Finite Group Databasebeta

← #13181643

Subgroups — #13181643

Order 1728.

5516 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#41×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×D3×#41C211yesmaximal, characteristic, complemented
4#11724597C211yesmaximal, characteristic, complemented
5#11724592C211yesmaximal, characteristic, complemented
6#11724591C211yesmaximal, characteristic, complemented
7#11724590C211yesmaximal, characteristic, complemented
8#11724589C213yesmaximal, complemented
9#11724588C213yesmaximal, complemented
10#11724587C213yesmaximal, complemented
11#11724582C213yesmaximal, complemented
12#11724578C213yesmaximal, complemented
13C3⋊D3×#235C213yesmaximal, complemented
14D3×#3828C213yesmaximal, complemented
15C2×#89020C213yesmaximal, complemented
16#10596756—31nomaximal
17#10596695—34nomaximal
18C33×#41C2211yescharacteristic, complemented
19#89080C2211yescharacteristic, complemented
20Q8×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21#89078C2213yescomplemented
22D4×C3⋊(C3⋊D3)C2213yescomplemented
23#89076C2213yescomplemented
24C2×C4×C3⋊(C3⋊D3)C2213yescomplemented
25C3×#3832C2211yescharacteristic, complemented
26C3×Q8×C3⋊D3C2211yescharacteristic, complemented
27C3×#3830C2213yescomplemented
28C3×D4×C3⋊D3C2213yescomplemented
29C3×#3828C2213yescomplemented
30C2×C3×C4×C3⋊D3C2213yescomplemented
31C32×#239C2211yescharacteristic, complemented
32C32×D3×Q8C2211yescharacteristic, complemented
33C32×#237C2213yescomplemented
34C32×D3×D4C2213yescomplemented
35C32×#235C2213yescomplemented
36C2×C32×C4×D3C2213yescomplemented
37#89039C2216yescomplemented
38C3⋊D3×#67C2216yescomplemented
39D3×#638C2216yescomplemented
40C2×#6293C2213yescomplemented
41C2×#6292C2213yescomplemented
42C2×#6291C2213yescomplemented
43C2×#6290C2213yescomplemented
44#89031C2216yescomplemented
45#89029C2216yescomplemented
46#89028C2216yescomplemented
47#89026C2213yescomplemented
48C3⋊D3×D12C2213yescomplemented
49D3×C4⋊(C3⋊D3)C2213yescomplemented
50C4×D3×C3⋊D3C2216yescomplemented
51#89022C2213yescomplemented
52#89021C2213yescomplemented
53#89020C2211yescharacteristic, complemented
54#89020C2213yescomplemented
55#89020C2213yescomplemented
56#89020C2213yescomplemented
57#89020C2213yescomplemented
58#89020C2213yescomplemented
59#89020C2213yescomplemented
60#89020C2213yescomplemented
61#89019C2213yescomplemented
62#89018C2213yescomplemented
63#89017C2213yescomplemented
64C3⋊D3×Dic6C2213yescomplemented
65#89015C2213yescomplemented
66#89014C2213yescomplemented
67D3×#634C2213yescomplemented
68C2×C32×#41—31no—
69#64367—31no—
70#64367—33no—
71#64366—31no—
72#64366—33no—
73#41×C3⋊D3—31no—
74#41×C3⋊D3—33no—
75#41×C3⋊D3—33no—
76#41×C3⋊D3—34no—
77#41×C3⋊D3—64no—
78#41×C3⋊D3D311yescharacteristic, complemented
79#64364—31no—
80#64364—31no—
81#64361—33no—
