Subgroups — #59709

Order 256.

768 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2798	C₂	1	2	yes	maximal
2	#2789	C₂	1	2	yes	maximal, complemented
3	#2604	C₂	1	2	yes	maximal
4	#2594	C₂	1	2	yes	maximal
5	#2550	C₂	1	1	yes	maximal, characteristic, complemented
6	#2528	C₂	1	2	yes	maximal, complemented
7	#2525	C₂	1	2	yes	maximal
8	#2514	C₂	1	1	yes	maximal, characteristic, complemented
9	#2511	C₂	1	1	yes	maximal, characteristic, complemented
10	#2509	C₂	1	2	yes	maximal, complemented
11	#2494	C₂	1	1	yes	maximal, characteristic
12	#2492	C₂	1	1	yes	maximal, characteristic
13	#2489	C₂	1	1	yes	maximal, characteristic
14	#2453	C₂	1	1	yes	maximal, characteristic, complemented
15	#2441	C₂	1	1	yes	maximal, characteristic
16	#2370	C₂	1	1	yes	maximal, characteristic, complemented
17	#2370	C₂	1	1	yes	maximal, characteristic, complemented
18	#2362	C₂	1	1	yes	maximal, characteristic
19	#2356	C₂	1	2	yes	maximal, complemented
20	#2346	C₂	1	1	yes	maximal, characteristic
21	C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#126	C₂	1	1	yes	maximal, characteristic
23	#2295	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×#126	C₂²	1	1	yes	characteristic
26	C₂×#125	C₂²	1	1	yes	characteristic
27	C₂×#125	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈	C₂²	1	2	yes	—
30	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
31	C₂×#117	C₂²	1	1	yes	characteristic
32	#401	C₂²	1	2	yes	—
33	#401	C₂²	1	2	yes	—
34	#400	C₂²	1	2	yes	—
35	#400	C₂²	1	2	yes	—
36	#400	C₂²	1	2	yes	—
37	#400	C₂²	1	2	yes	—
38	#400	C₂²	1	2	yes	—
39	#400	C₂²	1	2	yes	—
40	#399	C₂²	1	2	yes	—
41	#398	C₂²	1	2	yes	—
42	#398	C₂²	1	2	yes	—
43	#397	C₂²	1	2	yes	—
44	#397	C₂²	1	2	yes	—
45	#396	C₂²	1	2	yes	—
46	#395	C₂²	1	2	yes	—
47	#393	C₂²	1	2	yes	—
48	#391	C₂²	1	2	yes	—
49	#391	C₂²	1	2	yes	—
50	#391	C₂²	1	2	yes	—
51	#391	C₂²	1	1	yes	characteristic
52	#391	C₂²	1	1	yes	characteristic
53	#391	C₂²	1	1	yes	characteristic
54	#391	C₂²	1	1	yes	characteristic
55	#391	C₂²	1	1	yes	characteristic
56	#389	C₂²	1	2	yes	—
57	#389	C₂²	1	1	yes	characteristic
58	#389	C₂²	1	1	yes	characteristic
59	#389	C₂²	1	1	yes	characteristic
60	#389	C₂²	1	1	yes	characteristic
61	#389	C₂²	1	2	yes	—
62	#389	C₂²	1	2	yes	—
63	#389	C₂²	1	1	yes	characteristic
64	#389	C₂²	1	1	yes	characteristic
65	#389	C₂²	1	2	yes	—
66	#389	C₂²	1	2	yes	—
67	#389	C₂²	1	1	yes	characteristic
68	#389	C₂²	1	2	yes	—
69	#388	C₂²	1	1	yes	characteristic
70	#388	C₂²	1	1	yes	characteristic
71	#388	C₂²	1	1	yes	characteristic
72	#388	C₂²	1	2	yes	—
73	#388	C₂²	1	2	yes	—
74	#388	C₂²	1	2	yes	—
75	#388	C₂²	1	2	yes	—
76	#388	C₂²	1	2	yes	—
77	#388	C₂²	1	2	yes	—
78	#388	C₂²	1	2	yes	—
79	#387	C₂²	1	1	yes	characteristic
80	#387	C₂²	1	1	yes	characteristic
81	#387	C₂²	1	1	yes	characteristic
82	#387	C₂²	1	2	yes	—
83	#387	C₂²	1	2	yes	—
84	#387	C₂²	1	2	yes	—
