Finite Group Databasebeta

← #13164789

Subgroups — #13164789

Order 1728.

3309 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11722675C211yesmaximal, characteristic, complemented
2#11722638C211yesmaximal, characteristic, complemented
3#41×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
4#11722521C212yesmaximal, complemented
5#11722519C212yesmaximal, complemented
6#11722507C216yesmaximal, complemented
7D4×((C3⋊D3)⋊C3)⋊C2C216yesmaximal, complemented
8#11722493C213yesmaximal, complemented
9#11722492C213yesmaximal, complemented
10#11722490C213yesmaximal, complemented
11C2×#88654C213yesmaximal, complemented
12#10596692—31nomaximal
13D3×#1009—31nomaximal
14C22×((C3⋊D3)⋊C3)⋊C2C2216yescomplemented
15#41×H(3,𝔽3)C2211yescharacteristic, complemented
16#88748C2212yescomplemented
17D4×#272C2216yescomplemented
18#88740C2213yescomplemented
19C2×C4⋊#272C2213yescomplemented
20#88722C2212yescomplemented
21#88722C2211yescharacteristic, complemented
22Q8×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
23#3830⋊C3C2213yescomplemented
24D4×(C3⋊D3)⋊C3C2213yescomplemented
25D4×(C3⋊D3)⋊C3C2216yescomplemented
26#3828⋊C3C2213yescomplemented
27#3828⋊C3C2213yescomplemented
28C2×C4⋊((C3⋊D3)⋊C3)C2213yescomplemented
29C2×C4×(C3⋊D3)⋊C3C2213yescomplemented
30#88677C22112yescomplemented
31#88676C2216yescomplemented
32#88676C22112yescomplemented
33C2×#6200C2216yescomplemented
34#88671C2216yescomplemented
35#88655C2216yescomplemented
36#88654C2216yescomplemented
37#88654C2213yescomplemented
38#88654C2216yescomplemented
39#88654C2216yescomplemented
40#88654C2216yescomplemented
41C4×((C3⋊D3)⋊C3)⋊C2C2216yescomplemented
42#88652C2216yescomplemented
43#88652C2213yescomplemented
44#88650C2216yescomplemented
45#88649C2216yescomplemented
46#88648C2213yescomplemented
47((C3⋊D3)⋊C3)⋊Q8C2211yescharacteristic, complemented
48#64366D311yescharacteristic, complemented
49#41×C3⋊D3D311yescharacteristic, complemented
50C3×#1009—31no—
51C3×#1009—31no—
52C3×#1009—31no—
53C3×#1009—61no—
54C3×D3×#41—31no—
55#64320—32no—
56#64320—32no—
57#64319—32no—
58D3×#239—32no—
59#64314—36no—
60#64313—36no—
61D32×D4—36no—
62D32×D4—36no—
63#64308—33no—
64#64307—33no—
65#64307—33no—
66#64307—33no—
67#64306—33no—
68D3×#235—33no—
69C2×#3802—33no—
70C2×D3×D12—33no—
71C22×#272C2316yescomplemented
72C22×(C3⋊D3)⋊C3C2313yes—
73C22×(C3⋊D3)⋊C3C2316yescomplemented
74C2×((C3⋊D3)⋊C3)⋊C2—412no—
75C2×((C3⋊D3)⋊C3)⋊C2C2316yes—