82#64361—33no—
83C2×#3828—33no—
84C2×#3828—33no—
85C3×D3×#41—34no—
86C3×D3×#41D314yescomplemented
87#64320—34no—
88#64316—34no—
89#64315—34no—
90#64315—34no—
91#64314—312no—
92#64314—312no—
93#64313—312no—
94#64309—312no—
95#64306—312no—
96D3×#235—312no—
97D3×#235—312no—
98C2×#3798—312no—
99C22×C3⋊(C3⋊D3)C2313yes—
100C22×C3×C3⋊D3C2313yes—
101C22×C32×D3C2313yes—
102C2×D3×C3⋊D3C2316yes—
103C33×Q8C2311yescharacteristic
104C33×D4C2313yes—
105C2×C33×C4C2313yes—
106#6312C2316yes—
107C2×C3⋊(C3⋊Dic3)C2313yes—
108C4⋊(C3⋊(C3⋊D3))C2313yes—
109C4×C3⋊(C3⋊D3)C2313yes—
110C4×C3⋊(C3⋊D3)C2313yes—
111C4×C3⋊(C3⋊D3)C2311yescharacteristic
112C4×C3⋊(C3⋊D3)C2313yes—
113#6308C2313yes—
114C3×#638C2316yes—
115C2×C3×C3⋊Dic3C2313yes—
116C3×C4⋊(C3⋊D3)C2313yes—
117C3×C4×C3⋊D3C2313yes—
118C3×C4×C3⋊D3C2313yes—
119C3×C4×C3⋊D3C2311yescharacteristic
120C3×C4×C3⋊D3C2313yes—
121C3×#634C2313yes—
122C32×#67C2316yes—
123C2×C32×Dic3C2313yes—
124C32×D12C2313yes—
125C32×C4×D3C2313yes—
126C32×C4×D3C2311yescharacteristic
127C32×C4×D3C2313yes—
128C32×C4×D3C2313yes—
129C32×Dic6C2313yes—
130#6293C2313yes—
131#6293C2313yes—
132#6293C2313yes—
133#6293C2311yescharacteristic
134#6292C2313yes—
135#6292C2313yes—
136#6292C2311yescharacteristic
137#6292C2313yes—
138#6291C2313yes—
139#6291C2311yescharacteristic
140#6291C2313yes—
141#6291C2313yes—
142#6290C2313yes—
143#6290C2311yescharacteristic
144#6290C2313yes—
145#6290C2313yes—
146#6289C2316yes—
147Dic3×C3⋊D3C2316yes—
148D3×C3⋊Dic3C2316yes—
149#5964—94no—
150#5964—91no—
151C32×#41—24no—
152C32×#41—31no—
153C32×#41—33no—
154C32×#41—33no—
155C32×#41C2×D314yescomplemented
156C32×#41C2×D311yescharacteristic, complemented
157C2×C32×Q8—31no—
158C2×C32×D4—33no—
159C22×C32×C4—33no—
160C2×#638—33no—
161C2×#638—36no—
162C2×#638—33no—
163#3832—31no—
164#3832—34no—
165#3832—33no—
166#3832—33no—
167#3832—64no—
168#3832C2×D311yescharacteristic, complemented
169Q8×C3⋊D3—31no—
170Q8×C3⋊D3—34no—
171Q8×C3⋊D3—33no—
172Q8×C3⋊D3—33no—
173Q8×C3⋊D3—64no—
174Q8×C3⋊D3C2×D311yescharacteristic, complemented
175#3830—33no—
176#3830—312no—
177#3830—36no—
178#3830—36no—
179#3830—33no—
180#3830—33no—
181#3830—612no—
182#3830C2×D313yescomplemented
183D4×C3⋊D3—36no—
184D4×C3⋊D3—33no—
185D4×C3⋊D3—312no—
186D4×C3⋊D3—36no—
187D4×C3⋊D3—33no—
188D4×C3⋊D3—33no—
189D4×C3⋊D3—612no—
190D4×C3⋊D3C2×D313yescomplemented
191#3828—33no—
192#3828—312no—
193#3828—36no—
194#3828—33no—
195#3828—33no—
196#3828—31no—
197#3828—33no—
198#3828—33no—
199#3828—33no—
200#3828—33no—
201#3828—33no—
202#3828—33no—
203#3828—33no—
204#3828—612no—
205#3828C2×D313yescomplemented
206C2×C4⋊(C3⋊D3)—33no—
207C2×C4⋊(C3⋊D3)—33no—
208C2×C4×C3⋊D3—33no—
209C2×C4×C3⋊D3—312no—
210C2×C4×C3⋊D3—36no—
211C2×C4×C3⋊D3—612no—
212C2×C4×C3⋊D3C2×D313yescomplemented
213C2×#634—33no—
214C2×#634—33no—
215C3×#239—34no—
