Finite Group Databasebeta

← #13152001

Subgroups — #13152001

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#11721874C211yesmaximal, characteristic, complemented
2C9×#953C211yesmaximal, characteristic, complemented
3C3×#63515C211yesmaximal, characteristic, complemented
4#11721289C211yesmaximal, characteristic, complemented
5#11721282C211yesmaximal, characteristic, complemented
6#11721281C211yesmaximal, characteristic, complemented
7#11721280C211yesmaximal, characteristic, complemented
8#11721275C211yesmaximal, characteristic, complemented
9#11721271C211yesmaximal, characteristic, complemented
10#11721270C211yesmaximal, characteristic, complemented
11#11721269C211yesmaximal, characteristic, complemented
12#11721262C211yesmaximal, characteristic, complemented
13#11721256C211yesmaximal, characteristic, complemented
14#11721247C211yesmaximal, characteristic, complemented
15#11721246C211yesmaximal, characteristic, complemented
16#10595505—31nomaximal
17#10589697—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C9×#67C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C2×#6195C2211yescharacteristic, complemented
29C2×#6194C2211yescharacteristic, complemented
30C2×D3×Dic9C2211yescharacteristic, complemented
31C2×#6192C2211yescharacteristic, complemented
32C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
33C2×Dic3×D9C2211yescharacteristic, complemented
34#88551C2211yescharacteristic
35#88551C2211yescharacteristic
36#88551C2211yescharacteristic
37C9×#217C2211yescharacteristic
38C9×#217C2211yescharacteristic
39C9×#217C2211yescharacteristic
40C3×#3676C2211yescharacteristic
41C3×#3676C2211yescharacteristic
42C3×#3676C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic, complemented
44#88445C2211yescharacteristic, complemented
45(C2×D9)⋊Dic3C2211yescharacteristic, complemented
46Dic3⋊Dic9C2211yescharacteristic, complemented
47Dic3⋊Dic9C2211yescharacteristic, complemented
48#88442C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64162—31no—
54C3×#953—31no—
55C3×#953D311yescharacteristic
56#63979—31no—
57#63975—31no—
58#63971—31no—
59#63971—31no—
60#63970—31no—
61#63970—31no—
62#63969—31no—
63#63969—31no—
64#63958—31no—
65#63958—31no—
66#63956—31no—
67#63956—31no—
68C9×#120—31no—
69#63515—31no—
70#63515—61no—
71#63515D311yescharacteristic, complemented
72#63502—31no—
73#63501—31no—
74#63501—31no—
75#63500—31no—
76#63500—31no—
77#63497—31no—
78#63446—31no—
79#63446—31no—
80#63445—31no—
81#63445—31no—
82#63441—31no—
83#63441—31no—
84C23×C3×C9—41no—
85C23×C3×C9—41no—
86C23×C3×C9—41no—
87C23×C3×C9C2311yescharacteristic
88C23×C3×C9C2311yescharacteristic
89C23×C3×C9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93#6233—41no—
94#6233—41no—
95#6233—41no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C9×#67—41no—
100C9×#67—41no—
101C9×#67—41no—
102C3×#611—41no—
103C3×#611—41no—
104C3×#611—41no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111#6195—41no—
112#6194—41no—
113D3×Dic9—41no—
114#6192—41no—
115(C3⋊D9)⋊C4—41no—
116Dic3×D9—41no—
117#5595—91no—
118#5595—91no—
119C24×C32C2×D311yescharacteristic
120C2×#638—31no—
121C2×#638—31no—
122C2×#638—31no—
123C2×C3×#67—31no—
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67C2×D311yescharacteristic
127C2×C3×#67C2×D311yescharacteristic
128C2×C3×#67C2×D311yescharacteristic
129C2×#626—31no—
130C2×#626—31no—
131C2×#625—31no—
132C2×#624—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C24×C9—21no—
136C24×C9C2×D311yescharacteristic
137#3757—31no—
138#3757—31no—
139#3757—31no—
140C3×#217—31no—
141C3×#217—31no—
142C3×#217—31no—
143C3×#217C2×D311yescharacteristic
144C3×#217C2×D311yescharacteristic
145C3×#217C2×D311yescharacteristic
146#3724—31no—
147#3724—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150Dic3⋊Dic3—31no—
151Dic3⋊Dic3—31no—
