Subgroups — #61215

Order 256.

1100 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	#3333	C₂	1	2	yes	maximal, complemented
4	#3332	C₂	1	2	yes	maximal, complemented
5	#3325	C₂	1	2	yes	maximal, complemented
6	#3324	C₂	1	2	yes	maximal, complemented
7	#3305	C₂	1	2	yes	maximal, complemented
8	#3304	C₂	1	2	yes	maximal, complemented
9	#3295	C₂	1	2	yes	maximal, complemented
10	#3294	C₂	1	2	yes	maximal, complemented
11	C₂×#486	C₂	1	1	yes	maximal, characteristic, complemented
12	#3096	C₂	1	2	yes	maximal, complemented
13	#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	#3062	C₂	1	2	yes	maximal, complemented
15	#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	#3012	C₂	1	2	yes	maximal, complemented
17	C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	#2931	C₂	1	1	yes	maximal, characteristic, complemented
19	#2897	C₂	1	2	yes	maximal, complemented
20	C₂×H(5,𝔽₂)	C₂²	1	2	yes	—
21	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×#135	C₂²	1	1	yes	characteristic
23	C₂×#131	C₂²	1	2	yes	complemented
24	#556	C₂²	1	2	yes	complemented
25	#555	C₂²	1	2	yes	complemented
26	#554	C₂²	1	2	yes	complemented
27	#553	—	2	2	no	—
28	#550	C₂²	1	2	yes	—
29	#550	C₂²	1	2	yes	—
30	#548	—	2	2	no	—
31	#547	C₂²	1	2	yes	complemented
32	D₄²	—	2	2	no	—
33	D₄²	—	2	2	no	—
34	D₄²	C₂²	1	2	yes	—
35	D₄²	C₂²	1	2	yes	—
36	#542	—	2	2	no	—
37	#537	C₂²	1	2	yes	complemented
38	#535	—	2	2	no	—
39	#535	C₂²	1	2	yes	—
40	#533	—	2	1	no	—
41	#532	—	2	1	no	—
42	#532	—	2	1	no	—
43	#532	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×#127	—	2	1	no	—
46	C₂×#127	C₂²	1	1	yes	characteristic
47	#520	C₂²	1	2	yes	complemented
48	C₄×#41	C₂²	1	1	yes	characteristic
49	C₄×#41	C₂²	1	1	yes	characteristic, complemented
50	#486	C₂²	1	2	yes	complemented
51	#486	C₂²	1	2	yes	complemented
52	#486	C₂²	1	2	yes	complemented
53	#486	C₂²	1	2	yes	complemented
54	#482	C₂²	1	4	yes	complemented
55	#482	C₂²	1	4	yes	complemented
56	#481	C₂²	1	4	yes	complemented
57	#480	C₂²	1	4	yes	complemented
58	#477	C₂²	1	2	yes	complemented
59	#476	C₂²	1	2	yes	complemented
60	#475	C₂²	1	2	yes	complemented
61	#474	C₂²	1	2	yes	complemented
62	#469	C₂²	1	4	yes	complemented
63	#468	C₂²	1	4	yes	complemented
64	#466	C₂²	1	4	yes	complemented
65	#465	C₂²	1	4	yes	complemented
66	#460	C₂²	1	2	yes	complemented
67	#460	C₂²	1	2	yes	complemented
68	#459	C₂²	1	2	yes	complemented
69	#459	C₂²	1	2	yes	complemented
70	#452	C₂²	1	4	yes	complemented
71	#450	C₂²	1	4	yes	complemented
72	#449	C₂²	1	4	yes	complemented
73	#447	C₂²	1	4	yes	complemented
74	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
