Subgroups — #60298

Order 256.

886 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3475	C₂	1	1	yes	maximal, characteristic
2	#2994	C₂	1	2	yes	maximal, complemented
3	#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	#2992	C₂	1	2	yes	maximal, complemented
6	#2990	C₂	1	1	yes	maximal, characteristic, complemented
7	#2988	C₂	1	1	yes	maximal, characteristic, complemented
8	#2986	C₂	1	1	yes	maximal, characteristic, complemented
9	#2985	C₂	1	1	yes	maximal, characteristic, complemented
10	#2977	C₂	1	2	yes	maximal, complemented
11	#2976	C₂	1	2	yes	maximal, complemented
12	#2974	C₂	1	1	yes	maximal, characteristic, complemented
13	#2972	C₂	1	1	yes	maximal, characteristic, complemented
14	#2970	C₂	1	1	yes	maximal, characteristic, complemented
15	#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	#2968	C₂	1	2	yes	maximal, complemented
17	#2966	C₂	1	2	yes	maximal, complemented
18	#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
20	#2925	C₂	1	1	yes	maximal, characteristic, complemented
21	#2924	C₂	1	2	yes	maximal, complemented
22	#2922	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#433	C₂	1	2	yes	maximal, complemented
24	#556	C₄	1	1	yes	characteristic
25	#555	C₄	1	1	yes	characteristic
26	#554	C₄	1	1	yes	characteristic
27	#553	C₄	1	2	yes	—
28	#552	C₄	1	2	yes	—
29	#552	C₄	1	1	yes	characteristic
30	#552	C₄	1	1	yes	characteristic
31	#551	C₄	1	2	yes	—
32	#551	C₄	1	2	yes	—
33	#547	C₄	1	1	yes	characteristic
34	#546	C₄	1	1	yes	characteristic
35	#546	C₄	1	1	yes	characteristic
36	#533	C₂²	1	1	yes	characteristic
37	#529	C₂²	1	2	yes	—
38	#529	C₂²	1	1	yes	characteristic
39	#529	C₂²	1	2	yes	—
40	#529	C₂²	1	1	yes	characteristic
41	#525	C₂²	1	2	yes	—
42	C₄×#41	C₂²	1	1	yes	characteristic
43	C₄×#41	C₂²	1	1	yes	characteristic
44	C₄×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×#117	C₂²	1	2	yes	—
47	#446	C₂²	1	2	yes	complemented
48	#446	C₂²	1	1	yes	characteristic, complemented
49	#446	C₂²	1	2	yes	complemented
50	#446	C₂²	1	2	yes	complemented
51	#446	C₂²	1	1	yes	characteristic, complemented
52	#446	C₂²	1	1	yes	characteristic, complemented
53	#446	C₂²	1	1	yes	characteristic, complemented
54	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₈×Q₈	C₂²	1	2	yes	complemented
58	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
59	#436	C₂²	1	1	yes	characteristic
60	#436	C₂²	1	1	yes	characteristic
61	#436	C₂²	1	2	yes	complemented
62	#436	C₂²	1	2	yes	complemented
63	#435	C₂²	1	2	yes	—
64	#435	C₂²	1	2	yes	—
65	#435	C₂²	1	2	yes	complemented
66	#435	C₂²	1	2	yes	complemented
67	#435	C₂²	1	2	yes	complemented
68	#435	C₂²	1	2	yes	complemented
69	#435	C₂²	1	2	yes	complemented
70	#435	C₂²	1	2	yes	complemented
71	#435	C₂²	1	2	yes	complemented
72	#435	C₂²	1	2	yes	complemented
73	C₈×D₄	C₂²	1	1	yes	characteristic
74	C₈×D₄	C₂²	1	1	yes	characteristic
75	C₈×D₄	C₂²	1	2	yes	—
76	C₈×D₄	C₂²	1	1	yes	characteristic
77	C₈×D₄	C₂²	1	2	yes	—
78	C₈×D₄	C₂²	1	1	yes	characteristic
79	C₈×D₄	C₂²	1	1	yes	characteristic
80	C₈×D₄	C₂²	1	1	yes	characteristic
81	C₈×D₄	C₂²	1	2	yes	complemented
