Subgroups — #60982

Order 256.

864 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	#3260	C₂	1	2	yes	maximal, complemented
4	#3258	C₂	1	2	yes	maximal, complemented
5	#3242	C₂	1	2	yes	maximal, complemented
6	#3234	C₂	1	1	yes	maximal, characteristic, complemented
7	#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	#3222	C₂	1	2	yes	maximal, complemented
9	#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	#3206	C₂	1	1	yes	maximal, characteristic, complemented
11	#3196	C₂	1	1	yes	maximal, characteristic, complemented
12	#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	#3190	C₂	1	1	yes	maximal, characteristic, complemented
14	#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	#3178	C₂	1	2	yes	maximal, complemented
16	#3174	C₂	1	2	yes	maximal, complemented
17	#3123	C₂	1	2	yes	maximal, complemented
18	#3120	C₂	1	2	yes	maximal, complemented
19	#3117	C₂	1	1	yes	maximal, characteristic, complemented
20	#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#555	—	2	1	no	—
25	#553	—	2	1	no	—
26	#553	—	2	1	no	—
27	#551	—	2	1	no	—
28	#551	—	2	1	no	—
29	#547	—	2	1	no	—
30	#546	—	2	1	no	—
31	#546	—	2	1	no	—
32	#544	C₂²	1	1	yes	characteristic
33	#542	C₂²	1	1	yes	characteristic
34	#542	C₂²	1	1	yes	characteristic
35	#541	—	2	1	no	—
36	#541	—	2	1	no	—
37	#541	—	2	1	no	—
38	#541	—	2	1	no	—
39	#541	C₂²	1	2	yes	—
40	#541	C₂²	1	2	yes	—
41	#541	C₂²	1	2	yes	complemented
42	#541	C₂²	1	2	yes	complemented
43	#540	C₂²	1	1	yes	characteristic
44	#540	C₂²	1	1	yes	characteristic
45	#535	C₂²	1	1	yes	characteristic
46	#532	C₂²	1	1	yes	characteristic
47	#532	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	#529	C₂²	1	1	yes	characteristic
50	#529	C₂²	1	1	yes	characteristic
51	C₂×#126	—	2	1	no	—
52	C₂×#126	—	2	1	no	—
53	C₂×#125	—	2	1	no	—
54	C₂×#125	—	2	1	no	—
55	C₂×#125	C₂²	1	1	yes	characteristic, complemented
56	#525	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×#121	C₂²	1	1	yes	characteristic
60	#520	C₂²	1	1	yes	characteristic
61	#518	C₂²	1	1	yes	characteristic
62	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₂×#117	C₂²	1	1	yes	characteristic
65	#501	C₂²	1	2	yes	complemented
66	#499	C₂²	1	2	yes	complemented
67	#497	C₂²	1	2	yes	complemented
68	#492	C₂²	1	2	yes	complemented
69	#491	C₂²	1	2	yes	complemented
70	#490	C₂²	1	2	yes	complemented
71	#488	C₂²	1	2	yes	complemented
72	#487	C₂²	1	2	yes	complemented
73	#485	C₂²	1	2	yes	—
74	#485	C₂²	1	2	yes	—
75	#484	C₂²	1	2	yes	—
76	#484	C₂²	1	1	yes	characteristic, complemented
77	#483	C₂²	1	2	yes	—
78	#483	C₂²	1	1	yes	characteristic, complemented
79	#481	C₂²	1	1	yes	characteristic
80	#481	C₂²	1	1	yes	characteristic
81	#481	C₂²	1	1	yes	characteristic, complemented
82	#480	C₂²	1	1	yes	characteristic
