Finite Group Databasebeta

← #13148409

Subgroups — #13148409

Order 1728.

1168 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic, complemented
2C2×D9×D12C211yesmaximal, characteristic, complemented
3#11721728C211yesmaximal, characteristic, complemented
4C9×#884C211yesmaximal, characteristic, complemented
5C3×#63445C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721291C211yesmaximal, characteristic, complemented
8#11721282C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
11#11721038C211yesmaximal, characteristic, complemented
12#11721017C211yesmaximal, characteristic, complemented
13#11720997C211yesmaximal, characteristic, complemented
14#11720958C211yesmaximal, characteristic, complemented
15#11720938C211yesmaximal, characteristic, complemented
16#10594264—31nomaximal
17#10589707—31nomaximal
18C23×C3⋊D9C2211yescharacteristic, complemented
19C22×D3×D9C2211yescharacteristic
20C22×D3×D9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic
23C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic, complemented
25C2×C9×#67C2211yescharacteristic, complemented
26C2×C3×#611C2211yescharacteristic
27C2×C9×D12C2211yescharacteristic, complemented
28C2×C4×D3×C9C2211yescharacteristic, complemented
29C2×C3×C4×D9C2211yescharacteristic, complemented
30#88668—24no—
31C2×#6195C2211yescharacteristic
32C2×#6195C2211yescharacteristic, complemented
33C2×#6195C2211yescharacteristic, complemented
34C2×#6195C2211yescharacteristic, complemented
35C2×D3×Dic9C2211yescharacteristic, complemented
36C2×#6192C2211yescharacteristic
37C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
38D9×D12—24no—
39C3×C9×C22⋊C4C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41#88536C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C9×Dic3⋊C4C2211yescharacteristic, complemented
46C3×C4⋊Dic9C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54#88442C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×D3×D12—31no—
57#64091—31no—
58C3×#884D311yescharacteristic
59C3×#883—31no—
60#63983—31no—
61#63981—31no—
62#63971—31no—
63#63923—31no—
64D3×(C2×D3)⋊C4—31no—
65#63909—31no—
66#63897—31no—
67#63886—31no—
68#63854—31no—
69#63850—31no—
70C2×D4×D9—31no—
71C2×D4×D9—31no—
72C9×#121—31no—
73#63501—31no—
74#63501—31no—
75#63499—31no—
76#63499—31no—
77#63492—31no—
78C2×(C2×D9)⋊C4—31no—
79#63456—31no—
80#63456—31no—
81#63445—31no—
82#63445D311yescharacteristic, complemented
83#63444—31no—
84#63444—31no—
85#63444—61no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—41no—
89C22×C3⋊D9—41no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×D3×C9C2311yescharacteristic
95C22×C3×D9C2311yescharacteristic
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×D3×D9—41no—
99C2×D3×D9—41no—
100C2×D3×D9—41no—
101C2×D3×D9D414yescomplemented
102C2×C3×C4×C9C2311yescharacteristic
103C2×C3×C4×C9C2311yescharacteristic
104#6233—41no—
105C2×C3⋊Dic9C2311yescharacteristic
106C4⋊(C3⋊D9)—22no—
107C4⋊(C3⋊D9)—41no—
108C9×#67—22no—
109C9×#67—41no—
110C3×#611—22no—
111C2×C9×Dic3C2311yescharacteristic
112C2×C9×Dic3C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C9×D12—22no—
117C4×D3×C9—41no—
118C3×C4×D9—22no—