82	C₈×D₄	C₂²	1	2	yes	complemented
83	C₈×D₄	C₂²	1	2	yes	complemented
84	C₈×D₄	C₂²	1	2	yes	complemented
85	C₈×D₄	C₂²	1	2	yes	complemented
86	C₈×D₄	C₂²	1	2	yes	complemented
87	#433	C₂²	1	1	yes	characteristic
88	#433	C₂²	1	2	yes	—
89	#433	C₂²	1	2	yes	—
90	#433	C₂²	1	2	yes	—
91	#433	C₂²	1	1	yes	characteristic
92	#433	C₂²	1	2	yes	—
93	#433	C₂²	1	2	yes	—
94	#433	C₂²	1	2	yes	complemented
95	#433	C₂²	1	2	yes	complemented
96	#433	C₂²	1	2	yes	complemented
97	#433	C₂²	1	2	yes	complemented
98	#433	C₂²	1	1	yes	characteristic, complemented
99	#433	C₂²	1	1	yes	characteristic, complemented
100	#433	C₂²	1	2	yes	complemented
101	#432	C₂²	1	1	yes	characteristic
102	#432	C₂²	1	2	yes	complemented
103	#432	C₂²	1	2	yes	complemented
104	#432	C₂²	1	1	yes	characteristic, complemented
105	#431	C₂²	1	1	yes	characteristic
106	#431	C₂²	1	1	yes	characteristic
107	#431	C₂²	1	1	yes	characteristic
108	#431	C₂²	1	1	yes	characteristic, complemented
109	#431	C₂²	1	1	yes	characteristic, complemented
110	#431	C₂²	1	2	yes	complemented
111	#431	C₂²	1	2	yes	complemented
112	#431	C₂²	1	1	yes	characteristic, complemented
113	#424	C₂²	1	1	yes	characteristic, complemented
114	#424	C₂²	1	1	yes	characteristic, complemented
115	#424	C₂²	1	2	yes	complemented
116	#424	C₂²	1	2	yes	complemented
117	#423	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
119	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
120	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
121	#408	C₂²	1	1	yes	characteristic
122	#408	C₂²	1	1	yes	characteristic
123	#408	C₂²	1	2	yes	—
124	#407	C₂²	1	2	yes	—
125	C₂×C₂²⋊C₈	C₂²	1	2	yes	—
126	C₂×C₂²⋊C₈	C₂²	1	2	yes	—
127	C₂×C₂²⋊C₈	C₂²	1	2	yes	—
128	#405	C₂²	1	2	yes	complemented
129	#405	C₂²	1	2	yes	complemented
130	#405	C₂²	1	2	yes	complemented
131	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
132	C₂×#97	C₂²	1	2	yes	complemented
133	C₂×C₄×C₈	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	C₂×C₄	1	1	yes	characteristic
136	C₂×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂²×D₄	C₂×C₄	1	1	yes	characteristic
139	C₂³×C₄	C₂³	1	2	yes	—
140	C₂×M₁₆	C₂³	1	1	yes	characteristic
141	C₂×M₁₆	C₂³	1	1	yes	characteristic
142	C₂×M₁₆	C₂³	1	2	yes	—
143	C₂×M₁₆	C₂³	1	2	yes	—
144	C₂×M₁₆	C₂³	1	2	yes	—
145	C₂²×C₈	C₂³	1	2	yes	—
146	C₂²×C₈	C₂³	1	2	yes	—
147	C₂²×C₈	C₂³	1	1	yes	characteristic
148	C₂²×C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₈	C₂³	1	2	yes	—
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₂²×C₈	C₂³	1	2	yes	—
152	C₂²×C₈	C₂³	1	2	yes	—
153	C₂²×C₈	C₂³	1	2	yes	—
154	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
155	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
156	#126	C₂×C₄	1	2	yes	—
157	#126	C₂×C₄	1	2	yes	—
158	#126	C₂×C₄	1	2	yes	—
159	#126	C₂×C₄	1	2	yes	—
160	#126	C₂×C₄	1	2	yes	—
161	#126	C₂×C₄	1	2	yes	—
162	#125	C₂×C₄	1	2	yes	—
163	#125	C₂×C₄	1	2	yes	—
164	#125	C₂×C₄	1	1	yes	characteristic
165	#125	C₂×C₄	1	1	yes	characteristic
166	#125	C₂×C₄	1	2	yes	—
167	#124	C₂×C₄	1	1	yes	characteristic
168	#124	C₂×C₄	1	1	yes	characteristic
