Finite Group Databasebeta

← #13148132

Subgroups — #13148132

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6192C211yesmaximal, characteristic, complemented
2C2×#88635C211yesmaximal, characteristic, complemented
3#11721728C211yesmaximal, characteristic, complemented
4C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
5C9×#878C211yesmaximal, characteristic, complemented
6#11721276C211yesmaximal, characteristic, complemented
7#11721274C211yesmaximal, characteristic, complemented
8#11721240C211yesmaximal, characteristic, complemented
9#11721005C211yesmaximal, characteristic, complemented
10#11721005C211yesmaximal, characteristic, complemented
11#11721004C211yesmaximal, characteristic, complemented
12#11721003C211yesmaximal, characteristic, complemented
13#11721002C211yesmaximal, characteristic, complemented
14#11720942C211yesmaximal, characteristic, complemented
15#11720938C211yesmaximal, characteristic, complemented
16#10594187—31nomaximal
17#10589732—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C23×C3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C22×C9×Dic3C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic, complemented
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×C9×Dic6C2211yescharacteristic, complemented
27C2×#6192—24no—
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×#6192C2211yescharacteristic, complemented
33C2×#6192C2211yescharacteristic, complemented
34C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37#88635—24no—
38C3×C9×C22⋊C4C2211yescharacteristic
39#88536C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic
42C3×#3676C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C9×C4⋊Dic3C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47C9×Dic3⋊C4C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×#626—31no—
56C2×#3799—31no—
57#64091—31no—
58C3×D3×C22⋊C4—31no—
59C3×#878D311yescharacteristic
60#63977—31no—
61#63974—31no—
62#63952—31no—
63#63910—31no—
64#63910—31no—
65#63909—31no—
66#63907—31no—
67#63904—31no—
68#63854—31no—
69#63850—31no—
70C2×#3701—31no—
71C22×D36—31no—
72C9×C22⋊Q8—31no—
73#63509—31no—
74C4×#611—31no—
75#63457—31no—
76#63457—31no—
77#63457—31no—
78#63456—31no—
79#63456—31no—
80#63455—31no—
81#63444—31no—
82#63444—31no—
83#63444—61no—
84C22⋊C4×D9—31no—
85C22⋊C4×D9D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—41no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C22×C3×D9—22no—
94C22×C3×D9—22no—
95C22×C3×D9—41no—
96C22×C3×D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101C2×C3⋊Dic9C2311yescharacteristic
102C4⋊(C3⋊D9)—22no—
103C4⋊(C3⋊D9)—41no—
104C2×C9×Dic3—22no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C3×C4×D9—22no—
112C3×C4×D9—41no—
113C9×Dic6—22no—
114#6192—22no—
115#6192—22no—
116#6192—22no—
117#6192—22no—
118#6192—41no—
119#6192D414yescomplemented
120(C3⋊D9)⋊C4—22no—
121(C3⋊D9)⋊C4—22no—
122(C3⋊D9)⋊C4—41no—
123#5630—91no—
124#5490—91no—
125C23×C3⋊D3—31no—
126C23×C3×D3—31no—
127C2×#638—31no—
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C22×C3×Dic3C2×D311yescharacteristic
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×Dic6C2×D311yescharacteristic
134C2×#626—31no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—64no—
141C2×#624—31no—
142C2×#624—31no—
143C2×#624—31no—
144#3799—64no—
145C23×D9—31no—
146C23×D9—61no—
147C23×D9C2×D311yescharacteristic
