C₂	semidirect
12. #5633	C₂	semidirect
13. #5631	C₂	semidirect
14. #5627	C₂	semidirect
15. D₃×C₂²⋊Q₈	C₂	semidirect
16. #5624	C₂	semidirect
17. #5622	C₂	semidirect
18. #5515	C₂	semidirect
19. #5513	C₂	semidirect
20. #5507	C₂	semidirect
21. #5504	C₂	semidirect
22. #5495	C₂	semidirect
23. #5490	C₂	semidirect
25. C₂²×C₃×Q₈	C₂²	semidirect
28. C₂×#239	C₂²	semidirect
29. C₂×D₃×Q₈	C₂²	semidirect
31. C₂×#235	C₂²	semidirect
36. C₃×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₂²⋊Q₈	C₂²	semidirect
38. C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₃×C₄⋊C₄	C₂²	semidirect
40. C₂×C₃×C₄⋊C₄	C₂²	semidirect
44. #947	C₂²	semidirect
45. #947	C₂²	semidirect
46. #946	C₂²	semidirect
47. #946	C₂²	semidirect
48. #946	C₂²	semidirect
49. #946	C₂²	semidirect
50. Q₈×Dic₃	C₂²	semidirect
51. Q₈×Dic₃	C₂²	semidirect
52. #944	C₂²	semidirect
53. #944	C₂²	semidirect
56. #930	C₂²	semidirect
58. #929	C₂²	semidirect
59. #929	C₂²	semidirect
70. C₄×#67	C₂²	semidirect
71. C₄×#67	C₂²	semidirect
73. #926	C₂²	semidirect
74. #926	C₂²	semidirect
76. #924	C₂²	semidirect
77. #924	C₂²	semidirect
80. #898	C₂²	semidirect
81. #898	C₂²	semidirect
82. #898	C₂²	semidirect
83. #897	C₂²	semidirect
84. #896	C₂²	semidirect
85. #896	C₂²	semidirect
86. #896	C₂²	semidirect
87. #895	C₂²	semidirect
88. #894	C₂²	semidirect
89. #894	C₂²	semidirect
90. #894	C₂²	semidirect
91. #893	C₂²	semidirect
92. #893	C₂²	semidirect
93. #893	C₂²	semidirect
94. #892	C₂²	semidirect
95. #892	C₂²	semidirect
96. #892	C₂²	semidirect
97. D₃×C₄⋊C₄	C₂²	semidirect
98. D₃×C₄⋊C₄	C₂²	semidirect
99. D₃×C₄⋊C₄	C₂²	semidirect
100. #890	C₂²	semidirect
101. #889	C₂²	semidirect
102. #889	C₂²	semidirect
103. #889	C₂²	semidirect
104. #888	C₂²	semidirect
105. #887	C₂²	semidirect
106. #887	C₂²	semidirect
107. #887	C₂²	semidirect
110. #885	C₂²	semidirect
114. #883	C₂²	semidirect
119. #879	C₂²	semidirect
120. #879	C₂²	semidirect
144. C₂×C₂²⋊Q₈	D₃	semidirect
258. C₂²×Q₈	C₂×D₃	semidirect
303. C₂²⋊Q₈	C₂×D₃	semidirect
304. C₂²⋊Q₈	C₂×D₃	semidirect
305. C₂²⋊Q₈	C₂×D₃	semidirect
346. C₂×C₄⋊C₄	C₂×D₃	semidirect
347. C₂×C₄⋊C₄	C₂×D₃	semidirect
390. #67	#41	semidirect
675. C₃	#3520	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₂²⋊Q₈	2
#5817	2
Q₈×#67	2
#5791	2
C₂×C₄×#67	2
#5641	2
#5640	2
#5639	2
#5638	2
#5637	2
#5636	2
#5633	2
#5631	2
#5627	2
D₃×C₂²⋊Q₈	2
#5624	2
#5622	2
#5515	2
#5513	2
#5507	2
#5504	2
#5495	2
#5490	2
#3520	3