Finite Group Databasebeta

← #13148288

Subgroups — #13148288

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×#6195C211yesmaximal, characteristic, complemented
2C2×#88642C211yesmaximal, characteristic, complemented
3#11721728C211yesmaximal, characteristic, complemented
4D3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#63440C211yesmaximal, characteristic, complemented
6#11721287C211yesmaximal, characteristic, complemented
7#11721274C211yesmaximal, characteristic, complemented
8#11721241C211yesmaximal, characteristic, complemented
9#11721039C211yesmaximal, characteristic, complemented
10#11721039C211yesmaximal, characteristic, complemented
11#11721038C211yesmaximal, characteristic, complemented
12#11721035C211yesmaximal, characteristic, complemented
13#11721030C211yesmaximal, characteristic, complemented
14#11720958C211yesmaximal, characteristic, complemented
15#11720954C211yesmaximal, characteristic, complemented
16#10594187—31nomaximal
17#10589592—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C23×D3×C9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C22×C3×Dic9C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×C4×D3×C9C2211yescharacteristic, complemented
26C2×C3×Dic18C2211yescharacteristic, complemented
27C2×#6195—24no—
28C2×#6195C2211yescharacteristic
29C2×#6195C2211yescharacteristic
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic
32C2×#6195C2211yescharacteristic, complemented
33C2×#6195C2211yescharacteristic, complemented
34C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37#88642—24no—
38C3×C9×C22⋊C4C2211yescharacteristic
39#88536C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic
42C3×#3676C2211yescharacteristic
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×C4⋊Dic9C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×#626—31no—
56C2×#3799—31no—
57#64091—31no—
58C3×D3×C22⋊C4D311yescharacteristic
59C3×#878—31no—
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—
70C22×#611—31no—
71C2×#3697—31no—
72C2×C9×C22⋊C4—31no—
73#63515—31no—
74#63492—31no—
75#63491—31no—
76C4×#611—31no—
77#63447—31no—
78#63446—31no—
79#63446—31no—
80#63445—31no—
81#63444—31no—
82#63444—61no—
83#611⋊C4—31no—
84C22⋊C4×D9—31no—
85#63440D311yescharacteristic, 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×D3×C9—22no—
94C22×D3×C9—22no—
95C22×D3×C9—41no—
96C22×D3×C9C2311yescharacteristic
97C22×D3×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101C2×C3⋊Dic9C2311yescharacteristic
102C4⋊(C3⋊D9)—22no—
103C4⋊(C3⋊D9)—41no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9—22no—
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C4×D3×C9—22no—
112C4×D3×C9—41no—
113C3×Dic18—22no—
114#6195—22no—
115#6195—22no—
116#6195—22no—
117#6195—22no—
118#6195—41no—
119#6195D414yescomplemented
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×D3C2×D311yescharacteristic
127C2×#638—31no—
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C22×C3×Dic3—31no—
131C2×C3×C4×D3C2×D311yescharacteristic
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×Dic6—31no—
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—
145C24×C9—31no—
146C23×D9—31no—
147C23×D9—61no—
148C32×C22⋊C4C2×D311yescharacteristic
149#3752—31no—
150#3752—31no—
151C3×#217—31no—
152C3×#217C2×D311yescharacteristic
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×C4⋊Dic3—31no—
156C3×Dic3⋊C4—31no—
157C3×Dic3⋊C4—31no—
158#3724—31no—
159#3722—31no—
160#3722—31no—
161#3722—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164Dic32—31no—
165C22×C4×C9—31no—
166C22×C4×C9—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—64no—
175C2×#611—61no—
176C22×Dic9C2×D311yescharacteristic
177#3697—64no—
178C2×D36—31no—
