Finite Group Databasebeta

← #13151298

Subgroups — #13151298

Order 1728.

850 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721839C211yesmaximal, characteristic, complemented
2C9×#939C211yesmaximal, characteristic, complemented
3C3×#63502C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7#11721277C211yesmaximal, characteristic, complemented
8#11721271C211yesmaximal, characteristic, complemented
9#11721270C211yesmaximal, characteristic, complemented
10#11721260C211yesmaximal, characteristic, complemented
11#11721259C211yesmaximal, characteristic, complemented
12#11721049C211yesmaximal, characteristic, complemented
13#11720981C211yesmaximal, characteristic, complemented
14#11720963C211yesmaximal, characteristic, complemented
15#11720934C211yesmaximal, characteristic, complemented
16#10595313—31nomaximal
17#10589722—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C22×C3⋊Dic9C2211yescharacteristic, complemented
23C2×C9×#67C2211yescharacteristic
24C2×C9×#67C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic, complemented
29C22×C9×Dic3C2211yescharacteristic, complemented
30C2×C3×D36C2211yescharacteristic
31C2×#6194C2211yescharacteristic
32C2×#6192C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic, complemented
34#88551C2211yescharacteristic, complemented
35#88536C2211yescharacteristic
36#88534C2211yescharacteristic, complemented
37C9×#217C2211yescharacteristic, complemented
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C3×C4×Dic9C2211yescharacteristic, complemented
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53#64148—31no—
54C3×#940—31no—
55C3×#939D311yescharacteristic
56#63983—31no—
57#63983—31no—
58#63980—31no—
59#63978—31no—
60#63971—31no—
61#63970—31no—
62#63962—31no—
63#63961—31no—
64#63922—31no—
65#63884—31no—
66#63868—31no—
67#63859—31no—
68C9×#121—31no—
69#63502D311yescharacteristic, complemented
70#63501—31no—
71#63501—31no—
72#63501—61no—
73#63500—31no—
74#63499—31no—
75#63499—31no—
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⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C2×D3×D9—41no—
93C3×D4×C9—41no—
94C2×C3×C4×C9C2311yescharacteristic
95#6233—41no—
96#6233—41no—
97C2×C3⋊Dic9—41no—
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C9×#67—41no—
102C9×#67—41no—
103C3×#611—41no—
104C3×#611—41no—
105C3×#611—41no—
106C3×#611—41no—
107C2×C9×Dic3—41no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C9×Dic3C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C3×D36—41no—
114#6194—41no—
115#6192—41no—
116Dic3×D9—41no—
117#5720—91no—
118#5620—91no—
119C22×D32—31no—
120C2×C32×D4C2×D311yescharacteristic
121C2×#638—31no—
122C2×#638—31no—
123C22×C3⋊Dic3—31no—
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67C2×D311yescharacteristic
129C2×C3×#67C2×D311yescharacteristic
130C22×C3×Dic3C2×D311yescharacteristic
131C2×C3×D12—31no—
132C2×#626—31no—
133C2×#625—31no—
134C2×D3×Dic3—31no—
135C23×D9—31no—
136#3757—31no—
137#3752—31no—
138#3750—31no—
139C3×#217C2×D311yescharacteristic
140C3×(C2×D3)⋊C4C2×D311yescharacteristic
141C3×Dic3⋊C4C2×D311yescharacteristic
142C3×C4×Dic3—31no—
143#3724—31no—
144#3724—31no—
145Dic3⋊Dic3—31no—
146Dic3⋊Dic3—31no—
147#3722—31no—
148#3722—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155C2×D4×C9—21no—
156C2×D4×C9—31no—
157C2×D4×C9—31no—
158C2×D4×C9C2×D311yescharacteristic, complemented
159C22×C4×C9—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—61no—
164C2×#611—61no—
165C2×#611C2×D311yescharacteristic
166C2×#611C2×D311yescharacteristic
167C2×#611C2×D311yescharacteristic, complemented
168C2×#611C2×D311yescharacteristic, complemented
169C22×Dic9—31no—
170C22×Dic9—61no—
171C2×D36—31no—
172C2×D36C2×D311yescharacteristic
173C2×C4×D9—31no—
174C9×C4⋊C4—31no—
