Subgroups — #3566

Order 128.

477 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#563	C₂	1	1	yes	maximal, characteristic, complemented
2	#562	C₂	1	1	yes	maximal, characteristic, complemented
3	#562	C₂	1	1	yes	maximal, characteristic, complemented
4	#560	C₂	1	1	yes	maximal, characteristic, complemented
5	#559	C₂	1	1	yes	maximal, characteristic, complemented
6	#556	C₂	1	1	yes	maximal, characteristic, complemented
7	#555	C₂	1	1	yes	maximal, characteristic, complemented
8	#553	C₂	1	1	yes	maximal, characteristic, complemented
9	#553	C₂	1	1	yes	maximal, characteristic, complemented
10	#553	C₂	1	1	yes	maximal, characteristic, complemented
11	#552	C₂	1	1	yes	maximal, characteristic, complemented
12	#552	C₂	1	1	yes	maximal, characteristic, complemented
13	#552	C₂	1	1	yes	maximal, characteristic, complemented
14	#551	C₂	1	1	yes	maximal, characteristic, complemented
15	#551	C₂	1	1	yes	maximal, characteristic, complemented
16	#551	C₂	1	1	yes	maximal, characteristic, complemented
17	#542	C₂	1	1	yes	maximal, characteristic, complemented
18	#542	C₂	1	1	yes	maximal, characteristic, complemented
19	#542	C₂	1	1	yes	maximal, characteristic, complemented
20	#541	C₂	1	1	yes	maximal, characteristic, complemented
21	#541	C₂	1	1	yes	maximal, characteristic, complemented
22	#540	C₂	1	1	yes	maximal, characteristic, complemented
23	#539	C₂	1	1	yes	maximal, characteristic, complemented
24	#539	C₂	1	1	yes	maximal, characteristic, complemented
25	#539	C₂	1	1	yes	maximal, characteristic, complemented
26	#538	C₂	1	1	yes	maximal, characteristic, complemented
27	#538	C₂	1	1	yes	maximal, characteristic, complemented
28	#538	C₂	1	1	yes	maximal, characteristic, complemented
29	#529	C₂	1	1	yes	maximal, characteristic, complemented
30	#529	C₂	1	1	yes	maximal, characteristic, complemented
31	#529	C₂	1	1	yes	maximal, characteristic, complemented
32	C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	#127	C₂²	1	1	yes	characteristic
36	#126	C₂²	1	1	yes	characteristic
37	#126	C₂²	1	1	yes	characteristic
38	#126	C₂²	1	1	yes	characteristic
39	#126	C₂²	1	1	yes	characteristic
40	#126	C₂²	1	1	yes	characteristic
41	#126	C₂²	1	1	yes	characteristic
42	#126	C₂²	1	1	yes	characteristic
43	#126	C₂²	1	1	yes	characteristic
44	#126	C₂²	1	1	yes	characteristic
45	#126	C₂²	1	1	yes	characteristic
46	#126	C₂²	1	1	yes	characteristic
47	#126	C₂²	1	1	yes	characteristic
48	#126	C₂²	1	1	yes	characteristic
49	#126	C₂²	1	1	yes	characteristic
50	#126	C₂²	1	1	yes	characteristic, complemented
51	#126	C₂²	1	1	yes	characteristic, complemented
52	#126	C₂²	1	1	yes	characteristic, complemented
53	#126	C₂²	1	1	yes	characteristic, complemented
54	#126	C₂²	1	1	yes	characteristic, complemented