152#3722—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C2×D4×C9—31no—
157C2×D4×C9—31no—
158C2×D4×C9—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611—61no—
165C2×#611—61no—
166C2×#611—61no—
167C2×#611C2×D311yescharacteristic
168C2×#611C2×D311yescharacteristic
169C2×#611C2×D311yescharacteristic
170C22×Dic9—31no—
171C2×D36—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C9×C22⋊C4—31no—
175C9×C22⋊C4—31no—
176C9×C22⋊C4—31no—
177#3676—31no—
178#3676—31no—
179#3676—31no—
180#3676—31no—
181#3676—61no—
182#3676—61no—
183#3676—61no—
184#3676C2×D311yescharacteristic
185#3676C2×D311yescharacteristic
186#3676C2×D311yescharacteristic
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189C4⋊Dic9—31no—
190C4⋊Dic9—31no—
191Dic9⋊C4—31no—
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×C9—21no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—44no—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
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⋊Dic9—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×#120—31no—
226C3×#120—91no—
227#953—31no—
228#953—91no—
229#953—91no—
230#953—181no—
231#953D911yescharacteristic, complemented
232#940—91no—
233#940—91no—
234#939—91no—
235#939—91no—
236#939—91no—
237#939—91no—
238#938—91no—
239#938—91no—
240#938—91no—
241#938—91no—
242#935—91no—
243#935—91no—
244#884—91no—
245#884—91no—
246#884—91no—
247#884—91no—
248#883—91no—
249#883—91no—
250#883—91no—
251#883—91no—
252#879—91no—
253#879—91no—
254#879—91no—
255#879—91no—
256C23×C32—41no—
257C23×C32—41no—
258C23×C32—41no—
259C23×C32C22×D311yescharacteristic
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3C22×D311yescharacteristic
265#638—121no—
266#638—121no—
267#638—121no—
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C3×#67—41no—
272C3×#67—41no—
273C3×#67—41no—
274C3×#67—121no—
275C3×#67—121no—
276C3×#67—121no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283#626—121no—
284#626—121no—
285#625—121no—
286#624—121no—
287D3×Dic3—121no—
288D3×Dic3—121no—
289C23×C9—21no—
290C23×C9—21no—
291C23×C9—21no—
292C23×C9—31no—
293C23×C9—41no—
294C23×C9—41no—
295C23×C9—41no—
296C23×C9—42no—
297C23×C9—42no—
298C23×C9—42no—
299C23×C9C22×D311yescharacteristic
300C23×C9C22×D311yescharacteristic
301C23×C9C22×D311yescharacteristic
302C22×D9—31no—
303C22×D9—61no—
304C22×D9C22×D311yescharacteristic
305D4×C9—121no—
306D4×C9—121no—
307D4×C9—121no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—31no—
311#611—41no—
312#611—41no—
313#611—41no—
314#611—121no—
315#611—121no—
316#611—121no—
317#611—121no—
318#611—121no—
319#611—122no—
320#611—122no—
321#611—122no—
322C2×Dic9—31no—
323C2×Dic9—31no—
324C2×Dic9—31no—
325C2×Dic9—61no—
326C2×Dic9—61no—
327C2×Dic9—61no—
328C2×Dic9—121no—
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331C2×Dic9C22×D311yescharacteristic
332D36—121no—
333C4×D9—121no—
334C4×D9—121no—
335#560—271noSylow
336C2×C3×C9—41no—
337C2×C3×C9—41no—
338C2×C3×C9—41no—
339C2×C3×C9H(5,𝔽2)11yescharacteristic
340C2×C3×C9H(5,𝔽2)11yescharacteristic
341C2×C3×C9H(5,𝔽2)11yescharacteristic
342C3⋊D9—41no—
343D3×C9—41no—
344C3×D9—41no—
345C24×C3—21no—
346C24×C3C2×D911yescharacteristic
347C24×C3D3211yescharacteristic
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—31no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—31no—
357C2×#67—91no—
358C2×#67—91no—
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—181no—
368C2×#67—181no—
369C2×#67—181no—
370C2×#67C2×D911yescharacteristic
371C2×#67C2×D911yescharacteristic
372C2×#67C2×D911yescharacteristic
373C22×Dic3—91no—
374C22×Dic3—91no—
375C2×D12—91no—
376C2×D12—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387#217—31no—
388#217—31no—
389#217—31no—
390#217—91no—
391#217—91no—
392#217—91no—
393#217—91no—
394#217—91no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—181no—