179C2×D36—31no—
180C2×D36—61no—
181C2×D36—61no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9—31no—
185C2×Dic18C2×D311yescharacteristic, complemented
186C9×C22⋊C4—21no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4C2×D311yescharacteristic
191#3676—31no—
192#3676—31no—
193#3676C2×D311yescharacteristic
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—61no—
200(C2×D9)⋊C4—61no—
201C4⋊Dic9C2×D311yescharacteristic, complemented
202Dic9⋊C4—31no—
203Dic9⋊C4C2×D311yescharacteristic, complemented
204Dic9⋊C4C2×D311yescharacteristic, complemented
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×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9—21no—
223C2×D3×C9—21no—
224C2×D3×C9—21no—
225C2×D3×C9—44no—
226C2×D3×C9C2×D412yes—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C9×Dic3—21no—
231C9×Dic3—21no—
232C3×Dic9—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C22×#67—91no—
237C2×#239—91no—
238C2×#235—91no—
239C22×D12—91no—
240C3×C22⋊Q8—91no—
241C2×C3×C22⋊C4—31no—
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—91no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4D911yescharacteristic, complemented
266#878—31no—
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—22no—
275C22×C3×D3—22no—
276C22×C3×D3—41no—
277C22×C3×D3C22×D311yescharacteristic
278C22×C3×D3C22×D311yescharacteristic
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—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C3×C4×D3—22no—
293C3×C4×D3—41no—
294C3×Dic6—62no—
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×C9—31no—
306C23×C9—31no—
307C23×C9—62no—
308C23×C9—62no—
309C23×C9—121no—
310C23×C9C22×D311yescharacteristic
311C22×D9—31no—
312C22×D9—31no—
313C22×D9—31no—
314C22×D9—61no—
315C22×D9—61no—
316C22×D9—61no—
317C22×D9—62no—
318C22×D9—62no—
319C22×D9—122no—
320C22×D9—122no—
321C22×D9—121no—
322C22×D9—122no—
323C2×C4×C9—21no—
324C2×C4×C9—21no—
325C2×C4×C9—31no—
326C2×C4×C9—31no—
327C2×C4×C9—62no—
328C2×C4×C9—121no—
329C2×C4×C9C22×D311yescharacteristic
330C2×C4×C9C22×D311yescharacteristic
331#611—34no—
332#611—62no—
333#611—62no—
334#611—62no—
335#611—62no—
336#611—62no—
337#611—122no—
338#611—121no—
339C2×Dic9—22no—
340C2×Dic9—31no—
341C2×Dic9—61no—
342C2×Dic9C22×D311yescharacteristic
343C2×Dic9C22×D311yescharacteristic
344C2×Dic9C22×D311yescharacteristic
345C2×Dic9C22×D311yescharacteristic
346D36—62no—
347D36—122no—
348D36—121no—
349D36—122no—
350C4×D9—62no—
351C4×D9—62no—
352C4×D9—121no—
353Dic18—22no—
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—
362D3×C9—22no—
363D3×C9—41no—
364C24×C3—31no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—181no—
368C23×D3C2×D911yescharacteristic
369C2×C3×Q8—91no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
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×Dic3—31no—
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—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3C2×D911yescharacteristic, complemented
406C2×C4×D3C2×D911yescharacteristic, complemented
407C2×Dic6—31no—
408C3×C4⋊C4—91no—
409C3×C4⋊C4—91no—
410C3×C4⋊C4—91no—
411C3×C22⋊C4—21no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—31no—
414C3×C22⋊C4—31no—
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—91no—
423(C2×D3)⋊C4—91no—
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—181no—
435(C2×D3)⋊C4—181no—
436(C2×D3)⋊C4C2×D911yescharacteristic, complemented
437(C2×D3)⋊C4C2×D911yescharacteristic, complemented
438C4⋊Dic3—31no—
439Dic3⋊C4—31no—
440Dic3⋊C4—31no—
441Dic3⋊C4—91no—
442Dic3⋊C4—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32#23512yes—
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—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—44no—