169	#124	C₂×C₄	1	2	yes	—
170	#124	C₂×C₄	1	2	yes	—
171	#123	C₂×C₄	1	2	yes	—
172	#123	C₂×C₄	1	2	yes	—
173	#123	C₂×C₄	1	2	yes	—
174	#123	C₂×C₄	1	2	yes	—
175	#123	C₂×C₄	1	2	yes	—
176	#123	C₂×C₄	1	2	yes	—
177	#123	C₂×C₄	1	2	yes	—
178	#123	C₂×C₄	1	2	yes	—
179	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
180	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
181	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
182	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
183	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
186	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
187	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
188	#121	C₂×C₄	1	2	yes	—
189	#121	C₂×C₄	1	2	yes	—
190	#121	C₂×C₄	1	2	yes	—
191	#121	C₂×C₄	1	2	yes	—
192	#121	C₂×C₄	1	1	yes	characteristic
193	#121	C₂×C₄	1	1	yes	characteristic
194	#120	C₂×C₄	1	2	yes	—
195	#120	C₂×C₄	1	2	yes	—
196	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
197	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
198	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
199	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
200	C₄×Q₈	C₂³	1	1	yes	characteristic
201	C₄×Q₈	C₂³	1	1	yes	characteristic
202	C₄×Q₈	C₂³	1	2	yes	—
203	C₄×D₄	C₂×C₄	1	1	yes	characteristic
204	C₄×D₄	C₂×C₄	1	2	yes	—
205	C₄×D₄	C₂×C₄	1	1	yes	characteristic
206	C₄×D₄	C₂×C₄	1	1	yes	characteristic
207	C₄×D₄	C₂×C₄	1	1	yes	characteristic
208	C₄×D₄	C₂×C₄	1	1	yes	characteristic
209	C₄×D₄	C₂×C₄	1	1	yes	characteristic
210	C₄×D₄	C₂×C₄	1	1	yes	characteristic
211	C₄×D₄	C₂×C₄	1	1	yes	characteristic
212	C₄×D₄	C₂×C₄	1	1	yes	characteristic
213	C₄×D₄	C₂×C₄	1	2	yes	—
214	C₄×D₄	C₂×C₄	1	2	yes	—
215	C₄×D₄	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄	C₂³	1	1	yes	characteristic
217	C₄×D₄	C₂³	1	2	yes	—
218	C₄×D₄	C₂³	1	1	yes	characteristic
219	C₄×D₄	C₂³	1	2	yes	—
220	C₄×D₄	C₂³	1	2	yes	—
221	C₄×D₄	C₂³	1	2	yes	—
222	C₄×D₄	C₂³	1	2	yes	—
223	#117	C₂×C₄	1	2	yes	—
224	#117	C₂×C₄	1	2	yes	—
225	#117	C₂×C₄	1	2	yes	—
226	#117	C₂×C₄	1	2	yes	—
227	#117	C₂×C₄	1	2	yes	—
228	#117	C₂×C₄	1	2	yes	—
229	#117	C₂×C₄	1	1	yes	characteristic
230	#117	C₂×C₄	1	1	yes	characteristic
231	#117	C₂³	1	1	yes	characteristic
232	#117	C₂³	1	2	yes	—
233	#117	C₂³	1	2	yes	—
234	#117	C₂³	1	2	yes	—
235	#117	C₂³	1	1	yes	characteristic
236	#117	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
241	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
243	C₂×C₄²	C₂³	1	2	yes	—
244	C₂×C₄²	C₂³	1	2	yes	—
245	C₂×C₄²	C₂³	1	1	yes	characteristic
246	C₂×C₄²	C₂³	1	1	yes	characteristic
247	C₂×C₄²	C₂³	1	1	yes	characteristic
248	C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₄⋊C₈	C₂³	1	2	yes	—
250	C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₄⋊C₈	C₂³	1	2	yes	—
252	C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₄⋊C₈	C₂³	1	2	yes	—
255	C₄⋊C₈	C₂³	1	2	yes	—
256	C₄⋊C₈	C₂³	1	2	yes	—
257	C₄⋊C₈	C₂³	1	2	yes	—
258	C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₄⋊C₈	C₂³	1	2	yes	—
267	C₄⋊C₈	C₂³	1	2	yes	—
268	C₄⋊C₈	C₂³	1	2	yes	—
269	C₄⋊C₈	C₂³	1	2	yes	—