76C2×((C3⋊D3)⋊C3)⋊C2C23112yescomplemented
77Q8×H(3,𝔽3)C2311yescharacteristic, complemented
78D4×H(3,𝔽3)C2313yescomplemented
79C2×C4×H(3,𝔽3)C2313yescomplemented
80#6235C2316yescomplemented
81C4⋊#272C2313yescomplemented
82C4⋊#272C2316yescomplemented
83C4×#272C2316yescomplemented
84#6229C2311yescharacteristic, complemented
85#638⋊C3C2316yescomplemented
86#638⋊C3C2316yescomplemented
87C2×(C3⋊Dic3)⋊C3C2313yescomplemented
88C4⋊((C3⋊D3)⋊C3)C2313yescomplemented
89C4⋊((C3⋊D3)⋊C3)C2316yescomplemented
90C4⋊((C3⋊D3)⋊C3)C2313yescomplemented
91C4×(C3⋊D3)⋊C3C2311yescharacteristic
92C4×(C3⋊D3)⋊C3C2313yes—
93C4×(C3⋊D3)⋊C3C2313yescomplemented
94C4×(C3⋊D3)⋊C3C2313yescomplemented
95C4×(C3⋊D3)⋊C3C2316yescomplemented
96#634⋊C3C2311yescharacteristic, complemented
97#634⋊C3C2313yescomplemented
98#6200C23112yescomplemented
99#6200C2316yescomplemented
100#6200C2316yescomplemented
101#6199C2316yescomplemented
102#6198C2316yescomplemented
103((C3⋊D3)⋊C3)⋊C4C2312yes—
104((C3⋊D3)⋊C3)⋊C4C2316yescomplemented
105#6196C2312yescomplemented
106D3×H(5,𝔽2)—91no—
107D3×H(5,𝔽2)—91no—
108C2×#1009—91no—
109C22×D32—36no—
110C22×D32—36no—
111C32×#41—21no—
112C32×#41C2×D311yescharacteristic, complemented
113C32×#41C2×D311yescharacteristic, complemented
114#3832C2×D312yescomplemented
115#3832C2×D311yescharacteristic, complemented
116Q8×C3⋊D3C2×D311yescharacteristic, complemented
117#3830C2×D313yescomplemented
118D4×C3⋊D3C2×D313yescomplemented
119D4×C3⋊D3C2×D316yescomplemented
120#3828C2×D313yescomplemented
121#3828C2×D313yescomplemented
122C2×C4⋊(C3⋊D3)C2×D313yescomplemented
123C2×C4×C3⋊D3C2×D313yescomplemented
124C3×#239—32no—
125C3×#239—32no—
126C3×#239—32no—
127C3×#239—31no—
128C3×#239—62no—
129C3×D3×Q8—31no—
130C3×#237—33no—
131C3×D3×D4—33no—
132C3×D3×D4—36no—
133C3×D3×D4—36no—
134C3×D3×D4—36no—
135C3×D3×D4—66no—
136C3×#235—33no—
137C3×#235—33no—
138C3×#235—33no—
139C3×#235—33no—
140C3×#235—63no—
141C2×C3×D12—33no—
142C2×C3×D12—33no—
143C2×C3×D12—33no—
144C2×C3×D12—63no—
145C2×C3×C4×D3—33no—
146#3811—36no—
147#3811—312no—
148D3×#67—36no—
149D3×#67—312no—
150D3×#67—312no—
151D3×#67—312no—
152C2×#626—36no—
153C2×#625—36no—
154#3805—36no—
155#3804—36no—
156#3802—33no—
157#3802—36no—
158#3802—36no—
159#3802—36no—
160#3802—36no—
161D3×D12—33no—
162D3×D12—36no—
163D3×D12—36no—
164D3×D12—36no—
165D3×D12—36no—
166D3×D12—36no—
167D3×D12—36no—
168C4×D32—36no—
169C4×D32—36no—
170#3799—33no—
171#3799—36no—