55	#126	C₂²	1	1	yes	characteristic, complemented
56	#125	C₂²	1	1	yes	characteristic, complemented
57	#125	C₂²	1	1	yes	characteristic, complemented
58	#125	C₂²	1	1	yes	characteristic, complemented
59	#125	C₂²	1	1	yes	characteristic, complemented
60	#125	C₂²	1	1	yes	characteristic, complemented
61	#125	C₂²	1	1	yes	characteristic, complemented
62	#125	C₂²	1	1	yes	characteristic, complemented
63	#125	C₂²	1	1	yes	characteristic, complemented
64	#125	C₂²	1	1	yes	characteristic, complemented
65	#125	C₂²	1	1	yes	characteristic, complemented
66	#125	C₂²	1	1	yes	characteristic, complemented
67	#125	C₂²	1	1	yes	characteristic, complemented
68	#124	C₂²	1	1	yes	characteristic
69	#124	C₂²	1	1	yes	characteristic
70	#124	C₂²	1	1	yes	characteristic
71	#124	C₂²	1	1	yes	characteristic
72	#124	C₂²	1	1	yes	characteristic
73	#124	C₂²	1	1	yes	characteristic
74	#124	C₂²	1	1	yes	characteristic
75	#124	C₂²	1	1	yes	characteristic
76	#124	C₂²	1	1	yes	characteristic
77	#124	C₂²	1	1	yes	characteristic, complemented
78	#124	C₂²	1	1	yes	characteristic, complemented
79	#124	C₂²	1	1	yes	characteristic, complemented
80	#123	C₂²	1	1	yes	characteristic
81	#123	C₂²	1	1	yes	characteristic
82	#123	C₂²	1	1	yes	characteristic
83	#123	C₂²	1	1	yes	characteristic
84	#123	C₂²	1	1	yes	characteristic
85	#123	C₂²	1	1	yes	characteristic
86	#123	C₂²	1	1	yes	characteristic
87	#123	C₂²	1	1	yes	characteristic
88	#123	C₂²	1	1	yes	characteristic
89	#123	C₂²	1	1	yes	characteristic
90	#123	C₂²	1	1	yes	characteristic
91	#123	C₂²	1	1	yes	characteristic
92	#123	C₂²	1	1	yes	characteristic
93	#123	C₂²	1	1	yes	characteristic
94	#123	C₂²	1	1	yes	characteristic
95	#123	C₂²	1	1	yes	characteristic
96	#123	C₂²	1	1	yes	characteristic
97	#123	C₂²	1	1	yes	characteristic
98	#123	C₂²	1	1	yes	characteristic, complemented
99	#123	C₂²	1	1	yes	characteristic, complemented
100	#123	C₂²	1	1	yes	characteristic, complemented
101	#123	C₂²	1	1	yes	characteristic, complemented
102	#123	C₂²	1	1	yes	characteristic, complemented
103	#123	C₂²	1	1	yes	characteristic, complemented
104	C₂²⋊Q₈	C₂²	1	1	yes	characteristic
105	C₂²⋊Q₈	C₂²	1	1	yes	characteristic
106	C₂²⋊Q₈	C₂²	1	1	yes	characteristic
107	C₂²⋊Q₈	C₂²	1	1	yes	characteristic
108	C₂²⋊Q₈	C₂²	1	1	yes	characteristic
109	C₂²⋊Q₈	C₂²	1	1	yes	characteristic
110	C₂²⋊Q₈	C₂²	1	1	yes	characteristic
111	C₂²⋊Q₈	C₂²	1	1	yes	characteristic
112	C₂²⋊Q₈	C₂²	1	1	yes	characteristic
113	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
114	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
119	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
120	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
121	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
