Subgroups — #33240280

Order 18688.

702 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989029	C₂	1	2	yes	maximal
2	#494×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14556614	C₂	1	1	yes	maximal, characteristic
4	#22611981	C₂	1	1	yes	maximal, characteristic, complemented
5	#22611979	C₂	1	2	yes	maximal, complemented
6	#22611977	C₂	1	1	yes	maximal, characteristic, complemented
7	#22611975	C₂	1	2	yes	maximal, complemented
8	#22611973	C₂	1	1	yes	maximal, characteristic, complemented
9	#22611685	C₂	1	1	yes	maximal, characteristic, complemented
10	#22611649	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2209	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556614	C₂²	1	1	yes	characteristic
13	C₂×Q₁₆×D₇₃	—	2	1	no	—
14	C₂×Q₁₆×D₇₃	C₂²	1	2	yes	—
15	C₄⋊Q₈×D₇₃	—	2	1	no	—
16	C₄×#11924029	—	2	1	no	—
17	#17989029	—	2	8	no	—
18	C₂×#14556537	C₂²	1	2	yes	—
19	C₂×#14556536	C₂²	1	2	yes	—
20	C₂×#14556534	C₂²	1	2	yes	—
21	C₂×#14556530	C₂²	1	2	yes	—
22	#17988967	C₂²	1	1	yes	characteristic
23	#17988966	—	2	1	no	—
24	#17988965	—	2	1	no	—
25	#17988965	C₂²	1	2	yes	—
26	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
27	C₄×#11924015	—	2	1	no	—
28	#17988672	—	2	1	no	—
29	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
30	#17988669	C₂²	1	1	yes	characteristic
31	#17988624	C₂²	1	1	yes	characteristic
32	#17988582	—	2	1	no	—
33	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
34	C₄⋊#11924003	C₂²	1	1	yes	characteristic
35	#17988405	C₂²	1	2	yes	—
36	#17988392	C₂²	1	2	yes	—
37	#17988391	C₂²	1	2	yes	—
38	#17988390	C₂²	1	2	yes	—
39	C₂×Q₃₂×C₇₃	C₂²	1	2	yes	—
40	#494×C₇₃	C₂²	1	1	yes	characteristic
41	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
42	C₄⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
43	#358×C₇₃	C₂²	1	2	yes	—
44	C₂×#11924029	—	2	1	no	—
45	C₂×Q₈×D₇₃	—	2	2	no	—
46	#14556614	—	2	2	no	—
47	#14556614	D₄	1	4	yes	—
48	C₂×Dic₂₉₂	—	2	1	no	—
49	C₂×Dic₂₉₂	C₂³	1	2	yes	—
50	C₂×#11924018	—	2	2	no	—
51	C₂×#11924018	—	2	2	no	—
52	Q₁₆×D₇₃	—	2	4	no	—
53	Q₁₆×D₇₃	—	2	4	no	—
54	Q₁₆×D₇₃	—	4	4	no	—
55	C₂×#11924015	—	2	1	no	—
56	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
58	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
59	#14556591	—	2	1	no	—
60	#14556590	—	4	1	no	—
61	#14556590	—	4	1	no	—
62	#14556589	—	2	2	no	—
63	Q₈×Dic₇₃	—	2	1	no	—
64	C₄×D₂₉₂	—	2	1	no	—
65	C₄×D₂₉₂	—	4	1	no	—
66	#14556553	—	2	1	no	—
67	#14556553	—	4	1	no	—
68	#14556549	—	2	1	no	—
69	#14556549	—	4	1	no	—
70	C₄⋊C₄×D₇₃	—	4	1	no	—
71	C₄⋊C₄×D₇₃	—	4	1	no	—
72	C₄²×D₇₃	—	4	1	no	—
73	C₄²×D₇₃	D₄	1	1	yes	characteristic
74	#14556537	—	2	4	no	—