172#3798—36no—
173#3798—36no—
174#3797—31no—
175#3796—33no—
176#3796—33no—
177#3796—36no—
178#3795—33no—
179#3795—36no—
180#3795—36no—
181D3×Dic6—31no—
182C22×H(3,𝔽3)C2413yes—
183C2×#272—46no—
184C2×#272C2416yes—
185C2×(C3⋊D3)⋊C3—26no—
186C2×(C3⋊D3)⋊C3—46no—
187C2×(C3⋊D3)⋊C3C2416yes—
188C2×(C3⋊D3)⋊C3C2413yes—
189C2×(C3⋊D3)⋊C3C2411yescharacteristic
190((C3⋊D3)⋊C3)⋊C2—212no—
191((C3⋊D3)⋊C3)⋊C2—412no—
192C4×H(3,𝔽3)C2411yescharacteristic
193C4×H(3,𝔽3)C2413yes—
194#1084C2412yes—
195(C3⋊Dic3)⋊C3C2411yescharacteristic
196(C3⋊Dic3)⋊C3C2412yes—
197(C3⋊Dic3)⋊C3C2413yes—
198C3×H(5,𝔽2)—91no—
199C3×H(5,𝔽2)—91no—
200C2×C3×#41—91no—
201#1009—31no—
202#1009—31no—
203#1009—31no—
204#1009—61no—
205#1009—91no—
206#1009—93no—
207#1009—93no—
208#1009—93no—
209#1009—93no—
210#1009—96no—
211#1009—92no—
212#1009—92no—
213#1009—92no—
214D3×#41—31no—
215D3×#41—91no—
216D3×#41—93no—
217D3×#41—93no—
218D3×#41—92no—
219D3×#41—92no—
220C2×#239—92no—
221#1004—93no—
222#1004—93no—
223#1004—96no—
224#1004—96no—
225C2×D3×D4—93no—
226C2×D3×D4—93no—
227C2×D3×D4—96no—
228C2×D3×D4—96no—
229C2×D3×D4—96no—
230C2×#235—93no—
231C22×D12—93no—
232C22×C3⋊D3C22×D313yes—
233C22×C3⋊D3C22×D316yescomplemented
234C22×C3×D3—33no—
235C22×C3×D3—36no—
236C22×C3×D3—36no—
237C22×C3×D3—36no—
238C22×C3×D3—66no—
239C2×D32—36no—
240C2×D32—36no—
241C2×D32—312no—
242C2×D32—312no—
243C2×D32—1212no—
244C2×D32—1212no—
245C32×Q8—21no—
246C32×Q8C22×D311yescharacteristic, complemented
247C32×Q8C22×D311yescharacteristic, complemented
248C32×D4—23no—
249C32×D4C22×D313yescomplemented
250C32×D4C22×D313yescomplemented
251C2×C32×C4—23no—
252C2×C32×C4C22×D313yescomplemented
253C2×C32×C4C22×D313yescomplemented
254#638C22×D316yescomplemented
255#638C22×D316yescomplemented
256C2×C3⋊Dic3C22×D313yescomplemented
257C4⋊(C3⋊D3)C22×D313yescomplemented
258C4⋊(C3⋊D3)C22×D316yescomplemented
259C4⋊(C3⋊D3)C22×D313yescomplemented
260C4×C3⋊D3C22×D311yescharacteristic
261C4×C3⋊D3C22×D313yes—
262C4×C3⋊D3C22×D313yescomplemented
263C4×C3⋊D3C22×D316yescomplemented
264C4×C3⋊D3C22×D313yescomplemented
265#634C22×D311yescharacteristic, complemented
266#634C22×D313yescomplemented
267C3×#67—36no—
268C3×#67—36no—
269C3×#67—36no—
270C3×#67—36no—
271C3×#67—66no—
272C2×C3×Dic3—33no—
273C3×D12—36no—
274C3×D12—33no—
275C3×D12—33no—
276C3×D12—33no—
277C3×D12—36no—
278C3×D12—36no—
279C3×D12—33no—
280C3×D12—63no—
281C3×D12—66no—
282C3×C4×D3—31no—
283C3×C4×D3—33no—
