Subgroups — #184366

Order 512.

665 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21137	C₂	1	1	yes	maximal, characteristic
2	#17868	C₂	1	1	yes	maximal, characteristic
3	C₈×#135	C₂	1	1	yes	maximal, characteristic
4	#17331	C₂	1	1	yes	maximal, characteristic, complemented
5	#17320	C₂	1	1	yes	maximal, characteristic, complemented
6	#8296	C₂	1	1	yes	maximal, characteristic, complemented
7	#8293	C₂	1	1	yes	maximal, characteristic, complemented
8	#8270	C₂	1	1	yes	maximal, characteristic, complemented
9	#8195	C₂	1	1	yes	maximal, characteristic, complemented
10	#8193	C₂	1	1	yes	maximal, characteristic, complemented
11	#8193	C₂	1	1	yes	maximal, characteristic, complemented
12	#8191	C₂	1	1	yes	maximal, characteristic, complemented
13	#8188	C₂	1	1	yes	maximal, characteristic, complemented
14	#8185	C₂	1	1	yes	maximal, characteristic, complemented
15	#7845	C₂	1	1	yes	maximal, characteristic, complemented
16	#2965	C₂²	1	1	yes	characteristic
17	C₈×#41	C₂²	1	1	yes	characteristic
18	C₈×#41	C₂²	1	1	yes	characteristic
19	C₈×#41	C₂²	1	1	yes	characteristic
20	C₄×#135	C₂²	1	1	yes	characteristic
21	#2922	C₂²	1	1	yes	characteristic
22	C₄×#131	C₂²	1	1	yes	characteristic
23	#1929	C₄	1	2	yes	—
24	#1922	C₄	1	2	yes	—
25	#1876	C₄	1	2	yes	—
26	#1866	C₄	1	2	yes	—
27	C₄×#108	C₂²	1	1	yes	characteristic
28	C₄×#104	C₂²	1	1	yes	characteristic
29	C₄×#104	C₂²	1	1	yes	characteristic
30	#1744	C₂²	1	1	yes	characteristic
31	#1744	C₂²	1	1	yes	characteristic
32	#1744	C₂²	1	1	yes	characteristic
33	#1588	C₄	1	2	yes	complemented
34	#1587	C₄	1	2	yes	complemented
35	#1586	C₄	1	2	yes	complemented
36	#1585	C₄	1	2	yes	complemented
37	C₈×Q₁₆	C₄	1	2	yes	complemented
38	C₈×SD₁₆	C₄	1	2	yes	complemented
39	C₈×SD₁₆	C₄	1	2	yes	complemented
40	C₈×D₈	C₄	1	2	yes	complemented
41	#1564	C₂²	1	1	yes	characteristic
42	#1564	C₂²	1	1	yes	characteristic
43	#1476	C₂²	1	1	yes	characteristic
44	#1476	C₂²	1	1	yes	characteristic
45	#1476	C₂²	1	1	yes	characteristic
46	#1476	C₂²	1	1	yes	characteristic
47	#1454	—	2	1	no	—
48	#1453	—	2	1	no	—
49	#1452	—	2	1	no	—
50	#1452	—	2	1	no	—
51	#1452	C₂²	1	1	yes	characteristic
52	#1451	—	2	1	no	—
53	#1451	—	2	1	no	—
54	#1451	C₂²	1	1	yes	characteristic
55	#1451	C₂²	1	1	yes	characteristic
56	#1451	C₂²	1	1	yes	characteristic
57	#1450	C₂²	1	1	yes	characteristic
58	C₈×M₁₆	—	2	1	no	—
59	C₈×M₁₆	C₂²	1	1	yes	characteristic
60	C₂×#322	—	2	1	no	—
61	C₂×#322	C₂²	1	1	yes	characteristic
62	C₂×#322	C₂²	1	1	yes	characteristic
63	C₂×#322	C₂²	1	1	yes	characteristic
64	C₂×C₈²	C₂²	1	1	yes	characteristic
65	#1278	C₂²	1	1	yes	characteristic
66	#1278	C₂²	1	1	yes	characteristic
67	#1278	C₂²	1	1	yes	characteristic
68	#1278	C₂²	1	1	yes	characteristic
69	#1276	C₂²	1	1	yes	characteristic
70	#1276	C₂²	1	1	yes	characteristic
71	C₂×#135	C₂×C₄	1	1	yes	characteristic
72	C₂×#131	C₂×C₄	1	2	yes	—
73	C₄×#41	C₂³	1	1	yes	characteristic
74	C₄×#41	C₂³	1	1	yes	characteristic
75	#446	C₂×C₄	1	2	yes	—
76	C₈×Q₈	C₂×C₄	1	2	yes	—
77	C₈×Q₈	C₂×C₄	1	2	yes	—
78	C₈×Q₈	C₂×C₄	1	2	yes	—
79	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
81	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