175C9×C22⋊C4—31no—
176C9×C22⋊C4—31no—
177#3676—31no—
178#3676—31no—
179#3676—31no—
180#3676—61no—
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—
189C4⋊Dic9—31no—
190C4⋊Dic9—31no—
191Dic9⋊C4—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—61no—
195C4×Dic9C2×D311yescharacteristic, complemented
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×D3×C9—21no—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×C3×D9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215D3×D9—44no—
216C3×C4×C9—21no—
217C3⋊Dic9—21no—
218C3⋊Dic9—21no—
219C3⋊Dic9—21no—
220C9×Dic3—21no—
221C9×Dic3—21no—
222C9×Dic3—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#127—91no—
226C3×#121—31no—
227#940—31no—
228#939—91no—
229#939—91no—
230#939—91no—
231#939—91no—
232#939—91no—
233#939—91no—
234#939—91no—
235#939—181no—
236#939D911yescharacteristic, complemented
237#938—91no—
238#937—91no—
239#937—91no—
240#937—91no—
241#937—91no—
242#937—91no—
243#935—91no—
244#935—91no—
245#935—91no—
246#930—91no—
247#929—91no—
248#898—91no—
249#894—91no—
250#886—91no—
251#884—91no—
252#882—91no—
253#879—91no—
254#876—91no—
255#876—91no—
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3—31no—
259C22×C3×D3—31no—
260C22×C3×D3—31no—
261C22×C3×D3C22×D311yescharacteristic
262C2×D32—121no—
263C2×D32—121no—
264C2×D32—121no—
265C32×D4—41no—
266C2×C32×C4C22×D311yescharacteristic
267#638—121no—
268#638—121no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—121no—
273C3×#67—41no—
274C3×#67—41no—
275C3×#67—121no—
276C3×#67—121no—
277C3×#67—121no—
278C3×#67—121no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—41no—
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C3×D12—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—61no—
296C22×D9—121no—
297C22×D9—121no—
298C22×D9—121no—
299C22×D9C22×D311yescharacteristic
300C22×D9C22×D311yescharacteristic
301D4×C9—41no—
302D4×C9—42no—
303D4×C9—121no—
304D4×C9—121no—
305C2×C4×C9—21no—
306C2×C4×C9—31no—
307C2×C4×C9—31no—
308C2×C4×C9—31no—
309C2×C4×C9—121no—
310C2×C4×C9C22×D311yescharacteristic
311#611—41no—
312#611—41no—
313#611—41no—
314#611—41no—
315#611—121no—
316#611—121no—
317#611—121no—
318#611—122no—
319#611—122no—
320C2×Dic9—31no—
321C2×Dic9—31no—
322C2×Dic9—31no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9—61no—
326C2×Dic9—121no—
327C2×Dic9—122no—
328C2×Dic9C22×D311yescharacteristic
329C2×Dic9C22×D311yescharacteristic
330D36—41no—
331D36—121no—
332C4×D9—121no—
333#560—271noSylow
334C2×C3×C9—41no—
335C2×C3×C9—41no—
336C2×C3×C9H(5,𝔽2)11yescharacteristic
337C2×C3×C9H(5,𝔽2)11yescharacteristic
338C2×C3×C9H(5,𝔽2)11yescharacteristic
339C3⋊D9—41no—
340D3×C9—41no—
341C3×D9—41no—
342C3×D9—41no—
343C23×D3—91no—
344C23×D3—91no—
345C2×C3×D4—21no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—91no—
349C2×C3×D4—91no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4C2×D911yescharacteristic, complemented
354C2×C3×D4D3211yescharacteristic
355C22×C3×C4—31no—
356C2×#67—31no—
357C2×#67—31no—
358C2×#67—31no—
359C2×#67—31no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—181no—
368C2×#67—181no—
369C2×#67C2×D911yescharacteristic
370C2×#67C2×D911yescharacteristic
371C22×Dic3—91no—
372C22×Dic3—91no—
373C22×Dic3—91no—
374C22×Dic3—181no—
375C22×Dic3C2×D911yescharacteristic, complemented
376C2×D12—31no—
377C2×D12—91no—
378C2×C4×D3—91no—
379C3×C4⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C42—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—91no—
387#217—91no—
388#217—91no—
389#217—91no—
390#217—91no—
391#217—181no—
392#217C2×D911yescharacteristic, complemented
393(C2×D3)⋊C4—91no—
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—181no—
406(C2×D3)⋊C4C2×D911yescharacteristic
407C4⋊Dic3—91no—
