Finite Group Databasebeta

← #13148015

Subgroups — #13148015

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×#88642C211yesmaximal, characteristic, complemented
3#11721728C211yesmaximal, characteristic, complemented
4C9×#884C211yesmaximal, characteristic, complemented
5C3×#63447C211yesmaximal, characteristic, complemented
6#11721291C211yesmaximal, characteristic, complemented
7#11721289C211yesmaximal, characteristic, complemented
8#11721262C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721050C211yesmaximal, characteristic, complemented
11#11721040C211yesmaximal, characteristic, complemented
12#11721035C211yesmaximal, characteristic, complemented
13#11721034C211yesmaximal, characteristic, complemented
14#11721005C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10594287—31nomaximal
17#10589709—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×C9×#67C2211yescharacteristic, complemented
25C2×C3×#611C2211yescharacteristic
26C2×C9×D12C2211yescharacteristic, complemented
27C2×C4×D3×C9C2211yescharacteristic, complemented
28C2×C3×Dic18C2211yescharacteristic, complemented
29#88668—24no—
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic
32C2×#6195C2211yescharacteristic, complemented
33C2×#6195C2211yescharacteristic, complemented
34C2×#6195C2211yescharacteristic, complemented
35C2×#6194C2211yescharacteristic, complemented
36C2×#6192C2211yescharacteristic
37C2×#6192C2211yescharacteristic, complemented
38C2×(C3⋊D9)⋊C4C2211yescharacteristic
39C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
40#88642—24no—
41C3×C9×C22⋊C4C2211yescharacteristic, complemented
42#88536C2211yescharacteristic
43#88536C2211yescharacteristic, complemented
44C3×#3676C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48C9×Dic3⋊C4C2211yescharacteristic, complemented
49C3×C4×Dic9C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51#88445C2211yescharacteristic
52#88445C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×#3799—31no—
57#64091—31no—
58C3×#885—31no—
59C3×#884D311yescharacteristic
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×D4×D9—31no—
71C2×#3697—31no—
72C9×#121—31no—
73#63502—31no—
74#63502—31no—
75#63500—31no—
76#63499—31no—
77#63499—31no—
78#63492—31no—
79#63457—31no—
80#63454—31no—
81#63447—31no—
82#63447D311yescharacteristic, 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×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101#6233—41no—
102C2×C3⋊Dic9C2311yescharacteristic
103C4⋊(C3⋊D9)—22no—
104C4⋊(C3⋊D9)—41no—
105C9×#67—22no—
106C9×#67—41no—
107C3×#611—22no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C9×D12—41no—
114C4×D3×C9—22no—
115C3×Dic18—22no—
116#6195—22no—
117#6195—22no—
118#6195—22no—
119#6195—41no—
120#6195—41no—
121#6194—41no—
122#6192—22no—
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×#67C2×D311yescharacteristic
135C2×C3×#67C2×D311yescharacteristic
136C2×C3×D12C2×D311yescharacteristic
137C2×C3×C4×D3C2×D311yescharacteristic
138C2×C3×Dic6—31no—
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×#217—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4C2×D311yescharacteristic
161C3×Dic3⋊C4C2×D311yescharacteristic
162C3×C4×Dic3—31no—
163Dic3⋊Dic3—31no—
164#3722—31no—
165#3722—31no—
166(C2×D3)⋊Dic3—31no—
167Dic32—31no—
168C2×D4×C9—31no—
169C2×D4×C9—31no—
170C2×D4×C9—31no—
171C22×C4×C9—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—31no—