122	#121	C₂²	1	1	yes	characteristic
123	#121	C₂²	1	1	yes	characteristic
124	#121	C₂²	1	1	yes	characteristic
125	#121	C₂²	1	1	yes	characteristic
126	#121	C₂²	1	1	yes	characteristic
127	#121	C₂²	1	1	yes	characteristic
128	#121	C₂²	1	1	yes	characteristic
129	#121	C₂²	1	1	yes	characteristic
130	#121	C₂²	1	1	yes	characteristic
131	#121	C₂²	1	1	yes	characteristic
132	#121	C₂²	1	1	yes	characteristic
133	#121	C₂²	1	1	yes	characteristic
134	#121	C₂²	1	1	yes	characteristic
135	#121	C₂²	1	1	yes	characteristic
136	#121	C₂²	1	1	yes	characteristic
137	#121	C₂²	1	1	yes	characteristic, complemented
138	#121	C₂²	1	1	yes	characteristic, complemented
139	#121	C₂²	1	1	yes	characteristic, complemented
140	#120	C₂²	1	1	yes	characteristic
141	#120	C₂²	1	1	yes	characteristic
142	#120	C₂²	1	1	yes	characteristic
143	#120	C₂²	1	1	yes	characteristic
144	C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
145	C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
146	C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
147	C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
148	C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
149	C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
150	C₄×D₄	C₂²	1	1	yes	characteristic
151	C₄×D₄	C₂²	1	1	yes	characteristic
152	C₄×D₄	C₂²	1	1	yes	characteristic
153	C₄×D₄	C₂²	1	1	yes	characteristic
154	C₄×D₄	C₂²	1	1	yes	characteristic
155	C₄×D₄	C₂²	1	1	yes	characteristic
156	C₄×D₄	C₂²	1	1	yes	characteristic
157	C₄×D₄	C₂²	1	1	yes	characteristic
158	C₄×D₄	C₂²	1	1	yes	characteristic
159	C₄×D₄	C₂²	1	1	yes	characteristic
160	C₄×D₄	C₂²	1	1	yes	characteristic
161	C₄×D₄	C₂²	1	1	yes	characteristic
162	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
163	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
164	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
165	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
166	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
167	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
168	#117	C₂²	1	1	yes	characteristic
169	#117	C₂²	1	1	yes	characteristic
170	#117	C₂²	1	1	yes	characteristic
171	#117	C₂²	1	1	yes	characteristic
172	#117	C₂²	1	1	yes	characteristic
173	#117	C₂²	1	1	yes	characteristic
174	#117	C₂²	1	1	yes	characteristic, complemented
175	#117	C₂²	1	1	yes	characteristic, complemented
176	#117	C₂²	1	1	yes	characteristic, complemented
177	#117	C₂²	1	1	yes	characteristic, complemented
178	#117	C₂²	1	1	yes	characteristic, complemented
179	#117	C₂²	1	1	yes	characteristic, complemented
180	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
181	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