75	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
76	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
77	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
78	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
79	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
82	#436	C₂²	1	2	yes	complemented
83	#436	C₂²	1	2	yes	complemented
84	C₈×D₄	C₂²	1	2	yes	complemented
85	C₈×D₄	C₂²	1	2	yes	complemented
86	#428	C₂²	1	2	yes	complemented
87	#427	C₂²	1	1	yes	characteristic, complemented
88	#423	C₂²	1	1	yes	characteristic, complemented
89	#418	C₂²	1	2	yes	complemented
90	#418	C₂²	1	4	yes	complemented
91	#417	C₂²	1	2	yes	—
92	#417	C₂²	1	4	yes	complemented
93	#416	C₂²	1	1	yes	characteristic
94	#416	C₂²	1	4	yes	complemented
95	#416	C₂²	1	1	yes	characteristic, complemented
96	C₂×#102	C₂²	1	2	yes	complemented
97	C₂×#102	C₂²	1	2	yes	complemented
98	C₂×#102	C₂²	1	4	yes	complemented
99	#408	C₂²	1	2	yes	complemented
100	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
101	H(5,𝔽₂)	—	2	8	no	—
102	H(5,𝔽₂)	—	4	4	no	—
103	C₂×#41	—	2	2	no	—
104	C₂×#41	—	2	2	no	—
105	C₂×#41	C₂³	1	1	yes	characteristic
106	C₂×#41	C₂³	1	4	yes	—
107	C₂×#41	C₂³	1	1	yes	characteristic
108	C₂×#41	C₂³	1	2	yes	—
109	C₂²×Q₈	—	2	1	no	—
110	C₂²×D₄	—	2	2	no	—
111	C₂²×D₄	—	2	4	no	—
112	C₂²×D₄	—	2	2	no	—
113	C₂²×D₄	—	2	2	no	—
114	C₂²×D₄	—	2	1	no	—
115	C₂²×D₄	—	2	1	no	—
116	C₂²×D₄	C₂³	1	2	yes	—
117	C₂²×D₄	C₂³	1	4	yes	—
118	AGL(1,ℤ/8)	—	4	4	no	—
119	#135	—	2	4	no	—
120	C₂×Q₁₆	C₂³	1	1	yes	characteristic
121	C₂×SD₁₆	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆	C₂³	1	1	yes	characteristic
123	C₂×SD₁₆	C₂³	1	4	yes	—
124	C₂×D₈	C₂³	1	1	yes	characteristic
125	C₂×D₈	C₂³	1	4	yes	—
126	#131	—	4	4	no	—
127	C₂×M₁₆	C₂³	1	2	yes	—
128	C₂×M₁₆	C₂³	1	4	yes	—
129	C₂²×C₈	C₂³	1	1	yes	characteristic
130	C₂²×C₈	C₂³	1	1	yes	characteristic
131	C₂²×C₈	C₂³	1	4	yes	—
132	C₄⋊Q₈	—	2	1	no	—
133	C₄⋊Q₈	—	2	1	no	—
134	C₄⋊Q₈	D₄	1	1	yes	characteristic
135	C₄⋊Q₈	C₂³	1	2	yes	—
136	C₄⋊Q₈	C₂³	1	2	yes	—
137	#127	—	2	2	no	—
138	#127	—	2	2	no	—
139	#127	—	2	2	no	—
140	#127	—	2	1	no	—
141	#127	—	2	1	no	—
142	#127	D₄	1	1	yes	characteristic
143	#127	C₂³	1	2	yes	—
144	#127	C₂³	1	2	yes	—
145	#126	—	2	4	no	—
146	#125	—	2	2	no	—
147	#124	—	2	2	no	—
148	#124	—	2	2	no	—
149	#124	—	2	4	no	—
150	#124	D₄	1	2	yes	—
151	#123	—	2	4	no	—
152	C₂²⋊Q₈	—	2	2	no	—
153	C₂²⋊Q₈	—	2	2	no	—
154	C₂²⋊Q₈	—	2	4	no	—
155	C₂²⋊Q₈	C₂³	1	4	yes	—
156	#121	—	2	2	no	—
157	#121	—	2	2	no	—
158	#121	—	2	4	no	—
159	#121	—	2	2	no	—
160	#121	—	2	2	no	—
161	#121	—	2	4	no	—
162	#121	—	2	4	no	—