465C2×C3×D3D3×D412yes—
466C32×C4—21no—
467C32×C4—21no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—32no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—22no—
479C22×C9—32no—
480C22×C9—41no—
481C22×C9—41no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9—61no—
485C22×C9—61no—
486C22×C9—61no—
487C22×C9—124no—
488C22×C9#23912yescomplemented
489C22×C9C23×D311yescharacteristic
490C2×D9—32no—
491C2×D9—62no—
492C2×D9—61no—
493C2×D9—61no—
494C2×D9—62no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—61no—
500C2×D9—61no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—121no—
504C2×D9—121no—
505C2×D9—121no—
506C2×D9—121no—
507C2×D9—121no—
508C2×D9—124no—
509C2×D9—128no—
510C4×C9—21no—
511C4×C9—21no—
512C4×C9—41no—
513C4×C9—41no—
514C4×C9—61no—
515C4×C9—61no—
516Dic9—21no—
517Dic9—21no—
518Dic9—21no—
519Dic9—61no—
520Dic9—121no—
521Dic9D3×D412yes—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—271no—
526#123—271no—
527C22⋊Q8—91no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—271no—
537C3×C9#54611yescharacteristic, complemented, Sylow
538C23×C3—21no—
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—62no—
542C23×C3—62no—
543C23×C3—121no—
544C23×C3C22×D911yescharacteristic
545C23×C3C2×D3211yescharacteristic
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—41no—
549C22×D3—91no—
550C22×D3—91no—
551C22×D3—91no—
552C22×D3—91no—
553C22×D3—91no—
554C22×D3—91no—
555C22×D3—181no—
556C22×D3—181no—
557C22×D3—181no—
558C22×D3—182no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—182no—
562C22×D3—362no—
563C22×D3—362no—
564C22×D3—361no—
565C22×D3—361no—
566C22×D3—362no—
567C22×D3C22×D911yescharacteristic
568C22×D3C22×D911yescharacteristic
569C3×Q8—182no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—62no—
575C2×C3×C4—91no—
576C2×C3×C4—91no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—121no—
580C2×C3×C4—182no—
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—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—62no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—181no—
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—22no—
617C4×D3—41no—
618C4×D3—182no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—182no—
622C4×D3—361no—
623C4×D3—361no—
624Dic6—62no—
625C2×C32—22no—
626C2×C32C2×#23511yescharacteristic
627C2×C32C2×D3×D411yescharacteristic
628C2×C32#100411yescharacteristic
629C3⋊D3—62no—
630C3⋊D3—121no—
631C3⋊D3—121no—
632C3×D3—22no—
633C3×D3—41no—
634C2×C9—22no—
635C2×C9—21no—
636C2×C9—21no—
637C2×C9—21no—
638C2×C9—42no—
639C2×C9—62no—
640C2×C9—121no—
641C2×C9C2×D3×D411yescharacteristic
642C2×C9C2×#23911yescharacteristic
643C2×C9#100911yescharacteristic
644D9—62no—
645D9—122no—
646D9—122no—
647D9—121no—
648D9—121no—
649D9—241no—
650C24—31no—
651C24—271no—
652#41—544no—
653C2×Q8—91no—
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—31no—
666C22×C4—91no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—91no—
671C4⋊C4—91no—
672C4⋊C4—91no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—31no—
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—21no—
692C22×C3—22no—
693C22×C3—32no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—124no—
702C22×C3#369712yescomplemented
703C22×C3C23×D911yescharacteristic
704C22×C3#379912yes—
705C22×C3C22×D3211yescharacteristic
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—44no—
712C2×D3—92no—
713C2×D3—92no—
714C2×D3—182no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—182no—
720C2×D3—181no—
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—361no—
733C2×D3—361no—
734C2×D3—361no—
735C2×D3—361no—
736C2×D3—361no—
737C2×D3—361no—
738C2×D3—361no—