399#217—181no—
400#217—181no—
401#217C2×D911yescharacteristic
402#217C2×D911yescharacteristic
403#217C2×D911yescharacteristic
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408C4⋊Dic3—91no—
409C4⋊Dic3—91no—
410C4⋊Dic3—91no—
411C4⋊Dic3—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
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×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—44no—
432C22×C32C23×D311yescharacteristic
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C3⋊Dic3—61no—
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—22no—
453C22×C9—22no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—21no—
460C22×C9—21no—
461C22×C9—21no—
462C22×C9—21no—
463C22×C9—21no—
464C22×C9—41no—
465C22×C9—41no—
466C22×C9—41no—
467C22×C9—41no—
468C22×C9—41no—
469C22×C9—41no—
470C22×C9—48no—
471C22×C9—44no—
472C22×C9—61no—
473C22×C9—61no—
474C22×C9—61no—
475C22×C9C23×D311yescharacteristic
476C2×D9—21no—
477C2×D9—21no—
478C2×D9—21no—
479C2×D9—61no—
480C2×D9—61no—
481C2×D9—61no—
482C2×D9—121no—
483C2×D9—121no—
484C2×D9—121no—
485C4×C9—61no—
486C4×C9—61no—
487C4×C9—61no—
488Dic9—21no—
489Dic9—21no—
490Dic9—21no—
491Dic9—61no—
492Dic9—61no—
493Dic9—61no—
494Dic9—121no—
495Dic9—121no—
496Dic9—121no—
497#127—271no—
498#126—271no—
499#126—271no—
500#123—271no—
501#123—271no—
502#123—271no—
503#121—271no—
504#121—271no—
505#121—271no—
506#121—271no—
507#121—271no—
508#121—271no—
509#120—31no—
510#120—91no—
511#120—271no—
512C3×C9#56011yescharacteristic, complemented, Sylow
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—31no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—42no—
524C23×C3—42no—
525C23×C3—42no—
526C23×C3—91no—
527C23×C3C22×D911yescharacteristic
528C23×C3C22×D911yescharacteristic
529C23×C3C22×D911yescharacteristic
530C23×C3C2×D3211yescharacteristic
531C23×C3C2×D3211yescharacteristic
532C23×C3C2×D3211yescharacteristic
533C22×D3—31no—
534C22×D3—91no—
535C22×D3—91no—
536C22×D3—181no—
537C22×D3C22×D911yescharacteristic
538C3×D4—121no—
539C3×D4—121no—
540C3×D4—121no—
541C3×D4—361no—
542C3×D4—361no—
543C3×D4—361no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—91no—
548C2×C3×C4—91no—
549C2×C3×C4—91no—
550#67—41no—
551#67—41no—
552#67—41no—
553#67—121no—
554#67—121no—
555#67—121no—
556#67—361no—
557#67—361no—
558#67—361no—
559#67—361no—
560#67—361no—
561#67—361no—
562#67—361no—
563#67—361no—
564#67—361no—
565#67—361no—
566#67—362no—
567#67—362no—
568#67—362no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—91no—
573C2×Dic3—91no—
574C2×Dic3—91no—
575C2×Dic3—91no—
576C2×Dic3—91no—
577C2×Dic3—91no—
578C2×Dic3—181no—
579C2×Dic3—181no—
580C2×Dic3—181no—
581C2×Dic3—361no—
582C2×Dic3—361no—
583C2×Dic3C22×D911yescharacteristic
584C2×Dic3C22×D911yescharacteristic
585C2×Dic3C22×D911yescharacteristic
586D12—361no—
587D12—361no—
588C4×D3—361no—
589C4×D3—361no—
590C4×D3—361no—
591C4×D3—361no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—41no—
595C2×C32#100411yescharacteristic
596C2×C32#100411yescharacteristic
597C2×C32#100411yescharacteristic
598C3⋊D3—121no—
599C3×D3—41no—
600C3×D3—121no—
601C2×C9—21no—
602C2×C9—21no—
603C2×C9—21no—
604C2×C9—42no—
605C2×C9—42no—
606C2×C9—42no—
607C2×C9—41no—
608C2×C9—41no—
609C2×C9—41no—
610C2×C9—121no—
611C2×C9#100411yescharacteristic
612C2×C9#100411yescharacteristic
613C2×C9#100411yescharacteristic
614D9—41no—
615D9—121no—
616D9—241no—
617C24D3×D911yescharacteristic
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—31no—
621C2×D4—91no—
622C2×D4—91no—
623C2×D4—91no—
624C2×D4—271no—
625C2×D4—271no—
626C2×D4—271no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4—271no—
630C22×C4—271no—
631C22×C4—271no—
632C22×C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C4⋊C4—271no—
636C4⋊C4—271no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—31no—