163	#121	D₄	1	2	yes	—
164	#121	D₄	1	2	yes	—
165	#121	C₂³	1	4	yes	—
166	#121	C₂³	1	4	yes	—
167	#121	C₂³	1	4	yes	—
168	#120	—	2	4	no	—
169	#120	—	2	4	no	—
170	#120	—	2	4	no	—
171	C₄×Q₈	—	2	2	no	—
172	C₄×Q₈	—	2	2	no	—
173	C₄×Q₈	C₂³	1	1	yes	characteristic
174	C₄×Q₈	C₂³	1	1	yes	characteristic
175	C₄×Q₈	C₂³	1	1	yes	characteristic
176	C₄×Q₈	C₂³	1	1	yes	characteristic
177	C₄×D₄	—	2	2	no	—
178	C₄×D₄	—	2	4	no	—
179	C₄×D₄	—	2	2	no	—
180	C₄×D₄	—	2	1	no	—
181	C₄×D₄	—	2	1	no	—
182	C₄×D₄	—	2	1	no	—
183	C₄×D₄	—	2	1	no	—
184	C₄×D₄	—	2	2	no	—
185	C₄×D₄	—	2	2	no	—
186	C₄×D₄	C₂³	1	1	yes	characteristic
187	C₄×D₄	C₂³	1	1	yes	characteristic
188	C₄×D₄	C₂³	1	1	yes	characteristic
189	C₄×D₄	C₂³	1	1	yes	characteristic
190	C₄×D₄	C₂³	1	2	yes	—
191	C₄×D₄	C₂³	1	2	yes	—
192	#117	—	2	2	no	—
193	#117	—	2	1	no	—
194	#117	—	2	1	no	—
195	#117	C₂³	1	1	yes	characteristic
196	#117	C₂³	1	1	yes	characteristic
197	#117	C₂³	1	4	yes	—
198	C₂×C₄⋊C₄	—	2	1	no	—
199	C₂×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂×C₄²	—	2	1	no	—
202	C₂×C₄²	—	2	1	no	—
203	C₂×C₄²	C₂³	1	1	yes	characteristic
204	#107	C₂³	1	1	yes	characteristic
205	#107	C₂³	1	1	yes	characteristic
206	#107	C₂³	1	4	yes	—
207	#106	C₂³	1	1	yes	characteristic
208	#106	C₂³	1	1	yes	characteristic
209	#106	C₂³	1	4	yes	—
210	C₄⋊C₈	C₂³	1	2	yes	—
211	C₄⋊C₈	C₂³	1	2	yes	—
212	#103	C₂³	1	1	yes	characteristic
213	#103	C₂³	1	1	yes	characteristic
214	#103	C₂³	1	4	yes	—
215	#103	C₂³	1	1	yes	characteristic
216	#103	C₂³	1	1	yes	characteristic
217	#102	C₂³	1	1	yes	characteristic
218	#102	C₂³	1	4	yes	—
219	#102	C₂³	1	4	yes	—
220	#102	C₂³	1	4	yes	—
221	#102	C₂³	1	4	yes	—
222	#102	C₂³	1	4	yes	—
223	#102	C₂³	1	4	yes	—
224	#102	C₂³	1	1	yes	characteristic
225	#102	C₂³	1	4	yes	—
226	#102	C₂³	1	1	yes	characteristic
227	#102	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈	C₂³	1	4	yes	—
229	C₂²⋊C₈	C₂³	1	4	yes	—
230	C₄×C₈	C₂³	1	1	yes	characteristic
231	C₄×C₈	C₂³	1	1	yes	characteristic
232	C₄×C₈	C₂³	1	1	yes	characteristic
233	C₄×C₈	C₂³	1	1	yes	characteristic
234	C₂⁴	—	2	4	no	—
235	C₂⁴	—	2	2	no	—
236	#41	—	2	4	no	—
237	#41	—	2	4	no	—
238	#41	—	2	2	no	—
239	#41	—	2	8	no	—
240	#41	—	2	2	no	—
241	#41	—	2	2	no	—
242	#41	—	4	4	no	—
243	#41	—	4	8	no	—
244	#41	—	8	4	no	—
245	#41	#41	1	4	yes	complemented
246	C₂×Q₈	—	2	2	no	—
247	C₂×Q₈	—	2	2	no	—
248	C₂×Q₈	—	8	2	no	—
249	C₂×Q₈	C₂×D₄	1	2	yes	—
250	C₂×Q₈	C₂⁴	1	1	yes	characteristic
251	C₂×Q₈	C₂⁴	1	1	yes	characteristic
252	C₂×D₄	—	2	1	no	—
253	C₂×D₄	—	2	8	no	—
254	C₂×D₄	—	2	1	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	—	4	8	no	—
269	C₂×D₄	—	4	16	no	—
