Finite Group Databasebeta

← #13151092

Subgroups — #13151092

Order 1728.

886 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721837C211yesmaximal, characteristic, complemented
2C9×#939C211yesmaximal, characteristic, complemented
3C3×#63500C211yesmaximal, characteristic, complemented
4#11721291C211yesmaximal, characteristic, complemented
5#11721289C211yesmaximal, characteristic, complemented
6#11721282C211yesmaximal, characteristic, complemented
7#11721281C211yesmaximal, characteristic, complemented
8#11721278C211yesmaximal, characteristic, complemented
9#11721277C211yesmaximal, characteristic, complemented
10#11721251C211yesmaximal, characteristic, complemented
11#11721247C211yesmaximal, characteristic, complemented
12#11721033C211yesmaximal, characteristic, complemented
13#11721020C211yesmaximal, characteristic, complemented
14#11720938C211yesmaximal, characteristic, complemented
15#11720921C211yesmaximal, characteristic, complemented
16#10595264—31nomaximal
17#10589722—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic, complemented
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic, complemented
26C22×C9×Dic3C2211yescharacteristic, complemented
27C2×C3×C4×D9C2211yescharacteristic, complemented
28C2×#6195C2211yescharacteristic
29C2×#6195C2211yescharacteristic
30C2×#6194C2211yescharacteristic, complemented
31C2×D3×Dic9C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic
33C2×#6192C2211yescharacteristic
34#88551C2211yescharacteristic
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37C9×#217C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C3×#3676C2211yescharacteristic, complemented
40C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C9×Dic3⋊C4C2211yescharacteristic, complemented
42C3×C4⋊Dic9C2211yescharacteristic, complemented
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic, complemented
48Dic3⋊Dic9C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64146—31no—
54C3×#939D311yescharacteristic
55C3×#938—31no—
56#63981—31no—
57#63981—31no—
58#63979—31no—
59#63978—31no—
60#63971—31no—
61#63970—31no—
62#63966—31no—
63#63956—31no—
64#63906—31no—
65#63890—31no—
66#63850—31no—
67#63848—31no—
68C9×#121—31no—
69#63502—31no—
70#63501—31no—
71#63501—31no—
72#63500D311yescharacteristic, complemented
73#63499—31no—
74#63499—31no—
75#63499—61no—
76#63492—31no—
77#63491—31no—
78#63460—31no—
79#63456—31no—
80#63448—31no—
81#63446—31no—
82#63444—31no—
83#63441—31no—
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C22×C3⋊D9—41no—
87C22×C3⋊D9—41no—
88C22×C3⋊D9—41no—
89C22×C3⋊D9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C3×D4×C9—41no—
94C2×C3×C4×C9C2311yescharacteristic
95#6233—41no—
96#6233—41no—
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C9×#67—41no—
100C9×#67—41no—
101C3×#611—41no—
102C3×#611—41no—
103C2×C9×Dic3—41no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C3×C4×D9—41no—
111#6195—41no—
112#6195—41no—
113#6194—41no—
114D3×Dic9—41no—
115#6192—41no—
116#6192—41no—
117#5620—91no—
118#5620—91no—
119C23×C3⋊D3—31no—
120C2×C32×D4C2×D311yescharacteristic
121C2×#638—31no—
122C2×#638—31no—
123C2×C3×#67—31no—
124C2×C3×#67—31no—
125C2×C3×#67C2×D311yescharacteristic
126C2×C3×#67C2×D311yescharacteristic
127C22×C3×Dic3C2×D311yescharacteristic
128C2×C3×C4×D3—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#625—31no—
134C2×D3×Dic3—31no—
135C23×D9—31no—
136C23×D9—61no—
137#3757—31no—
138#3752—31no—
139#3752—31no—
140C3×#217—31no—
141C3×#217—31no—
142C3×#217C2×D311yescharacteristic
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×C4⋊Dic3—31no—
145C3×Dic3⋊C4C2×D311yescharacteristic
146#3724—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150#3722—31no—
151#3722—31no—
152#3722—31no—
153#3722—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C2×D4×C9—21no—
157C2×D4×C9—31no—
158C2×D4×C9—31no—
159C2×D4×C9C2×D311yescharacteristic
160C22×C4×C9—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—61no—