83	#480	C₂²	1	1	yes	characteristic
84	#480	C₂²	1	1	yes	characteristic, complemented
85	#479	C₂²	1	2	yes	complemented
86	#479	C₂²	1	2	yes	complemented
87	#479	C₂²	1	2	yes	complemented
88	#478	C₂²	1	2	yes	complemented
89	#478	C₂²	1	2	yes	complemented
90	#478	C₂²	1	2	yes	complemented
91	#477	C₂²	1	2	yes	complemented
92	#475	C₂²	1	2	yes	complemented
93	#470	C₂²	1	2	yes	complemented
94	#468	C₂²	1	2	yes	—
95	#468	C₂²	1	2	yes	—
96	#468	C₂²	1	2	yes	complemented
97	#467	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	—
99	#465	C₂²	1	2	yes	—
100	#465	C₂²	1	2	yes	complemented
101	#464	C₂²	1	2	yes	complemented
102	#464	C₂²	1	2	yes	complemented
103	#462	C₂²	1	2	yes	complemented
104	#461	C₂²	1	2	yes	complemented
105	#461	C₂²	1	2	yes	complemented
106	#461	C₂²	1	2	yes	complemented
107	#460	C₂²	1	2	yes	complemented
108	#460	C₂²	1	2	yes	complemented
109	#452	C₂²	1	2	yes	—
110	#452	C₂²	1	2	yes	—
111	#451	C₂²	1	1	yes	characteristic, complemented
112	#451	C₂²	1	1	yes	characteristic, complemented
113	#450	C₂²	1	2	yes	—
114	#450	C₂²	1	2	yes	—
115	#448	C₂²	1	1	yes	characteristic
116	#448	C₂²	1	1	yes	characteristic
117	#448	C₂²	1	1	yes	characteristic
118	#448	C₂²	1	1	yes	characteristic
119	#448	C₂²	1	1	yes	characteristic, complemented
120	#448	C₂²	1	1	yes	characteristic, complemented
121	#441	C₂²	1	2	yes	complemented
122	#440	C₂²	1	2	yes	complemented
123	#440	C₂²	1	2	yes	complemented
124	#440	C₂²	1	2	yes	complemented
125	C₄×Q₁₆	C₂²	1	2	yes	complemented
126	C₄×SD₁₆	C₂²	1	2	yes	complemented
127	C₄×SD₁₆	C₂²	1	2	yes	complemented
128	C₄×SD₁₆	C₂²	1	2	yes	complemented
129	#433	C₂²	1	2	yes	—
130	#433	C₂²	1	2	yes	—
131	#432	C₂²	1	1	yes	characteristic, complemented
132	#432	C₂²	1	1	yes	characteristic, complemented
133	#431	C₂²	1	1	yes	characteristic, complemented
134	#431	C₂²	1	1	yes	characteristic, complemented
135	#424	C₂²	1	2	yes	complemented
136	#407	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	#405	C₂²	1	2	yes	complemented
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂²×Q₈	C₂³	1	1	yes	characteristic
143	C₂²×Q₈	C₂³	1	1	yes	characteristic
144	C₂²×D₄	—	2	1	no	—
145	C₂²×D₄	C₂³	1	1	yes	characteristic
146	C₂³×C₄	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆	C₂³	1	2	yes	—
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×M₁₆	C₂³	1	2	yes	—
156	C₂²×C₈	C₂³	1	2	yes	—
157	C₄⋊Q₈	—	2	1	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	C₂³	1	2	yes	—
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	#127	C₂³	1	1	yes	characteristic
165	#127	C₂³	1	1	yes	characteristic
166	#126	—	2	1	no	—
167	#126	—	2	1	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	2	no	—
176	#126	—	2	1	no	—
177	#126	—	2	1	no	—
178	#125	—	2	2	no	—