270	C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈	C₂³	1	2	yes	—
272	C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₂²⋊C₈	C₂³	1	2	yes	—
275	C₂²⋊C₈	C₂³	1	2	yes	—
276	C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂²⋊C₈	C₂³	1	2	yes	—
279	C₂²⋊C₈	C₂³	1	2	yes	—
280	C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂²⋊C₈	C₂³	1	2	yes	—
290	#97	C₂³	1	1	yes	characteristic
291	#97	C₂³	1	2	yes	—
292	#97	C₂³	1	2	yes	—
293	#97	C₂³	1	2	yes	—
294	#97	C₂³	1	1	yes	characteristic
295	#97	C₂³	1	2	yes	—
296	#97	C₂³	1	2	yes	—
297	#97	C₂³	1	2	yes	—
298	C₄×C₈	C₂³	1	1	yes	characteristic
299	C₄×C₈	C₂³	1	2	yes	—
300	C₄×C₈	C₂³	1	1	yes	characteristic
301	C₄×C₈	C₂³	1	1	yes	characteristic
302	C₄×C₈	C₂³	1	1	yes	characteristic
303	C₄×C₈	C₂³	1	2	yes	—
304	C₄×C₈	C₂³	1	2	yes	—
305	C₄×C₈	C₂³	1	1	yes	characteristic
306	C₄×C₈	C₂³	1	1	yes	characteristic
307	C₄×C₈	C₂³	1	2	yes	—
308	C₄×C₈	C₂³	1	2	yes	—
309	C₄×C₈	C₂³	1	2	yes	—
310	C₂⁴	C₂²×C₄	1	2	yes	—
311	#41	—	2	4	no	—
312	#41	—	2	4	no	—
313	#41	—	4	1	no	—
314	#41	—	4	1	no	—
315	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
317	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈	C₂²×C₄	1	2	yes	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	C₂²×C₄	1	2	yes	—
321	C₂×D₄	C₂²×C₄	1	2	yes	—
322	C₂×D₄	C₂²×C₄	1	2	yes	—
323	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
325	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄	C₂²×C₄	1	2	yes	—
328	C₂×D₄	C₂²×C₄	1	2	yes	—
329	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂²×C₄	1	2	yes	—
333	C₂²×C₄	C₂²×C₄	1	2	yes	—
334	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
336	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄	1	2	yes	—
339	C₂²×C₄	C₂²×C₄	1	2	yes	—
340	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄	1	2	yes	—
343	C₂²×C₄	C₂²×C₄	1	2	yes	—
344	C₂²×C₄	C₂²×C₄	1	2	yes	—
345	C₂²×C₄	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴	1	2	yes	—
347	C₂²×C₄	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴	1	2	yes	—
350	M₁₆	—	4	1	no	—
351	M₁₆	—	4	2	no	—
352	M₁₆	—	4	2	no	—
353	M₁₆	—	4	1	no	—
354	M₁₆	—	4	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	—	4	2	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	C₂⁴	1	1	yes	characteristic
365	C₂×C₈	C₂⁴	1	1	yes	characteristic
366	C₂×C₈	C₂⁴	1	1	yes	characteristic
367	C₂×C₈	C₂⁴	1	2	yes	—
368	C₂×C₈	C₂⁴	1	1	yes	characteristic
369	C₂×C₈	C₂⁴	1	1	yes	characteristic
370	C₂×C₈	C₂⁴	1	2	yes	—
371	C₂×C₈	C₂⁴	1	1	yes	characteristic
372	C₂×C₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₈	C₂⁴	1	2	yes	—
375	C₂×C₈	C₂⁴	1	2	yes	—
376	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
378	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×C₄	1	2	yes	—
380	C₄⋊C₄	C₂²×C₄	1	2	yes	—
381	C₄⋊C₄	C₂²×C₄	1	2	yes	—
382	C₄⋊C₄	C₂²×C₄	1	2	yes	—
383	C₄⋊C₄	C₂²×C₄	1	2	yes	—
384	C₄⋊C₄	C₂²×C₄	1	2	yes	—
385	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
386	C₄⋊C₄	C₂²×C₄	1	2	yes	—
387	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	C₄⋊C₄	C₂²×C₄	1	2	yes	—
390	C₄⋊C₄	C₂²×C₄	1	2	yes	—
391	C₄⋊C₄	C₂²×C₄	1	2	yes	—