75	#14556536	—	2	4	no	—
76	#14556534	—	2	4	no	—
77	#14556530	—	2	4	no	—
78	C₂×#11924003	C₂³	1	2	yes	—
79	#14556525	C₂³	1	1	yes	characteristic
80	#14556522	—	2	1	no	—
81	#14556515	—	2	1	no	—
82	#14556513	—	2	1	no	—
83	#14556511	—	2	1	no	—
84	C₄×#10596831	D₄	1	1	yes	characteristic
85	C₈×Dic₇₃	D₄	1	1	yes	characteristic
86	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₇₃	—	2	1	no	—
88	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
89	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₇₃	—	2	1	no	—
91	C₄×Q₈×C₇₃	—	2	1	no	—
92	Q₃₂×C₇₃	—	2	4	no	—
93	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
94	#107×C₇₃	C₂³	1	1	yes	characteristic
95	#103×C₇₃	—	2	1	no	—
96	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
97	#11924029	—	2	4	no	—
98	#11924029	—	4	2	no	—
99	C₂×Dic₁₄₆	—	2	2	no	—
100	C₂×Dic₁₄₆	—	4	2	no	—
101	Q₈×D₇₃	—	4	4	no	—
102	Q₈×D₇₃	—	4	4	no	—
103	C₂×D₂₉₂	—	2	1	no	—
104	C₂×D₂₉₂	—	4	1	no	—
105	C₂×C₄×D₇₃	—	4	1	no	—
106	C₂×C₄×D₇₃	—	4	2	no	—
107	C₂×C₄×D₇₃	—	4	1	no	—
108	C₂×C₄×D₇₃	—	4	1	no	—
109	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
110	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
112	Dic₂₉₂	—	2	2	no	—
113	Dic₂₉₂	—	2	2	no	—
114	Dic₂₉₂	—	4	2	no	—
115	#11924018	—	4	4	no	—
116	#11924018	—	4	4	no	—
117	#11924015	—	2	4	no	—
118	D₅₈₄	—	2	1	no	—
119	D₅₈₄	C₂×D₄	1	2	yes	—
120	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
121	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
122	C₈×D₇₃	—	2	2	no	—
123	C₈×D₇₃	C₂×D₄	1	2	yes	—
124	C₈×D₇₃	#41	1	2	yes	—
125	C₄⋊Dic₇₃	—	2	1	no	—
126	C₄⋊Dic₇₃	—	4	1	no	—
127	C₄⋊Dic₇₃	—	4	1	no	—
128	C₄⋊Dic₇₃	—	4	1	no	—
129	#11924007	—	4	2	no	—
130	#11924007	—	4	2	no	—
131	#11924005	—	4	1	no	—
132	#11924005	—	4	1	no	—
133	#11924005	—	4	1	no	—
134	C₄×Dic₇₃	—	4	1	no	—
135	C₄×Dic₇₃	—	4	1	no	—
136	C₄×Dic₇₃	D₈	1	1	yes	characteristic
137	C₄×Dic₇₃	D₈	1	1	yes	characteristic
138	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
139	#11924003	—	2	2	no	—
140	C₂×Q₈×C₇₃	—	2	1	no	—
141	C₂×Q₈×C₇₃	—	2	2	no	—
142	Q₁₆×C₇₃	—	2	2	no	—
143	Q₁₆×C₇₃	—	2	1	no	—
144	Q₁₆×C₇₃	—	2	2	no	—
145	Q₁₆×C₇₃	—	4	2	no	—
146	Q₁₆×C₇₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₇₃	—	2	1	no	—
150	C₄⋊C₄×C₇₃	—	4	1	no	—
151	C₄⋊C₄×C₇₃	—	4	1	no	—
152	C₄⋊C₄×C₇₃	—	4	1	no	—
153	C₄²×C₇₃	—	4	1	no	—
154	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₁₆×C₇₃	—	2	2	no	—
156	C₂²×D₇₃	—	4	1	no	—
157	C₂²×D₇₃	C₂×D₈	1	1	yes	characteristic
158	Q₈×C₇₃	—	2	2	no	—
159	Q₈×C₇₃	—	4	1	no	—
160	Q₈×C₇₃	—	4	2	no	—
161	Q₈×C₇₃	—	4	2	no	—
162	C₂×C₄×C₇₃	—	4	1	no	—
163	C₂×C₄×C₇₃	—	4	1	no	—
