Subgroups — #416798

Order 512.

649 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21177	C₂	1	1	yes	maximal, characteristic
2	#20755	C₂	1	1	yes	maximal, characteristic
3	#11368	C₂	1	2	yes	maximal
4	#11306	C₂	1	2	yes	maximal
5	#11306	C₂	1	2	yes	maximal
6	#11295	C₂	1	2	yes	maximal
7	#10856	C₂	1	1	yes	maximal, characteristic
8	#10853	C₂	1	1	yes	maximal, characteristic
9	#10853	C₂	1	1	yes	maximal, characteristic
10	C₄⋊#338	C₂	1	1	yes	maximal, characteristic
11	C₄×#344	C₂	1	1	yes	maximal, characteristic
12	C₂×#430	C₂²	1	2	yes	—
13	C₂×#423	C₂²	1	1	yes	characteristic
14	C₂×#423	C₂²	1	1	yes	characteristic
15	C₂×#423	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
19	C₄×#117	C₂²	1	1	yes	characteristic
20	#1950	—	2	2	no	—
21	#1950	—	2	2	no	—
22	#1832	—	2	2	no	—
23	#1831	—	2	2	no	—
24	C₂×#344	C₂²	1	1	yes	characteristic
25	C₂×#344	C₂²	1	1	yes	characteristic
26	C₂×#344	C₂²	1	1	yes	characteristic
27	C₂×#344	C₂²	1	1	yes	characteristic
28	C₂×#344	C₂²	1	2	yes	—
29	C₂×#344	C₂²	1	2	yes	—
30	#1738	C₂²	1	2	yes	—
31	C₂×#341	C₂²	1	2	yes	—
32	C₂×#341	C₂²	1	2	yes	—
33	C₂×#341	C₂²	1	2	yes	—
34	C₂×#341	C₂²	1	2	yes	—
35	C₂×#338	C₂²	1	2	yes	—
36	C₂×#338	C₂²	1	2	yes	—
37	#1729	C₂²	1	2	yes	—
38	#1729	C₂²	1	2	yes	—
39	C₂²×M₁₆	C₂³	1	2	yes	—
40	C₂²×M₁₆	C₂³	1	2	yes	—
41	C₂²×M₁₆	C₂³	1	1	yes	characteristic
42	C₂²×M₁₆	C₂³	1	1	yes	characteristic
43	C₂²×M₁₆	C₂³	1	1	yes	characteristic
44	C₂²×M₁₆	C₂³	1	1	yes	characteristic
45	C₂²×M₁₆	C₂³	1	2	yes	—
46	C₂³×C₈	C₂³	1	2	yes	—
47	C₂×#117	C₂³	1	1	yes	characteristic
48	C₂×#117	C₂³	1	1	yes	characteristic
49	C₂²×C₄²	C₂³	1	1	yes	characteristic
50	#430	—	2	4	no	—
51	#430	—	4	2	no	—
52	C₂×#108	—	2	4	no	—
53	#423	—	2	1	no	—
54	#423	—	2	1	no	—
55	#423	—	2	1	no	—
56	#423	—	2	1	no	—
57	#423	—	2	1	no	—
58	#423	—	2	1	no	—
59	#423	—	2	1	no	—
60	#423	—	2	1	no	—
61	#423	—	2	1	no	—
62	#423	—	2	1	no	—
63	#423	—	2	1	no	—
64	#423	—	2	1	no	—
65	C₂×C₄⋊C₈	—	2	1	no	—
66	C₂×C₄⋊C₈	—	2	1	no	—
67	C₂×C₄⋊C₈	—	2	1	no	—
68	C₂×C₄⋊C₈	—	2	1	no	—
69	C₂×C₄⋊C₈	—	2	1	no	—
70	C₂×C₄⋊C₈	—	2	1	no	—
71	C₂×C₄⋊C₈	—	2	1	no	—
72	C₂×C₄⋊C₈	—	2	1	no	—
73	C₂×C₄⋊C₈	—	2	1	no	—
74	C₂×C₄⋊C₈	—	2	1	no	—
75	C₂×C₄⋊C₈	D₄	1	2	yes	—
76	C₂×C₄⋊C₈	D₄	1	2	yes	—
77	C₄×M₁₆	—	2	1	no	—
78	C₄×M₁₆	—	2	1	no	—
79	C₄×M₁₆	—	2	1	no	—
80	C₄×M₁₆	—	2	1	no	—
81	C₄×M₁₆	—	2	1	no	—
82	C₄×M₁₆	—	2	1	no	—
83	C₄×M₁₆	—	2	1	no	—
84	C₄×M₁₆	—	2	1	no	—
85	C₂×#97	—	2	1	no	—
86	C₂×#97	—	2	1	no	—
87	C₂×C₄×C₈	—	2	1	no	—
88	C₂×C₄×C₈	—	2	1	no	—
89	C₄×C₄⋊C₄	—	2	1	no	—
90	C₄×C₄⋊C₄	—	2	1	no	—
91	C₄×C₂²⋊C₄	Q₈	1	2	yes	—
92	C₄×C₂²⋊C₄	Q₈	1	2	yes	—
93	#376	—	2	1	no	—
94	C₄³	—	2	1	no	—
95	#344	—	2	2	no	—
96	#344	—	2	2	no	—
97	#344	—	2	2	no	—
98	#344	—	2	2	no	—
99	#344	—	4	2	no	—
100	#344	—	4	2	no	—
101	#341	—	2	4	no	—
102	#341	—	2	4	no	—
103	#341	—	2	4	no	—
104	#341	—	4	2	no	—
105	#341	—	4	2	no	—
106	#338	—	2	4	no	—
107	#338	—	4	2	no	—