408C4⋊Dic3—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—181no—
418Dic3⋊C4C2×D911yescharacteristic, complemented
419C4×Dic3—31no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32C23×D311yescharacteristic
427C2×C3⋊D3—61no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—61no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439D32—124no—
440C32×C4—21no—
441C3⋊Dic3—61no—
442C3⋊Dic3—61no—
443C3⋊Dic3—61no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C22×C9—22no—
450C22×C9—21no—
451C22×C9—21no—
452C22×C9—21no—
453C22×C9—21no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—41no—
458C22×C9—41no—
459C22×C9—41no—
460C22×C9—41no—
461C22×C9—41no—
462C22×C9—61no—
463C22×C9—61no—
464C22×C9—61no—
465C22×C9C23×D311yescharacteristic
466C2×D9—21no—
467C2×D9—21no—
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—21no—
471C2×D9—21no—
472C2×D9—61no—
473C2×D9—61no—
474C2×D9—61no—
475C2×D9—121no—
476C2×D9—121no—
477C2×D9—121no—
478C2×D9—124no—
479C4×C9—21no—
480C4×C9—41no—
481C4×C9—61no—
482C4×C9—61no—
483C4×C9—61no—
484Dic9—21no—
485Dic9—21no—
486Dic9—62no—
487Dic9—61no—
488Dic9—61no—
489Dic9—61no—
490Dic9—121no—
491Dic9—121no—
492#127—91no—
493#126—271no—
494#126—271no—
495#123—271no—
496#123—271no—
497#123—271no—
498#121—31no—
499#121—271no—
500#121—271no—
501#121—271no—
502#121—271no—
503#121—271no—
504#120—271no—
505#120—271no—
506#120—271no—
507C3×C9#56011yescharacteristic, complemented, Sylow
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—31no—
511C23×C3—91no—
512C23×C3—91no—
513C23×C3C22×D911yescharacteristic
514C23×C3C22×D911yescharacteristic
515C23×C3C2×D3211yescharacteristic
516C23×C3C2×D3211yescharacteristic
517C22×D3—31no—
518C22×D3—31no—
519C22×D3—91no—
520C22×D3—91no—
521C22×D3—181no—
522C22×D3—361no—
523C22×D3—361no—
524C22×D3—361no—
525C22×D3—361no—
526C22×D3—361no—
527C22×D3—361no—
528C22×D3C22×D911yescharacteristic
529C3×D4—41no—
530C3×D4—41no—
531C3×D4—42no—
532C3×D4—121no—
533C3×D4—121no—
534C3×D4—361no—
535C3×D4—361no—
536C3×D4—361no—
537C3×D4—361no—
538C3×D4—361no—
539C2×C3×C4—21no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—91no—
544C2×C3×C4—91no—
545C2×C3×C4—121no—
546C2×C3×C4C22×D911yescharacteristic
547C2×C3×C4C2×D3211yescharacteristic
548#67—41no—
549#67—41no—
550#67—121no—
551#67—121no—
552#67—121no—
553#67—121no—
554#67—361no—
555#67—361no—
556#67—361no—
557#67—361no—
558#67—361no—
559#67—361no—
560#67—361no—
561#67—362no—
562#67—362no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—41no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—91no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—181no—
573C2×Dic3—181no—
574C2×Dic3—181no—
575C2×Dic3—361no—
576C2×Dic3—361no—
577C2×Dic3—361no—
578C2×Dic3—362no—
579C2×Dic3C22×D911yescharacteristic
580C2×Dic3C22×D911yescharacteristic
581C2×Dic3C22×D911yescharacteristic
582D12—121no—
583D12—361no—
584C4×D3—361no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32#100411yescharacteristic
588C2×C32#100411yescharacteristic
589C2×C32#100911yescharacteristic
590C3⋊D3—121no—
591C3×D3—41no—
592C3×D3—121no—
593C3×D3—121no—
594C2×C9—21no—
595C2×C9—21no—
596C2×C9—21no—
597C2×C9—42no—
598C2×C9—41no—
599C2×C9—41no—
600C2×C9—81no—
601C2×C9—121no—
602C2×C9#100411yescharacteristic
603C2×C9#100411yescharacteristic
604C2×C9#100411yescharacteristic
605D9—41no—
606D9—41no—
607D9—121no—
608D9—241no—
609C24—271no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—91no—
613C2×D4—91no—
614C2×D4—91no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C2×D4—271no—
621C2×D4D3×D911yescharacteristic, complemented
622C22×C4—31no—
623C22×C4—271no—
624C22×C4—271no—
625C4⋊C4—31no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C4⋊C4—271no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C42—91no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3—181no—