119#6195—22no—
120#6195—22no—
121#6195—22no—
122#6195—41no—
123D3×Dic9—41no—
124#6192—22no—
125(C3⋊D9)⋊C4—22no—
126#5653—91no—
127#5605—91no—
128C23×C3⋊D3—31no—
129C22×D32—31no—
130C22×D32—31no—
131C2×#638—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C3×#67—31no—
135C2×C3×#67C2×D311yescharacteristic
136C2×C3×#67C2×D311yescharacteristic
137C2×C3×D12C2×D311yescharacteristic
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3C2×D311yescharacteristic
140#3811—64no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#624—31no—
147C2×D3×Dic3—31no—
148D3×D12—64no—
149C23×D9—31no—
150C23×D9—31no—
151C23×D9—31no—
152C23×D9—61no—
153C32×C22⋊C4C2×D311yescharacteristic
154#3752—31no—
155#3752—31no—
156C3×#217—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4C2×D311yescharacteristic
159C3×C4⋊Dic3—31no—
160C3×Dic3⋊C4—31no—
161C3×Dic3⋊C4C2×D311yescharacteristic
162#3724—31no—
163#3722—31no—
164#3722—31no—
165#3722—31no—
166#3722—31no—
167(C2×D3)⋊Dic3—31no—
168(C2×D3)⋊Dic3—31no—
169C2×D4×C9—31no—
170C2×D4×C9—31no—
171C2×D4×C9—31no—
172C22×C4×C9—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—31no—
178C2×#611—61no—
179C2×#611C2×D311yescharacteristic
180C22×Dic9—31no—
181D4×D9—64no—
182D4×D9—64no—
183C2×D36—31no—
184C2×D36—31no—
185C2×D36—31no—
186C2×D36—61no—
187C2×D36—61no—
188C2×C4×D9—31no—
189C2×C4×D9C2×D311yescharacteristic, complemented
190C9×C4⋊C4—31no—
191C9×C22⋊C4—21no—
192C9×C22⋊C4—31no—
193C9×C22⋊C4C2×D311yescharacteristic, complemented
194#3676—31no—
195#3676C2×D311yescharacteristic, complemented
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—31no—
203(C2×D9)⋊C4—61no—
204(C2×D9)⋊C4—61no—
205(C2×D9)⋊C4C2×D311yescharacteristic, complemented
206C4⋊Dic9C2×D311yescharacteristic, complemented
207Dic9⋊C4—31no—
208Dic9⋊C4C2×D311yescharacteristic, complemented
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9C2411yescharacteristic
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×C3⋊D9—21no—
217C2×C3⋊D9—21no—
218C2×C3⋊D9—21no—
219C2×C3⋊D9—21no—
220C2×C3⋊D9—21no—
221C2×C3⋊D9—44no—
222C2×C3⋊D9C2×D412yes—
223C2×D3×C9—21no—
224C2×D3×C9—21no—
225C2×D3×C9—21no—
226C2×D3×C9—21no—
227C2×D3×C9—21no—
228C2×D3×C9C2×D412yes—
229C2×C3×D9—21no—
230C2×C3×D9—21no—
231C2×C3×D9C2×D412yes—
232D3×D9—44no—
233D3×D9—44no—
234C3×C4×C9—21no—
235C3×C4×C9—21no—
236C3⋊Dic9—21no—
237C9×Dic3—21no—
238C9×Dic3—21no—
239C3×Dic9—21no—
240C3×Dic9—21no—
241C3×Dic9—21no—
242C2×D3×D4—91no—
243C2×D3×D4—91no—
244C2×D3×D4—91no—
245C22×D12—91no—
246C3×#123—91no—
247C3×#121—31no—
248#939—91no—
249#939—91no—
250#937—91no—
251#937—91no—
252#937—91no—
253#930—91no—
254#929—91no—
255C2×(C2×D3)⋊C4—91no—
256#895—91no—
257#895—91no—
258#894—91no—
259#894—91no—
260#894—91no—
261#894—91no—
262#884—91no—
263#884D911yescharacteristic, complemented
264#883—31no—
265#883—91no—
266#882—91no—
267#882—91no—
268#882—91no—
269#882—91no—
270#882—91no—
271#882—181no—
272D3×C22⋊C4—91no—
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—31no—
277C22×C3⋊D3—62no—
278C22×C3⋊D3—121no—
279C22×C3⋊D3—121no—
280C22×C3×D3—31no—
281C22×C3×D3C22×D311yescharacteristic
282C22×C3×D3C22×D311yescharacteristic
283C2×D32—34no—