164	C₂×C₄×C₇₃	—	4	2	no	—
165	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×Dic₇₃	—	4	1	no	—
169	C₂×Dic₇₃	—	4	2	no	—
170	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
171	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
172	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
173	D₂₉₂	—	2	2	no	—
174	D₂₉₂	—	4	4	no	—
175	D₂₉₂	—	4	1	no	—
176	C₄×D₇₃	—	2	2	no	—
177	C₄×D₇₃	—	2	2	no	—
178	C₄×D₇₃	—	4	4	no	—
179	C₄×D₇₃	—	8	4	no	—
180	C₄×D₇₃	—	8	2	no	—
181	C₄×D₇₃	—	8	2	no	—
182	C₄×D₇₃	#121	1	2	yes	—
183	C₄×D₇₃	AGL(1,ℤ/8)	1	2	yes	—
184	Dic₁₄₆	—	4	2	no	—
185	Dic₁₄₆	—	4	2	no	—
186	Dic₁₄₆	—	8	4	no	—
187	C₈×C₇₃	—	2	1	no	—
188	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
189	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
190	#10596831	—	2	1	no	—
191	#10596831	#121	1	2	yes	—
192	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
193	C₂×D₇₃	—	2	1	no	—
194	C₂×D₇₃	—	2	1	no	—
195	C₂×D₇₃	—	4	2	no	—
196	C₂×D₇₃	—	8	1	no	—
197	C₂×D₇₃	—	8	1	no	—
198	C₂×D₇₃	#459	1	2	yes	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	—	4	2	no	—
201	C₄×C₇₃	—	8	1	no	—
202	C₄×C₇₃	—	8	2	no	—
203	C₄×C₇₃	#510	1	2	yes	complemented
204	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
205	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	Dic₇₃	—	2	1	no	—
207	Dic₇₃	—	8	1	no	—
208	Dic₇₃	—	8	2	no	—
209	Dic₇₃	#459	1	2	yes	—
210	Dic₇₃	#510	1	2	yes	complemented
211	#33583	—	73	1	no	maximal, Sylow
212	C₂×C₇₃	C₂×#459	1	1	yes	characteristic
213	C₂×C₇₃	C₂×#510	1	1	yes	characteristic
214	C₂×C₇₃	C₂×#510	1	1	yes	characteristic
215	D₇₃	—	2	2	no	—
216	D₇₃	—	8	2	no	—
217	C₂×#510	—	73	2	no	—
218	C₂×#494	—	73	1	no	—
219	C₄×#135	—	73	1	no	—
220	#2209	—	73	2	no	—
221	#2209	—	73	1	no	—
222	#2209	D₇₃	1	1	yes	characteristic, complemented
223	#2208	—	73	1	no	—
224	#2208	—	73	1	no	—
225	#2208	—	73	2	no	—
226	#2150	—	73	1	no	—
227	#2141	—	73	2	no	—
228	C₇₃	#33583	1	1	yes	characteristic, complemented, Sylow
229	C₂×#135	—	73	1	no	—
230	C₂²×Q₁₆	—	73	2	no	—
231	C₂²×Q₁₆	—	146	1	no	—
232	C₂×C₄⋊Q₈	—	146	1	no	—
233	C₄×#41	—	146	1	no	—
234	#510	—	146	8	no	—
235	C₂×Q₃₂	—	73	2	no	—
236	C₂×Q₃₂	C₂×D₇₃	1	2	yes	—
237	C₂×SD₃₂	—	73	2	no	—
238	C₂×SD₃₂	—	73	2	no	—
239	C₂×M₃₂	—	73	2	no	—
240	#494	—	73	2	no	—
241	#494	—	73	1	no	—
242	#494	—	146	1	no	—
243	#494	—	146	1	no	—
244	#494	C₂×D₇₃	1	1	yes	characteristic
245	C₄×Q₁₆	—	73	1	no	—
246	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
247	C₄×SD₁₆	—	146	1	no	—
248	C₄×SD₁₆	—	146	1	no	—
249	C₄×D₈	—	73	1	no	—
250	C₄×D₈	—	73	1	no	—
251	#427	—	73	1	no	—
252	#416	—	146	1	no	—
253	C₂×C₄×C₈	—	73	1	no	—
254	C₄⋊C₁₆	—	73	2	no	—