148C32×C22⋊C4C2×D311yescharacteristic
149#3752—31no—
150#3752—31no—
151C3×#217—31no—
152C3×#217C2×D311yescharacteristic
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×C4⋊Dic3C2×D311yescharacteristic
156C3×Dic3⋊C4C2×D311yescharacteristic
157C3×Dic3⋊C4C2×D311yescharacteristic
158#3724—31no—
159#3722—31no—
160#3722—31no—
161#3722—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164Dic32—31no—
165C2×Q8×C9—31no—
166C22×C4×C9—31no—
167C2×#611—31no—
168C2×#611—61no—
169#3701—64no—
170C2×D36—31no—
171C2×D36—31no—
172C2×D36—31no—
173C2×D36—31no—
174C2×D36—31no—
175C2×D36—31no—
176C2×D36—31no—
177C2×D36—31no—
178C2×D36—64no—
179C2×D36—61no—
180C2×D36—61no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9C2×D311yescharacteristic, complemented
185C2×C4×D9C2×D311yescharacteristic, complemented
186C9×C4⋊C4—31no—
187C9×C4⋊C4—31no—
188C9×C4⋊C4—31no—
189C9×C22⋊C4—21no—
190C9×C22⋊C4—31no—
191C9×C22⋊C4C2×D311yescharacteristic
192#3676C2×D311yescharacteristic
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—61no—
201(C2×D9)⋊C4—61no—
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203(C2×D9)⋊C4C2×D311yescharacteristic, complemented
204Dic9⋊C4—31no—
205C4×Dic9—31no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9#4112yescomplemented
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×C3⋊D9—21no—
217C2×C3⋊D9—21no—
218C2×C3⋊D9—44no—
219C2×C3⋊D9C2×D412yes—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—44no—
226C2×C3×D9C2×D412yes—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C9×Dic3—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3C2×D412yes—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C22×#67—91no—
237C2×#239—91no—
238C2×#235—91no—
239C22×D12—91no—
240C3×C22⋊Q8—31no—
241C2×C3×C22⋊C4—91no—
242#953—91no—
243#947—91no—
244#930—91no—
245#929—91no—
246C4×#67—91no—
247C4×#67—91no—
248#895—91no—
249#895—91no—
250#895—91no—
251#894—91no—
252#894—91no—
253#893—91no—
254#885—91no—
255#884—91no—
256#884—91no—
257#883—91no—
258#882—91no—
259#882—91no—
260#882—91no—
261#882—181no—
262#67⋊C4—91no—
263D3×C22⋊C4—31no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266#878D911yescharacteristic, complemented
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3⋊D3—31no—
270C22×C3⋊D3—31no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3—62no—
273C22×C3⋊D3—121no—
274C22×C3×D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—62no—
277C22×C3×D3—62no—
278C22×C3×D3—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282C2×C3⋊Dic3—31no—
283C4⋊(C3⋊D3)—62no—
284C4⋊(C3⋊D3)—121no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C3×C4×D3—62no—
293C3×C4×D3—121no—
294C3×Dic6—22no—
295#626—34no—
296#626—62no—
297#626—62no—
298#626—62no—
299#626—62no—
300#626—121no—
301#624—62no—
302#624—62no—
303#624—121no—
304C23×C9—21no—
305C23×C9C22×D311yescharacteristic
306C22×D9—22no—
307C22×D9—22no—
308C22×D9—31no—
309C22×D9—31no—
310C22×D9—31no—
311C22×D9—41no—
312C22×D9—61no—
313C22×D9—61no—
314C22×D9—61no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—122no—
318C22×D9—122no—
319C22×D9—121no—
320C22×D9—122no—
321C22×D9C22×D311yescharacteristic
322C22×D9C22×D311yescharacteristic
323Q8×C9—62no—
324C2×C4×C9—21no—
325C2×C4×C9—21no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328C2×C4×C9—31no—
329C2×C4×C9—31no—
330C2×C4×C9—62no—
331C2×C4×C9C22×D311yescharacteristic
332C2×C4×C9C22×D311yescharacteristic