392	C₄⋊C₄	C₂²×C₄	1	2	yes	—
393	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
394	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
395	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×C₄	1	2	yes	—
398	C₄⋊C₄	C₂²×C₄	1	2	yes	—
399	C₄⋊C₄	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄	C₂²×C₄	1	2	yes	—
401	C₄⋊C₄	C₂²×C₄	1	2	yes	—
402	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
403	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
404	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
405	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
406	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
407	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
408	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
409	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
410	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
411	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
412	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
413	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
414	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
415	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
417	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
419	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
420	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
421	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
422	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
424	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
426	C₄²	C₂²×C₄	1	2	yes	—
427	C₄²	C₂²×C₄	1	2	yes	—
428	C₄²	C₂²×C₄	1	2	yes	—
429	C₄²	C₂²×C₄	1	2	yes	—
430	C₄²	C₂²×C₄	1	1	yes	characteristic
431	C₄²	C₂²×C₄	1	1	yes	characteristic
432	C₄²	C₂²×C₄	1	1	yes	characteristic
433	C₄²	C₂²×C₄	1	1	yes	characteristic
434	C₄²	C₂²×C₄	1	1	yes	characteristic
435	C₄²	C₂²×C₄	1	1	yes	characteristic
436	C₄²	C₂⁴	1	1	yes	characteristic
437	C₄²	C₂⁴	1	1	yes	characteristic
438	C₄²	C₂⁴	1	1	yes	characteristic
439	C₄²	C₂⁴	1	2	yes	—
440	C₄²	C₂⁴	1	2	yes	—
441	C₄²	C₂⁴	1	1	yes	characteristic
442	C₂³	—	2	4	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	C₂³×C₄	1	2	yes	—
446	C₂³	C₂³×C₄	1	1	yes	characteristic
447	C₂³	C₂³×C₄	1	1	yes	characteristic
448	C₂³	C₂³×C₄	1	1	yes	characteristic
449	C₂³	C₂³×C₄	1	2	yes	—
450	Q₈	—	2	2	no	—
451	Q₈	—	2	2	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	1	no	—
454	D₄	—	2	4	no	—
455	D₄	—	2	4	no	—
456	D₄	—	2	4	no	—
457	D₄	—	2	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	1	no	—
461	D₄	—	4	1	no	—
462	D₄	—	4	1	no	—
463	D₄	#131	1	4	yes	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	C₂³×C₄	1	2	yes	—
488	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
489	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
497	C₂×C₄	C₂³×C₄	1	2	yes	—
498	C₂×C₄	C₂³×C₄	1	2	yes	—
499	C₂×C₄	C₂³×C₄	1	2	yes	—
500	C₂×C₄	C₂³×C₄	1	2	yes	—
501	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
502	C₂×C₄	C₂³×C₄	1	2	yes	—
503	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
504	C₂×C₄	C₂⁵	1	1	yes	characteristic
