Finite Group Databasebeta

← #13148014

Subgroups — #13148014

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic, complemented
2C2×#88635C211yesmaximal, characteristic, complemented
3#11721728C211yesmaximal, characteristic, complemented
4C9×#885C211yesmaximal, characteristic, complemented
5C3×#63446C211yesmaximal, characteristic, complemented
6#11721289C211yesmaximal, characteristic, complemented
7#11721278C211yesmaximal, characteristic, complemented
8#11721256C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721049C211yesmaximal, characteristic, complemented
11#11721039C211yesmaximal, characteristic, complemented
12#11721033C211yesmaximal, characteristic, complemented
13#11721006C211yesmaximal, characteristic, complemented
14#11721003C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10594287—31nomaximal
17#10589776—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic, complemented
26C2×C3×D36C2211yescharacteristic, complemented
27C2×C3×C4×D9C2211yescharacteristic, complemented
28C2×C9×Dic6C2211yescharacteristic, complemented
29#88668—24no—
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic, complemented
32C2×#6194C2211yescharacteristic, complemented
33C2×#6192C2211yescharacteristic
34C2×#6192C2211yescharacteristic
35C2×#6192C2211yescharacteristic, complemented
36C2×#6192C2211yescharacteristic, complemented
37C2×#6192C2211yescharacteristic, complemented
38C2×(C3⋊D9)⋊C4C2211yescharacteristic
39C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
40#88635—24no—
41C3×C9×C22⋊C4C2211yescharacteristic, complemented
42#88536C2211yescharacteristic
43#88536C2211yescharacteristic, complemented
44C9×#217C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48C4×C9×Dic3C2211yescharacteristic, complemented
49C3×Dic9⋊C4C2211yescharacteristic, complemented
50#88445C2211yescharacteristic
51#88445C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×#3799—31no—
57#64091—31no—
58C3×#885D311yescharacteristic
59C3×#884—31no—
60#63981—31no—
61#63979—31no—
62#63958—31no—
63#63923—31no—
64#63922—31no—
65#63911—31no—
66#63910—31no—
67#63907—31no—
68#63906—31no—
69#63836—31no—
70C2×#3701—31no—
71C2×D4×D9—31no—
72C9×#124—31no—
73#63509—31no—
74#63502—31no—
75#63446—31no—
76#63446—31no—
77#63446—31no—
78#63446D311yescharacteristic, complemented
79#63444—31no—
80#63444—31no—
81#63444—31no—
82#63444—31no—
83#63444—61no—
84#63436—31no—
85#63434—31no—
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×C3×D9C2311yescharacteristic
95C22×C3×D9C2311yescharacteristic
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×D3×D9—41no—
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101#6233—41no—
102C2×C3⋊Dic9C2311yescharacteristic
103C4⋊(C3⋊D9)—22no—
104C4⋊(C3⋊D9)—41no—
105C9×#67—22no—
106C3×#611—22no—
107C3×#611—41no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C9×Dic3C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C3×D36—41no—
114C3×C4×D9—22no—
115C9×Dic6—22no—
116#6195—22no—
117#6195—41no—
118#6194—41no—
119#6192—22no—
120#6192—22no—
121#6192—22no—
122#6192—41no—
123#6192—41no—
124(C3⋊D9)⋊C4—22no—
125(C3⋊D9)⋊C4D414yescomplemented
126#5674—91no—
127#5607—91no—
128C23×C3⋊D3—31no—
129C22×D32—31no—
130C2×#638—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67C2×D311yescharacteristic
136C2×C3×D12—31no—
137C2×C3×C4×D3—31no—
138C2×C3×Dic6C2×D311yescharacteristic
139#3811—64no—
140C2×#626—31no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#625—31no—
148C2×#624—31no—
149C2×#624—31no—
150#3799—64no—
151C23×D9—31no—
152C23×D9—31no—