182	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
183	C₂×C₂²⋊C₄	C₂²	1	1	yes	characteristic
184	C₂×C₂²⋊C₄	C₂²	1	1	yes	characteristic
185	C₂×C₂²⋊C₄	C₂²	1	1	yes	characteristic
186	C₂×C₄²	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴	C₂³	1	1	yes	characteristic
188	C₂×Q₈	C₂³	1	1	yes	characteristic
189	C₂×Q₈	C₂³	1	1	yes	characteristic
190	C₂×Q₈	C₂³	1	1	yes	characteristic
191	C₂×Q₈	C₂³	1	1	yes	characteristic
192	C₂×Q₈	C₂³	1	1	yes	characteristic
193	C₂×Q₈	C₂³	1	1	yes	characteristic
194	C₂×D₄	C₂³	1	1	yes	characteristic
195	C₂×D₄	C₂³	1	1	yes	characteristic
196	C₂×D₄	C₂³	1	1	yes	characteristic
197	C₂×D₄	C₂³	1	1	yes	characteristic
198	C₂×D₄	C₂³	1	1	yes	characteristic
199	C₂×D₄	C₂³	1	1	yes	characteristic
200	C₂×D₄	C₂³	1	1	yes	characteristic
201	C₂×D₄	C₂³	1	1	yes	characteristic
202	C₂×D₄	C₂³	1	1	yes	characteristic
203	C₂×D₄	C₂³	1	1	yes	characteristic
204	C₂×D₄	C₂³	1	1	yes	characteristic
205	C₂×D₄	C₂³	1	1	yes	characteristic
206	C₂×D₄	C₂³	1	1	yes	characteristic
207	C₂×D₄	C₂³	1	1	yes	characteristic
208	C₂×D₄	C₂³	1	1	yes	characteristic
209	C₂×D₄	C₂³	1	1	yes	characteristic
210	C₂×D₄	C₂³	1	1	yes	characteristic
211	C₂×D₄	C₂³	1	1	yes	characteristic
212	C₂²×C₄	C₂³	1	1	yes	characteristic
213	C₂²×C₄	C₂³	1	1	yes	characteristic
214	C₂²×C₄	C₂³	1	1	yes	characteristic
215	C₂²×C₄	C₂³	1	1	yes	characteristic
216	C₂²×C₄	C₂³	1	1	yes	characteristic
217	C₂²×C₄	C₂³	1	1	yes	characteristic
218	C₂²×C₄	C₂³	1	1	yes	characteristic
219	C₂²×C₄	C₂³	1	1	yes	characteristic
220	C₂²×C₄	C₂³	1	1	yes	characteristic
221	C₂²×C₄	C₂³	1	1	yes	characteristic
222	C₂²×C₄	C₂³	1	1	yes	characteristic
223	C₂²×C₄	C₂³	1	1	yes	characteristic
224	C₂²×C₄	C₂³	1	1	yes	characteristic
225	C₂²×C₄	C₂³	1	1	yes	characteristic
226	C₂²×C₄	C₂³	1	1	yes	characteristic
227	C₂²×C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₄	C₂³	1	1	yes	characteristic
230	C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₂²⋊C₄	C₂³	1	1	yes	characteristic
290	C₂²⋊C₄	C₂³	1	1	yes	characteristic
291	C₂²⋊C₄	C₂³	1	1	yes	characteristic
292	C₂²⋊C₄	C₂³	1	1	yes	characteristic
293	C₂²⋊C₄	C₂³	1	1	yes	characteristic
294	C₂²⋊C₄	C₂³	1	1	yes	characteristic
295	C₂²⋊C₄	C₂³	1	1	yes	characteristic
296	C₂²⋊C₄	C₂³	1	1	yes	characteristic
297	C₂²⋊C₄	C₂³	1	1	yes	characteristic
298	C₂²⋊C₄	C₂³	1	1	yes	characteristic
299	C₂²⋊C₄	C₂³	1	1	yes	characteristic
300	C₂²⋊C₄	C₂³	1	1	yes	characteristic
301	C₂²⋊C₄	C₂³	1	1	yes	characteristic
302	C₂²⋊C₄	C₂³	1	1	yes	characteristic
303	C₂²⋊C₄	C₂³	1	1	yes	characteristic
304	C₂²⋊C₄	C₂³	1	1	yes	characteristic
305	C₂²⋊C₄	C₂³	1	1	yes	characteristic
306	C₂²⋊C₄	C₂³	1	1	yes	characteristic
307	C₂²⋊C₄	C₂³	1	1	yes	characteristic
308	C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	C₂²⋊C₄	C₂³	1	1	yes	characteristic