216C3×#239C2×D314yescomplemented
217C3×D3×Q8—34no—
218C3×D3×Q8C2×D314yescomplemented
219C3×#237—312no—
220C3×#237C2×D3112yescomplemented
221C3×D3×D4—312no—
222C3×D3×D4C2×D3112yescomplemented
223C3×#235—312no—
224C3×#235C2×D3112yescomplemented
225C2×C3×C4×D3—312no—
226C2×C3×C4×D3C2×D3112yescomplemented
227#3811—324no—
228D3×#67—324no—
229D3×#67—324no—
230C2×#627—312no—
231C2×#626—312no—
232C2×#626—312no—
233C2×#625—312no—
234#3805—324no—
235#3804—324no—
236#3804—324no—
237#3802—312no—
238D3×D12—312no—
239D3×D12—312no—
240C4×D32—324no—
241#3799—312no—
242#3799—312no—
243#3798—34no—
244#3798—312no—
245#3798—312no—
246#3798—312no—
247#3798—312no—
248#3798—312no—
249#3798—312no—
250#3798—312no—
251#3797—312no—
252#3796—312no—
253#3796—312no—
254#3795—312no—
255#3795—312no—
256D3×Dic6—312no—
257D3×Dic6—312no—
258C22×C33C2413yes—
259C2×C3⋊(C3⋊D3)—43no—
260C2×C3⋊(C3⋊D3)C2413yes—
261C2×C3⋊(C3⋊D3)C2411yescharacteristic
262C2×C3×C3⋊D3—43no—
263C2×C3×C3⋊D3C2413yes—
264C2×C3×C3⋊D3C2411yescharacteristic
265C2×C32×D3—43no—
266C2×C32×D3C2413yes—
267C2×C32×D3C2411yescharacteristic
268D3×C3⋊D3—46no—
269C33×C4C2413yes—
270C33×C4C2411yescharacteristic
271C3⋊(C3⋊Dic3)C2413yes—
272C3⋊(C3⋊Dic3)C2411yescharacteristic
273C3×C3⋊Dic3C2413yes—
274C3×C3⋊Dic3C2411yescharacteristic
275C32×Dic3C2413yes—
276C32×Dic3C2411yescharacteristic
277C2×C3×#41—34no—
278C2×C3×#41—91no—
279#1010—912no—
280#1010—94no—
281#1010—91no—
282#1010—93no—
283#1009—912no—
284#1009—94no—
285#1009—91no—
286#1009—93no—
287D3×#41—34no—
288D3×#41—912no—
289D3×#41—912no—
290D3×#41—94no—
291D3×#41—91no—
292D3×#41—93no—
293D3×#41—93no—
294D3×#41—184no—
295D3×#41C3⋊D311yescharacteristic, complemented
296#1007—94no—
297#1007—94no—
298#1007—91no—
299#1007—91no—
300#1004—912no—
301#1004—912no—
302#1004—93no—
303#1004—93no—
304C2×#235—912no—
305C2×#235—912no—
306C2×#235—93no—
307C2×#235—93no—
308C23×C32—33no—
309C22×C3⋊D3—33no—
310C22×C3⋊D3—36no—
311C22×C3⋊D3—312no—
312C22×C3⋊D3—612no—
313C22×C3⋊D3C22×D313yes—
314C22×C3×D3—312no—
315C22×C3×D3C22×D3112yes—
316C2×D32—324no—
317C32×Q8—24no—
318C32×Q8—33no—
319C32×Q8C22×D314yes—
320C32×Q8C22×D311yescharacteristic
321C32×D4—212no—
322C32×D4—36no—
323C32×D4—33no—
324C32×D4C22×D3112yes—
325C32×D4C22×D313yes—
326C2×C32×C4—212no—
327C2×C32×C4—33no—
328C2×C32×C4—33no—
329C2×C32×C4—33no—
330C2×C32×C4—31no—
331C2×C32×C4—33no—
332C2×C32×C4C22×D3112yes—
333C2×C32×C4C22×D313yes—
334#638—36no—
335#638—33no—
336#638—31no—
337#638—33no—
338#638—33no—
339#638—31no—
340#638—33no—
341#638—33no—
342#638—33no—
343#638—324no—
344#638—624no—
345#638C22×D316yes—
346C2×C3⋊Dic3—33no—
347C2×C3⋊Dic3—36no—
348C2×C3⋊Dic3—312no—
349C2×C3⋊Dic3—612no—
350C2×C3⋊Dic3C22×D313yes—
351C4⋊(C3⋊D3)—33no—
352C4⋊(C3⋊D3)—31no—
353C4⋊(C3⋊D3)—33no—
354C4⋊(C3⋊D3)—33no—
355C4⋊(C3⋊D3)—33no—
356C4⋊(C3⋊D3)—312no—