179	#125	—	2	2	no	—
180	#125	—	2	2	no	—
181	#125	—	2	2	no	—
182	#125	—	2	2	no	—
183	#125	—	2	2	no	—
184	#125	—	2	2	no	—
185	#125	—	2	2	no	—
186	#125	—	2	1	no	—
187	#125	—	2	1	no	—
188	#125	—	2	1	no	—
189	#125	C₂³	1	2	yes	—
190	#125	C₂³	1	2	yes	—
191	#125	C₂³	1	1	yes	characteristic
192	#125	C₂³	1	1	yes	characteristic
193	#124	—	2	1	no	—
194	#124	—	2	1	no	—
195	#124	—	2	1	no	—
196	#124	—	2	1	no	—
197	#124	C₂³	1	1	yes	characteristic
198	#124	C₂³	1	1	yes	characteristic
199	#123	—	2	1	no	—
200	#123	—	2	1	no	—
201	#123	—	2	1	no	—
202	#123	—	2	1	no	—
203	#123	—	2	1	no	—
204	#123	—	2	1	no	—
205	#123	—	2	1	no	—
206	#123	—	2	1	no	—
207	#123	—	2	1	no	—
208	C₂²⋊Q₈	—	2	1	no	—
209	C₂²⋊Q₈	—	2	1	no	—
210	C₂²⋊Q₈	—	2	1	no	—
211	C₂²⋊Q₈	—	2	1	no	—
212	C₂²⋊Q₈	—	2	1	no	—
213	C₂²⋊Q₈	—	2	1	no	—
214	C₂²⋊Q₈	—	2	1	no	—
215	C₂²⋊Q₈	—	2	1	no	—
216	C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	#121	—	2	1	no	—
223	#121	—	2	1	no	—
224	#121	—	2	1	no	—
225	#121	—	2	1	no	—
226	#121	—	2	1	no	—
227	#121	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	—	2	1	no	—
230	#121	—	2	1	no	—
231	#121	—	2	1	no	—
232	#121	C₂³	1	1	yes	characteristic
233	#121	C₂³	1	1	yes	characteristic
234	#121	C₂³	1	1	yes	characteristic
235	#121	C₂³	1	1	yes	characteristic
236	#121	C₂³	1	1	yes	characteristic
237	#121	C₂³	1	1	yes	characteristic
238	#120	—	2	1	no	—
239	#120	—	2	1	no	—
240	#120	—	2	1	no	—
241	C₄×Q₈	—	2	1	no	—
242	C₄×Q₈	—	2	1	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×Q₈	C₂³	1	2	yes	—
246	C₄×Q₈	C₂³	1	2	yes	—
247	C₄×Q₈	C₂³	1	2	yes	—
248	C₄×Q₈	C₂³	1	2	yes	—
249	C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	C₂³	1	1	yes	characteristic
262	C₄×D₄	C₂³	1	1	yes	characteristic
263	C₄×D₄	C₂³	1	1	yes	characteristic
264	C₄×D₄	C₂³	1	1	yes	characteristic
265	C₄×D₄	C₂³	1	1	yes	characteristic
266	C₄×D₄	C₂³	1	1	yes	characteristic
267	#117	—	2	1	no	—
268	#117	—	2	1	no	—
269	#117	—	2	1	no	—
270	#117	D₄	1	1	yes	characteristic
271	#117	D₄	1	1	yes	characteristic
272	#117	D₄	1	1	yes	characteristic
273	#117	D₄	1	1	yes	characteristic
274	#117	C₂³	1	1	yes	characteristic
275	#117	C₂³	1	1	yes	characteristic
276	#117	C₂³	1	1	yes	characteristic
277	#117	C₂³	1	1	yes	characteristic
278	#117	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
289	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³	1	1	yes	characteristic
303	C₂×C₄²	C₂³	1	1	yes	characteristic
304	#107	C₂³	1	2	yes	—
305	#107	C₂³	1	2	yes	—
306	#107	C₂³	1	2	yes	—
307	#107	C₂³	1	2	yes	—
308	#106	C₂³	1	2	yes	—
309	#106	C₂³	1	2	yes	—
310	#106	C₂³	1	2	yes	—
311	#106	C₂³	1	2	yes	—
312	C₄⋊C₈	C₂³	1	2	yes	—
313	C₄⋊C₈	C₂³	1	2	yes	—
314	C₄⋊C₈	C₂³	1	2	yes	—
315	C₄⋊C₈	C₂³	1	2	yes	—
316	#103	C₂³	1	2	yes	—
317	#103	C₂³	1	2	yes	—