255	C₄⋊C₁₆	—	73	1	no	—
256	C₄⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic
257	#358	—	73	2	no	—
258	#358	—	73	2	no	—
259	#358	—	73	2	no	—
260	#358	C₂×D₇₃	1	2	yes	—
261	C₂×#41	—	146	1	no	—
262	C₂²×Q₈	—	146	2	no	—
263	#135	—	73	4	no	—
264	#135	—	146	2	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂×Q₁₆	—	292	4	no	—
267	C₂×Q₁₆	—	73	2	no	—
268	C₂×Q₁₆	—	146	4	no	—
269	C₂×Q₁₆	—	146	4	no	—
270	C₂×Q₁₆	—	146	2	no	—
271	C₂×Q₁₆	—	146	2	no	—
272	C₂×Q₁₆	—	146	1	no	—
273	C₂×Q₁₆	C₂²×D₇₃	1	2	yes	—
274	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
275	C₂×SD₁₆	—	146	1	no	—
276	C₂×D₈	—	73	1	no	—
277	C₂²×C₈	—	73	1	no	—
278	C₂²×C₈	—	73	1	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	292	1	no	—
281	C₄⋊Q₈	—	292	1	no	—
282	C₄⋊Q₈	—	146	2	no	—
283	C₄⋊Q₈	—	146	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	—	146	1	no	—
286	C₄×D₄	—	292	1	no	—
287	C₄×D₄	—	292	1	no	—
288	C₄×D₄	—	146	1	no	—
289	C₄×D₄	—	146	1	no	—
290	#117	—	292	1	no	—
291	#117	—	146	1	no	—
292	C₂×C₄⋊C₄	—	292	1	no	—
293	C₂×C₄⋊C₄	—	292	1	no	—
294	C₂×C₄²	—	292	1	no	—
295	C₂×C₄²	—	73	1	no	—
296	Q₃₂	—	2	4	no	—
297	Q₃₂	—	146	4	no	—
298	SD₃₂	—	146	4	no	—
299	SD₃₂	—	146	4	no	—
300	M₃₂	—	146	4	no	—
301	C₂×C₁₆	—	73	2	no	—
302	C₂×C₁₆	C₂²×D₇₃	1	2	yes	—
303	#107	—	73	1	no	—
304	#107	C₂²×D₇₃	1	1	yes	characteristic
305	#106	—	146	1	no	—
306	#103	—	2	1	no	—
307	#103	—	146	1	no	—
308	#102	—	146	1	no	—
309	#102	—	146	1	no	—
310	C₄×C₈	—	73	1	no	—
311	C₄×C₈	—	73	1	no	—
312	C₄×C₈	—	73	1	no	—
313	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
314	#41	—	292	2	no	—
315	#41	—	146	4	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	292	2	no	—
319	C₂×Q₈	—	292	4	no	—
320	C₂×Q₈	—	292	4	no	—
321	C₂×Q₈	—	146	2	no	—
322	C₂×D₄	—	292	1	no	—
323	C₂×D₄	—	146	1	no	—
324	C₂²×C₄	—	292	1	no	—
325	C₂²×C₄	—	292	2	no	—
326	C₂²×C₄	—	292	1	no	—
327	C₂²×C₄	—	292	1	no	—
328	C₂²×C₄	—	73	1	no	—
329	C₂²×C₄	—	73	1	no	—
330	C₂²×C₄	—	73	1	no	—
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	1	no	—
333	Q₁₆	—	2	2	no	—
334	Q₁₆	—	4	2	no	—
335	Q₁₆	—	292	2	no	—
336	Q₁₆	—	292	4	no	—
337	Q₁₆	—	292	4	no	—
338	Q₁₆	—	146	2	no	—
339	Q₁₆	—	146	2	no	—
340	Q₁₆	D₄×D₇₃	1	2	yes	—
341	SD₁₆	—	146	4	no	—
342	D₈	—	73	2	no	—
343	D₈	—	146	1	no	—
344	C₂×C₈	—	73	1	no	—
345	C₂×C₈	—	73	2	no	—
346	C₂×C₈	—	73	2	no	—
347	C₂×C₈	—	73	1	no	—
348	C₂×C₈	—	146	2	no	—
349	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
350	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	292	2	no	—
356	C₄⋊C₄	—	292	2	no	—
357	C₄⋊C₄	—	292	1	no	—
358	C₄⋊C₄	—	292	1	no	—
359	C₄⋊C₄	—	292	1	no	—
360	C₄⋊C₄	—	146	1	no	—