108	#336	—	2	4	no	—
109	#336	—	2	4	no	—
110	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
111	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
112	C₂³×C₄	C₂⁴	1	1	yes	characteristic
113	C₂×M₁₆	—	2	2	no	—
114	C₂×M₁₆	—	2	1	no	—
115	C₂×M₁₆	—	2	1	no	—
116	C₂×M₁₆	—	2	2	no	—
117	C₂×M₁₆	—	2	2	no	—
118	C₂×M₁₆	—	2	2	no	—
119	C₂×M₁₆	—	2	1	no	—
120	C₂×M₁₆	—	2	2	no	—
121	C₂×M₁₆	—	2	2	no	—
122	C₂×M₁₆	—	2	1	no	—
123	C₂×M₁₆	—	2	1	no	—
124	C₂×M₁₆	—	2	1	no	—
125	C₂×M₁₆	—	2	1	no	—
126	C₂×M₁₆	—	2	1	no	—
127	C₂×M₁₆	—	2	1	no	—
128	C₂×M₁₆	—	2	1	no	—
129	C₂×M₁₆	—	2	1	no	—
130	C₂×M₁₆	—	2	1	no	—
131	C₂×M₁₆	—	2	1	no	—
132	C₂×M₁₆	—	2	1	no	—
133	C₂×M₁₆	—	2	1	no	—
134	C₂×M₁₆	—	2	1	no	—
135	C₂×M₁₆	—	2	1	no	—
136	C₂×M₁₆	—	2	1	no	—
137	C₂×M₁₆	—	2	1	no	—
138	C₂×M₁₆	—	2	1	no	—
139	C₂×M₁₆	—	2	2	no	—
140	C₂×M₁₆	—	2	2	no	—
141	C₂×M₁₆	—	2	2	no	—
142	C₂×M₁₆	—	2	2	no	—
143	C₂×M₁₆	—	2	2	no	—
144	C₂×M₁₆	—	2	2	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂×M₁₆	—	2	2	no	—
151	C₂×M₁₆	#41	1	2	yes	—
152	C₂×M₁₆	#41	1	2	yes	—
153	C₂×M₁₆	#41	1	2	yes	—
154	C₂×M₁₆	#41	1	2	yes	—
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	—	2	1	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	2	2	no	—
160	C₂²×C₈	—	2	2	no	—
161	C₂²×C₈	—	2	2	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	—	2	2	no	—
164	C₂²×C₈	—	2	2	no	—
165	C₂²×C₈	—	2	2	no	—
166	C₂²×C₈	—	2	2	no	—
167	C₂²×C₈	—	2	2	no	—
168	C₂²×C₈	C₂×D₄	1	4	yes	—
169	#117	—	2	1	no	—
170	#117	—	2	1	no	—
171	#117	—	2	1	no	—
172	#117	—	2	1	no	—
173	#117	—	2	1	no	—
174	#117	—	2	1	no	—
175	#117	—	2	1	no	—
176	#117	—	2	1	no	—
177	C₂×C₄⋊C₄	—	2	1	no	—
178	C₂×C₄⋊C₄	—	2	1	no	—
179	C₂×C₂²⋊C₄	C₂×Q₈	1	2	yes	—
180	C₂×C₂²⋊C₄	C₂×Q₈	1	2	yes	—
181	C₂×C₄²	—	2	2	no	—
182	C₂×C₄²	—	2	1	no	—
183	C₂×C₄²	—	2	1	no	—
184	C₂×C₄²	—	2	2	no	—
185	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
186	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
187	C₂×C₄²	#41	1	1	yes	characteristic
188	C₂×C₄²	#41	1	1	yes	characteristic
189	C₂×C₄²	#41	1	1	yes	characteristic
190	C₂×C₄²	#41	1	1	yes	characteristic
191	C₂×C₄²	#41	1	1	yes	characteristic
192	C₂×C₄²	#41	1	1	yes	characteristic
193	C₂×C₄²	#41	1	1	yes	characteristic
194	C₂×C₄²	#41	1	1	yes	characteristic
195	C₂×C₄²	#41	1	1	yes	characteristic
196	C₂×C₄²	#41	1	1	yes	characteristic
197	#108	—	4	8	no	—
198	C₄⋊C₈	—	2	2	no	—
199	C₄⋊C₈	—	2	2	no	—
200	C₄⋊C₈	—	2	2	no	—
201	C₄⋊C₈	—	2	2	no	—
202	C₄⋊C₈	—	4	1	no	—
203	C₄⋊C₈	—	4	1	no	—
204	C₄⋊C₈	—	4	1	no	—
205	C₄⋊C₈	—	4	1	no	—
206	C₄⋊C₈	—	4	1	no	—
207	C₄⋊C₈	—	4	1	no	—
208	C₄⋊C₈	—	4	1	no	—
209	C₄⋊C₈	—	4	1	no	—
210	C₄⋊C₈	—	4	1	no	—
211	C₄⋊C₈	—	4	1	no	—
212	C₄⋊C₈	—	4	1	no	—
213	C₄⋊C₈	—	4	1	no	—
214	#97	—	4	1	no	—
215	#97	—	4	1	no	—
216	#97	—	4	1	no	—
217	#97	—	4	1	no	—
218	C₄×C₈	—	4	1	no	—
219	C₄×C₈	—	4	1	no	—
220	C₄×C₈	—	4	1	no	—
221	C₄×C₈	—	4	1	no	—
222	#95	—	2	2	no	—
223	#95	—	2	2	no	—