284C2×D32—62no—
285C2×D32—121no—
286C2×D32—121no—
287C2×D32—121no—
288C2×D32—121no—
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—121no—
292C2×C3⋊Dic3—31no—
293C4⋊(C3⋊D3)—62no—
294C4⋊(C3⋊D3)—121no—
295C3×#67—22no—
296C3×#67—41no—
297C3×#67—62no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D311yescharacteristic
303C3×D12—22no—
304C3×C4×D3—41no—
305C3×C4×D3—62no—
306#626—62no—
307#626—62no—
308#626—62no—
309#626—62no—
310#626—121no—
311#624—62no—
312D3×Dic3—121no—
313C23×C9—21no—
314C23×C9—31no—
315C23×C9—31no—
316C23×C9C22×D311yescharacteristic
317C22×D9—31no—
318C22×D9—34no—
319C22×D9—31no—
320C22×D9—31no—
321C22×D9—61no—
322C22×D9—61no—
323C22×D9—61no—
324C22×D9—62no—
325C22×D9—62no—
326C22×D9—122no—
327C22×D9—121no—
328C22×D9—121no—
329C22×D9—121no—
330C22×D9—121no—
331C22×D9—121no—
332C22×D9—121no—
333C22×D9—122no—
334C22×D9—122no—
335C22×D9C22×D311yescharacteristic
336D4×C9—62no—
337D4×C9—62no—
338D4×C9—121no—
339C2×C4×C9—21no—
340C2×C4×C9—21no—
341C2×C4×C9—31no—
342C2×C4×C9—31no—
343C2×C4×C9—121no—
344C2×C4×C9C22×D311yescharacteristic
345C2×C4×C9C22×D311yescharacteristic
346#611—22no—
347#611—62no—
348#611—62no—
349#611—62no—
350#611—121no—
351#611—121no—
352#611—122no—
353C2×Dic9—31no—
354C2×Dic9—61no—
355C2×Dic9—121no—
356C2×Dic9C22×D311yescharacteristic
357C2×Dic9C22×D311yescharacteristic
358C2×Dic9C22×D311yescharacteristic
359D36—62no—
360D36—62no—
361D36—122no—
362D36—121no—
363D36—122no—
364C4×D9—22no—
365C4×D9—62no—
366#534—271noSylow
367C2×C3×C9—41no—
368C2×C3×C9C22×D411yescharacteristic
369C2×C3×C9H(5,𝔽2)11yescharacteristic
370C2×C3×C9H(5,𝔽2)11yescharacteristic
371C3⋊D9—22no—
372C3⋊D9—41no—
373C3⋊D9—41no—
374D3×C9—22no—
375D3×C9—41no—
376C3×D9—22no—
377C23×D3—91no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—91no—
381C23×D3—91no—
382C23×D3—91no—
383C23×D3—181no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—31no—
387C2×C3×D4—91no—
388C22×C3×C4—31no—
389C22×C3×C4—91no—
390C2×#67—31no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—181no—
399C2×#67C2×D911yescharacteristic, complemented
400C2×#67C2×D911yescharacteristic, complemented
401C22×Dic3—91no—
402D3×D4—184no—
403D3×D4—184no—
404D3×D4—184no—
405C2×D12—91no—
406C2×D12—91no—
407C2×D12—91no—
408C2×D12—91no—
409C2×D12—91no—
410C2×D12—91no—
411C2×D12—91no—
412C2×D12—91no—
413C2×D12—91no—
414C2×D12—181no—
415C2×D12—181no—
416C2×D12—184no—
417C2×D12C2×D911yescharacteristic, complemented
418C2×C4×D3—31no—
419C2×C4×D3—91no—
420C2×C4×D3—91no—
421C2×C4×D3—91no—
422C2×C4×D3C2×D911yescharacteristic, complemented
423C3×C4⋊C4—31no—
424C3×C4⋊C4—91no—
425C3×C4⋊C4—91no—
426C3×C22⋊C4—21no—
427C3×C22⋊C4—31no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4C2×D911yescharacteristic, complemented
431C3×C22⋊C4D3211yescharacteristic
432#217—31no—
433#217—91no—
434#217—91no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—91no—
449(C2×D3)⋊C4—91no—
450(C2×D3)⋊C4—181no—
451(C2×D3)⋊C4—181no—
452(C2×D3)⋊C4C2×D911yescharacteristic, complemented
453C4⋊Dic3—31no—
454Dic3⋊C4—31no—
455Dic3⋊C4—91no—
456Dic3⋊C4—91no—
457Dic3⋊C4C2×D911yescharacteristic, complemented