284C3×C4×D3—36no—
285C3×C4×D3—33no—
286C3×C4×D3—33no—
287C3×C4×D3—36no—
288C3×C4×D3—36no—
289C3×C4×D3—66no—
290C3×Dic6—31no—
291C3×Dic6—33no—
292C3×Dic6—31no—
293C3×Dic6—31no—
294C3×Dic6—61no—
295#627—32no—
296#627—32no—
297#626—36no—
298#626—36no—
299#626—36no—
300#626—312no—
301#626—36no—
302#625—312no—
303#625—36no—
304#625—36no—
305#624—32no—
306#624—36no—
307D3×Dic3—32no—
308D3×Dic3—36no—
309D3×Dic3—36no—
310D3×Dic3—36no—
311C2×H(5,𝔽2)—271noSylow
312C2×H(3,𝔽3)—23no—
313C2×H(3,𝔽3)C2511yescharacteristic
314#272—26no—
315(C3⋊D3)⋊C3—26no—
316(C3⋊D3)⋊C3—23no—
317(C3⋊D3)⋊C3H(5,𝔽2)12yescomplemented
318C23×D3—96no—
319C23×D3—96no—
320C23×D3—96no—
321C3×#41—31no—
322C3×#41—31no—
323C3×#41—61no—
324C3×#41—93no—
325C3×#41—93no—
326C3×#41—93no—
327C3×#41—92no—
328C3×#41—91no—
329C3×#41—92no—
330C3×#41—93no—
331C3×#41D3211yescharacteristic
332C2×C3×Q8—91no—
333C2×C3×D4—93no—
334C2×C3×D4—93no—
335C2×C3×D4—96no—
336C2×C3×D4—96no—
337C2×C3×D4—93no—
338C22×C3×C4—93no—
339C2×#67—96no—
340C2×#67—912no—
341C2×#67—96no—
342C2×#67—912no—
343C2×#67—96no—
344#239—32no—
345#239—32no—
346#239—31no—
347#239—32no—
348#239—62no—
349#239—92no—
350#239—91no—
351#239—93no—
352#239—96no—
353#239—96no—
354#239—93no—
355D3×Q8—31no—
356D3×Q8—91no—
357D3×Q8—91no—
358D3×Q8—91no—
359#237—33no—
360#237—93no—
361#237—93no—
362#237—96no—
363#237—93no—
364#237—96no—
365#237—96no—
366#237—96no—
367D3×D4—36no—
368D3×D4—36no—
369D3×D4—33no—
370D3×D4—36no—
371D3×D4—66no—
372D3×D4—93no—
373D3×D4—96no—
374D3×D4—93no—
375D3×D4—96no—
376D3×D4—96no—
377D3×D4—96no—
378D3×D4—96no—
379D3×D4—96no—
380D3×D4—96no—
381D3×D4—93no—
382D3×D4—96no—
383D3×D4—96no—
384D3×D4—96no—
385D3×D4—96no—
386D3×D4—96no—
387D3×D4—912no—
388D3×D4—96no—
389D3×D4—912no—
390D3×D4—912no—
391D3×D4—912no—
392#235—33no—
393#235—33no—
394#235—33no—
395#235—33no—
396#235—63no—
397#235—93no—
398#235—93no—
399#235—96no—
400#235—93no—
401#235—96no—
402#235—96no—
403#235—96no—
404#235—93no—
405#235—96no—
406#235—96no—
407C2×D12—33no—
408C2×D12—33no—
409C2×D12—33no—
410C2×D12—63no—
411C2×D12—93no—
412C2×D12—96no—
413C2×D12—93no—
414C2×D12—96no—
415C2×D12—96no—
416C2×D12—96no—
417C2×D12—96no—
418C2×D12—96no—
419C2×C4×D3—33no—
420C2×C4×D3—93no—
421C2×C4×D3—96no—
422C2×C4×D3—96no—
423C2×C4×D3—96no—
424C2×Dic6—91no—
425C22×C32—23no—
426C22×C32C23×D313yes—
427C22×C32C23×D313yes—
428C2×C3⋊D3—26no—
429C2×C3⋊D3—46no—
430C2×C3⋊D3C23×D316yes—
431C2×C3⋊D3C23×D313yes—