224	C₂⁴	C₂²×Q₈	1	1	yes	characteristic
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	4	2	no	—
228	C₂²×C₄	—	8	1	no	—
229	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
230	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
231	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
232	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
233	C₂²×C₄	#125	1	1	yes	characteristic
234	C₂²×C₄	#125	1	1	yes	characteristic
235	C₂²×C₄	#125	1	1	yes	characteristic
236	C₂²×C₄	#125	1	1	yes	characteristic
237	C₂²×C₄	#125	1	1	yes	characteristic
238	C₂²×C₄	#125	1	1	yes	characteristic
239	C₂²×C₄	#125	1	1	yes	characteristic
240	C₂²×C₄	#125	1	1	yes	characteristic
241	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
242	C₂²×C₄	C₂×#41	1	1	yes	characteristic
243	C₂²×C₄	C₂×#41	1	1	yes	characteristic
244	C₂²×C₄	C₂×#41	1	1	yes	characteristic
245	C₂²×C₄	C₂×#41	1	1	yes	characteristic
246	C₂²×C₄	C₂×#41	1	1	yes	characteristic
247	C₂²×C₄	C₂×#41	1	1	yes	characteristic
248	C₂²×C₄	C₂×#41	1	1	yes	characteristic
249	C₂²×C₄	C₂×#41	1	1	yes	characteristic
250	C₂²×C₄	C₂×#41	1	1	yes	characteristic
251	C₂²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
253	C₂²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
254	C₂²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
255	M₁₆	—	2	2	no	—
256	M₁₆	—	2	2	no	—
257	M₁₆	—	2	2	no	—
258	M₁₆	—	2	2	no	—
259	M₁₆	—	2	2	no	—
260	M₁₆	—	2	2	no	—
261	M₁₆	—	2	2	no	—
262	M₁₆	—	2	2	no	—
263	M₁₆	—	4	2	no	—
264	M₁₆	—	4	2	no	—
265	M₁₆	—	4	1	no	—
266	M₁₆	—	4	1	no	—
267	M₁₆	—	4	1	no	—
268	M₁₆	—	4	1	no	—
269	M₁₆	—	4	1	no	—
270	M₁₆	—	4	1	no	—
271	M₁₆	—	4	1	no	—
272	M₁₆	—	4	2	no	—
273	M₁₆	—	4	1	no	—
274	M₁₆	—	4	2	no	—
275	M₁₆	—	4	2	no	—
276	M₁₆	—	4	2	no	—
277	M₁₆	—	4	2	no	—
278	M₁₆	—	4	2	no	—
279	M₁₆	—	4	2	no	—
280	M₁₆	—	4	2	no	—
281	M₁₆	—	4	2	no	—
282	M₁₆	—	4	2	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	—	4	2	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₄²	—	4	4	no	—
320	C₄²	—	4	1	no	—
321	C₄²	—	4	1	no	—
322	C₄²	—	4	1	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	8	2	no	—
325	C₄²	#123	1	1	yes	characteristic
326	C₄²	#123	1	1	yes	characteristic
327	C₄²	#123	1	1	yes	characteristic
328	C₄²	#123	1	1	yes	characteristic
329	C₄²	#124	1	1	yes	characteristic
330	C₄²	#124	1	1	yes	characteristic
331	C₄²	#124	1	1	yes	characteristic
332	C₄²	#124	1	1	yes	characteristic
333	C₄²	#126	1	1	yes	characteristic
334	C₄²	#126	1	1	yes	characteristic
335	C₄²	#126	1	1	yes	characteristic
336	C₄²	#126	1	1	yes	characteristic
337	C₄²	#126	1	1	yes	characteristic
338	C₄²	#126	1	1	yes	characteristic
339	C₄²	#126	1	1	yes	characteristic
340	C₄²	#126	1	1	yes	characteristic
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	C₂×C₂²⋊Q₈	1	1	yes	characteristic
344	C₂³	C₂×#125	1	1	yes	characteristic
345	C₂³	C₂×#125	1	1	yes	characteristic