167C2×#611—61no—
168C2×#611C2×D311yescharacteristic
169C2×#611C2×D311yescharacteristic, complemented
170C22×Dic9—31no—
171C2×D36—31no—
172C2×D36—31no—
173C2×C4×D9C2×D311yescharacteristic, complemented
174C9×C4⋊C4—31no—
175C9×C22⋊C4—31no—
176C9×C22⋊C4—31no—
177#3676—31no—
178#3676—61no—
179#3676C2×D311yescharacteristic
180#3676C2×D311yescharacteristic, complemented
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—61no—
189(C2×D9)⋊C4—61no—
190C4⋊Dic9—31no—
191C4⋊Dic9C2×D311yescharacteristic, complemented
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195C4×Dic9—31no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9C2411yescharacteristic
203C2×C3⋊D9—21no—
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—44no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C3×C4×C9—21no—
217C3⋊Dic9—21no—
218C3⋊Dic9—21no—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#121—31no—
226C3×#121—91no—
227#940—91no—
228#940—91no—
229#939—91no—
230#939—91no—
231#939—91no—
232#939D911yescharacteristic, complemented
233#938—31no—
234#938—91no—
235#937—91no—
236#937—91no—
237#937—91no—
238#937—91no—
239#937—181no—
240#930—91no—
241#930—91no—
242#929—91no—
243#929—91no—
244#898—91no—
245#898—91no—
246#894—91no—
247#894—91no—
248#886—91no—
249#886—91no—
250#884—91no—
251#884—91no—
252#882—91no—
253#882—91no—
254#879—91no—
255#879—91no—
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3—31no—
259C22×C3⋊D3—31no—
260C22×C3⋊D3—121no—
261C22×C3⋊D3—121no—
262C22×C3⋊D3—121no—
263C22×C3×D3—31no—
264C22×C3×D3C22×D311yescharacteristic
265C32×D4—41no—
266C2×C32×C4C22×D311yescharacteristic
267#638—121no—
268#638—121no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C3×#67—41no—
272C3×#67—41no—
273C3×#67—121no—
274C3×#67—121no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—41no—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C3×C4×D3—121no—
283#626—121no—
284#626—121no—
285#626—121no—
286#626—121no—
287#625—121no—
288D3×Dic3—121no—
289C23×C9—21no—
290C23×C9—21no—
291C23×C9—31no—
292C23×C9C22×D311yescharacteristic
293C23×C9C22×D311yescharacteristic
294C22×D9—31no—
295C22×D9—31no—
296C22×D9—61no—
297C22×D9—61no—
298C22×D9—121no—
299C22×D9—121no—
300C22×D9—121no—
301C22×D9—122no—
302C22×D9—122no—
303C22×D9—122no—
304C22×D9C22×D311yescharacteristic
305D4×C9—41no—
306D4×C9—42no—
307D4×C9—121no—
308D4×C9—121no—
309C2×C4×C9—21no—
310C2×C4×C9—31no—
311C2×C4×C9—31no—
312C2×C4×C9—31no—
313C2×C4×C9—121no—
314C2×C4×C9C22×D311yescharacteristic
315#611—41no—
316#611—41no—
317#611—121no—
318#611—121no—
319#611—121no—
320#611—121no—
321#611—121no—
322#611—122no—
323#611—122no—
324C2×Dic9—31no—
325C2×Dic9—31no—
326C2×Dic9—61no—
327C2×Dic9—61no—
328C2×Dic9—121no—
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331C2×Dic9C22×D311yescharacteristic
332D36—121no—
333D36—121no—
334C4×D9—41no—
335#560—271noSylow
336C2×C3×C9—41no—
337C2×C3×C9—41no—
338C2×C3×C9H(5,𝔽2)11yescharacteristic
339C2×C3×C9H(5,𝔽2)11yescharacteristic
340C2×C3×C9H(5,𝔽2)11yescharacteristic
341C3⋊D9—41no—
342C3⋊D9—41no—
343D3×C9—41no—
344C3×D9—41no—
345C23×D3—91no—
346C23×D3—91no—
347C23×D3—181no—
348C2×C3×D4—21no—
349C2×C3×D4—31no—
350C2×C3×D4—31no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4C2×D911yescharacteristic
354C2×C3×D4D3211yescharacteristic
355C22×C3×C4—31no—
356C22×C3×C4—91no—
357C2×#67—31no—
358C2×#67—31no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—181no—
370C2×#67—181no—
371C2×#67C2×D911yescharacteristic
372C2×#67C2×D911yescharacteristic, complemented
373C22×Dic3—91no—
374C22×Dic3C2×D911yescharacteristic, complemented
375C2×D12—91no—
376C2×D12—91no—
377C2×D12—91no—
378C2×D12—91no—
379C2×C4×D3—31no—
380C2×C4×D3—91no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—91no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387#217—31no—
388#217—31no—
389#217—91no—
390#217—91no—
391#217—91no—
392#217—181no—
393#217C2×D911yescharacteristic