153C23×D9—61no—
154C32×C22⋊C4C2×D311yescharacteristic
155#3752—31no—
156#3752—31no—
157C3×#217C2×D311yescharacteristic
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4C2×D311yescharacteristic
160C3×(C2×D3)⋊C4C2×D311yescharacteristic
161C3×Dic3⋊C4—31no—
162C3×C4×Dic3C2×D311yescharacteristic
163Dic3⋊Dic3—31no—
164#3722—31no—
165#3722—31no—
166(C2×D3)⋊Dic3—31no—
167Dic32—31no—
168C2×Q8×C9—31no—
169C2×D4×C9—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—61no—
175C2×#611C2×D311yescharacteristic
176C2×#611C2×D311yescharacteristic, complemented
177#3701—64no—
178D4×D9—64no—
179C2×D36—31no—
180C2×D36—31no—
181C2×D36—31no—
182C2×D36—31no—
183C2×D36—31no—
184C2×D36—31no—
185C2×D36—31no—
186C2×D36—61no—
187C2×D36—61no—
188C2×D36C2×D311yescharacteristic, complemented
189C2×C4×D9—31no—
190C2×C4×D9—31no—
191C2×C4×D9C2×D311yescharacteristic, complemented
192C9×C22⋊C4—21no—
193C9×C22⋊C4—31no—
194C9×C22⋊C4—31no—
195C9×C22⋊C4—31no—
196C9×C22⋊C4C2×D311yescharacteristic, complemented
197C42×C9—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
206Dic9⋊C4—31no—
207Dic9⋊C4C2×D311yescharacteristic, complemented
208C4×Dic9—31no—
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×C3×D9—21no—
227C2×C3×D9—21no—
228C2×C3×D9—21no—
229C2×C3×D9—21no—
230C2×C3×D9—21no—
231C2×C3×D9—21no—
232D3×D9—44no—
233C3×C4×C9—21no—
234C3×C4×C9—21no—
235C3⋊Dic9—21no—
236C9×Dic3—21no—
237C9×Dic3—21no—
238C9×Dic3C2×D412yes—
239C3×Dic9—21no—
240C3×Dic9C2×D412yes—
241C2×#239—91no—
242C2×D3×D4—91no—
243C2×D3×D4—91no—
244C2×#235—91no—
245C3×#124—31no—
246C3×#121—91no—
247#947—91no—
248#940—91no—
249#940—91no—
250#940—91no—
251#938—91no—
252#937—91no—
253#937—91no—
254#930—91no—
255#895—91no—
256#892—91no—
257#885—91no—
258#885D911yescharacteristic, complemented
259#884—31no—
260#884—91no—
261#884—91no—
262#884—91no—
263#882—91no—
264#882—91no—
265#882—91no—
266#882—91no—
267#882—91no—
268#882—91no—
269#882—181no—
270#874—91no—
271#872—91no—
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—31no—
274C22×C3⋊D3—31no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—62no—
277C22×C3⋊D3—121no—
278C22×C3⋊D3—121no—
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C22×C3×D3C22×D311yescharacteristic
282C2×D32—62no—
283C2×D32—121no—
284C2×D32—121no—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287#638—121no—
288C2×C3⋊Dic3—31no—
289C4⋊(C3⋊D3)—62no—
290C4⋊(C3⋊D3)—121no—
291C3×#67—22no—
292C3×#67—62no—
293C3×#67—121no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D311yescharacteristic
299C3×D12—121no—
300C3×C4×D3—62no—
301C3×Dic6—22no—
302#626—62no—
303#626—62no—
304#626—62no—
305#626—62no—
306#626—121no—
307#626—121no—
308#626—121no—
309#625—121no—
310#624—34no—
311#624—62no—
312C23×C9—21no—
313C23×C9—31no—
314C23×C9C22×D311yescharacteristic
315C22×D9—31no—
316C22×D9—31no—
317C22×D9—31no—
318C22×D9—61no—
319C22×D9—61no—
320C22×D9—61no—
321C22×D9—62no—
322C22×D9—62no—
323C22×D9—122no—
324C22×D9—121no—
325C22×D9—121no—
326C22×D9—121no—
327C22×D9—121no—
328C22×D9—122no—
329C22×D9—122no—
330C22×D9C22×D311yescharacteristic
331C22×D9C22×D311yescharacteristic
332Q8×C9—62no—
333D4×C9—62no—
334C2×C4×C9—21no—
335C2×C4×C9—21no—
336C2×C4×C9—31no—
337C2×C4×C9—31no—
338C2×C4×C9—31no—
339C2×C4×C9C22×D311yescharacteristic
340C2×C4×C9C22×D311yescharacteristic
341#611—22no—
342#611—41no—
343#611—62no—
344#611—121no—
345#611—121no—
346#611—121no—
347#611—122no—
348C2×Dic9—31no—
349C2×Dic9—61no—
350C2×Dic9C22×D311yescharacteristic
351C2×Dic9C22×D311yescharacteristic
352D36—41no—