82	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
83	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
84	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
85	C₄×D₈	C₂×C₄	1	1	yes	characteristic
86	C₄×D₈	C₂×C₄	1	1	yes	characteristic
87	#436	C₂×C₄	1	2	yes	—
88	#435	—	2	2	no	—
89	C₈×D₄	—	2	2	no	—
90	C₈×D₄	—	2	2	no	—
91	C₈×D₄	—	2	2	no	—
92	C₈×D₄	C₂×C₄	1	2	yes	—
93	C₈×D₄	C₂×C₄	1	2	yes	—
94	C₈×D₄	C₂×C₄	1	2	yes	—
95	#433	—	2	2	no	—
96	#431	—	2	1	no	—
97	#431	—	2	1	no	—
98	#431	—	2	1	no	—
99	#431	—	2	1	no	—
100	#431	—	2	1	no	—
101	#431	—	2	1	no	—
102	#431	C₂³	1	1	yes	characteristic
103	#431	C₂³	1	1	yes	characteristic
104	#431	C₂³	1	1	yes	characteristic
105	#431	C₂³	1	1	yes	characteristic
106	C₂×#108	C₂×C₄	1	2	yes	—
107	#427	C₂×C₄	1	1	yes	characteristic
108	#424	C₂×C₄	1	2	yes	—
109	C₂×#104	C₂×C₄	1	2	yes	—
110	C₂×#104	C₂×C₄	1	2	yes	—
111	#416	C₂×C₄	1	1	yes	characteristic
112	#416	C₂×C₄	1	1	yes	characteristic
113	#408	C₂×C₄	1	2	yes	—
114	#405	—	2	2	no	—
115	#405	C₂×C₄	1	2	yes	—
116	C₄×M₁₆	—	2	1	no	—
117	C₄×M₁₆	—	2	1	no	—
118	C₄×M₁₆	C₂³	1	1	yes	characteristic
119	C₄×M₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₄×C₈	—	2	1	no	—
121	C₂×C₄×C₈	—	2	1	no	—
122	C₂×C₄×C₈	—	2	1	no	—
123	C₂×C₄×C₈	—	2	1	no	—
124	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
125	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
126	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
128	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
129	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
130	C₄³	C₂³	1	1	yes	characteristic
131	#341	C₂×C₄	1	2	yes	—
132	#339	C₂×C₄	1	2	yes	—
133	#339	C₂×C₄	1	2	yes	—
134	#336	—	2	2	no	—
135	#336	—	2	2	no	—
136	#336	C₂×C₄	1	2	yes	—
137	#336	C₂×C₄	1	2	yes	—
138	#335	C₂×C₄	1	2	yes	—
139	#335	C₂×C₄	1	2	yes	—
140	#334	C₂×C₄	1	2	yes	—
141	#334	C₂×C₄	1	2	yes	—
142	Q₈⋊C₈	C₂×C₄	1	2	yes	—
143	Q₈⋊C₈	C₂×C₄	1	2	yes	—
144	Q₈⋊C₈	C₂×C₄	1	2	yes	—
145	Q₈⋊C₈	C₂×C₄	1	2	yes	—
146	D₄⋊C₈	C₂×C₄	1	2	yes	—
147	D₄⋊C₈	C₂×C₄	1	2	yes	—
148	D₄⋊C₈	C₂×C₄	1	2	yes	—
149	D₄⋊C₈	C₂×C₄	1	2	yes	—
150	#322	—	2	1	no	—
151	#322	—	2	1	no	—
152	#322	—	2	1	no	—
153	#322	—	2	1	no	—
154	#322	—	2	1	no	—
155	#322	—	2	1	no	—
156	#322	—	2	1	no	—
157	#322	—	2	1	no	—
158	#322	—	2	1	no	—
159	#322	—	2	1	no	—
160	#322	—	2	2	no	—
161	#322	C₂×C₄	1	2	yes	—
162	#322	C₂×C₄	1	2	yes	—
163	#322	D₄	1	1	yes	characteristic
164	#322	D₄	1	1	yes	characteristic
165	#322	D₄	1	1	yes	characteristic
166	#322	D₄	1	1	yes	characteristic
167	C₈²	—	2	1	no	—
168	C₈²	—	2	1	no	—
169	C₈²	C₂×C₄	1	2	yes	—
170	C₈²	C₂×C₄	1	2	yes	—
171	C₂×#41	C₂²×C₄	1	1	yes	characteristic
172	C₂×#41	C₂²×C₄	1	1	yes	characteristic
173	#135	—	2	4	no	—
174	C₂×Q₁₆	C₄²	1	1	yes	characteristic
175	C₂×SD₁₆	C₄²	1	1	yes	characteristic
176	C₂×SD₁₆	C₄²	1	1	yes	characteristic
177	C₂×D₈	C₄²	1	1	yes	characteristic
178	#131	—	2	4	no	—
179	#131	—	4	2	no	—
180	C₂×M₁₆	—	2	2	no	—
181	C₂×M₁₆	—	2	2	no	—
182	C₂×M₁₆	C₂²×C₄	1	2	yes	—
183	C₂×M₁₆	C₂²×C₄	1	2	yes	—
184	C₂²×C₈	—	2	1	no	—
185	C₂²×C₈	—	2	1	no	—
186	C₂²×C₈	—	2	2	no	—
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	—	2	2	no	—
189	C₂²×C₈	—	2	2	no	—
190	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₈	C₂²×C₄	1	2	yes	—