85	#387	C₂²	1	2	yes	—
86	#387	C₂²	1	2	yes	—
87	#387	C₂²	1	2	yes	—
88	#387	C₂²	1	2	yes	—
89	#387	C₂²	1	2	yes	—
90	#387	C₂²	1	2	yes	—
91	#387	C₂²	1	2	yes	—
92	#387	C₂²	1	2	yes	—
93	#387	C₂²	1	2	yes	—
94	#387	C₂²	1	2	yes	—
95	#384	C₂²	1	1	yes	characteristic
96	#383	C₂²	1	1	yes	characteristic
97	#383	C₂²	1	2	yes	—
98	#382	C₂²	1	2	yes	—
99	#382	C₂²	1	2	yes	—
100	#382	C₂²	1	1	yes	characteristic
101	#380	C₂²	1	1	yes	characteristic
102	#380	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	#376	C₂²	1	2	yes	—
121	#376	C₂²	1	2	yes	—
122	C₄³	C₂²	1	1	yes	characteristic
123	C₂²×Q₈	C₂³	1	1	yes	characteristic
124	C₂²×Q₈	C₂³	1	2	yes	—
125	C₂³×C₄	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈	—	2	4	no	—
127	#126	—	2	4	no	—
128	#125	—	2	4	no	—
129	#125	—	2	4	no	—
130	C₂²⋊Q₈	—	2	4	no	—
131	C₄×Q₈	—	2	4	no	—
132	C₄×Q₈	—	2	8	no	—
133	#117	—	2	4	no	—
134	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₄²	C₂³	1	2	yes	—
174	C₂×C₄²	C₂³	1	1	yes	characteristic
175	C₂×C₄²	C₂³	1	2	yes	—
176	C₂×C₄²	C₂³	1	2	yes	—
177	C₂×C₄²	C₂³	1	2	yes	—
178	C₂×C₄²	C₂³	1	1	yes	characteristic
179	C₂×C₄²	C₂³	1	1	yes	characteristic
180	C₂×C₄²	C₂³	1	1	yes	characteristic
181	C₂×C₄²	C₂³	1	1	yes	characteristic
182	C₂×C₄²	C₂³	1	1	yes	characteristic
183	C₂×C₄²	C₂³	1	1	yes	characteristic
184	C₂×C₄²	C₂³	1	1	yes	characteristic
185	C₂×C₄²	C₂³	1	1	yes	characteristic
186	C₂×C₄²	C₂³	1	2	yes	—
187	C₂×C₄²	C₂³	1	2	yes	—
188	C₂×C₄²	C₂³	1	2	yes	—
189	C₂×C₄²	C₂³	1	2	yes	—
190	C₂×C₄²	C₂³	1	1	yes	characteristic
191	#95	C₂³	1	1	yes	characteristic
192	#95	C₂³	1	2	yes	—
193	#95	C₂³	1	2	yes	—
194	#95	C₂³	1	2	yes	—
195	#95	C₂³	1	2	yes	—
196	#95	C₂³	1	2	yes	—
197	#95	C₂³	1	2	yes	—
198	#95	C₂³	1	1	yes	characteristic
199	#95	C₂³	1	1	yes	characteristic
200	#95	C₂³	1	1	yes	characteristic
201	#95	C₂³	1	1	yes	characteristic
202	#95	C₂³	1	1	yes	characteristic
203	#95	C₂³	1	1	yes	characteristic
204	#95	C₂³	1	1	yes	characteristic
205	#95	C₂³	1	2	yes	—
206	#95	C₂³	1	2	yes	—
207	#95	C₂³	1	1	yes	characteristic
208	#95	C₂³	1	2	yes	—
209	#95	C₂³	1	2	yes	—
210	#95	C₂³	1	2	yes	—
211	#95	C₂³	1	2	yes	—
212	#95	C₂³	1	2	yes	—
213	#95	C₂³	1	1	yes	characteristic
214	#95	C₂³	1	1	yes	characteristic
215	#95	C₂³	1	2	yes	—
216	#95	C₂³	1	2	yes	—
217	#95	C₂³	1	1	yes	characteristic
218	#95	C₂³	1	2	yes	—
219	#95	C₂³	1	2	yes	—
220	#95	C₂³	1	2	yes	—
221	#95	C₂³	1	2	yes	—
222	#95	C₂³	1	2	yes	—
223	#95	C₂³	1	2	yes	—
224	#95	C₂³	1	2	yes	—
225	#95	C₂³	1	2	yes	—
226	#95	C₂³	1	2	yes	—
227	#95	C₂³	1	2	yes	—
228	#95	C₂³	1	2	yes	—
229	#95	C₂³	1	2	yes	—
230	C₂⁴	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈	—	2	4	no	—
232	C₂×Q₈	—	2	2	no	—
233	C₂×Q₈	—	2	2	no	—
234	C₂×Q₈	—	2	4	no	—
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	—	4	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄	C₂⁴	1	2	yes	—
