Subgroups — #33068471

Order 18688.

620 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620517	C₂	1	1	yes	maximal, characteristic, complemented
2	#22620003	C₂	1	2	yes	maximal
3	C₈×#11924028	C₂	1	1	yes	maximal, characteristic
4	#22609362	C₂	1	2	yes	maximal, complemented
5	#22609355	C₂	1	2	yes	maximal, complemented
6	#22609326	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609321	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609302	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609297	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608595	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989144	C₂²	1	2	yes	—
13	C₄×#11924028	C₂²	1	1	yes	characteristic
14	#17988992	C₂²	1	1	yes	characteristic
15	#17988967	C₂²	1	1	yes	characteristic
16	#17988938	C₂²	1	2	yes	—
17	#17988929	—	2	2	no	—
18	#17988873	C₂²	1	2	yes	—
19	#17988868	C₂²	1	2	yes	—
20	#17988828	—	2	1	no	—
21	#17988828	—	2	1	no	—
22	#17988798	C₂²	1	2	yes	—
23	#17988793	C₂²	1	2	yes	—
24	#17988751	—	2	2	no	—
25	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
27	C₄×Dic₂₉₂	—	2	2	no	—
28	C₄×Dic₂₉₂	—	2	1	no	—
29	C₄×Dic₂₉₂	—	2	1	no	—
30	C₄×#11924017	—	2	2	no	—
31	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
32	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
33	C₈×C₂²⋊D₇₃	—	2	1	no	—
34	C₈×C₂²⋊D₇₃	—	2	1	no	—
35	#17988640	C₂²	1	1	yes	characteristic
36	#17988638	—	2	1	no	—
37	C₄×C₈×D₇₃	—	2	1	no	—
38	#17988334	C₂²	1	2	yes	—
39	#17988334	C₂²	1	2	yes	—
40	#17988332	C₂²	1	2	yes	—
41	#17988332	C₂²	1	2	yes	—
42	#431×C₇₃	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
44	#335×C₇₃	C₂²	1	1	yes	characteristic
45	#335×C₇₃	C₂²	1	1	yes	characteristic
46	#334×C₇₃	C₂²	1	2	yes	—
47	C₂×#11924028	D₄	1	1	yes	characteristic
48	C₂×Dic₂₉₂	—	2	2	no	—
49	C₂×Dic₂₉₂	—	2	1	no	—
50	C₂×Dic₂₉₂	—	2	1	no	—
51	C₂×#11924017	—	2	2	no	—
52	C₂×C₈×D₇₃	—	2	1	no	—
53	C₂×C₈×D₇₃	—	2	1	no	—
54	#14556591	C₂³	1	2	yes	—
55	#14556591	C₂³	1	2	yes	—
56	#14556583	—	2	2	no	—
57	#14556570	—	2	2	no	—
58	#14556570	—	2	2	no	—
59	C₄×Dic₁₄₆	—	2	2	no	—
60	C₄×Dic₁₄₆	—	2	2	no	—
61	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
62	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
63	C₄×D₂₉₂	D₄	1	1	yes	characteristic
64	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₇₃	—	2	1	no	—
66	C₄×C₂²⋊D₇₃	—	2	1	no	—
67	#14556550	—	2	2	no	—
68	#14556550	D₄	1	1	yes	characteristic
69	#14556548	—	2	1	no	—
70	C₄²×D₇₃	—	2	1	no	—
71	#14556525	—	2	2	no	—
72	#14556525	—	2	1	no	—
73	#14556525	—	2	1	no	—
74	#14556523	—	2	2	no	—
75	C₄⋊#10596831	C₂³	1	1	yes	characteristic
76	C₄⋊#10596831	C₂³	1	1	yes	characteristic
77	#14556520	—	2	1	no	—
78	#14556520	—	2	1	no	—
79	#14556516	—	2	2	no	—
80	#14556516	—	2	2	no	—
81	#14556516	—	2	2	no	—
82	#14556516	—	2	2	no	—
83	#14556516	—	2	2	no	—
84	#14556513	—	2	2	no	—
85	C₂²⋊#10596831	—	2	1	no	—
86	#14556503	—	2	1	no	—
87	#14556503	—	2	1	no	—
88	C₄×#10596831	—	2	1	no	—
89	C₈×Dic₇₃	—	2	1	no	—
90	C₈×Dic₇₃	—	2	1	no	—
91	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
95	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
96	C₂²⋊C₈×C₇₃	—	2	2	no	—