361	C₂²⋊C₄	—	292	1	no	—
362	C₂²⋊C₄	—	292	1	no	—
363	C₂²⋊C₄	—	292	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	292	1	no	—
366	C₄²	—	292	1	no	—
367	C₄²	—	73	1	no	—
368	C₄²	—	73	1	no	—
369	C₄²	—	73	1	no	—
370	C₄²	D₄×D₇₃	1	1	yes	characteristic
371	C₁₆	—	2	2	no	—
372	C₁₆	—	146	2	no	—
373	C₂³	—	292	1	no	—
374	C₂³	—	73	1	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	4	1	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	292	2	no	—
380	Q₈	—	292	2	no	—
381	Q₈	—	584	4	no	—
382	D₄	—	292	4	no	—
383	D₄	—	292	1	no	—
384	D₄	—	146	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	292	4	no	—
389	C₂×C₄	—	292	1	no	—
390	C₂×C₄	—	292	2	no	—
391	C₂×C₄	—	584	4	no	—
392	C₂×C₄	—	584	2	no	—
393	C₂×C₄	—	584	2	no	—
394	C₂×C₄	—	73	1	no	—
395	C₂×C₄	—	73	1	no	—
396	C₂×C₄	—	73	2	no	—
397	C₂×C₄	—	73	2	no	—
398	C₂×C₄	—	73	1	no	—
399	C₂×C₄	—	146	2	no	—
400	C₂×C₄	—	146	2	no	—
401	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
402	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
404	C₈	—	2	1	no	—
405	C₈	—	73	2	no	—
406	C₈	—	146	1	no	—
407	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
408	C₈	#41×D₇₃	1	1	yes	characteristic
409	C₂²	—	292	2	no	—
410	C₂²	—	584	1	no	—
411	C₂²	—	584	1	no	—
412	C₂²	—	73	2	no	—
413	C₂²	—	146	1	no	—
414	C₂²	—	146	1	no	—
415	C₂²	C₂×D₈×D₇₃	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	584	1	no	—
421	C₄	—	584	2	no	—
422	C₄	—	73	2	no	—
423	C₄	—	73	2	no	—
424	C₄	—	146	1	no	—
425	C₄	#17989029	1	2	yes	complemented
426	C₄	#121×D₇₃	1	1	yes	characteristic
427	C₄	AGL(1,ℤ/8)×D₇₃	1	1	yes	characteristic
428	C₂	—	584	2	no	—
429	C₂	—	146	2	no	—
430	C₂	#459×D₇₃	1	1	yes	characteristic
431	C₂	#510×D₇₃	1	1	yes	characteristic
432	C₂	C₂×#17989029	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2209	C₂
socle	C₂²×C₇₃	C₂²×D₈
prime radical	C₂×#14556614	C₂²
hypercenter	#2209	D₇₃
hypocenter	C₇₃	#33583
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2209

Complements

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

N	H ≅ G/N	type
2. #494×D₇₃	C₂	semidirect
4. #22611981	C₂	semidirect
5. #22611979	C₂	semidirect
6. #22611977	C₂	semidirect
7. #22611975	C₂	semidirect
8. #22611973	C₂	semidirect
9. #22611685	C₂	semidirect
10. #22611649	C₂	semidirect
11. C₇₃×#2209	C₂	semidirect
203. C₄×C₇₃	#510	semidirect
210. Dic₇₃	#510	semidirect
222. #2209	D₇₃	semidirect
228. C₇₃	#33583	semidirect
425. C₄	#17989029	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989029	2
#494×D₇₃	2
C₄×#14556614	2
#22611981	2
#22611979	2
#22611977	2
#22611975	2
#22611973	2
#22611685	2
#22611649	2
C₇₃×#2209	2
#33583	73