432C2×C3⋊D3C23×D311yescharacteristic
433C2×C3×D3—31no—
434C2×C3×D3—36no—
435C2×C3×D3—33no—
436C2×C3×D3—36no—
437C2×C3×D3—36no—
438C2×C3×D3—66no—
439C2×C3×D3—66no—
440C2×C3×D3—126no—
441C2×C3×D3—126no—
442C2×C3×D3—126no—
443C2×C3×D3—246no—
444D32—612no—
445D32—612no—
446D32—1212no—
447D32—1212no—
448C32×C4—21no—
449C32×C4—23no—
450C32×C4C23×D311yescharacteristic
451C32×C4C23×D311yescharacteristic
452C32×C4C23×D313yes—
453C32×C4C23×D313yes—
454C3⋊Dic3C23×D313yes—
455C3⋊Dic3C23×D312yes—
456C3⋊Dic3C23×D311yescharacteristic
457C3×Dic3—32no—
458C3×Dic3—33no—
459C3×Dic3—31no—
460C3×Dic3—32no—
461C3×Dic3—32no—
462C3×Dic3—62no—
463H(5,𝔽2)—91no—
464H(5,𝔽2)—91no—
465H(5,𝔽2)—276no—
466H(5,𝔽2)—273no—
467H(5,𝔽2)—273no—
468H(5,𝔽2)—272no—
469C2×#41—91no—
470C2×#41—273no—
471C2×#41—272no—
472C22×D4—273no—
473C22×D4—276no—
474H(3,𝔽3)C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
475C23×C3—93no—
476C23×C3—96no—
477C23×C3—96no—
478C22×D3—33no—
479C22×D3—36no—
480C22×D3—36no—
481C22×D3—36no—
482C22×D3—66no—
483C22×D3—93no—
484C22×D3—96no—
485C22×D3—96no—
486C22×D3—912no—
487C22×D3—96no—
488C22×D3—96no—
489C22×D3—912no—
490C22×D3—912no—
491C22×D3—3612no—
492C22×D3—3612no—
493C22×D3—3612no—
494C3×Q8—31no—
495C3×Q8—31no—
496C3×Q8—61no—
497C3×Q8—91no—
498C3×Q8—93no—
499C3×Q8—91no—
500C3×Q8C2×D3211yescharacteristic
501C3×D4—33no—
502C3×D4—33no—
503C3×D4—63no—
504C3×D4—93no—
505C3×D4—93no—
506C3×D4—96no—
507C3×D4—96no—
508C3×D4—96no—
509C3×D4—96no—
510C3×D4—96no—
511C3×D4—93no—
512C3×D4C2×D3213yes—
513C2×C3×C4—33no—
514C2×C3×C4—33no—
515C2×C3×C4—63no—
516C2×C3×C4—91no—
517C2×C3×C4—93no—
518C2×C3×C4—96no—
519C2×C3×C4—93no—
520C2×C3×C4—93no—
521C2×C3×C4—93no—
522C2×C3×C4—96no—
523C2×C3×C4C2×D3213yes—
524#67—36no—
525#67—36no—
526#67—36no—
527#67—36no—
528#67—66no—
529#67—96no—
530#67—96no—
531#67—912no—
532#67—96no—
533#67—96no—
534#67—96no—
535#67—96no—
536#67—96no—
537#67—912no—
538#67—96no—
539C2×Dic3—33no—
540C2×Dic3—93no—
541C2×Dic3—96no—
542C2×Dic3—92no—
543C2×Dic3—96no—
544D12—33no—
545D12—33no—
546D12—36no—
547D12—36no—
548D12—33no—
549D12—36no—
550D12—33no—
551D12—63no—
552D12—66no—
553D12—93no—
554D12—96no—
555D12—93no—
556D12—96no—
557D12—96no—
558D12—912no—
559D12—96no—
560C4×D3—36no—
561C4×D3—36no—
562C4×D3—31no—
563C4×D3—33no—
564C4×D3—33no—
565C4×D3—33no—
566C4×D3—36no—
567C4×D3—66no—
568C4×D3—91no—
569C4×D3—93no—
570C4×D3—93no—
571C4×D3—93no—
572C4×D3—96no—