333#611—62no—
334#611—122no—
335C2×Dic9—31no—
336C2×Dic9—61no—
337C2×Dic9C22×D311yescharacteristic
338C2×Dic9C22×D311yescharacteristic
339D36—34no—
340D36—62no—
341D36—62no—
342D36—62no—
343D36—62no—
344D36—62no—
345D36—122no—
346D36—121no—
347D36—122no—
348D36—121no—
349C4×D9—22no—
350C4×D9—41no—
351C4×D9—62no—
352C4×D9—62no—
353C4×D9—121no—
354#546—271noSylow
355C2×C3×C9—22no—
356C2×C3×C9C22×D411yescharacteristic
357C2×C3×C9C2×#4111yescharacteristic
358C2×C3×C9H(5,𝔽2)11yescharacteristic
359C3⋊D9—22no—
360C3⋊D9—41no—
361C3⋊D9—41no—
362C3×D9—22no—
363C3×D9—41no—
364C24×C3—91no—
365C23×D3—31no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—181no—
369C2×C3×Q8—31no—
370C22×C3×C4—31no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—181no—
382C2×#67—184no—
383C22×Dic3C2×D911yescharacteristic
384#239—184no—
385#235—184no—
386C2×D12—91no—
387C2×D12—91no—
388C2×D12—91no—
389C2×D12—91no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12—91no—
395C2×D12—91no—
396C2×D12—181no—
397C2×D12—181no—
398C2×D12—184no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—91no—
407C2×Dic6C2×D911yescharacteristic, complemented
408C3×C4⋊C4—31no—
409C3×C4⋊C4—31no—
410C3×C4⋊C4—31no—
411C3×C22⋊C4—21no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—91no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4C2×D911yescharacteristic
417C3×C22⋊C4D3211yescharacteristic
418#217—31no—
419#217—91no—
420#217—91no—
421#217C2×D911yescharacteristic
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—181no—
437(C2×D3)⋊C4—181no—
438C4⋊Dic3C2×D911yescharacteristic, complemented
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4C2×D911yescharacteristic, complemented
442Dic3⋊C4C2×D911yescharacteristic, complemented
443C4×Dic3—91no—
444C4×Dic3—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32#23912yes—
448C22×C32C23×D311yescharacteristic
449C2×C3⋊D3—32no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—61no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—124no—
459C2×C3×D3—32no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465C2×C3×D3—124no—
466C32×C4—21no—
467C32×C4—21no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3D3×D412yes—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—22no—
479C22×C9—41no—
480C22×C9—41no—
481C22×C9#23512yescomplemented
482C22×C9C23×D311yescharacteristic
483C2×D9—21no—
484C2×D9—21no—
485C2×D9—21no—
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—32no—
489C2×D9—44no—
490C2×D9—62no—
491C2×D9—61no—
492C2×D9—61no—
493C2×D9—62no—
494C2×D9—61no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—61no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—121no—
504C2×D9—121no—
505C2×D9—121no—
506C2×D9—121no—
507C2×D9—124no—
508C2×D9—128no—
509C2×D9D3×D412yes—
510C4×C9—21no—
511C4×C9—21no—
512C4×C9—32no—
513C4×C9—41no—
514C4×C9—41no—
515C4×C9—61no—
516C4×C9—61no—
517C4×C9—61no—
518Dic9—21no—
519Dic9—21no—
520Dic9—61no—
521Dic9—121no—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—271no—
526#123—271no—
527C22⋊Q8—31no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—271no—
537C3×C9#54611yescharacteristic, complemented, Sylow
538C23×C3—21no—
539C23×C3—91no—
540C23×C3—91no—
541C23×C3—182no—
542C23×C3—182no—
543C23×C3—361no—
544C23×C3C22×D911yescharacteristic
545C23×C3C2×D3211yescharacteristic
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—91no—