311	C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₂²⋊C₄	C₂³	1	1	yes	characteristic
313	C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₂²⋊C₄	C₂³	1	1	yes	characteristic
315	C₂²⋊C₄	C₂³	1	1	yes	characteristic
316	C₂²⋊C₄	C₂³	1	1	yes	characteristic
317	C₂²⋊C₄	C₂³	1	1	yes	characteristic
318	C₂²⋊C₄	C₂³	1	1	yes	characteristic
319	C₂²⋊C₄	C₂³	1	1	yes	characteristic
320	C₂²⋊C₄	C₂³	1	1	yes	characteristic
321	C₂²⋊C₄	C₂³	1	1	yes	characteristic
322	C₂²⋊C₄	C₂³	1	1	yes	characteristic
323	C₂²⋊C₄	C₂³	1	1	yes	characteristic
324	C₂²⋊C₄	C₂³	1	1	yes	characteristic
325	C₂²⋊C₄	C₂³	1	1	yes	characteristic
326	C₄²	C₂³	1	1	yes	characteristic
327	C₄²	C₂³	1	1	yes	characteristic
328	C₄²	C₂³	1	1	yes	characteristic
329	C₄²	C₂³	1	1	yes	characteristic
330	C₄²	C₂³	1	1	yes	characteristic
331	C₄²	C₂³	1	1	yes	characteristic
332	C₄²	C₂³	1	1	yes	characteristic
333	C₄²	C₂³	1	1	yes	characteristic
334	C₄²	C₂³	1	1	yes	characteristic
335	C₄²	C₂³	1	1	yes	characteristic
336	C₄²	C₂³	1	1	yes	characteristic
337	C₄²	C₂³	1	1	yes	characteristic
338	C₄²	C₂³	1	1	yes	characteristic
339	C₄²	C₂³	1	1	yes	characteristic
340	C₄²	C₂³	1	1	yes	characteristic
341	C₄²	C₂³	1	1	yes	characteristic
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	C₂⁴	1	1	yes	characteristic
346	C₂³	C₂⁴	1	1	yes	characteristic
347	C₂³	C₂⁴	1	1	yes	characteristic
348	C₂³	C₂⁴	1	1	yes	characteristic
349	C₂³	C₂⁴	1	1	yes	characteristic
350	C₂³	C₂⁴	1	1	yes	characteristic
351	C₂³	C₂⁴	1	1	yes	characteristic
352	Q₈	—	4	1	no	—
353	Q₈	—	4	1	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	1	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	C₂⁴	1	1	yes	characteristic
395	C₂×C₄	C₂⁴	1	1	yes	characteristic
396	C₂×C₄	C₂⁴	1	1	yes	characteristic
397	C₂×C₄	C₂⁴	1	1	yes	characteristic
398	C₂×C₄	C₂⁴	1	1	yes	characteristic
399	C₂×C₄	C₂⁴	1	1	yes	characteristic
400	C₂×C₄	C₂⁴	1	1	yes	characteristic
401	C₂×C₄	C₂⁴	1	1	yes	characteristic
402	C₂×C₄	C₂⁴	1	1	yes	characteristic
403	C₂×C₄	C₂⁴	1	1	yes	characteristic
404	C₂×C₄	C₂⁴	1	1	yes	characteristic
405	C₂×C₄	C₂⁴	1	1	yes	characteristic
406	C₂×C₄	C₂⁴	1	1	yes	characteristic
407	C₂×C₄	C₂⁴	1	1	yes	characteristic
408	C₂×C₄	C₂⁴	1	1	yes	characteristic
409	C₂×C₄	C₂⁴	1	1	yes	characteristic
410	C₂×C₄	C₂⁴	1	1	yes	characteristic
411	C₂×C₄	C₂⁴	1	1	yes	characteristic
412	C₂×C₄	C₂⁴	1	1	yes	characteristic
413	C₂×C₄	C₂⁴	1	1	yes	characteristic
414	C₂×C₄	C₂⁴	1	1	yes	characteristic
415	C₂×C₄	C₂⁴	1	1	yes	characteristic
416	C₂×C₄	C₂⁴	1	1	yes	characteristic
417	C₂×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	8	2	no	—
440	C₂²	C₂⁵	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₂	—	4	1	no	—
466	C₂	—	4	1	no	—
467	C₂	—	4	1	no	—
468	C₂	—	4	1	no	—