178C2×#611—31no—
179C2×#611—61no—
180C2×#611C2×D311yescharacteristic
181D4×D9—64no—
182#3697—64no—
183C2×D36—31no—
184C2×D36—31no—
185C2×D36—31no—
186C2×D36—31no—
187C2×D36—61no—
188C2×D36—61no—
189C2×C4×D9—31no—
190C2×C4×D9—31no—
191C2×Dic18C2×D311yescharacteristic, complemented
192C9×C4⋊C4—31no—
193C9×C22⋊C4—21no—
194C9×C22⋊C4—31no—
195C9×C22⋊C4C2×D311yescharacteristic, complemented
196#3676—31no—
197#3676C2×D311yescharacteristic, complemented
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—61no—
203(C2×D9)⋊C4—61no—
204(C2×D9)⋊C4C2×D311yescharacteristic, complemented
205(C2×D9)⋊C4C2×D311yescharacteristic, complemented
206C4⋊Dic9—31no—
207C4×Dic9—31no—
208C4×Dic9C2×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×C9—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×Dic3C2×D412yes—
238C3×Dic9—21no—
239C3×Dic9—21no—
240C3×Dic9C2×D412yes—
241C2×#239—91no—
242C2×D3×D4—91no—
243C2×D3×D4—91no—
244C2×#235—91no—
245C3×#124—91no—
246C3×#121—31no—
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—31no—
258#885—91no—
259#884—91no—
260#884—91no—
261#884—91no—
262#884D911yescharacteristic, complemented
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×D3C22×D311yescharacteristic
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—41no—
293C3×#67—62no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D311yescharacteristic
299C3×D12—41no—
300C3×C4×D3—22no—
301C3×Dic6—62no—
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×C9—31no—
315C23×C9C22×D311yescharacteristic
316C22×D9—31no—
317C22×D9—31no—
318C22×D9—31no—
319C22×D9—61no—
320C22×D9—61no—
321C22×D9—61no—
322C22×D9—62no—
323C22×D9—62no—
324C22×D9—122no—
325C22×D9—121no—
326C22×D9—121no—
327C22×D9—121no—
328C22×D9—121no—
329C22×D9—122no—
330C22×D9—122no—
331C22×D9C22×D311yescharacteristic
332D4×C9—62no—
333D4×C9—121no—
334D4×C9—121no—
335C2×C4×C9—21no—
336C2×C4×C9—21no—
337C2×C4×C9—31no—
338C2×C4×C9—31no—
339C2×C4×C9—62no—
340C2×C4×C9C22×D311yescharacteristic
341C2×C4×C9C22×D311yescharacteristic
342#611—22no—
343#611—62no—
344#611—62no—
345#611—62no—
346#611—121no—
347#611—121no—
348#611—121no—
349#611—121no—
350#611—122no—
351C2×Dic9—31no—
352C2×Dic9—61no—
353C2×Dic9C22×D311yescharacteristic
354C2×Dic9C22×D311yescharacteristic
355C2×Dic9C22×D311yescharacteristic
356D36—62no—
357D36—62no—
358D36—122no—
359D36—121no—
360D36—122no—
361D36—121no—
362C4×D9—34no—
363C4×D9—62no—
364Dic18—22no—
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—
374D3×C9—41no—
375C3×D9—41no—
376C23×D3—91no—
377C23×D3—91no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—181no—
381C2×C3×Q8—91no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—91no—
386C22×C3×C4—31no—
387C2×#67—31no—
388C2×#67—91no—
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—181no—
400C2×#67C2×D911yescharacteristic
401C2×#67C2×D911yescharacteristic, complemented
402#239—184no—
403D3×D4—184no—
404D3×D4—184no—
405#235—184no—
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—91no—
415C2×D12—91no—
416C2×D12—91no—
417C2×D12—181no—
418C2×D12—181no—
419C2×D12C2×D911yescharacteristic, complemented
420C2×C4×D3—91no—
421C2×C4×D3—91no—
422C2×C4×D3—91no—
423C2×C4×D3—91no—
424C2×C4×D3C2×D911yescharacteristic, complemented
425C2×Dic6—31no—
426C3×C4⋊C4—31no—
427C3×C22⋊C4—21no—
428C3×C22⋊C4—31no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4—91no—