318	#103	C₂³	1	2	yes	—
319	#103	C₂³	1	2	yes	—
320	#103	C₂³	1	2	yes	—
321	#103	C₂³	1	2	yes	—
322	#103	C₂³	1	2	yes	—
323	#103	C₂³	1	2	yes	—
324	#103	C₂³	1	2	yes	—
325	#103	C₂³	1	2	yes	—
326	#102	C₂³	1	2	yes	—
327	#102	C₂³	1	2	yes	—
328	#102	C₂³	1	2	yes	—
329	#102	C₂³	1	2	yes	—
330	#102	C₂³	1	2	yes	—
331	#102	C₂³	1	2	yes	—
332	C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈	C₂³	1	2	yes	—
335	C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈	C₂³	1	2	yes	—
338	#97	C₂³	1	2	yes	—
339	#97	C₂³	1	2	yes	—
340	C₄×C₈	C₂³	1	2	yes	—
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	C₂×D₄	1	1	yes	characteristic
344	#41	—	4	2	no	—
345	#41	—	8	2	no	—
346	#41	—	8	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	—	4	2	no	—
353	C₂×Q₈	C₂⁴	1	1	yes	characteristic
354	C₂×Q₈	C₂⁴	1	2	yes	—
355	C₂×Q₈	C₂⁴	1	2	yes	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	8	2	no	—
370	C₂×D₄	C₂⁴	1	1	yes	characteristic
371	C₂×D₄	C₂⁴	1	1	yes	characteristic
372	C₂×D₄	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴	1	1	yes	characteristic
396	Q₁₆	—	4	2	no	—
397	Q₁₆	—	4	2	no	—
398	SD₁₆	—	4	2	no	—
399	SD₁₆	—	4	2	no	—
400	SD₁₆	—	4	2	no	—
401	SD₁₆	—	4	2	no	—
402	SD₁₆	—	4	2	no	—
403	SD₁₆	—	4	2	no	—
404	M₁₆	—	4	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	C₂⁴	1	2	yes	—
407	C₂×C₈	C₂⁴	1	2	yes	—
408	C₂×C₈	C₂⁴	1	2	yes	—
409	C₂×C₈	C₂⁴	1	2	yes	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄	C₂⁴	1	2	yes	—
448	C₄⋊C₄	C₂⁴	1	2	yes	—
449	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
484	C₄²	—	2	2	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	C₂×D₄	1	1	yes	characteristic
492	C₄²	C₂×D₄	1	1	yes	characteristic
493	C₄²	C₂×D₄	1	1	yes	characteristic
494	C₄²	C₂×D₄	1	1	yes	characteristic
495	C₄²	C₂⁴	1	1	yes	characteristic
496	C₄²	C₂⁴	1	1	yes	characteristic
497	C₄²	C₂⁴	1	1	yes	characteristic
498	C₄²	C₂⁴	1	1	yes	characteristic
499	C₂³	—	2	2	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	8	1	no	—
507	C₂³	—	8	1	no	—
508	C₂³	C₂²×D₄	1	1	yes	characteristic
509	C₂³	C₂²×D₄	1	1	yes	characteristic
510	C₂³	C₂²×D₄	1	1	yes	characteristic
511	Q₈	—	2	2	no	—
512	Q₈	—	2	2	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	4	2	no	—
518	Q₈	—	8	1	no	—
519	Q₈	—	8	1	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	8	1	no	—
529	D₄	—	8	1	no	—
530	D₄	—	8	1	no	—
531	D₄	—	8	1	no	—
532	D₄	—	8	1	no	—
533	D₄	—	8	1	no	—
534	D₄	—	8	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	8	1	no	—
560	C₂×C₄	—	8	1	no	—
561	C₂×C₄	—	8	1	no	—
562	C₂×C₄	—	8	1	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	—	8	1	no	—
565	C₂×C₄	—	8	1	no	—
566	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄	C₂⁵	1	1	yes	characteristic
578	C₈	—	2	2	no	—
579	C₈	—	2	2	no	—