97	C₄×C₈×C₇₃	—	2	2	no	—
98	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
102	#11924028	—	2	2	no	—
103	#11924028	—	2	2	no	—
104	C₂×Dic₁₄₆	—	2	2	no	—
105	C₂×Dic₁₄₆	—	2	2	no	—
106	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
107	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
108	C₂×C₂²⋊D₇₃	—	2	1	no	—
109	C₂×C₄×D₇₃	—	2	1	no	—
110	C₂×C₄×D₇₃	—	2	1	no	—
111	C₂×C₄×D₇₃	—	2	1	no	—
112	Dic₂₉₂	—	4	2	no	—
113	Dic₂₉₂	—	4	4	no	—
114	Dic₂₉₂	—	4	2	no	—
115	#11924017	—	4	4	no	—
116	C₂×#10596831	—	2	1	no	—
117	C₂×#10596831	—	2	1	no	—
118	C₈×D₇₃	—	4	2	no	—
119	C₈×D₇₃	—	4	2	no	—
120	C₄⋊Dic₇₃	—	2	2	no	—
121	C₄⋊Dic₇₃	—	2	2	no	—
122	C₄⋊Dic₇₃	—	2	2	no	—
123	C₄⋊Dic₇₃	—	2	2	no	—
124	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
125	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
126	#11924007	—	2	1	no	—
127	#11924007	—	2	1	no	—
128	#11924007	—	4	2	no	—
129	#11924007	—	4	2	no	—
130	C₂²⋊Dic₇₃	—	2	1	no	—
131	C₂²⋊Dic₇₃	—	4	2	no	—
132	#11924005	—	2	1	no	—
133	#11924005	—	2	1	no	—
134	C₄×Dic₇₃	—	2	1	no	—
135	C₄×Dic₇₃	—	2	1	no	—
136	C₄×Dic₇₃	—	2	1	no	—
137	C₄×Dic₇₃	—	4	2	no	—
138	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₂×C₈×C₇₃	—	4	1	no	—
145	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₇₃	#41	1	1	yes	characteristic
152	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
153	C₂³×C₇₃	#121	1	1	yes	characteristic
154	C₂²×D₇₃	—	2	1	no	—
155	C₂×C₄×C₇₃	—	2	1	no	—
156	C₂×C₄×C₇₃	—	2	1	no	—
157	C₂×C₄×C₇₃	—	2	1	no	—
158	C₂×C₄×C₇₃	—	2	1	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
166	C₂²⋊D₇₃	—	2	4	no	—
167	C₂×Dic₇₃	—	2	1	no	—
168	C₂×Dic₇₃	—	2	1	no	—
169	C₂×Dic₇₃	—	2	1	no	—
170	C₂×Dic₇₃	—	4	2	no	—
171	C₂×Dic₇₃	—	4	2	no	—
172	D₂₉₂	—	2	1	no	—
173	D₂₉₂	#135	1	2	yes	—
174	C₄×D₇₃	—	2	4	no	—
175	C₄×D₇₃	—	4	1	no	—
176	C₄×D₇₃	—	4	1	no	—
177	C₄×D₇₃	—	4	2	no	—
178	Dic₁₄₆	—	2	1	no	—
179	Dic₁₄₆	—	4	2	no	—
180	Dic₁₄₆	—	4	2	no	—
181	Dic₁₄₆	—	4	2	no	—
182	Dic₁₄₆	—	4	2	no	—
183	Dic₁₄₆	#135	1	2	yes	—
184	C₈×C₇₃	—	2	1	no	—
185	C₈×C₇₃	—	2	1	no	—
186	C₈×C₇₃	—	2	1	no	—
187	C₈×C₇₃	—	4	2	no	—
188	C₈×C₇₃	—	4	2	no	—
189	C₈×C₇₃	#135	1	2	yes	—
190	#10596831	—	4	1	no	—
191	#10596831	—	4	1	no	—
192	C₂²×C₇₃	—	2	1	no	—
193	C₂²×C₇₃	—	2	1	no	—
194	C₂²×C₇₃	—	2	1	no	—
195	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
196	C₂×D₇₃	—	2	2	no	—
197	C₂×D₇₃	—	4	1	no	—
198	C₂×D₇₃	—	4	1	no	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	—	2	1	no	—
201	C₄×C₇₃	—	2	1	no	—
202	C₄×C₇₃	#473	1	2	yes	—
203	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
204	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
205	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
206	C₄×C₇₃	#575	1	1	yes	characteristic
207	Dic₇₃	—	2	2	no	—
208	Dic₇₃	—	4	1	no	—
209	Dic₇₃	—	4	1	no	—
210	Dic₇₃	—	8	2	no	—
211	Dic₇₃	—	8	2	no	—
212	#19129	—	73	1	no	maximal, Sylow
213	C₂×C₇₃	—	4	1	no	—
214	C₂×C₇₃	#3035	1	1	yes	characteristic
215	C₂×C₇₃	#3050	1	1	yes	characteristic
216	C₂×C₇₃	C₂×#473	1	1	yes	characteristic
217	D₇₃	—	4	2	no	—
218	#3170	—	73	1	no	—
219	#3107	—	73	2	no	—
220	C₈×#41	—	73	1	no	—
221	#1680	—	73	2	no	—
222	#1679	—	73	2	no	—