270	C₂×D₄	—	8	2	no	—
271	C₂×D₄	—	8	2	no	—
272	C₂×D₄	—	8	4	no	—
273	C₂×D₄	—	8	4	no	—
274	C₂×D₄	C₂×D₄	1	2	yes	—
275	C₂×D₄	C₂×D₄	1	4	yes	—
276	C₂×D₄	C₂×D₄	1	2	yes	—
277	C₂×D₄	C₂×D₄	1	2	yes	—
278	C₂×D₄	C₂⁴	1	4	yes	—
279	C₂×D₄	C₂⁴	1	1	yes	characteristic
280	C₂×D₄	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄	C₂⁴	1	4	yes	—
293	C₂²×C₄	C₂⁴	1	1	yes	characteristic
294	Q₁₆	—	2	2	no	—
295	SD₁₆	—	2	2	no	—
296	SD₁₆	—	2	2	no	—
297	SD₁₆	—	4	4	no	—
298	D₈	—	2	2	no	—
299	D₈	—	4	4	no	—
300	M₁₆	—	2	4	no	—
301	M₁₆	—	4	4	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	C₂⁴	1	1	yes	characteristic
306	C₂×C₈	C₂⁴	1	1	yes	characteristic
307	C₂×C₈	C₂⁴	1	1	yes	characteristic
308	C₂×C₈	C₂⁴	1	1	yes	characteristic
309	C₂×C₈	C₂⁴	1	4	yes	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	C₂×D₄	1	2	yes	—
320	C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄	C₂⁴	1	4	yes	—
323	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	2	1	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	C₂×D₄	1	4	yes	—
338	C₂²⋊C₄	C₂×D₄	1	4	yes	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	4	no	—
346	C₄²	C₂×D₄	1	1	yes	characteristic
347	C₄²	C₂×D₄	1	1	yes	characteristic
348	C₄²	C₂⁴	1	1	yes	characteristic
349	C₄²	C₂⁴	1	1	yes	characteristic
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	4	8	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	8	2	no	—
356	C₂³	—	8	2	no	—
357	C₂³	—	8	4	no	—
358	C₂³	—	8	4	no	—
359	C₂³	C₂²×D₄	1	4	yes	—
360	C₂³	C₂²×D₄	1	1	yes	characteristic
361	Q₈	—	2	4	no	—
362	Q₈	—	2	1	no	—
363	Q₈	—	2	1	no	—
364	Q₈	—	2	1	no	—
365	Q₈	—	4	4	no	—
366	Q₈	—	8	2	no	—
367	Q₈	C₂×#41	1	2	yes	—
368	D₄	—	2	4	no	—
369	D₄	—	2	8	no	—
370	D₄	—	2	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	1	no	—
374	D₄	—	2	4	no	—
375	D₄	—	2	1	no	—
376	D₄	—	2	1	no	—
377	D₄	—	2	4	no	—
378	D₄	—	4	8	no	—
379	D₄	—	4	8	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	4	no	—
384	D₄	—	8	2	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	4	no	—
387	D₄	—	8	4	no	—
388	D₄	—	8	4	no	—
389	D₄	C₂×#41	1	2	yes	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	—	8	4	no	—
410	C₂×C₄	C₂²×D₄	1	4	yes	—
411	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂×#41	1	2	yes	—
417	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄	C₂⁵	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	4	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	16	4	no	—
439	C₂²	—	16	8	no	—
440	C₂²	#546	1	2	yes	—
441	C₂²	C₂³×D₄	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	#546	1	2	yes	—
453	C₄	#576	1	2	yes	—
454	C₄	#577	1	2	yes	—
455	C₄	C₂²×#41	1	1	yes	characteristic