573C4×D3—92no—
574C4×D3—96no—
575C4×D3—92no—
576C4×D3—96no—
577C4×D3—96no—
578C4×D3—96no—
579Dic6—31no—
580Dic6—31no—
581Dic6—31no—
582Dic6—33no—
583Dic6—61no—
584Dic6—91no—
585Dic6—93no—
586Dic6—92no—
587Dic6—92no—
588Dic6—92no—
589C2×C32—23no—
590C2×C32—23no—
591C2×C32—21no—
592C2×C32—43no—
593C2×C32C24×D311yescharacteristic
594C2×C32C24×D311yescharacteristic
595C3⋊D3—23no—
596C3⋊D3—26no—
597C3⋊D3#100912yescomplemented
598C3×D3—32no—
599C3×D3—66no—
600C3×D3—66no—
601C3×D3—63no—
602C3×D3—66no—
603C3×D3—126no—
604C24—276no—
605#41—91no—
606#41—92no—
607#41—92no—
608#41—93no—
609#41—93no—
610#41—93no—
611#41—93no—
612#41—276no—
613#41—276no—
614#41—273no—
615#41—273no—
616#41—276no—
617#41—276no—
618#41((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
619C2×Q8—91no—
620C2×Q8—271no—
621C2×D4—93no—
622C2×D4—96no—
623C2×D4—96no—
624C2×D4—93no—
625C2×D4—93no—
626C2×D4—273no—
627C2×D4—276no—
628C2×D4—276no—
629C2×D4—276no—
630C2×D4—276no—
631C2×D4—276no—
632C2×D4—276no—
633C2×D4—276no—
634C2×D4—2712no—
635C2×D4—2712no—
636C22×C4—93no—
637C22×C4—276no—
638C22×C3—33no—
639C22×C3—33no—
640C22×C3—63no—
641C22×C3—91no—
642C22×C3—96no—
643C22×C3—93no—
644C22×C3—96no—
645C22×C3—186no—
646C22×C3—366no—
647C22×C3—366no—
648C22×C3C22×D3213yes—
649C2×D3—31no—
650C2×D3—36no—
651C2×D3—36no—
652C2×D3—33no—
653C2×D3—36no—
654C2×D3—66no—
655C2×D3—66no—
656C2×D3—91no—
657C2×D3—96no—
658C2×D3—93no—
659C2×D3—126no—
660C2×D3—126no—
661C2×D3—126no—
662C2×D3—186no—
663C2×D3—1812no—
664C2×D3—1812no—
665C2×D3—1812no—
666C2×D3—246no—
667C2×D3—366no—
668C2×D3—3612no—
669C2×D3—3612no—
670C2×D3—3612no—
671C3×C4—31no—
672C3×C4—31no—
673C3×C4—33no—
674C3×C4—33no—
675C3×C4—61no—
676C3×C4—63no—
677C3×C4—91no—
678C3×C4—92no—
679C3×C4—93no—
680C3×C4—92no—
681C3×C4C22×D3213yes—
682C3×C4C22×D3211yescharacteristic
683Dic3—32no—
684Dic3—32no—
685Dic3—33no—
686Dic3—32no—
687Dic3—31no—
688Dic3—62no—
689Dic3—92no—
690Dic3—91no—
691Dic3—93no—
692C32—21no—
693C32C2×#100911yescharacteristic, complemented
694C32D3×H(5,𝔽2)11yescharacteristic, complemented
695C23—93no—
696C23—96no—
697C23—96no—
698C23—276no—
699C23—2712no—
700C23—10812no—
701Q8—93no—
702Q8—91no—
703Q8—91no—
704Q8—272no—
705Q8C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
706D4—96no—
707D4—96no—
708D4—96no—
709D4—96no—
710D4—93no—
711D4—96no—
712D4—93no—
713D4—93no—
714D4—276no—
715D4—276no—
716D4—276no—
717D4—2712no—