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32C23×D311yescharacteristic
462C2×C3⋊D3—32no—
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—61no—
470C2×C3⋊D3—61no—
471C2×C3⋊D3—124no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—32no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480C2×C3×D3D3×D412yes—
481D32—124no—
482D32—124no—
483C32×C4—21no—
484C32×C4—21no—
485C3⋊Dic3—61no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—61no—
489C3×Dic3—61no—
490C3×Dic3—61no—
491C22×C9—22no—
492C22×C9—21no—
493C22×C9—21no—
494C22×C9—21no—
495C22×C9—21no—
496C22×C9—32no—
497C22×C9—41no—
498C22×C9—41no—
499C22×C9—61no—
500C22×C9—61no—
501C22×C9—61no—
502C22×C9—61no—
503C22×C9—61no—
504C22×C9C23×D311yescharacteristic
505C2×D9—21no—
506C2×D9—21no—
507C2×D9—32no—
508C2×D9—62no—
509C2×D9—61no—
510C2×D9—61no—
511C2×D9—62no—
512C2×D9—61no—
513C2×D9—61no—
514C2×D9—61no—
515C2×D9—61no—
516C2×D9—61no—
517C2×D9—61no—
518C2×D9—121no—
519C2×D9—121no—
520C2×D9—121no—
521C2×D9—121no—
522C2×D9—121no—
523C2×D9—121no—
524C2×D9—121no—
525C2×D9—124no—
526C2×D9—124no—
527C2×D9—124no—
528C2×D9—128no—
529C2×D9D3×D412yes—
530C4×C9—21no—
531C4×C9—21no—
532C4×C9—41no—
533C4×C9—41no—
534C4×C9—61no—
535C4×C9—61no—
536Dic9—21no—
537Dic9—21no—
538Dic9—21no—
539Dic9—61no—
540Dic9—121no—
541C22×D4—271no—
542C22×D4—271no—
543#123—91no—
544#123—271no—
545#123—271no—
546#123—271no—
547#121—31no—
548#121—271no—
549#121—271no—
550#121—271no—
551#120—271no—
552#120—271no—
553#120—271no—
554#120—271no—
555C2×C22⋊C4—271no—
556C3×C9#53411yescharacteristic, complemented, Sylow
557C23×C3—21no—
558C23×C3—31no—
559C23×C3—31no—
560C23×C3—91no—
561C23×C3C22×D911yescharacteristic
562C23×C3C2×D3211yescharacteristic
563C22×D3—31no—
564C22×D3—94no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—94no—
568C22×D3—91no—
569C22×D3—91no—
570C22×D3—91no—
571C22×D3—91no—
572C22×D3—181no—
573C22×D3—181no—
574C22×D3—181no—
575C22×D3—182no—
576C22×D3—182no—
577C22×D3—182no—
578C22×D3—182no—
579C22×D3—362no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—361no—
584C22×D3—361no—
585C22×D3—361no—
586C22×D3—361no—
587C22×D3—361no—
588C22×D3—361no—
589C22×D3—361no—
590C22×D3—361no—
591C22×D3—361no—
592C22×D3—362no—
593C22×D3—362no—
594C22×D3C22×D911yescharacteristic
595C22×D3C22×D911yescharacteristic
596C3×D4—62no—
597C3×D4—62no—
598C3×D4—121no—
599C3×D4—182no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—91no—
605C2×C3×C4—91no—
606C2×C3×C4—91no—
607C2×C3×C4—121no—
608C2×C3×C4—182no—
609C2×C3×C4C22×D911yescharacteristic
610C2×C3×C4C22×D911yescharacteristic
611C2×C3×C4C2×D3211yescharacteristic
612C2×C3×C4C2×D3211yescharacteristic
613#67—22no—
614#67—41no—
615#67—62no—
616#67—182no—
617#67—182no—
618#67—182no—
619#67—182no—
620#67—361no—
621#67—361no—
622#67—361no—
623#67—362no—
624C2×Dic3—31no—
625C2×Dic3—31no—
626C2×Dic3—31no—
627C2×Dic3—91no—
628C2×Dic3—91no—
629C2×Dic3—181no—
630C2×Dic3—361no—
631C2×Dic3C22×D911yescharacteristic
632C2×Dic3C22×D911yescharacteristic
633D12—22no—
634D12—182no—
635D12—182no—
636D12—182no—
637D12—182no—
638D12—182no—
639D12—182no—
640D12—362no—
641D12—361no—
642D12—361no—
643D12—362no—
644D12—361no—