432C3×C22⋊C4C2×D911yescharacteristic, complemented
433C3×C22⋊C4D3211yescharacteristic
434C3×C42—91no—
435#217—31no—
436#217—91no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—31no—
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—181no—
449(C2×D3)⋊C4—181no—
450(C2×D3)⋊C4C2×D911yescharacteristic, complemented
451C4⋊Dic3—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4C2×D911yescharacteristic, complemented
454C4×Dic3—31no—
455C4×Dic3—91no—
456C4×Dic3—91no—
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—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
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—32no—
486C3×Dic3—61no—
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×C9—61no—
500C22×C9—61no—
501C22×C9—61no—
502C22×C9C23×D311yescharacteristic
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—
533Dic9—21no—
534Dic9—21no—
535Dic9—61no—
536Dic9—121no—
537Dic9D3×D412yes—
538C2×#41—271no—
539C22×D4—271no—
540#127—271no—
541#127—271no—
542#124—91no—
543#124—271no—
544#121—31no—
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—31no—
557C23×C3—91no—
558C23×C3C22×D911yescharacteristic
559C23×C3C2×D3211yescharacteristic
560C22×D3—31no—
561C22×D3—91no—
562C22×D3—91no—
563C22×D3—91no—
564C22×D3—91no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—181no—
568C22×D3—181no—
569C22×D3—181no—
570C22×D3—182no—
571C22×D3—182no—
572C22×D3—182no—
573C22×D3—182no—
574C22×D3—362no—
575C22×D3—361no—
576C22×D3—361no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—362no—
584C22×D3—362no—
585C22×D3C22×D911yescharacteristic
586C22×D3C22×D911yescharacteristic
587C3×Q8—182no—
588C3×D4—62no—
589C3×D4—121no—
590C3×D4—121no—
591C3×D4—182no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—62no—
597C2×C3×C4—91no—
598C2×C3×C4—91no—
599C2×C3×C4—91no—
600C2×C3×C4C22×D911yescharacteristic
601C2×C3×C4C22×D911yescharacteristic
602C2×C3×C4C2×D3211yescharacteristic
603C2×C3×C4C2×D3211yescharacteristic
604#67—22no—
605#67—41no—
606#67—62no—
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—31no—
622C2×Dic3—91no—
623C2×Dic3—91no—
624C2×Dic3—181no—
625C2×Dic3C22×D911yescharacteristic
626C2×Dic3C22×D911yescharacteristic
627D12—41no—
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—22no—
642C4×D3—94no—
643C4×D3—94no—
644C4×D3—182no—
645C4×D3—182no—
646Dic6—62no—
647C2×C32—41no—
648C2×C32C2×D3×D411yescharacteristic
649C2×C32#100411yescharacteristic
650C2×C32#100911yescharacteristic
651C3⋊D3—62no—
652C3⋊D3—121no—
653C3⋊D3—121no—
654C3×D3—41no—
655C3×D3—41no—
656C3×D3—121no—
657C2×C9—21no—
658C2×C9—21no—
659C2×C9—21no—
660C2×C9—42no—
661C2×C9—41no—
662C2×C9—121no—
663C2×C9—121no—
664C2×C9C2×D3×D411yescharacteristic
665C2×C9#100911yescharacteristic
666C2×C9#100911yescharacteristic
667D9—41no—
668D9—62no—
669D9—122no—
670D9—122no—
671D9—121no—
672D9—121no—
673D9—241no—
674C24—271no—
675C24—271no—
676#41—544no—
677C2×Q8—91no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
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—31no—
695C22×C4—271no—
696C22×C4—271no—
697C4⋊C4—31no—
698C4⋊C4—271no—
699C22⋊C4—31no—
700C22⋊C4—91no—
701C22⋊C4—91no—
702C22⋊C4—91no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C22⋊C4D3×D911yescharacteristic, complemented
709C42—91no—
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—61no—
725C22×C3—61no—