551C22×D3—91no—
552C22×D3—91no—
553C22×D3—91no—
554C22×D3—91no—
555C22×D3—91no—
556C22×D3—121no—
557C22×D3—181no—
558C22×D3—181no—
559C22×D3—181no—
560C22×D3—182no—
561C22×D3—182no—
562C22×D3—182no—
563C22×D3—182no—
564C22×D3—362no—
565C22×D3—362no—
566C22×D3—361no—
567C22×D3—361no—
568C22×D3—362no—
569C3×Q8—62no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—62no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—182no—
580C2×C3×C4—361no—
581C2×C3×C4C22×D911yescharacteristic
582C2×C3×C4C22×D911yescharacteristic
583C2×C3×C4C2×D3211yescharacteristic
584C2×C3×C4C2×D3211yescharacteristic
585#67—94no—
586#67—182no—
587#67—182no—
588#67—182no—
589#67—182no—
590#67—182no—
591#67—182no—
592#67—362no—
593#67—361no—
594C2×Dic3—22no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—181no—
600C2×Dic3C22×D911yescharacteristic
601C2×Dic3C22×D911yescharacteristic
602C2×Dic3C22×D911yescharacteristic
603C2×Dic3C22×D911yescharacteristic
604D12—94no—
605D12—182no—
606D12—182no—
607D12—182no—
608D12—182no—
609D12—182no—
610D12—182no—
611D12—362no—
612D12—361no—
613D12—361no—
614D12—362no—
615D12—361no—
616C4×D3—62no—
617C4×D3—121no—
618C4×D3—182no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—182no—
622C4×D3—361no—
623C4×D3—361no—
624Dic6—22no—
625C2×C32—22no—
626C2×C32C2×D3×D411yescharacteristic
627C2×C32C2×#23911yescharacteristic
628C2×C32#100911yescharacteristic
629C3⋊D3—62no—
630C3⋊D3—121no—
631C3⋊D3—121no—
632C3×D3—62no—
633C3×D3—121no—
634C2×C9—22no—
635C2×C9—21no—
636C2×C9—21no—
637C2×C9—21no—
638C2×C9—42no—
639C2×C9C2×#23511yescharacteristic
640C2×C9C2×D3×D411yescharacteristic
641C2×C9#100411yescharacteristic
642D9—22no—
643D9—41no—
644D9—62no—
645D9—122no—
646D9—122no—
647D9—121no—
648D9—121no—
649D9—241no—
650C24—91no—
651C24—271no—
652#41—544no—
653C2×Q8—31no—
654C2×D4—271no—
655C2×D4—271no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—544no—
664C22×C4—31no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—31no—
671C4⋊C4—31no—
672C4⋊C4—31no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—91no—
676C22⋊C4—91no—
677C22⋊C4—91no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4D3×D911yescharacteristic
686C42—271no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—22no—
692C22×C3—21no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—92no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3—364no—
702C22×C3#370112yescomplemented
703C22×C3C23×D911yescharacteristic
704C22×C3#379912yes—
705C22×C3C22×D3211yescharacteristic
706C2×D3—32no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—92no—
713C2×D3—92no—
714C2×D3—124no—
715C2×D3—182no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—181no—
720C2×D3—182no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C2×D3—181no—
731C2×D3—181no—
732C2×D3—181no—
733C2×D3—361no—
734C2×D3—361no—
735C2×D3—361no—
736C2×D3—361no—
737C2×D3—361no—
738C2×D3—361no—
739C2×D3—361no—
740C2×D3—364no—
741C2×D3—364no—
742C2×D3—368no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—32no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4—181no—
754C3×C4—181no—
755Dic3—21no—
756Dic3—21no—
757Dic3—21no—
758Dic3—61no—
759Dic3—61no—
760Dic3—181no—
761Dic3—181no—
762Dic3—361no—
763Dic3D4×D912yes—
764C32#563011yescharacteristic
765C9—21no—
766C9#549011yescharacteristic, complemented
767C23—91no—
768C23—91no—
769C23—182no—
770C23—182no—