669C22×C3—181no—
670C22×C3—181no—
671C22×C3—181no—
672C22×C3C23×D911yescharacteristic
673C22×C3C22×D3211yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—361no—
690C2×D3—361no—
691C2×D3—361no—
692C2×D3—364no—
693C2×D3—364no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—41no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—181no—
701C3×C4—181no—
702Dic3—21no—
703Dic3—21no—
704Dic3—21no—
705Dic3—61no—
706Dic3—61no—
707Dic3—182no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—181no—
712Dic3—181no—
713Dic3—181no—
714Dic3—361no—
715Dic3—361no—
716C32#562011yescharacteristic
717C9—21no—
718C9#572011yescharacteristic, complemented
719C23—31no—
720C23—91no—
721C23—91no—
722C23—271no—
723C23—1081no—
724C23—1081no—
725C23—1081no—
726C23C2×D3×D911yescharacteristic
727C23C2×D3×D911yescharacteristic
728D4—41no—
729D4—121no—
730D4—121no—
731D4—361no—
732D4—361no—
733D4—361no—
734D4—361no—
735D4—361no—
736D4—1081no—
737D4—1081no—
738D4—1081no—
739D4—1081no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—121no—
746C2×C4—271no—
747C2×C4—271no—
748C2×C4—271no—
749C2×C4—1081no—
750C2×C4—1081no—
751C2×C4C2×D3×D911yescharacteristic
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—42no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—81no—
761C2×C3—121no—
762C2×C3—361no—
763C2×C3—361no—
764C2×C3#6371011yescharacteristic
765C2×C3#6371011yescharacteristic
766C2×C3#6371511yescharacteristic
767C2×C3#6431311yescharacteristic
768C2×C3#6431411yescharacteristic
769C2×C3#6433011yescharacteristic
770D3—41no—
771D3—121no—
772D3—121no—
773D3—361no—
774D3—361no—
775D3—721no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—181no—
786C22—181no—
787C22—181no—
788C22—181no—
789C22—181no—
790C22—181no—
791C22—541no—
792C22—541no—
793C22—541no—
794C22—1084no—
795C22C22×D3×D911yescharacteristic
796C4—21no—
797C4—61no—
798C4—61no—
799C4—61no—
800C4—181no—
801C4—181no—
802C4—541no—
803C4—541no—
804C4—541no—
805C3—21no—
806C3#1058972211yescharacteristic, complemented
807C3#1059531311yescharacteristic
808C2—41no—
809C2—41no—
810C2—121no—
811C2—361no—
812C2—361no—
813C2—1081no—
814C2#1172249911yescharacteristic
815C2#1172250111yescharacteristic
816C2#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. #11721839C2semidirect
2. C9×#939C2semidirect
3. C3×#63502C2semidirect
4. #11721292C2semidirect
5. #11721292C2semidirect
6. #11721290C2semidirect
7. #11721277C2semidirect
8. #11721271C2semidirect
9. #11721270C2semidirect
10. #11721260C2semidirect
11. #11721259C2semidirect
12. #11721049C2semidirect
13. #11720981C2semidirect
14. #11720963C2semidirect
15. #11720934C2semidirect
19. C2×C3×D4×C9C22semidirect
22. C22×C3⋊Dic9C22semidirect
27. C2×C3×#611C22semidirect
28. C2×C3×#611C22semidirect
29. C22×C9×Dic3C22semidirect
33. C2×Dic3×D9C22semidirect
34. #88551C22semidirect
36. #88534C22semidirect
37. C9×#217C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C3×C4×Dic9C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. #88442C22semidirect
69. #63502D3semidirect
158. C2×D4×C9C2×D3semidirect
167. C2×#611C2×D3semidirect
168. C2×#611C2×D3semidirect
195. C4×Dic9C2×D3semidirect
236. #939D9semidirect
353. C2×C3×D4C2×D9semidirect
375. C22×Dic3C2×D9semidirect
392. #217C2×D9semidirect
418. Dic3⋊C4C2×D9semidirect
507. C3×C9#560semidirect
621. C2×D4D3×D9semidirect
718. C9#5720semidirect
806. C3#10589722semidirect

Maximal subgroups

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

subgroupindex
#117218392
C9×#9392
C3×#635022
#117212922
#117212902
#117212772
#117212712
#117212702
#117212602
#117212592
#117210492
#117209812
#117209632
#117209342
#105953133
#105897223