353D36—62no—
354D36—62no—
355D36—62no—
356D36—62no—
357D36—122no—
358D36—121no—
359D36—122no—
360D36—121no—
361D36—121no—
362C4×D9—22no—
363C4×D9—34no—
364C4×D9—62no—
365#535—271noSylow
366C2×C3×C9—41no—
367C2×C3×C9C22×D411yescharacteristic
368C2×C3×C9H(5,𝔽2)11yescharacteristic
369C2×C3×C9H(5,𝔽2)11yescharacteristic
370C3⋊D9—22no—
371C3⋊D9—41no—
372C3⋊D9—41no—
373D3×C9—41no—
374C3×D9—41no—
375C3×D9—41no—
376C23×D3—91no—
377C23×D3—91no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—181no—
381C2×C3×Q8—31no—
382C2×C3×D4—31no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C2×C3×D4—91no—
386C22×C3×C4—91no—
387C2×#67—31no—
388C2×#67—31no—
389C2×#67—91no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—91no—
399C2×#67—91no—
400C2×#67—181no—
401C2×#67C2×D911yescharacteristic
402#239—184no—
403D3×D4—184no—
404D3×D4—184no—
405#235—184no—
406C2×D12—31no—
407C2×D12—91no—
408C2×D12—91no—
409C2×D12—91no—
410C2×D12—91no—
411C2×D12—91no—
412C2×D12—91no—
413C2×D12—91no—
414C2×D12—91no—
415C2×D12—91no—
416C2×D12—91no—
417C2×D12—91no—
418C2×D12—181no—
419C2×D12—181no—
420C2×C4×D3—31no—
421C2×C4×D3—91no—
422C2×C4×D3—91no—
423C2×C4×D3—91no—
424C2×C4×D3—91no—
425C2×Dic6C2×D911yescharacteristic, complemented
426C3×C4⋊C4—91no—
427C3×C22⋊C4—21no—
428C3×C22⋊C4—31no—
429C3×C22⋊C4—31no—
430C3×C22⋊C4—31no—
431C3×C22⋊C4—91no—
432C3×C22⋊C4C2×D911yescharacteristic, complemented
433C3×C22⋊C4D3211yescharacteristic
434C3×C42—31no—
435#217—91no—
436#217C2×D911yescharacteristic, complemented
437(C2×D3)⋊C4—31no—
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—181no—
448(C2×D3)⋊C4—181no—
449(C2×D3)⋊C4C2×D911yescharacteristic, complemented
450(C2×D3)⋊C4C2×D911yescharacteristic, complemented
451C4⋊Dic3—91no—
452Dic3⋊C4—31no—
453Dic3⋊C4—91no—
454C4×Dic3—91no—
455C4×Dic3—91no—
456C4×Dic3C2×D911yescharacteristic, complemented
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32C23×D311yescharacteristic
461C2×C3⋊D3—32no—
462C2×C3⋊D3—61no—
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—124no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480D32—124no—
481C32×C4—21no—
482C32×C4—21no—
483C3⋊Dic3—61no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—32no—
487C3×Dic3—61no—
488C3×Dic3D3×D412yes—
489C22×C9—22no—
490C22×C9—21no—
491C22×C9—21no—
492C22×C9—21no—
493C22×C9—21no—
494C22×C9—41no—
495C22×C9—41no—
496C22×C9—61no—
497C22×C9—61no—
498C22×C9—61no—
499C22×C9C23×D311yescharacteristic
500C2×D9—21no—
501C2×D9—21no—
502C2×D9—21no—
503C2×D9—21no—
504C2×D9—21no—
505C2×D9—21no—
506C2×D9—32no—
507C2×D9—62no—
508C2×D9—61no—
509C2×D9—61no—
510C2×D9—62no—
511C2×D9—61no—
512C2×D9—61no—
513C2×D9—61no—
514C2×D9—61no—
515C2×D9—61no—
516C2×D9—61no—
517C2×D9—121no—
518C2×D9—121no—
519C2×D9—121no—
520C2×D9—121no—
521C2×D9—121no—
522C2×D9—121no—
523C2×D9—121no—
524C2×D9—124no—
525C2×D9—124no—
526C2×D9—128no—
527C4×C9—21no—
528C4×C9—21no—
529C4×C9—32no—
530C4×C9—41no—
531C4×C9—41no—
532C4×C9—61no—
533C4×C9—61no—
534Dic9—21no—
535Dic9—61no—
536Dic9—121no—
537Dic9D3×D412yes—
538C2×#41—271no—
539C22×D4—271no—
540#127—271no—
541#127—271no—
542#124—31no—
543#124—271no—
544#121—91no—
545#121—271no—
546#121—271no—
547#121—271no—
548#120—271no—
549#120—271no—
550#120—271no—
551#120—271no—
552#117—271no—
553C3×C9#53511yescharacteristic, complemented, Sylow
554C23×C3—21no—
555C23×C3—31no—
556C23×C3—91no—
557C23×C3—91no—
558C23×C3C22×D911yescharacteristic
559C23×C3C2×D3211yescharacteristic
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—91no—
563C22×D3—91no—