469	C₂	—	4	1	no	—
470	C₂	—	4	1	no	—
471	C₂	—	4	1	no	—
472	C₂	#585	1	1	yes	characteristic
473	C₂	#585	1	1	yes	characteristic
474	C₂	#585	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #563	C₂	semidirect
2. #562	C₂	semidirect
3. #562	C₂	semidirect
4. #560	C₂	semidirect
5. #559	C₂	semidirect
6. #556	C₂	semidirect
7. #555	C₂	semidirect
8. #553	C₂	semidirect
9. #553	C₂	semidirect
10. #553	C₂	semidirect
11. #552	C₂	semidirect
12. #552	C₂	semidirect
13. #552	C₂	semidirect
14. #551	C₂	semidirect
15. #551	C₂	semidirect
16. #551	C₂	semidirect
17. #542	C₂	semidirect
18. #542	C₂	semidirect
19. #542	C₂	semidirect
20. #541	C₂	semidirect
21. #541	C₂	semidirect
22. #540	C₂	semidirect
23. #539	C₂	semidirect
24. #539	C₂	semidirect
25. #539	C₂	semidirect
26. #538	C₂	semidirect
27. #538	C₂	semidirect
28. #538	C₂	semidirect
29. #529	C₂	semidirect
30. #529	C₂	semidirect
31. #529	C₂	semidirect
32. C₄⋊Q₈	C₂²	semidirect
33. C₄⋊Q₈	C₂²	semidirect
34. C₄⋊Q₈	C₂²	semidirect
50. #126	C₂²	semidirect
51. #126	C₂²	semidirect
52. #126	C₂²	semidirect
53. #126	C₂²	semidirect
54. #126	C₂²	semidirect
55. #126	C₂²	semidirect
56. #125	C₂²	semidirect
57. #125	C₂²	semidirect
58. #125	C₂²	semidirect
59. #125	C₂²	semidirect
60. #125	C₂²	semidirect
61. #125	C₂²	semidirect
62. #125	C₂²	semidirect
63. #125	C₂²	semidirect
64. #125	C₂²	semidirect
65. #125	C₂²	semidirect
66. #125	C₂²	semidirect
67. #125	C₂²	semidirect
77. #124	C₂²	semidirect
78. #124	C₂²	semidirect
79. #124	C₂²	semidirect
98. #123	C₂²	semidirect
99. #123	C₂²	semidirect
100. #123	C₂²	semidirect
101. #123	C₂²	semidirect
102. #123	C₂²	semidirect
103. #123	C₂²	semidirect
113. C₂²⋊Q₈	C₂²	semidirect
114. C₂²⋊Q₈	C₂²	semidirect
115. C₂²⋊Q₈	C₂²	semidirect
116. C₂²⋊Q₈	C₂²	semidirect
117. C₂²⋊Q₈	C₂²	semidirect
118. C₂²⋊Q₈	C₂²	semidirect
119. C₂²⋊Q₈	C₂²	semidirect
120. C₂²⋊Q₈	C₂²	semidirect
121. C₂²⋊Q₈	C₂²	semidirect
137. #121	C₂²	semidirect
138. #121	C₂²	semidirect
139. #121	C₂²	semidirect
144. C₄×Q₈	C₂²	semidirect
145. C₄×Q₈	C₂²	semidirect
146. C₄×Q₈	C₂²	semidirect
147. C₄×Q₈	C₂²	semidirect
148. C₄×Q₈	C₂²	semidirect
149. C₄×Q₈	C₂²	semidirect
162. C₄×D₄	C₂²	semidirect
163. C₄×D₄	C₂²	semidirect
164. C₄×D₄	C₂²	semidirect
165. C₄×D₄	C₂²	semidirect
166. C₄×D₄	C₂²	semidirect
167. C₄×D₄	C₂²	semidirect
174. #117	C₂²	semidirect
175. #117	C₂²	semidirect
176. #117	C₂²	semidirect
177. #117	C₂²	semidirect
178. #117	C₂²	semidirect
179. #117	C₂²	semidirect
180. C₂×C₄⋊C₄	C₂²	semidirect
181. C₂×C₄⋊C₄	C₂²	semidirect
182. C₂×C₄⋊C₄	C₂²	semidirect
186. C₂×C₄²	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#563	2
#562	2
#560	2
#559	2
#556	2
#555	2
#553	2
#552	2
#551	2
#542	2
#541	2
#540	2
#539	2
#538	2
#529	2