739C2×D3—364no—
740C2×D3—364no—
741C2×D3—368no—
742C2×D3D4×D912yes—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—61no—
750C3×C4—61no—
751C3×C4—92no—
752C3×C4—181no—
753C3×C4—181no—
754C3×C4—181no—
755Dic3—21no—
756Dic3—21no—
757Dic3—32no—
758Dic3—61no—
759Dic3—61no—
760Dic3—61no—
761Dic3—181no—
762Dic3—181no—
763Dic3—361no—
764C32#549011yescharacteristic
765C9—21no—
766C9#563011yescharacteristic, complemented
767C23—31no—
768C23—31no—
769C23—62no—
770C23—62no—
771C23—121no—
772C23—271no—
773C23—271no—
774C23—271no—
775C23—542no—
776C23—542no—
777C23—1081no—
778C23C2×D3×D911yescharacteristic
779Q8—182no—
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—62no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—121no—
797C2×C4—182no—
798C2×C4—271no—
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—62no—
811C2×C3—121no—
812C2×C3C2×#369711yescharacteristic
813C2×C3C2×D4×D911yescharacteristic
814C2×C3#6371011yescharacteristic
815C2×C3C2×#379911yescharacteristic
816C2×C3D32×D411yescharacteristic
817C2×C3#6431411yescharacteristic
818D3—22no—
819D3—41no—
820D3—182no—
821D3—182no—
822D3—362no—
823D3—362no—
824D3—361no—
825D3—361no—
826D3—361no—
827D3—361no—
828D3—721no—
829C22—21no—
830C22—21no—
831C22—32no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—124no—
838C22—272no—
839C22—541no—
840C22—541no—
841C22—541no—
842C22—541no—
843C22—541no—
844C22—541no—
845C22—541no—
846C22—541no—
847C22—1084no—
848C22#8864212yescomplemented
849C22C22×D3×D911yescharacteristic
850C4—21no—
851C4—21no—
852C4—61no—
853C4—61no—
854C4—92no—
855C4—181no—
856C4—181no—
857C4—181no—
858C4—541no—
859C3—21no—
860C3#1058959211yescharacteristic, complemented
861C3#1059418711yescharacteristic
862C2—22no—
863C2—62no—
864C2—121no—
865C2—542no—
866C2—1081no—
867C2—1081no—
868C2C2×#8864211yescharacteristic
869C2D3×D4×D911yescharacteristic
870C2#1172250011yescharacteristic
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×#6195C2semidirect
2. C2×#88642C2semidirect
3. #11721728C2semidirect
4. D3×C9×C22⋊C4C2semidirect
5. C3×#63440C2semidirect
6. #11721287C2semidirect
7. #11721274C2semidirect
8. #11721241C2semidirect
9. #11721039C2semidirect
10. #11721039C2semidirect
11. #11721038C2semidirect
12. #11721035C2semidirect
13. #11721030C2semidirect
14. #11720958C2semidirect
15. #11720954C2semidirect
21. C2×C4⋊(C3⋊D9)C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C4×D3×C9C22semidirect
25. C2×C4×D3×C9C22semidirect
26. C2×C3×Dic18C22semidirect
32. C2×#6195C22semidirect
33. C2×#6195C22semidirect
34. C2×(C3⋊D9)⋊C4C22semidirect
35. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
39. #88536C22semidirect
40. #88536C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C3×C4⋊Dic9C22semidirect
46. C3×Dic9⋊C4C22semidirect
47. C3×Dic9⋊C4C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
51. #88445C22semidirect
52. #88445C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
85. #63440D3semidirect
119. #6195D4semidirect
185. C2×Dic18C2×D3semidirect
201. C4⋊Dic9C2×D3semidirect
203. Dic9⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
208. C22×C3×C9#41semidirect
265. D3×C22⋊C4D9semidirect
405. C2×C4×D3C2×D9semidirect
406. C2×C4×D3C2×D9semidirect
436. (C2×D3)⋊C4C2×D9semidirect
437. (C2×D3)⋊C4C2×D9semidirect
488. C22×C9#239semidirect
537. C3×C9#546semidirect
702. C22×C3#3697semidirect
766. C9#5630semidirect
848. C22#88642semidirect
860. C3#10589592semidirect

Maximal subgroups

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

subgroupindex
C22×#61952
C2×#886422
#117217282
D3×C9×C22⋊C42
C3×#634402
#117212872
#117212742
#117212412
#117210392
#117210382
#117210352
#117210302
#117209582
#117209542
#105941873
#105895923