193	C₂²×C₈	#41	1	2	yes	—
194	C₂²×C₈	#41	1	2	yes	—
195	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
196	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
197	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
198	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
199	C₄×D₄	—	2	1	no	—
200	C₄×D₄	—	2	1	no	—
201	C₄×D₄	—	2	1	no	—
202	C₄×D₄	—	2	1	no	—
203	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
204	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
205	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
206	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
207	#117	—	2	1	no	—
208	#117	—	2	1	no	—
209	#117	C₂²×C₄	1	1	yes	characteristic
210	#117	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₄²	—	2	1	no	—
212	C₂×C₄²	—	2	1	no	—
213	C₂×C₄²	—	2	1	no	—
214	C₂×C₄²	—	2	1	no	—
215	C₂×C₄²	C₂²×C₄	1	2	yes	—
216	C₂×C₄²	C₂⁴	1	1	yes	characteristic
217	#108	—	4	2	no	—
218	#107	C₄²	1	1	yes	characteristic
219	#107	C₄²	1	1	yes	characteristic
220	#106	C₄²	1	1	yes	characteristic
221	#106	C₄²	1	1	yes	characteristic
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	—	2	2	no	—
225	C₄⋊C₈	—	2	2	no	—
226	C₄⋊C₈	—	2	2	no	—
227	C₄⋊C₈	—	2	2	no	—
228	C₄⋊C₈	C₂²×C₄	1	2	yes	—
229	C₄⋊C₈	C₂²×C₄	1	2	yes	—
230	C₄⋊C₈	C₂²×C₄	1	2	yes	—
231	C₄⋊C₈	C₂²×C₄	1	2	yes	—
232	#104	—	2	4	no	—
233	#104	—	4	2	no	—
234	#103	C₄²	1	1	yes	characteristic
235	#103	C₄²	1	1	yes	characteristic
236	#103	C₄²	1	1	yes	characteristic
237	#103	C₄²	1	1	yes	characteristic
238	#102	C₄²	1	1	yes	characteristic
239	#102	C₄²	1	1	yes	characteristic
240	#102	C₄²	1	1	yes	characteristic
241	#102	C₄²	1	1	yes	characteristic
242	C₂²⋊C₈	—	2	1	no	—
243	C₂²⋊C₈	—	2	1	no	—
244	C₂²⋊C₈	—	2	1	no	—
245	C₂²⋊C₈	—	2	1	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	2	2	no	—
249	C₂²⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	#97	—	2	2	no	—
253	#97	—	2	2	no	—
254	#97	—	2	1	no	—
255	#97	—	2	1	no	—
256	C₄×C₈	—	2	2	no	—
257	C₄×C₈	—	2	2	no	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	—	2	1	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	C₂²×C₄	1	2	yes	—
269	C₄×C₈	C₂²×C₄	1	2	yes	—
270	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
271	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
272	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
273	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
274	C₄×C₈	C₂²×C₄	1	2	yes	—
275	C₄×C₈	C₂²×C₄	1	2	yes	—
276	C₄×C₈	C₂×D₄	1	1	yes	characteristic
277	C₄×C₈	C₂×D₄	1	1	yes	characteristic
278	C₄×C₈	C₂×D₄	1	1	yes	characteristic
279	C₄×C₈	C₂×D₄	1	1	yes	characteristic
280	C₄×C₈	C₂×D₄	1	1	yes	characteristic
281	C₄×C₈	C₂×D₄	1	1	yes	characteristic
282	C₄×C₈	#41	1	2	yes	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	#131	1	4	yes	—
287	C₂×Q₈	C₂×C₄²	1	1	yes	characteristic
288	C₂×Q₈	C₂×C₄²	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	C₂×C₄²	1	1	yes	characteristic
292	C₂×D₄	C₂×C₄²	1	1	yes	characteristic
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
301	C₂²×C₄	C₂×#41	1	1	yes	characteristic
302	C₂²×C₄	C₂×#41	1	1	yes	characteristic
303	Q₁₆	—	2	2	no	—
304	SD₁₆	—	2	2	no	—