771C23—271no—
772C23—271no—
773C23—271no—
774C23—361no—
775C23—542no—
776C23—542no—
777C23—1081no—
778C23C2×D3×D911yescharacteristic
779Q8—62no—
780D4—274no—
781D4—542no—
782D4—542no—
783D4—542no—
784D4—542no—
785D4—542no—
786D4—542no—
787D4—1081no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—31no—
793C2×C4—62no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—182no—
797C2×C4—271no—
798C2×C4—361no—
799C2×C4—542no—
800C2×C4—542no—
801C2×C4—1081no—
802C2×C4C2×D3×D911yescharacteristic
803C2×C4C2×D3×D911yescharacteristic
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—42no—
810C2×C3—182no—
811C2×C3—361no—
812C2×C3C2×D4×D911yescharacteristic
813C2×C3C2×#370111yescharacteristic
814C2×C3#6371511yescharacteristic
815C2×C3C2×#379911yescharacteristic
816C2×C3D32×D411yescharacteristic
817C2×C3#6431411yescharacteristic
818D3—62no—
819D3—121no—
820D3—182no—
821D3—182no—
822D3—362no—
823D3—362no—
824D3—361no—
825D3—361no—
826D3—361no—
827D3—361no—
828D3—721no—
829C22—21no—
830C22—21no—
831C22—92no—
832C22—181no—
833C22—181no—
834C22—181no—
835C22—181no—
836C22—181no—
837C22—272no—
838C22—364no—
839C22—541no—
840C22—541no—
841C22—541no—
842C22—541no—
843C22—541no—
844C22—541no—
845C22—541no—
846C22—541no—
847C22—1084no—
848C22#8863512yescomplemented
849C22C22×D3×D911yescharacteristic
850C4—21no—
851C4—21no—
852C4—32no—
853C4—61no—
854C4—61no—
855C4—61no—
856C4—181no—
857C4—181no—
858C4—541no—
859C3—21no—
860C3#1058973211yescharacteristic, complemented
861C3#1059418711yescharacteristic
862C2—22no—
863C2—182no—
864C2—361no—
865C2—542no—
866C2—1081no—
867C2—1081no—
868C2C2×#8863511yescharacteristic
869C2D3×D4×D911yescharacteristic
870C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6192C2semidirect
2. C2×#88635C2semidirect
3. #11721728C2semidirect
4. C3×C22⋊C4×D9C2semidirect
5. C9×#878C2semidirect
6. #11721276C2semidirect
7. #11721274C2semidirect
8. #11721240C2semidirect
9. #11721005C2semidirect
10. #11721005C2semidirect
11. #11721004C2semidirect
12. #11721003C2semidirect
13. #11721002C2semidirect
14. #11720942C2semidirect
15. #11720938C2semidirect
21. C2×C4⋊(C3⋊D9)C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C3×C4×D9C22semidirect
25. C2×C3×C4×D9C22semidirect
26. C2×C9×Dic6C22semidirect
32. C2×#6192C22semidirect
33. C2×#6192C22semidirect
34. C2×(C3⋊D9)⋊C4C22semidirect
35. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
39. #88536C22semidirect
40. #88536C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C9×C4⋊Dic3C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. C9×Dic3⋊C4C22semidirect
48. #88445C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
85. C22⋊C4×D9D3semidirect
119. #6192D4semidirect
184. C2×C4×D9C2×D3semidirect
185. C2×C4×D9C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
208. C22×C3×C9#41semidirect
266. #878D9semidirect
407. C2×Dic6C2×D9semidirect
438. C4⋊Dic3C2×D9semidirect
441. Dic3⋊C4C2×D9semidirect
442. Dic3⋊C4C2×D9semidirect
481. C22×C9#235semidirect
537. C3×C9#546semidirect
702. C22×C3#3701semidirect
766. C9#5490semidirect
848. C22#88635semidirect
860. C3#10589732semidirect

Maximal subgroups

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

subgroupindex
C22×#61922
C2×#886352
#117217282
C3×C22⋊C4×D92
C9×#8782
#117212762
#117212742
#117212402
#117210052
#117210042
#117210032
#117210022
#117209422
#117209382
#105941873
#105897323