580	C₈	—	2	2	no	—
581	C₈	—	2	2	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	8	2	no	—
600	C₂²	—	16	2	no	—
601	C₂²	#577	1	2	yes	—
602	C₂²	C₂³×D₄	1	1	yes	characteristic
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	4	2	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	#585	1	2	yes	—
624	C₂	—	2	2	no	—
625	C₂	—	4	1	no	—
626	C₂	—	4	1	no	—
627	C₂	—	8	1	no	—
628	C₂	—	8	1	no	—
629	C₂	—	8	1	no	—
630	C₂	#3449	1	1	yes	characteristic
631	C₂	C₂×#577	1	1	yes	characteristic
632	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#541	C₂	semidirect
3. #3260	C₂	semidirect
4. #3258	C₂	semidirect
5. #3242	C₂	semidirect
6. #3234	C₂	semidirect
7. #3232	C₂	semidirect
8. #3222	C₂	semidirect
9. #3218	C₂	semidirect
10. #3206	C₂	semidirect
11. #3196	C₂	semidirect
12. #3193	C₂	semidirect
13. #3190	C₂	semidirect
14. #3187	C₂	semidirect
15. #3178	C₂	semidirect
16. #3174	C₂	semidirect
17. #3123	C₂	semidirect
18. #3120	C₂	semidirect
19. #3117	C₂	semidirect
20. #3112	C₂	semidirect
21. #3108	C₂	semidirect
22. #3103	C₂	semidirect
23. #2924	C₂	semidirect
41. #541	C₂²	semidirect
42. #541	C₂²	semidirect
48. C₂×C₄⋊Q₈	C₂²	semidirect
55. C₂×#125	C₂²	semidirect
62. C₂×C₄×Q₈	C₂²	semidirect
63. C₂×C₄×Q₈	C₂²	semidirect
65. #501	C₂²	semidirect
66. #499	C₂²	semidirect
67. #497	C₂²	semidirect
68. #492	C₂²	semidirect
69. #491	C₂²	semidirect
70. #490	C₂²	semidirect
71. #488	C₂²	semidirect
72. #487	C₂²	semidirect
76. #484	C₂²	semidirect
78. #483	C₂²	semidirect
81. #481	C₂²	semidirect
84. #480	C₂²	semidirect
85. #479	C₂²	semidirect
86. #479	C₂²	semidirect
87. #479	C₂²	semidirect
88. #478	C₂²	semidirect
89. #478	C₂²	semidirect
90. #478	C₂²	semidirect
91. #477	C₂²	semidirect
92. #475	C₂²	semidirect
93. #470	C₂²	semidirect
96. #468	C₂²	semidirect
97. #467	C₂²	semidirect
100. #465	C₂²	semidirect
101. #464	C₂²	semidirect
102. #464	C₂²	semidirect
103. #462	C₂²	semidirect
104. #461	C₂²	semidirect
105. #461	C₂²	semidirect
106. #461	C₂²	semidirect
107. #460	C₂²	semidirect
108. #460	C₂²	semidirect
111. #451	C₂²	semidirect
112. #451	C₂²	semidirect
119. #448	C₂²	semidirect
120. #448	C₂²	semidirect
121. #441	C₂²	semidirect
122. #440	C₂²	semidirect
123. #440	C₂²	semidirect
124. #440	C₂²	semidirect
125. C₄×Q₁₆	C₂²	semidirect
126. C₄×SD₁₆	C₂²	semidirect
127. C₄×SD₁₆	C₂²	semidirect
128. C₄×SD₁₆	C₂²	semidirect
131. #432	C₂²	semidirect
132. #432	C₂²	semidirect
133. #431	C₂²	semidirect
134. #431	C₂²	semidirect
135. #424	C₂²	semidirect
138. #405	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3494	2
C₂×#541	2
#3260	2
#3258	2
#3242	2
#3234	2
#3232	2
#3222	2
#3218	2
#3206	2
#3196	2
#3193	2
#3190	2
#3187	2
#3178	2
#3174	2
#3123	2
#3120	2
#3117	2
#3112	2
#3108	2
#3103	2
#2924	2