642C22⋊C4—91no—
643C22⋊C4—91no—
644C22⋊C4—91no—
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—22no—
654C22×C3—22no—
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—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—44no—
681C22×C3—48no—
682C22×C3—44no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—181no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3C23×D911yescharacteristic
690C22×C3C22×D3211yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C2×D3—181no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—361no—
704C2×D3—361no—
705C2×D3—361no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—181no—
710C3×C4—181no—
711C3×C4—181no—
712Dic3—21no—
713Dic3—21no—
714Dic3—21no—
715Dic3—61no—
716Dic3—61no—
717Dic3—61no—
718Dic3—181no—
719Dic3—181no—
720Dic3—181no—
721Dic3—181no—
722Dic3—181no—
723Dic3—181no—
724Dic3—361no—
725Dic3—361no—
726Dic3—361no—
727C32#559511yescharacteristic
728C9—21no—
729C9#559511yescharacteristic, complemented
730C23—31no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—91no—
735C23—271no—
736C23C2×D3×D911yescharacteristic
737C23C2×D3×D911yescharacteristic
738C23C2×D3×D911yescharacteristic
739D4—121no—
740D4—121no—
741D4—121no—
742D4—361no—
743D4—361no—
744D4—361no—
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—271no—
758C2×C4—271no—
759C2×C4—271no—
760C2×C4—1081no—
761C2×C4—1081no—
762C2×C4—1081no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3—42no—
768C2×C3—42no—
769C2×C3—41no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—41no—
774C2×C3—41no—
775C2×C3—121no—
776C2×C3—361no—
777C2×C3#6371011yescharacteristic
778C2×C3#6371011yescharacteristic
779C2×C3#6371011yescharacteristic
780C2×C3#6433011yescharacteristic
781C2×C3#6433011yescharacteristic
782C2×C3#6433011yescharacteristic
783D3—41no—
784D3—121no—
785D3—361no—
786D3—361no—
787D3—721no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—44no—
798C22—61no—
799C22—61no—
800C22—61no—
801C22—181no—
802C22—181no—
803C22—181no—
804C22—541no—
805C22—541no—
806C22—541no—
807C22C22×D3×D911yescharacteristic
808C4—61no—
809C4—61no—
810C4—61no—
811C4—181no—
812C4—181no—
813C4—181no—
814C4—541no—
815C4—541no—
816C4—541no—
817C3—21no—
818C3#1058969711yescharacteristic, complemented
819C3#1059550511yescharacteristic
820C2—41no—
821C2—41no—
822C2—41no—
823C2—121no—
824C2—361no—
825C2—1081no—
826C2#1172253511yescharacteristic
827C2#1172253511yescharacteristic
828C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC24×C3×C9C22
socleC22×C32C23×D3
hypercenterC24D3×D9
hypocenterC3×C9#560
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. #11721874C2semidirect
2. C9×#953C2semidirect
3. C3×#63515C2semidirect
4. #11721289C2semidirect
5. #11721282C2semidirect
6. #11721281C2semidirect
7. #11721280C2semidirect
8. #11721275C2semidirect
9. #11721271C2semidirect
10. #11721270C2semidirect
11. #11721269C2semidirect
12. #11721262C2semidirect
13. #11721256C2semidirect
14. #11721247C2semidirect
15. #11721246C2semidirect
28. C2×#6195C22semidirect
29. C2×#6194C22semidirect
30. C2×D3×Dic9C22semidirect
31. C2×#6192C22semidirect
32. C2×(C3⋊D9)⋊C4C22semidirect
33. C2×Dic3×D9C22semidirect
43. (C2×D3)⋊Dic9C22semidirect
44. #88445C22semidirect
45. (C2×D9)⋊Dic3C22semidirect
46. Dic3⋊Dic9C22semidirect
47. Dic3⋊Dic9C22semidirect
48. #88442C22semidirect
49. #88442C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
71. #63515D3semidirect
231. #953D9semidirect
512. C3×C9#560semidirect
729. C9#5595semidirect
818. C3#10589697semidirect

Maximal subgroups

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

subgroupindex
#117218742
C9×#9532
C3×#635152
#117212892
#117212822
#117212812
#117212802
#117212752
#117212712
#117212702
#117212692
#117212622
#117212562
#117212472
#117212462
#105955053
#105896973