357C4⋊(C3⋊D3)—612no—
358C4⋊(C3⋊D3)C22×D313yes—
359C4×C3⋊D3—36no—
360C4×C3⋊D3—31no—
361C4×C3⋊D3—33no—
362C4×C3⋊D3—33no—
363C4×C3⋊D3—33no—
364C4×C3⋊D3—36no—
365C4×C3⋊D3—312no—
366C4×C3⋊D3—312no—
367C4×C3⋊D3—34no—
368C4×C3⋊D3—312no—
369C4×C3⋊D3—64no—
370C4×C3⋊D3—612no—
371C4×C3⋊D3—612no—
372C4×C3⋊D3—612no—
373C4×C3⋊D3C22×D313yes—
374C4×C3⋊D3C22×D311yescharacteristic
375C4×C3⋊D3C22×D313yes—
376C4×C3⋊D3C22×D313yes—
377#634—33no—
378#634—31no—
379#634—33no—
380#634—33no—
381#634—33no—
382#634—312no—
383#634—612no—
384#634C22×D313yes—
385C3×#67—324no—
386C3×#67C22×D3124yes—
387C2×C3×Dic3—312no—
388C2×C3×Dic3C22×D3112yes—
389C3×D12—312no—
390C3×D12C22×D3112yes—
391C3×C4×D3—312no—
392C3×C4×D3—312no—
393C3×C4×D3—34no—
394C3×C4×D3—312no—
395C3×C4×D3C22×D3112yes—
396C3×C4×D3C22×D3112yes—
397C3×C4×D3C22×D314yes—
398C3×C4×D3C22×D3112yes—
399C3×Dic6—312no—
400C3×Dic6C22×D3112yes—
401#627—312no—
402#627—312no—
403#627—312no—
404#627—34no—
405#626—312no—
406#626—34no—
407#626—312no—
408#626—312no—
409#626—312no—
410#626—34no—
411#626—312no—
412#626—312no—
413#625—312no—
414#625—312no—
415#625—34no—
416#625—312no—
417#624—324no—
418D3×Dic3—324no—
419D3×Dic3—324no—
420#585—271noSylow
421C2×C33—23no—
422C2×C33C2511yescharacteristic
423C3⋊(C3⋊D3)—21no—
424C3⋊(C3⋊D3)—23no—
425C3×C3⋊D3—23no—
426C3×C3⋊D3—21no—
427C32×D3—23no—
428C32×D3—21no—
429C3×#41—24no—
430C3×#41—34no—
431C3×#41—312no—
432C3×#41—312no—
433C3×#41—91no—
434C3×#41—93no—
435C3×#41—93no—
436C3×#41D3214yescomplemented
437C3×#41C2×C3⋊D311yescharacteristic, complemented
438C2×C3×Q8—34no—
439C2×C3×Q8—91no—
440C2×C3×D4—312no—
441C2×C3×D4—93no—
442C22×C3×C4—312no—
443C22×C3×C4—93no—
444C2×#67—912no—
445C2×#67—924no—
446C2×#67—912no—
447C2×#67—93no—
448C2×#67—96no—
449C2×#67—93no—
450#239—34no—
451#239—912no—
452#239—912no—
453#239—94no—
454#239—91no—
455#239—93no—
456#239—93no—
457#239—184no—
458#239C2×C3⋊D311yescharacteristic, complemented
459D3×Q8—34no—
460D3×Q8—912no—
461D3×Q8—912no—
462D3×Q8—94no—
463D3×Q8—91no—
464D3×Q8—93no—
465D3×Q8—93no—
466D3×Q8—184no—
467D3×Q8C2×C3⋊D311yescharacteristic, complemented
468#237—312no—
469#237—912no—
470#237—912no—
471#237—924no—
472#237—924no—
473#237—912no—
474#237—93no—
475#237—96no—
476#237—96no—
477#237—93no—
478#237—93no—
479#237—1812no—
480#237C2×C3⋊D313yescomplemented
481D3×D4—312no—
482D3×D4—912no—
483D3×D4—912no—
484D3×D4—924no—
485D3×D4—924no—
486D3×D4—96no—
487D3×D4—912no—
488D3×D4—93no—
489D3×D4—96no—
490D3×D4—93no—
491D3×D4—93no—
492D3×D4—1812no—
493D3×D4C2×C3⋊D313yescomplemented
494#235—312no—
495#235—912no—
496#235—94no—
497#235—912no—
498#235—912no—
499#235—912no—
500#235—912no—
501#235—912no—
502#235—912no—
503#235—912no—
504#235—912no—
505#235—924no—
506#235—912no—
507#235—93no—
508#235—96no—
509#235—93no—
510#235—93no—