305	SD₁₆	—	2	2	no	—
306	D₈	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	2	2	no	—
310	M₁₆	—	2	2	no	—
311	M₁₆	—	4	4	no	—
312	M₁₆	—	4	4	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	4	4	no	—
328	C₂×C₈	—	4	4	no	—
329	C₂×C₈	—	4	2	no	—
330	C₂×C₈	—	4	2	no	—
331	C₂×C₈	—	8	2	no	—
332	C₂×C₈	—	8	2	no	—
333	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
336	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
337	C₂×C₈	C₄×D₄	1	2	yes	—
338	C₂×C₈	C₄×D₄	1	2	yes	—
339	C₂×C₈	C₄×D₄	1	2	yes	—
340	C₂×C₈	C₄×D₄	1	2	yes	—
341	C₂×C₈	C₄×D₄	1	2	yes	—
342	C₂×C₈	C₄×D₄	1	2	yes	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	C₂×C₄²	1	1	yes	characteristic
348	C₄⋊C₄	C₂×C₄²	1	1	yes	characteristic
349	C₄⋊C₄	C₂×C₄²	1	1	yes	characteristic
350	C₄⋊C₄	C₂×C₄²	1	1	yes	characteristic
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	4	2	no	—
366	C₄²	—	4	2	no	—
367	C₄²	C₂³×C₄	1	1	yes	characteristic
368	C₄²	C₂³×C₄	1	1	yes	characteristic
369	C₄²	C₂²×D₄	1	1	yes	characteristic
370	C₄²	C₂×#41	1	1	yes	characteristic
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	C₄×#41	1	1	yes	characteristic
374	Q₈	—	2	1	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	#405	1	2	yes	—
378	D₄	—	2	4	no	—
379	D₄	—	2	1	no	—
380	D₄	—	2	1	no	—
381	D₄	—	2	1	no	—
382	D₄	—	4	2	no	—
383	D₄	#405	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	C₂²×C₄²	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
403	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
404	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
405	C₂×C₄	C₄×#41	1	1	yes	characteristic
406	C₂×C₄	C₄×#41	1	1	yes	characteristic
407	C₂×C₄	C₂×#131	1	2	yes	—
408	C₂×C₄	#568	1	2	yes	—
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	C₄²×D₄	1	1	yes	characteristic
436	C₂²	#2968	1	2	yes	—
437	C₄	—	2	2	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	8	2	no	—
446	C₄	C₂×#405	1	1	yes	characteristic
447	C₄	#2875	1	1	yes	characteristic
448	C₄	#2933	1	2	yes	—
449	C₄	#2955	1	2	yes	—
450	C₄	#2957	1	2	yes	—
451	C₂	—	2	2	no	—
452	C₂	—	4	2	no	—
453	C₂	—	8	1	no	—
454	C₂	#20493	1	1	yes	characteristic
455	C₂	#20510	1	1	yes	characteristic
456	C₂	#20514	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×D₄
commutator	C₂×C₄	C₂²×C₄²
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂²	C₄²×D₄
prime radical	C₂×#135	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄² ◁ C₂×#322 ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #17331	C₂	semidirect
5. #17320	C₂	semidirect
6. #8296	C₂	semidirect
7. #8293	C₂	semidirect
8. #8270	C₂	semidirect
9. #8195	C₂	semidirect
10. #8193	C₂	semidirect
11. #8193	C₂	semidirect
12. #8191	C₂	semidirect
13. #8188	C₂	semidirect
14. #8185	C₂	semidirect
15. #7845	C₂	semidirect
33. #1588	C₄	semidirect
34. #1587	C₄	semidirect
35. #1586	C₄	semidirect
36. #1585	C₄	semidirect
37. C₈×Q₁₆	C₄	semidirect
38. C₈×SD₁₆	C₄	semidirect
39. C₈×SD₁₆	C₄	semidirect
40. C₈×D₈	C₄	semidirect

Maximal subgroups

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

subgroup	index
#21137	2
#17868	2
C₈×#135	2
#17331	2
#17320	2
#8296	2
#8293	2
#8270	2
#8195	2
#8193	2
#8191	2
#8188	2
#8185	2
#7845	2