645C4×D3—41no—
646C4×D3—62no—
647C4×D3—182no—
648C4×D3—182no—
649C4×D3—361no—
650C2×C32—41no—
651C2×C32C2×D3×D411yescharacteristic
652C2×C32#100411yescharacteristic
653C2×C32#100911yescharacteristic
654C3⋊D3—62no—
655C3⋊D3—121no—
656C3⋊D3—121no—
657C3×D3—22no—
658C3×D3—41no—
659C3×D3—62no—
660C2×C9—21no—
661C2×C9—21no—
662C2×C9—21no—
663C2×C9—42no—
664C2×C9—41no—
665C2×C9—62no—
666C2×C9—121no—
667C2×C9C2×D3×D411yescharacteristic
668C2×C9#100911yescharacteristic
669C2×C9#100911yescharacteristic
670D9—22no—
671D9—62no—
672D9—122no—
673D9—122no—
674D9—121no—
675D9—121no—
676D9—241no—
677C24—271no—
678C24—271no—
679C24—271no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—91no—
684C2×D4—271no—
685C2×D4—271no—
686C2×D4—271no—
687C2×D4—271no—
688C2×D4—271no—
689C2×D4—271no—
690C2×D4—271no—
691C2×D4—271no—
692C2×D4—544no—
693C2×D4—544no—
694C22×C4—31no—
695C22×C4—91no—
696C22×C4—271no—
697C22×C4—271no—
698C4⋊C4—31no—
699C4⋊C4—91no—
700C4⋊C4—91no—
701C4⋊C4—271no—
702C22⋊C4—31no—
703C22⋊C4—91no—
704C22⋊C4—91no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C22⋊C4—271no—
709C22⋊C4—271no—
710C22⋊C4—271no—
711C22⋊C4—271no—
712C22⋊C4—271no—
713C22⋊C4D3×D911yescharacteristic, complemented
714C22×C3—22no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—32no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—92no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3C23×D911yescharacteristic
734C22×C3C22×D3211yescharacteristic
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—32no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—92no—
744C2×D3—92no—
745C2×D3—182no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—182no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—181no—
757C2×D3—181no—
758C2×D3—181no—
759C2×D3—181no—
760C2×D3—181no—
761C2×D3—181no—
762C2×D3—181no—
763C2×D3—361no—
764C2×D3—361no—
765C2×D3—361no—
766C2×D3—361no—
767C2×D3—361no—
768C2×D3—361no—
769C2×D3—361no—
770C2×D3—364no—
771C2×D3—364no—
772C2×D3—364no—
773C2×D3—364no—
774C2×D3—364no—
775C2×D3—364no—
776C2×D3—368no—
777C2×D3D4×D912yes—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—181no—
787C3×C4—181no—
788C3×C4—181no—
789Dic3—21no—
790Dic3—21no—
791Dic3—61no—
792Dic3—61no—
793Dic3—61no—
794Dic3—181no—
795Dic3—181no—
796Dic3—361no—
797C32#560511yescharacteristic
798C9—21no—
799C9#565311yescharacteristic, complemented
800C23—31no—
801C23—31no—
802C23—91no—
803C23—274no—
804C23—271no—
805C23—271no—
806C23—271no—
807C23—542no—
808C23—542no—
809C23—1081no—
810C23—1081no—
811C23—1081no—
812C23—1081no—
813C23—1081no—
814C23—1081no—
815C23C2×D3×D911yescharacteristic
816D4—62no—
817D4—62no—
818D4—121no—
819D4—182no—
820D4—542no—
821D4—542no—
822D4—542no—
823D4—542no—
824D4—542no—
825D4—1081no—
826D4—1081no—
827D4—1081no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—91no—
831C2×C4—91no—
832C2×C4—91no—
833C2×C4—121no—
834C2×C4—182no—
835C2×C4—271no—
836C2×C4—542no—
837C2×C4—1081no—
838C2×C4C2×D3×D911yescharacteristic
839C2×C4C2×D3×D911yescharacteristic
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—42no—
844C2×C3—41no—
845C2×C3—41no—
846C2×C3—62no—
847C2×C3—121no—