456	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	4	4	no	—
459	C₂	—	4	2	no	—
460	C₂	—	8	1	no	—
461	C₂	—	8	4	no	—
462	C₂	C₂×#546	1	1	yes	characteristic
463	C₂	C₂×#576	1	1	yes	characteristic
464	C₂	C₂×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #532 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3511	C₂	semidirect
2. #3498	C₂	semidirect
3. #3333	C₂	semidirect
4. #3332	C₂	semidirect
5. #3325	C₂	semidirect
6. #3324	C₂	semidirect
7. #3305	C₂	semidirect
8. #3304	C₂	semidirect
9. #3295	C₂	semidirect
10. #3294	C₂	semidirect
11. C₂×#486	C₂	semidirect
12. #3096	C₂	semidirect
13. #3079	C₂	semidirect
14. #3062	C₂	semidirect
15. #3038	C₂	semidirect
16. #3012	C₂	semidirect
17. C₄×#135	C₂	semidirect
18. #2931	C₂	semidirect
19. #2897	C₂	semidirect
21. C₂×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×#131	C₂²	semidirect
24. #556	C₂²	semidirect
25. #555	C₂²	semidirect
26. #554	C₂²	semidirect
31. #547	C₂²	semidirect
37. #537	C₂²	semidirect
44. C₂×C₄⋊Q₈	C₂²	semidirect
47. #520	C₂²	semidirect
49. C₄×#41	C₂²	semidirect
50. #486	C₂²	semidirect
51. #486	C₂²	semidirect
52. #486	C₂²	semidirect
53. #486	C₂²	semidirect
54. #482	C₂²	semidirect
55. #482	C₂²	semidirect
56. #481	C₂²	semidirect
57. #480	C₂²	semidirect
58. #477	C₂²	semidirect
59. #476	C₂²	semidirect
60. #475	C₂²	semidirect
61. #474	C₂²	semidirect
62. #469	C₂²	semidirect
63. #468	C₂²	semidirect
64. #466	C₂²	semidirect
65. #465	C₂²	semidirect
66. #460	C₂²	semidirect
67. #460	C₂²	semidirect
68. #459	C₂²	semidirect
69. #459	C₂²	semidirect
70. #452	C₂²	semidirect
71. #450	C₂²	semidirect
72. #449	C₂²	semidirect
73. #447	C₂²	semidirect
74. C₄×Q₁₆	C₂²	semidirect
75. C₄×Q₁₆	C₂²	semidirect
76. C₄×SD₁₆	C₂²	semidirect
77. C₄×SD₁₆	C₂²	semidirect
78. C₄×SD₁₆	C₂²	semidirect
79. C₄×SD₁₆	C₂²	semidirect
80. C₄×D₈	C₂²	semidirect
81. C₄×D₈	C₂²	semidirect
82. #436	C₂²	semidirect
83. #436	C₂²	semidirect
84. C₈×D₄	C₂²	semidirect
85. C₈×D₄	C₂²	semidirect
86. #428	C₂²	semidirect
87. #427	C₂²	semidirect
88. #423	C₂²	semidirect
89. #418	C₂²	semidirect
90. #418	C₂²	semidirect
92. #417	C₂²	semidirect
94. #416	C₂²	semidirect
95. #416	C₂²	semidirect
96. C₂×#102	C₂²	semidirect
97. C₂×#102	C₂²	semidirect
98. C₂×#102	C₂²	semidirect
99. #408	C₂²	semidirect
100. C₂×C₄×C₈	C₂²	semidirect
245. #41	#41	semidirect

Maximal subgroups

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

subgroup	index
#3511	2
#3498	2
#3333	2
#3332	2
#3325	2
#3324	2
#3305	2
#3304	2
#3295	2
#3294	2
C₂×#486	2
#3096	2
#3079	2
#3062	2
#3038	2
#3012	2
C₄×#135	2
#2931	2
#2897	2