564C22×D3—91no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—91no—
568C22×D3—181no—
569C22×D3—181no—
570C22×D3—181no—
571C22×D3—182no—
572C22×D3—182no—
573C22×D3—182no—
574C22×D3—182no—
575C22×D3—362no—
576C22×D3—361no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—361no—
584C22×D3—362no—
585C22×D3—362no—
586C22×D3C22×D911yescharacteristic
587C3×Q8—62no—
588C3×D4—62no—
589C3×D4—182no—
590C3×D4—361no—
591C3×D4—361no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—91no—
598C2×C3×C4—91no—
599C2×C3×C4—182no—
600C2×C3×C4C22×D911yescharacteristic
601C2×C3×C4C22×D911yescharacteristic
602C2×C3×C4C2×D3211yescharacteristic
603C2×C3×C4C2×D3211yescharacteristic
604#67—22no—
605#67—62no—
606#67—121no—
607#67—182no—
608#67—182no—
609#67—182no—
610#67—182no—
611#67—361no—
612#67—361no—
613#67—361no—
614#67—361no—
615#67—361no—
616#67—361no—
617#67—361no—
618#67—362no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—91no—
622C2×Dic3—91no—
623C2×Dic3—181no—
624C2×Dic3C22×D911yescharacteristic
625C2×Dic3C22×D911yescharacteristic
626C2×Dic3C22×D911yescharacteristic
627D12—121no—
628D12—182no—
629D12—182no—
630D12—182no—
631D12—182no—
632D12—182no—
633D12—182no—
634D12—362no—
635D12—361no—
636D12—361no—
637D12—362no—
638D12—361no—
639D12—361no—
640D12—361no—
641C4×D3—62no—
642C4×D3—94no—
643C4×D3—94no—
644C4×D3—182no—
645C4×D3—182no—
646Dic6—22no—
647C2×C32—41no—
648C2×C32C2×D3×D411yescharacteristic
649C2×C32#100911yescharacteristic
650C2×C32#100911yescharacteristic
651C3⋊D3—62no—
652C3⋊D3—121no—
653C3⋊D3—121no—
654C3×D3—41no—
655C3×D3—121no—
656C3×D3—121no—
657C2×C9—21no—
658C2×C9—21no—
659C2×C9—21no—
660C2×C9—42no—
661C2×C9—41no—
662C2×C9—121no—
663C2×C9C2×D3×D411yescharacteristic
664C2×C9#100411yescharacteristic
665C2×C9#100911yescharacteristic
666D9—41no—
667D9—41no—
668D9—62no—
669D9—122no—
670D9—122no—
671D9—121no—
672D9—121no—
673D9—241no—
674C24—271no—
675C24—271no—
676#41—544no—
677C2×Q8—31no—
678C2×D4—31no—
679C2×D4—91no—
680C2×D4—91no—
681C2×D4—91no—
682C2×D4—271no—
683C2×D4—271no—
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—271no—
693C2×D4—544no—
694C22×C4—91no—
695C22×C4—271no—
696C22×C4—271no—
697C4⋊C4—91no—
698C4⋊C4—271no—
699C22⋊C4—31no—
700C22⋊C4—31no—
701C22⋊C4—31no—
702C22⋊C4—91no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C22⋊C4D3×D911yescharacteristic, complemented
709C42—31no—
710C42—271no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—181no—
725C22×C3—181no—
726C22×C3—181no—
727C22×C3—181no—
728C22×C3—181no—
729C22×C3—181no—
730C22×C3C23×D911yescharacteristic
731C22×C3C22×D3211yescharacteristic
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—92no—
742C2×D3—92no—
743C2×D3—182no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—182no—
749C2×D3—181no—
750C2×D3—181no—
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—361no—
762C2×D3—361no—
763C2×D3—361no—
764C2×D3—361no—
765C2×D3—361no—
766C2×D3—361no—
767C2×D3—361no—
768C2×D3—364no—
769C2×D3—364no—
770C2×D3—364no—
771C2×D3—364no—
772C2×D3—368no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—32no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—92no—
783C3×C4—181no—
784Dic3—21no—
785Dic3—21no—
786Dic3—32no—
787Dic3—61no—
788Dic3—181no—
789Dic3—181no—
790Dic3—361no—
791Dic3D4×D912yes—
792C32#567411yescharacteristic
793C9—21no—
794C9#560711yescharacteristic, complemented
795C23—31no—
796C23—91no—
797C23—91no—
798C23—271no—
799C23—271no—
800C23—271no—
801C23—542no—
802C23—542no—
803C23—1081no—
804C23—1081no—
805C23—1081no—
806C23—1081no—