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—181no—
408(C2×D3)⋊C4—181no—
409(C2×D3)⋊C4C2×D911yescharacteristic, complemented
410C4⋊Dic3—31no—
411C4⋊Dic3—91no—
412C4⋊Dic3—91no—
413C4⋊Dic3—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4C2×D911yescharacteristic, complemented
420C4×Dic3—91no—
421C4×Dic3—91no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—124no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C32×C4—21no—
443C3⋊Dic3—61no—
444C3⋊Dic3—61no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—61no—
451C22×C9—22no—
452C22×C9—21no—
453C22×C9—21no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—41no—
460C22×C9—41no—
461C22×C9—41no—
462C22×C9—41no—
463C22×C9—41no—
464C22×C9—61no—
465C22×C9—61no—
466C22×C9—61no—
467C22×C9C23×D311yescharacteristic
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—21no—
471C2×D9—62no—
472C2×D9—62no—
473C2×D9—61no—
474C2×D9—61no—
475C2×D9—61no—
476C2×D9—61no—
477C2×D9—61no—
478C2×D9—61no—
479C2×D9—121no—
480C2×D9—121no—
481C2×D9—121no—
482C2×D9—121no—
483C2×D9—128no—
484C2×D9—124no—
485C4×C9—21no—
486C4×C9—41no—
487C4×C9—61no—
488C4×C9—61no—
489C4×C9—61no—
490Dic9—21no—
491Dic9—21no—
492Dic9—21no—
493Dic9—61no—
494Dic9—61no—
495Dic9—121no—
496Dic9—121no—
497#127—271no—
498#126—271no—
499#126—271no—
500#123—271no—
501#123—271no—
502#123—271no—
503#121—31no—
504#121—91no—
505#121—271no—
506#121—271no—
507#121—271no—
508#121—271no—
509#120—271no—
510#120—271no—
511#120—271no—
512C3×C9#56011yescharacteristic, complemented, Sylow
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—91no—
517C23×C3C22×D911yescharacteristic
518C23×C3C22×D911yescharacteristic
519C23×C3C2×D3211yescharacteristic
520C23×C3C2×D3211yescharacteristic
521C22×D3—31no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—91no—
526C22×D3—181no—
527C22×D3—181no—
528C22×D3—361no—
529C22×D3—361no—
530C22×D3—361no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—362no—
535C22×D3—362no—
536C22×D3—362no—
537C22×D3C22×D911yescharacteristic
538C3×D4—41no—
539C3×D4—41no—
540C3×D4—42no—
541C3×D4—121no—
542C3×D4—121no—
543C3×D4—361no—
544C3×D4—361no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—91no—
550C2×C3×C4—91no—
551C2×C3×C4—91no—
552C2×C3×C4—121no—
553C2×C3×C4—361no—
554C2×C3×C4C22×D911yescharacteristic
555C2×C3×C4C2×D3211yescharacteristic
556#67—41no—
557#67—41no—
558#67—121no—
559#67—121no—
560#67—361no—
561#67—361no—
562#67—361no—
563#67—361no—
564#67—361no—
565#67—361no—
566#67—361no—
567#67—361no—
568#67—361no—
569#67—361no—
570#67—362no—
571#67—362no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—41no—
576C2×Dic3—91no—
577C2×Dic3—91no—
578C2×Dic3—91no—
579C2×Dic3—91no—
580C2×Dic3—181no—
581C2×Dic3—181no—
582C2×Dic3—361no—
583C2×Dic3C22×D911yescharacteristic
584C2×Dic3C22×D911yescharacteristic
585C2×Dic3C22×D911yescharacteristic
586D12—361no—
587D12—361no—
588D12—361no—
589D12—361no—
590C4×D3—121no—
591C4×D3—361no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32#100411yescharacteristic
595C2×C32#100411yescharacteristic
596C2×C32#100911yescharacteristic
597C3⋊D3—121no—
598C3⋊D3—121no—
599C3×D3—41no—
600C3×D3—121no—
601C2×C9—21no—
602C2×C9—21no—
603C2×C9—21no—
604C2×C9—42no—
605C2×C9—41no—
606C2×C9—41no—
607C2×C9—81no—
608C2×C9—121no—
609C2×C9#100411yescharacteristic
610C2×C9#100411yescharacteristic
611C2×C9#100911yescharacteristic
612D9—41no—
613D9—122no—
614D9—122no—
615D9—121no—
616D9—121no—
617C24—271no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—91no—
621C2×D4—91no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4—271no—
625C2×D4—271no—
626C2×D4—271no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4D3×D911yescharacteristic
630C22×C4—31no—
631C22×C4—91no—
632C22×C4—271no—
633C4⋊C4—31no—
634C4⋊C4—91no—
635C4⋊C4—271no—
636C4⋊C4—271no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—91no—
642C22⋊C4—91no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22⋊C4—271no—