223	#1674	—	73	1	no	—
224	#1673	—	73	1	no	—
225	#1670	—	73	1	no	—
226	#1669	—	73	1	no	—
227	#1564	D₇₃	1	1	yes	characteristic, complemented
228	#1544	—	73	2	no	—
229	C₇₃	#19129	1	1	yes	characteristic, complemented, Sylow
230	#533	—	73	2	no	—
231	C₄×#41	—	73	1	no	—
232	#500	—	73	1	no	—
233	#494	—	73	1	no	—
234	#487	—	73	2	no	—
235	#485	—	146	2	no	—
236	#475	—	73	2	no	—
237	#474	—	73	2	no	—
238	#467	—	146	1	no	—
239	#467	—	146	1	no	—
240	#462	—	73	2	no	—
241	#461	—	73	2	no	—
242	#452	—	146	2	no	—
243	C₈×Q₈	—	73	1	no	—
244	C₈×Q₈	—	73	1	no	—
245	C₄×Q₁₆	—	146	2	no	—
246	C₄×Q₁₆	—	146	1	no	—
247	C₄×Q₁₆	—	146	1	no	—
248	C₄×SD₁₆	—	146	2	no	—
249	C₈×D₄	—	73	1	no	—
250	C₈×D₄	—	73	1	no	—
251	C₈×D₄	—	146	1	no	—
252	C₈×D₄	—	146	1	no	—
253	#431	—	73	1	no	—
254	#431	—	146	1	no	—
255	#431	C₂×D₇₃	1	2	yes	—
256	C₂×C₄×C₈	—	146	1	no	—
257	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
258	#335	C₂×D₇₃	1	1	yes	characteristic
259	#335	C₂×D₇₃	1	1	yes	characteristic
260	#334	C₂×D₇₃	1	2	yes	—
261	#332	—	73	2	no	—
262	#332	—	73	2	no	—
263	#332	—	73	2	no	—
264	#332	—	73	2	no	—
265	C₂×#41	—	73	1	no	—
266	C₂×Q₁₆	—	146	2	no	—
267	C₂×Q₁₆	—	146	1	no	—
268	C₂×Q₁₆	—	146	1	no	—
269	C₂×SD₁₆	—	146	2	no	—
270	C₂²×C₈	—	146	1	no	—
271	C₂²×C₈	—	146	1	no	—
272	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
273	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
274	C₄⋊Q₈	—	73	2	no	—
275	C₄⋊Q₈	—	73	2	no	—
276	#125	—	146	2	no	—
277	C₂²⋊Q₈	—	146	2	no	—
278	C₂²⋊Q₈	—	146	2	no	—
279	C₄×Q₈	—	73	1	no	—
280	C₄×Q₈	—	73	1	no	—
281	C₄×Q₈	—	146	2	no	—
282	C₄×Q₈	—	146	2	no	—
283	C₄×D₄	—	73	1	no	—
284	C₄×D₄	—	73	1	no	—
285	C₄×D₄	—	146	1	no	—
286	C₄×D₄	—	146	1	no	—
287	#117	—	73	1	no	—
288	#117	—	146	2	no	—
289	#117	—	146	1	no	—
290	C₂×C₄²	—	146	1	no	—
291	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
292	#107	—	146	2	no	—
293	#107	—	146	1	no	—
294	#107	—	146	1	no	—
295	#106	—	146	2	no	—
296	C₄⋊C₈	—	73	1	no	—
297	C₄⋊C₈	—	73	1	no	—
298	C₄⋊C₈	—	146	1	no	—
299	C₄⋊C₈	—	146	1	no	—
300	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
301	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
302	#103	—	146	2	no	—
303	#103	—	146	2	no	—
304	#103	—	146	2	no	—
305	#103	—	146	2	no	—
306	#103	—	146	2	no	—
307	#102	—	146	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	146	1	no	—
310	C₂²⋊C₈	—	146	1	no	—
311	C₂²⋊C₈	—	146	1	no	—
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	—	146	1	no	—
314	C₄×C₈	—	146	1	no	—
315	C₄×C₈	—	146	1	no	—
316	C₄×C₈	D₂₉₂	1	1	yes	characteristic
317	C₄×C₈	D₂₉₂	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
320	#41	—	146	2	no	—
321	#41	—	146	2	no	—
322	C₂×Q₈	—	73	1	no	—
323	C₂×Q₈	—	146	2	no	—
324	C₂×Q₈	—	146	2	no	—
325	C₂×D₄	—	73	1	no	—
326	C₂×D₄	—	146	1	no	—
327	C₂²×C₄	—	146	1	no	—
328	C₂²×C₄	—	146	1	no	—
329	C₂²×C₄	—	146	1	no	—
330	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
332	C₂²×C₄	#11924029	1	1	yes	characteristic
333	Q₁₆	—	292	2	no	—
334	Q₁₆	—	292	4	no	—
335	Q₁₆	—	292	2	no	—
336	SD₁₆	—	292	4	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	292	2	no	—
342	C₂×C₈	—	292	2	no	—