807C23C2×D3×D911yescharacteristic
808Q8—62no—
809D4—62no—
810D4—182no—
811D4—361no—
812D4—361no—
813D4—542no—
814D4—542no—
815D4—542no—
816D4—542no—
817D4—542no—
818D4—1081no—
819D4—1081no—
820D4—1081no—
821D4—1081no—
822D4—1081no—
823D4—1081no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—91no—
828C2×C4—91no—
829C2×C4—182no—
830C2×C4—274no—
831C2×C4—271no—
832C2×C4—542no—
833C2×C4C2×D3×D911yescharacteristic
834C2×C4C2×D3×D911yescharacteristic
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—42no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—121no—
842C2×C3—361no—
843C2×C3—361no—
844C2×C3C2×D4×D911yescharacteristic
845C2×C3#6371511yescharacteristic
846C2×C3#6371511yescharacteristic
847C2×C3#6430811yescharacteristic
848C2×C3D32×D411yescharacteristic
849C2×C3#6431411yescharacteristic
850D3—41no—
851D3—121no—
852D3—121no—
853D3—182no—
854D3—182no—
855D3—362no—
856D3—362no—
857D3—361no—
858D3—361no—
859D3—361no—
860D3—361no—
861D3—721no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—61no—
866C22—61no—
867C22—61no—
868C22—181no—
869C22—181no—
870C22—181no—
871C22—181no—
872C22—181no—
873C22—181no—
874C22—272no—
875C22—541no—
876C22—541no—
877C22—541no—
878C22—541no—
879C22—541no—
880C22—541no—
881C22—541no—
882C22—541no—
883C22—1084no—
884C22—1084no—
885C22C22×D3×D911yescharacteristic
886C4—21no—
887C4—21no—
888C4—32no—
889C4—61no—
890C4—61no—
891C4—92no—
892C4—181no—
893C4—541no—
894C3—21no—
895C3#1058977611yescharacteristic, complemented
896C3#1059428711yescharacteristic
897C2—41no—
898C2—121no—
899C2—361no—
900C2—361no—
901C2—542no—
902C2—1081no—
903C2—1081no—
904C2#1172247811yescharacteristic
905C2D3×D4×D911yescharacteristic
906C2#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#535
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×#88635C2semidirect
3. #11721728C2semidirect
4. C9×#885C2semidirect
5. C3×#63446C2semidirect
6. #11721289C2semidirect
7. #11721278C2semidirect
8. #11721256C2semidirect
9. #11721051C2semidirect
10. #11721049C2semidirect
11. #11721039C2semidirect
12. #11721033C2semidirect
13. #11721006C2semidirect
14. #11721003C2semidirect
15. #11720898C2semidirect
20. C2×#6233C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
25. C2×C3×#611C22semidirect
26. C2×C3×D36C22semidirect
27. C2×C3×C4×D9C22semidirect
28. C2×C9×Dic6C22semidirect
31. C2×#6195C22semidirect
32. C2×#6194C22semidirect
35. C2×#6192C22semidirect
36. C2×#6192C22semidirect
37. C2×#6192C22semidirect
39. C2×(C3⋊D9)⋊C4C22semidirect
41. C3×C9×C22⋊C4C22semidirect
43. #88536C22semidirect
44. C9×#217C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C9×(C2×D3)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. C4×C9×Dic3C22semidirect
49. C3×Dic9⋊C4C22semidirect
51. #88445C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
78. #63446D3semidirect
125. (C3⋊D9)⋊C4D4semidirect
176. C2×#611C2×D3semidirect
188. C2×D36C2×D3semidirect
191. C2×C4×D9C2×D3semidirect
196. C9×C22⋊C4C2×D3semidirect
205. (C2×D9)⋊C4C2×D3semidirect
207. Dic9⋊C4C2×D3semidirect
258. #885D9semidirect
425. C2×Dic6C2×D9semidirect
432. C3×C22⋊C4C2×D9semidirect
436. #217C2×D9semidirect
449. (C2×D3)⋊C4C2×D9semidirect
450. (C2×D3)⋊C4C2×D9semidirect
456. C4×Dic3C2×D9semidirect
553. C3×C9#535semidirect
708. C22⋊C4D3×D9semidirect
794. C9#5607semidirect
895. C3#10589776semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#886352
#117217282
C9×#8852
C3×#634462
#117212892
#117212782
#117212562
#117210512
#117210492
#117210392
#117210332
#117210062
#117210032
#117208982
#105942873
#105897763