650C22⋊C4—271no—
651C42—271no—
652C22×C3—22no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3—181no—
677C22×C3C23×D911yescharacteristic
678C22×C3C22×D3211yescharacteristic
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—182no—
686C2×D3—182no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—181no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—361no—
700C2×D3—361no—
701C2×D3—361no—
702C2×D3—361no—
703C2×D3—364no—
704C2×D3—368no—
705C2×D3—364no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—41no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—181no—
713C3×C4—181no—
714C3×C4—181no—
715Dic3—21no—
716Dic3—21no—
717Dic3—21no—
718Dic3—61no—
719Dic3—61no—
720Dic3—61no—
721Dic3—181no—
722Dic3—181no—
723Dic3—181no—
724Dic3—181no—
725Dic3—361no—
726Dic3—361no—
727C32#562011yescharacteristic
728C9—21no—
729C9#562011yescharacteristic, complemented
730C23—31no—
731C23—91no—
732C23—271no—
733C23—271no—
734C23—1081no—
735C23—1081no—
736C23—1081no—
737C23C2×D3×D911yescharacteristic
738C23C2×D3×D911yescharacteristic
739D4—41no—
740D4—121no—
741D4—121no—
742D4—361no—
743D4—361no—
744D4—1081no—
745D4—1081no—
746D4—1081no—
747D4—1081no—
748D4—1081no—
749D4—1081no—
750D4—1081no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—121no—
758C2×C4—271no—
759C2×C4—271no—
760C2×C4—361no—
761C2×C4—1081no—
762C2×C4C2×D3×D911yescharacteristic
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3—41no—
768C2×C3—41no—
769C2×C3—41no—
770C2×C3—41no—
771C2×C3—81no—
772C2×C3—121no—
773C2×C3—361no—
774C2×C3#6371011yescharacteristic
775C2×C3#6371011yescharacteristic
776C2×C3#6371511yescharacteristic
777C2×C3#6431411yescharacteristic
778C2×C3#6431411yescharacteristic
779C2×C3#6433011yescharacteristic
780D3—41no—
781D3—121no—
782D3—362no—
783D3—362no—
784D3—361no—
785D3—361no—
786D3—361no—
787D3—361no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—61no—
795C22—61no—
796C22—61no—
797C22—181no—
798C22—181no—
799C22—181no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22—1084no—
807C22C22×D3×D911yescharacteristic
808C4—21no—
809C4—61no—
810C4—61no—
811C4—61no—
812C4—181no—
813C4—181no—
814C4—181no—
815C4—541no—
816C4—541no—
817C3—21no—
818C3#1058972211yescharacteristic, complemented
819C3#1059526411yescharacteristic
820C2—41no—
821C2—41no—
822C2—121no—
823C2—361no—
824C2—1081no—
825C2—1081no—
826C2#1172250011yescharacteristic
827C2#1172250111yescharacteristic
828C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#560
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11721837C2semidirect
2. C9×#939C2semidirect
3. C3×#63500C2semidirect
4. #11721291C2semidirect
5. #11721289C2semidirect
6. #11721282C2semidirect
7. #11721281C2semidirect
8. #11721278C2semidirect
9. #11721277C2semidirect
10. #11721251C2semidirect
11. #11721247C2semidirect
12. #11721033C2semidirect
13. #11721020C2semidirect
14. #11720938C2semidirect
15. #11720921C2semidirect
23. C2×C9×#67C22semidirect
25. C2×C3×#611C22semidirect
26. C22×C9×Dic3C22semidirect
27. C2×C3×C4×D9C22semidirect
30. C2×#6194C22semidirect
31. C2×D3×Dic9C22semidirect
39. C3×#3676C22semidirect
40. C9×(C2×D3)⋊C4C22semidirect
41. C9×Dic3⋊C4C22semidirect
42. C3×C4⋊Dic9C22semidirect
47. (C2×D9)⋊Dic3C22semidirect
48. Dic3⋊Dic9C22semidirect
49. #88442C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
72. #63500D3semidirect
169. C2×#611C2×D3semidirect
173. C2×C4×D9C2×D3semidirect
180. #3676C2×D3semidirect
191. C4⋊Dic9C2×D3semidirect
232. #939D9semidirect
372. C2×#67C2×D9semidirect
374. C22×Dic3C2×D9semidirect
409. (C2×D3)⋊C4C2×D9semidirect
419. Dic3⋊C4C2×D9semidirect
512. C3×C9#560semidirect
729. C9#5620semidirect
818. C3#10589722semidirect

Maximal subgroups

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

subgroupindex
#117218372
C9×#9392
C3×#635002
#117212912
#117212892
#117212822
#117212812
#117212782
#117212772
#117212512
#117212472
#117210332
#117210202
#117209382
#117209212
#105952643
#105897223