718D4C2×((C3⋊D3)⋊C3)⋊C213yescomplemented
719C2×C4—93no—
720C2×C4—91no—
721C2×C4—93no—
722C2×C4—93no—
723C2×C4—93no—
724C2×C4—96no—
725C2×C4—96no—
726C2×C4—272no—
727C2×C4—276no—
728C2×C4—276no—
729C2×C4C2×((C3⋊D3)⋊C3)⋊C213yescomplemented
730C2×C3—23no—
731C2×C3—31no—
732C2×C3—31no—
733C2×C3—63no—
734C2×C3—63no—
735C2×C3—61no—
736C2×C3—92no—
737C2×C3—123no—
738C2×C3—186no—
739C2×C3—183no—
740C2×C3—186no—
741C2×C3C23×D3211yescharacteristic
742D3—32no—
743D3—66no—
744D3—66no—
745D3—63no—
746D3—66no—
747D3—92no—
748D3—126no—
749D3—183no—
750D3—186no—
751C22—91no—
752C22—93no—
753C22—96no—
754C22—96no—
755C22—186no—
756C22—366no—
757C22—366no—
758C22—5412no—
759C22—10812no—
760C22C22×((C3⋊D3)⋊C3)⋊C213yes—
761C4—91no—
762C4—92no—
763C4—92no—
764C4—93no—
765C4C22×((C3⋊D3)⋊C3)⋊C213yes—
766C4C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
767C3—31no—
768C3—31no—
769C3—61no—
770C3D3×#100911yescharacteristic
771C2—23no—
772C2—92no—
773C2—183no—
774C2—186no—
775C2—186no—
776C2C23×((C3⋊D3)⋊C3)⋊C211yescharacteristic
subgroupG/H
centerC2C23×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC2×H(3,𝔽3)C25
Frattini, socleC2×C3C23×D32
Fitting#41×H(3,𝔽3)C22
hypercenter#41((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×H(5,𝔽2)
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #11722675C2semidirect
2. #11722638C2semidirect
3. #41×(C3⋊D3)⋊C3C2semidirect
4. #11722521C2semidirect
5. #11722519C2semidirect
6. #11722507C2semidirect
7. D4×((C3⋊D3)⋊C3)⋊C2C2semidirect
8. #11722493C2semidirect
9. #11722492C2semidirect
10. #11722490C2semidirect
11. C2×#88654C2semidirect
14. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
15. #41×H(3,𝔽3)C22semidirect
16. #88748C22semidirect
17. D4×#272C22semidirect
18. #88740C22semidirect
19. C2×C4⋊#272C22semidirect
20. #88722C22semidirect
21. #88722C22semidirect
22. Q8×(C3⋊D3)⋊C3C22semidirect
23. #3830⋊C3C22semidirect
24. D4×(C3⋊D3)⋊C3C22semidirect
25. D4×(C3⋊D3)⋊C3C22semidirect
26. #3828⋊C3C22semidirect
27. #3828⋊C3C22semidirect
28. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
29. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. #88677C22semidirect
31. #88676C22semidirect
32. #88676C22semidirect
33. C2×#6200C22semidirect
34. #88671C22semidirect
35. #88655C22semidirect
36. #88654C22semidirect
37. #88654C22semidirect
38. #88654C22semidirect
39. #88654C22semidirect
40. #88654C22semidirect
41. C4×((C3⋊D3)⋊C3)⋊C2C22semidirect