848C2×C3—182no—
849C2×C3C2×D4×D911yescharacteristic
850C2×C3#6371011yescharacteristic
851C2×C3#6371511yescharacteristic
852C2×C3#6430811yescharacteristic
853C2×C3D32×D411yescharacteristic
854C2×C3#6431411yescharacteristic
855D3—22no—
856D3—41no—
857D3—62no—
858D3—182no—
859D3—182no—
860D3—362no—
861D3—362no—
862D3—361no—
863D3—361no—
864D3—361no—
865D3—361no—
866D3—721no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—32no—
871C22—61no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—92no—
877C22—181no—
878C22—181no—
879C22—272no—
880C22—541no—
881C22—541no—
882C22—541no—
883C22—541no—
884C22—541no—
885C22—541no—
886C22—541no—
887C22—541no—
888C22—1084no—
889C22—1084no—
890C22—1084no—
891C22C22×D3×D911yescharacteristic
892C4—21no—
893C4—21no—
894C4—61no—
895C4—61no—
896C4—181no—
897C4—181no—
898C4—181no—
899C4—541no—
900C3—21no—
901C3#1058970711yescharacteristic, complemented
902C3#1059426411yescharacteristic
903C2—41no—
904C2—62no—
905C2—121no—
906C2—182no—
907C2—542no—
908C2—1081no—
909C2—1081no—
910C2#1172247811yescharacteristic
911C2D3×D4×D911yescharacteristic
912C2#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#534
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. C2×#88668C2semidirect
2. C2×D9×D12C2semidirect
3. #11721728C2semidirect
4. C9×#884C2semidirect
5. C3×#63445C2semidirect
6. #11721292C2semidirect
7. #11721291C2semidirect
8. #11721282C2semidirect
9. #11721051C2semidirect
10. D3×(C2×D9)⋊C4C2semidirect
11. #11721038C2semidirect
12. #11721017C2semidirect
13. #11720997C2semidirect
14. #11720958C2semidirect
15. #11720938C2semidirect
18. C23×C3⋊D9C22semidirect
20. C22×D3×D9C22semidirect
21. C2×#6233C22semidirect
23. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C9×#67C22semidirect
25. C2×C9×#67C22semidirect
27. C2×C9×D12C22semidirect
28. C2×C4×D3×C9C22semidirect
29. C2×C3×C4×D9C22semidirect
32. C2×#6195C22semidirect
33. C2×#6195C22semidirect
34. C2×#6195C22semidirect
35. C2×D3×Dic9C22semidirect
37. C2×(C3⋊D9)⋊C4C22semidirect
39. C3×C9×C22⋊C4C22semidirect
40. #88536C22semidirect
41. #88536C22semidirect
42. C3×#3676C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C9×Dic3⋊C4C22semidirect
46. C3×C4⋊Dic9C22semidirect
47. C3×Dic9⋊C4C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. #88445C22semidirect
52. #88445C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. #88442C22semidirect
82. #63445D3semidirect
101. C2×D3×D9D4semidirect
189. C2×C4×D9C2×D3semidirect
193. C9×C22⋊C4C2×D3semidirect
195. #3676C2×D3semidirect
205. (C2×D9)⋊C4C2×D3semidirect
206. C4⋊Dic9C2×D3semidirect
208. Dic9⋊C4C2×D3semidirect
263. #884D9semidirect
399. C2×#67C2×D9semidirect
400. C2×#67C2×D9semidirect
417. C2×D12C2×D9semidirect
422. C2×C4×D3C2×D9semidirect
430. C3×C22⋊C4C2×D9semidirect
452. (C2×D3)⋊C4C2×D9semidirect
457. Dic3⋊C4C2×D9semidirect
556. C3×C9#534semidirect
713. C22⋊C4D3×D9semidirect
799. C9#5653semidirect
901. C3#10589707semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×D9×D122
#117217282
C9×#8842
C3×#634452
#117212922
#117212912
#117212822
#117210512
D3×(C2×D9)⋊C42
#117210382
#117210172
#117209972
#117209582
#117209382
#105942643
#105897073