346	C₂³	#533	1	1	yes	characteristic
347	C₂³	#533	1	1	yes	characteristic
348	C₂³	#544	1	1	yes	characteristic
349	C₂³	#544	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	#400	1	1	yes	characteristic
369	C₂×C₄	#400	1	1	yes	characteristic
370	C₂×C₄	#400	1	1	yes	characteristic
371	C₂×C₄	#400	1	1	yes	characteristic
372	C₂×C₄	#400	1	1	yes	characteristic
373	C₂×C₄	#400	1	1	yes	characteristic
374	C₂×C₄	#400	1	1	yes	characteristic
375	C₂×C₄	#400	1	1	yes	characteristic
376	C₂×C₄	C₂×#123	1	1	yes	characteristic
377	C₂×C₄	C₂×#124	1	1	yes	characteristic
378	C₂×C₄	C₂×#126	1	1	yes	characteristic
379	C₂×C₄	C₂×#126	1	1	yes	characteristic
380	C₂×C₄	#529	1	1	yes	characteristic
381	C₂×C₄	#529	1	1	yes	characteristic
382	C₂×C₄	#529	1	1	yes	characteristic
383	C₂×C₄	#529	1	1	yes	characteristic
384	C₂×C₄	#540	1	1	yes	characteristic
385	C₂×C₄	#541	1	1	yes	characteristic
386	C₂×C₄	#542	1	1	yes	characteristic
387	C₂×C₄	#542	1	1	yes	characteristic
388	C₂×C₄	#546	1	1	yes	characteristic
389	C₂×C₄	#547	1	1	yes	characteristic
390	C₂×C₄	#548	1	1	yes	characteristic
391	C₂×C₄	#550	1	1	yes	characteristic
392	C₂×C₄	#552	1	1	yes	characteristic
393	C₂×C₄	#552	1	1	yes	characteristic
394	C₂×C₄	#552	1	1	yes	characteristic
395	C₂×C₄	#553	1	1	yes	characteristic
396	C₂×C₄	#553	1	1	yes	characteristic
397	C₂×C₄	#553	1	1	yes	characteristic
398	C₂×C₄	#555	1	1	yes	characteristic
399	C₂×C₄	#556	1	1	yes	characteristic
400	C₂×C₄	#556	1	1	yes	characteristic
401	C₂×C₄	#556	1	1	yes	characteristic
402	C₂×C₄	#559	1	1	yes	characteristic
403	C₂×C₄	#559	1	1	yes	characteristic
404	C₈	—	4	4	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	8	2	no	—
410	C₈	—	8	2	no	—
411	C₈	—	8	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	C₂×#400	1	1	yes	characteristic
423	C₂²	#2439	1	1	yes	characteristic
424	C₂²	#2441	1	1	yes	characteristic
425	C₂²	#2570	1	1	yes	characteristic
426	C₂²	#2570	1	1	yes	characteristic
427	C₂²	#2647	1	1	yes	characteristic
428	C₂²	#2864	1	1	yes	characteristic
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	2	no	—
438	C₄	#2103	1	2	yes	—
439	C₄	#2447	1	1	yes	characteristic
440	C₄	#2448	1	1	yes	characteristic
441	C₄	#2489	1	1	yes	characteristic
442	C₄	#2490	1	1	yes	characteristic
443	C₄	#2494	1	1	yes	characteristic
444	C₄	#2495	1	1	yes	characteristic
445	C₄	#2513	1	1	yes	characteristic
446	C₄	#2514	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	#15232	1	1	yes	characteristic
454	C₂	C₂×#2103	1	1	yes	characteristic
455	C₂	#23753	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#124
commutator, Frattini, cosocle	C₂³×C₄	C₂⁴
socle	C₂²	C₂×#400
prime radical	C₂⁴	C₂²×Q₈
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

Maximal subgroups

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

subgroup	index
#21177	2
#20755	2
#11368	2
#11306	2
#11295	2
#10856	2
#10853	2
C₄⋊#338	2
C₄×#344	2