42. #88652C22semidirect
43. #88652C22semidirect
44. #88650C22semidirect
45. #88649C22semidirect
46. #88648C22semidirect
47. ((C3⋊D3)⋊C3)⋊Q8C22semidirect
48. #64366D3semidirect
49. #41×C3⋊D3D3semidirect
71. C22×#272C23semidirect
73. C22×(C3⋊D3)⋊C3C23semidirect
76. C2×((C3⋊D3)⋊C3)⋊C2C23semidirect
77. Q8×H(3,𝔽3)C23semidirect
78. D4×H(3,𝔽3)C23semidirect
79. C2×C4×H(3,𝔽3)C23semidirect
80. #6235C23semidirect
81. C4⋊#272C23semidirect
82. C4⋊#272C23semidirect
83. C4×#272C23semidirect
84. #6229C23semidirect
85. #638⋊C3C23semidirect
86. #638⋊C3C23semidirect
87. C2×(C3⋊Dic3)⋊C3C23semidirect
88. C4⋊((C3⋊D3)⋊C3)C23semidirect
89. C4⋊((C3⋊D3)⋊C3)C23semidirect
90. C4⋊((C3⋊D3)⋊C3)C23semidirect
93. C4×(C3⋊D3)⋊C3C23semidirect
94. C4×(C3⋊D3)⋊C3C23semidirect
95. C4×(C3⋊D3)⋊C3C23semidirect
96. #634⋊C3C23semidirect
97. #634⋊C3C23semidirect
98. #6200C23semidirect
99. #6200C23semidirect
100. #6200C23semidirect
101. #6199C23semidirect
102. #6198C23semidirect
104. ((C3⋊D3)⋊C3)⋊C4C23semidirect
105. #6196C23semidirect
112. C32×#41C2×D3semidirect
113. C32×#41C2×D3semidirect
114. #3832C2×D3semidirect
115. #3832C2×D3semidirect
116. Q8×C3⋊D3C2×D3semidirect
117. #3830C2×D3semidirect
118. D4×C3⋊D3C2×D3semidirect
119. D4×C3⋊D3C2×D3semidirect
120. #3828C2×D3semidirect
121. #3828C2×D3semidirect
122. C2×C4⋊(C3⋊D3)C2×D3semidirect
123. C2×C4×C3⋊D3C2×D3semidirect
233. C22×C3⋊D3C22×D3semidirect
246. C32×Q8C22×D3semidirect
247. C32×Q8C22×D3semidirect
249. C32×D4C22×D3semidirect
250. C32×D4C22×D3semidirect
252. C2×C32×C4C22×D3semidirect
253. C2×C32×C4C22×D3semidirect
254. #638C22×D3semidirect
255. #638C22×D3semidirect
256. C2×C3⋊Dic3C22×D3semidirect
257. C4⋊(C3⋊D3)C22×D3semidirect
258. C4⋊(C3⋊D3)C22×D3semidirect
259. C4⋊(C3⋊D3)C22×D3semidirect
262. C4×C3⋊D3C22×D3semidirect
263. C4×C3⋊D3C22×D3semidirect
264. C4×C3⋊D3C22×D3semidirect
265. #634C22×D3semidirect
266. #634C22×D3semidirect
317. (C3⋊D3)⋊C3H(5,𝔽2)semidirect
474. H(3,𝔽3)C2×H(5,𝔽2)semidirect
597. C3⋊D3#1009semidirect
618. #41((C3⋊D3)⋊C3)⋊C2semidirect
693. C32C2×#1009semidirect
694. C32D3×H(5,𝔽2)semidirect
705. Q8C2×((C3⋊D3)⋊C3)⋊C2semidirect
718. D4C2×((C3⋊D3)⋊C3)⋊C2semidirect
729. C2×C4C2×((C3⋊D3)⋊C3)⋊C2semidirect

Maximal subgroups

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

subgroupindex
#117226752
#117226382
#41×(C3⋊D3)⋊C32
#117225212
#117225192
#117225072
D4×((C3⋊D3)⋊C3)⋊C22
#117224932
#117224922
#117224902
C2×#886542
#105966923
D3×#10093