343	C₂×C₈	—	146	1	no	—
344	C₂×C₈	—	146	1	no	—
345	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
346	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
347	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
348	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
349	C₄⋊C₄	—	292	2	no	—
350	C₄⋊C₄	—	292	2	no	—
351	C₄⋊C₄	—	73	1	no	—
352	C₄⋊C₄	—	73	1	no	—
353	C₄⋊C₄	—	146	2	no	—
354	C₄⋊C₄	—	146	2	no	—
355	C₄⋊C₄	—	146	2	no	—
356	C₄⋊C₄	—	146	2	no	—
357	C₄⋊C₄	—	146	1	no	—
358	C₄⋊C₄	—	146	1	no	—
359	C₂²⋊C₄	—	292	2	no	—
360	C₂²⋊C₄	—	146	1	no	—
361	C₂²⋊C₄	—	146	1	no	—
362	C₂²⋊C₄	—	146	1	no	—
363	C₄²	—	292	2	no	—
364	C₄²	—	146	1	no	—
365	C₄²	—	146	1	no	—
366	C₄²	—	146	1	no	—
367	C₄²	D₄×D₇₃	1	1	yes	characteristic
368	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
369	C₄²	#11924029	1	1	yes	characteristic
370	C₄²	C₂³×D₇₃	1	1	yes	characteristic
371	C₂³	—	146	1	no	—
372	C₂³	#14556566	1	1	yes	characteristic
373	Q₈	—	292	2	no	—
374	Q₈	—	292	2	no	—
375	Q₈	—	292	2	no	—
376	Q₈	—	292	2	no	—
377	Q₈	—	73	2	no	—
378	Q₈	—	146	1	no	—
379	D₄	—	73	2	no	—
380	D₄	—	146	4	no	—
381	D₄	—	146	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	292	1	no	—
388	C₂×C₄	—	292	1	no	—
389	C₂×C₄	—	292	2	no	—
390	C₂×C₄	—	292	2	no	—
391	C₂×C₄	—	292	2	no	—
392	C₂×C₄	—	146	4	no	—
393	C₂×C₄	—	146	1	no	—
394	C₂×C₄	—	146	1	no	—
395	C₂×C₄	—	146	1	no	—
396	C₂×C₄	#14556566	1	1	yes	characteristic
397	C₂×C₄	#14556566	1	1	yes	characteristic
398	C₂×C₄	#14556566	1	1	yes	characteristic
399	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
401	C₂×C₄	C₂×#11924029	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	292	1	no	—
408	C₈	—	292	1	no	—
409	C₈	#14556613	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	292	1	no	—
414	C₂²	—	292	1	no	—
415	C₂²	—	146	2	no	—
416	C₂²	C₂×#14556566	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	292	1	no	—
421	C₄	—	292	1	no	—
422	C₄	—	584	2	no	—
423	C₄	—	584	2	no	—
424	C₄	—	146	2	no	—
425	C₄	#17988863	1	2	yes	—
426	C₄	#135×D₇₃	1	1	yes	characteristic
427	C₄	#135×D₇₃	1	1	yes	characteristic
428	C₄	C₂×#14556613	1	1	yes	characteristic
429	C₄	#17989387	1	1	yes	characteristic
430	C₂	—	4	1	no	—
431	C₂	—	292	2	no	—
432	C₂	#22619388	1	1	yes	characteristic
433	C₂	#22619513	1	1	yes	characteristic
434	C₂	C₂×#17988863	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14556566
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1564	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	C₂×#11924028	D₄
hypercenter	#1564	D₇₃
hypocenter	C₇₃	#19129
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #22620517	C₂	semidirect
4. #22609362	C₂	semidirect
5. #22609355	C₂	semidirect
6. #22609326	C₂	semidirect
7. #22609321	C₂	semidirect
8. #22609302	C₂	semidirect
9. #22609297	C₂	semidirect
10. #22608595	C₂	semidirect
11. C₇₃×#1564	C₂	semidirect
227. #1564	D₇₃	semidirect
229. C₇₃	#19129	semidirect

Maximal subgroups

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

subgroup	index
#22620517	2
#22620003	2
C₈×#11924028	2
#22609362	2
#22609355	2
#22609326	2
#22609321	2
#22609302	2
#22609297	2
#22608595	2
C₇₃×#1564	2
#19129	73