243	C₂²×C₄	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄	C₂⁴	1	2	yes	—
249	C₂²×C₄	C₂⁴	1	2	yes	—
250	C₂²×C₄	C₂⁴	1	2	yes	—
251	C₂²×C₄	C₂⁴	1	2	yes	—
252	C₂²×C₄	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄	C₂⁴	1	2	yes	—
255	C₂²×C₄	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄	C₂⁴	1	2	yes	—
258	C₂²×C₄	C₂⁴	1	2	yes	—
259	C₂²×C₄	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄	C₂⁴	1	1	yes	characteristic
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	4	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	2	4	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	4	2	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	#41	1	4	yes	—
290	C₄⋊C₄	#41	1	4	yes	—
291	C₂²⋊C₄	—	2	4	no	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	4	1	no	—
298	C₂²⋊C₄	—	4	1	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	4	no	—
304	C₄²	—	2	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	4	2	no	—
314	C₄²	—	4	2	no	—
315	C₄²	—	4	2	no	—
316	C₄²	—	4	1	no	—
317	C₄²	—	4	2	no	—
318	C₄²	#41	1	4	yes	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	C₂⁵	1	1	yes	characteristic
327	Q₈	—	4	8	no	—
328	Q₈	—	4	4	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	C₂×#41	1	2	yes	—
388	C₂×C₄	C₂×#41	1	4	yes	—
389	C₂×C₄	C₂×#41	1	2	yes	—
390	C₂×C₄	C₂×#41	1	2	yes	—
391	C₂×C₄	C₂×#41	1	4	yes	—
392	C₂×C₄	C₂×#41	1	2	yes	—
393	C₂×C₄	C₂×#41	1	2	yes	—
394	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
395	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	C₂²×#41	1	1	yes	characteristic
404	C₂²	C₂²×#41	1	1	yes	characteristic
405	C₂²	C₂²×#41	1	1	yes	characteristic
406	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
407	C₂²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
408	C₂²	#585	1	1	yes	characteristic
409	C₂²	#585	1	1	yes	characteristic
410	C₄	—	2	4	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	2	no	—
431	C₄	#556	1	4	yes	—
432	C₂	—	8	1	no	—
433	C₂	C₂×#556	1	1	yes	characteristic
434	C₂	#3475	1	1	yes	characteristic
435	C₂	#3480	1	1	yes	characteristic
436	C₂	#3509	1	1	yes	characteristic
437	C₂	#3515	1	1	yes	characteristic
438	C₂	#3516	1	1	yes	characteristic
439	C₂	#3565	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂³	C₂⁵
prime radical	C₂⁴	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2789	C₂	semidirect
5. #2550	C₂	semidirect
6. #2528	C₂	semidirect
8. #2514	C₂	semidirect
9. #2511	C₂	semidirect
10. #2509	C₂	semidirect
14. #2453	C₂	semidirect
16. #2370	C₂	semidirect
17. #2370	C₂	semidirect
19. #2356	C₂	semidirect
21. C₄×C₄⋊Q₈	C₂	semidirect
23. #2295	C₂	semidirect

Maximal subgroups

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

subgroup	index
#2798	2
#2789	2
#2604	2
#2594	2
#2550	2
#2528	2
#2525	2
#2514	2
#2511	2
#2509	2
#2494	2
#2492	2
#2489	2
#2453	2
#2441	2
#2370	2
#2362	2
#2356	2
#2346	2
C₄×C₄⋊Q₈	2
C₄×#126	2
#2295	2