726C22×C3—61no—
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—21no—
736C2×D3—21no—
737C2×D3—21no—
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—92no—
782C3×C4—181no—
783C3×C4—181no—
784Dic3—21no—
785Dic3—32no—
786Dic3—61no—
787Dic3—61no—
788Dic3—181no—
789Dic3—181no—
790Dic3—361no—
791Dic3D4×D912yes—
792C32#560711yescharacteristic
793C9—21no—
794C9#567411yescharacteristic, complemented
795C23—31no—
796C23—31no—
797C23—91no—
798C23—271no—
799C23—271no—
800C23—271no—
801C23—542no—
802C23—542no—
803C23—1081no—
804C23—1081no—
805C23—1081no—
806C23—1081no—
807C23C2×D3×D911yescharacteristic
808Q8—182no—
809D4—62no—
810D4—121no—
811D4—121no—
812D4—182no—
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—62no—
827C2×C4—91no—
828C2×C4—91no—
829C2×C4—91no—
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—121no—
843C2×C3—361no—
844C2×C3C2×D4×D911yescharacteristic
845C2×C3#6371011yescharacteristic
846C2×C3#6371511yescharacteristic
847C2×C3#6430811yescharacteristic
848C2×C3D32×D411yescharacteristic
849C2×C3#6431411yescharacteristic
850D3—41no—
851D3—41no—
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—61no—
869C22—61no—
870C22—61no—
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—92no—
891C4—181no—
892C4—181no—
893C4—541no—
894C3—21no—
895C3#1058970911yescharacteristic, complemented
896C3#1059428711yescharacteristic
897C2—41no—
898C2—121no—
899C2—121no—
900C2—361no—
901C2—542no—
902C2—1081no—
903C2—1081no—
904C2#1172247811yescharacteristic
905C2D3×D4×D911yescharacteristic
906C2#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#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×#88642C2semidirect
3. #11721728C2semidirect
4. C9×#884C2semidirect
5. C3×#63447C2semidirect
6. #11721291C2semidirect
7. #11721289C2semidirect
8. #11721262C2semidirect
9. #11721051C2semidirect
10. #11721050C2semidirect
11. #11721040C2semidirect
12. #11721035C2semidirect
13. #11721034C2semidirect
14. #11721005C2semidirect
15. #11720899C2semidirect
20. C2×#6233C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C9×#67C22semidirect
26. C2×C9×D12C22semidirect
27. C2×C4×D3×C9C22semidirect
28. C2×C3×Dic18C22semidirect
32. C2×#6195C22semidirect
33. C2×#6195C22semidirect
34. C2×#6195C22semidirect
35. C2×#6194C22semidirect
37. C2×#6192C22semidirect
39. C2×(C3⋊D9)⋊C4C22semidirect
41. C3×C9×C22⋊C4C22semidirect
43. #88536C22semidirect
44. C3×#3676C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. C9×Dic3⋊C4C22semidirect
49. C3×C4×Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
52. #88445C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic3×Dic9C22semidirect
82. #63447D3semidirect
125. (C3⋊D9)⋊C4D4semidirect
191. C2×Dic18C2×D3semidirect
195. C9×C22⋊C4C2×D3semidirect
197. #3676C2×D3semidirect
204. (C2×D9)⋊C4C2×D3semidirect
205. (C2×D9)⋊C4C2×D3semidirect
208. C4×Dic9C2×D3semidirect
262. #884D9semidirect
401. C2×#67C2×D9semidirect
419. C2×D12C2×D9semidirect
424. C2×C4×D3C2×D9semidirect
432. C3×C22⋊C4C2×D9semidirect
450. (C2×D3)⋊C4C2×D9semidirect
453. Dic3⋊C4C2×D9semidirect
553. C3×C9#535semidirect
708. C22⋊C4D3×D9semidirect
794. C9#5674semidirect
895. C3#10589709semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#886422
#117217282
C9×#8842
C3×#634472
#117212912
#117212892
#117212622
#117210512
#117210502
#117210402
#117210352
#117210342
#117210052
#117208992
#105942873
#105897093