505	C₈	—	2	1	no	—
506	C₈	—	2	2	no	—
507	C₈	—	2	1	no	—
508	C₈	—	2	1	no	—
509	C₈	—	2	2	no	—
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	2	2	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	2	no	—
516	C₈	—	2	1	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	8	4	no	—
532	C₂²	C₂×#131	1	4	yes	—
533	C₂²	C₂⁴×C₄	1	1	yes	characteristic
534	C₄	—	2	1	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	C₂×#131	1	2	yes	—
551	C₄	#585	1	1	yes	characteristic
552	C₄	#585	1	1	yes	characteristic
553	C₂	—	2	4	no	—
554	C₂	—	4	1	no	—
555	C₂	—	4	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	4	1	no	—
558	C₂	#3428	1	1	yes	characteristic
559	C₂	C₂²×#131	1	1	yes	characteristic
560	C₂	#3573	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂⁵
commutator, socle	C₂²	C₂⁴×C₄
prime radical	#3475	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2994	C₂	semidirect
3. #2994	C₂	semidirect
4. #2993	C₂	semidirect
5. #2992	C₂	semidirect
6. #2990	C₂	semidirect
7. #2988	C₂	semidirect
8. #2986	C₂	semidirect
9. #2985	C₂	semidirect
10. #2977	C₂	semidirect
11. #2976	C₂	semidirect
12. #2974	C₂	semidirect
13. #2972	C₂	semidirect
14. #2970	C₂	semidirect
15. #2969	C₂	semidirect
16. #2968	C₂	semidirect
17. #2966	C₂	semidirect
18. #2966	C₂	semidirect
19. C₈×#41	C₂	semidirect
20. #2925	C₂	semidirect
21. #2924	C₂	semidirect
22. #2922	C₂	semidirect
23. C₂×#433	C₂	semidirect
47. #446	C₂²	semidirect
48. #446	C₂²	semidirect
49. #446	C₂²	semidirect
50. #446	C₂²	semidirect
51. #446	C₂²	semidirect
52. #446	C₂²	semidirect
53. #446	C₂²	semidirect
54. C₈×Q₈	C₂²	semidirect
55. C₈×Q₈	C₂²	semidirect
56. C₈×Q₈	C₂²	semidirect
57. C₈×Q₈	C₂²	semidirect
58. C₈×Q₈	C₂²	semidirect
61. #436	C₂²	semidirect
62. #436	C₂²	semidirect
65. #435	C₂²	semidirect
66. #435	C₂²	semidirect
67. #435	C₂²	semidirect
68. #435	C₂²	semidirect
69. #435	C₂²	semidirect
70. #435	C₂²	semidirect
71. #435	C₂²	semidirect
72. #435	C₂²	semidirect
81. C₈×D₄	C₂²	semidirect
82. C₈×D₄	C₂²	semidirect
83. C₈×D₄	C₂²	semidirect
84. C₈×D₄	C₂²	semidirect
85. C₈×D₄	C₂²	semidirect
86. C₈×D₄	C₂²	semidirect
94. #433	C₂²	semidirect
95. #433	C₂²	semidirect
96. #433	C₂²	semidirect
97. #433	C₂²	semidirect
98. #433	C₂²	semidirect
99. #433	C₂²	semidirect
100. #433	C₂²	semidirect
102. #432	C₂²	semidirect
103. #432	C₂²	semidirect
104. #432	C₂²	semidirect
108. #431	C₂²	semidirect
109. #431	C₂²	semidirect
110. #431	C₂²	semidirect
111. #431	C₂²	semidirect
112. #431	C₂²	semidirect
113. #424	C₂²	semidirect
114. #424	C₂²	semidirect
115. #424	C₂²	semidirect
116. #424	C₂²	semidirect
117. #423	C₂²	semidirect
118. C₂×C₄⋊C₈	C₂²	semidirect
119. C₂×C₄⋊C₈	C₂²	semidirect
120. C₂×C₄⋊C₈	C₂²	semidirect
128. #405	C₂²	semidirect
129. #405	C₂²	semidirect
130. #405	C₂²	semidirect
131. C₄×M₁₆	C₂²	semidirect
132. C₂×#97	C₂²	semidirect
133. C₂×C₄×C₈	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3475	2
#2994	2
#2993	2
#2992	2
#2990	2
#2988	2
#2986	2
#2985	2
#2977	2
#2976	2
#2974	2
#2972	2
#2970	2
#2969	2
#2968	2
#2966	2
C₈×#41	2
#2925	2
#2924	2
#2922	2
C₂×#433	2