511#235—91no—
512#235—93no—
513#235—93no—
514#235—93no—
515#235—93no—
516#235—93no—
517#235—93no—
518#235—93no—
519#235—1812no—
520#235C2×C3⋊D313yescomplemented
521C2×D12—912no—
522C2×D12—912no—
523C2×D12—93no—
524C2×D12—93no—
525C2×C4×D3—312no—
526C2×C4×D3—924no—
527C2×C4×D3—912no—
528C2×C4×D3—93no—
529C2×C4×D3—96no—
530C2×C4×D3—1812no—
531C2×C4×D3C2×C3⋊D313yescomplemented
532C2×Dic6—912no—
533C2×Dic6—912no—
534C2×Dic6—93no—
535C2×Dic6—93no—
536C22×C32—212no—
537C22×C32—33no—
538C22×C32—31no—
539C22×C32—123no—
540C22×C32C23×D3112yes—
541C22×C32C23×D313yes—
542C2×C3⋊D3—33no—
543C2×C3⋊D3—31no—
544C2×C3⋊D3—312no—
545C2×C3⋊D3—34no—
546C2×C3⋊D3—43no—
547C2×C3⋊D3—64no—
548C2×C3⋊D3—612no—
549C2×C3⋊D3—126no—
550C2×C3⋊D3—123no—
551C2×C3⋊D3—1212no—
552C2×C3⋊D3—1224no—
553C2×C3⋊D3C23×D313yes—
554C2×C3⋊D3C23×D311yescharacteristic
555C2×C3×D3—312no—
556C2×C3×D3—34no—
557C2×C3×D3—412no—
558C2×C3×D3—1212no—
559C2×C3×D3C23×D3112yes—
560C2×C3×D3C23×D314yes—
561D32—1224no—
562C32×C4—212no—
563C32×C4—24no—
564C32×C4—31no—
565C32×C4—33no—
566C32×C4C23×D3112yes—
567C32×C4C23×D314yes—
568C32×C4C23×D313yes—
569C32×C4C23×D311yescharacteristic
570C3⋊Dic3—33no—
571C3⋊Dic3—31no—
572C3⋊Dic3—312no—
573C3⋊Dic3—34no—
574C3⋊Dic3—612no—
575C3⋊Dic3—64no—
576C3⋊Dic3C23×D311yescharacteristic
577C3⋊Dic3C23×D313yes—
578C3×Dic3—312no—
579C3×Dic3—34no—
580C3×Dic3C23×D3112yes—
581C3×Dic3C23×D314yes—
5822−1+4—271no—
5832−1+4—271no—
5842−1+4—271no—
5852−1+4—273no—
586H(5,𝔽2)—273no—
587H(5,𝔽2)—273no—
588H(5,𝔽2)—273no—
589H(5,𝔽2)—271no—
590C2×#41—31no—
591C2×#41—91no—
592C2×#41—273no—
593C2×#41—273no—
594C2×#41—273no—
595C2×#41—273no—
596C2×#41—271no—
597C33#58511yescharacteristic, complemented, Sylow
598C23×C3—312no—
599C23×C3—93no—
600C22×D3—312no—
601C22×D3—924no—
602C22×D3—912no—
603C22×D3—93no—
604C22×D3—96no—
605C22×D3—1812no—
606C22×D3C22×C3⋊D313yes—
607C3×Q8—24no—
608C3×Q8—312no—
609C3×Q8—93no—
610C3×Q8C2×D3214yes—
611C3×Q8C22×C3⋊D311yescharacteristic
612C3×D4—212no—
613C3×D4—324no—
614C3×D4—312no—
615C3×D4—96no—
616C3×D4—93no—
617C3×D4C2×D32112yes—
618C3×D4C22×C3⋊D313yes—
619C2×C3×C4—212no—
620C2×C3×C4—312no—
621C2×C3×C4—312no—
622C2×C3×C4—312no—
623C2×C3×C4—34no—
624C2×C3×C4—312no—
625C2×C3×C4—93no—
626C2×C3×C4—93no—
627C2×C3×C4—93no—
628C2×C3×C4—91no—
629C2×C3×C4—93no—
630C2×C3×C4C2×D32112yes—
631C2×C3×C4C22×C3⋊D313yes—
632#67—324no—
633#67—912no—
634#67—94no—
635#67—912no—
636#67—912no—
637#67—94no—
638#67—912no—
639#67—912no—
640#67—912no—
641#67—924no—
642#67—96no—
643#67—93no—
644#67—91no—
645#67—93no—
646#67—93no—
647#67—91no—
648#67—93no—
649#67—93no—
650#67—93no—
651#67—1824no—
652#67C22×C3⋊D316yes—
653C2×Dic3—312no—
654C2×Dic3—924no—
655C2×Dic3—912no—
656C2×Dic3—93no—
657C2×Dic3—96no—
658C2×Dic3—1812no—
659C2×Dic3C22×C3⋊D313yes—
660D12—312no—
661D12—94no—
662D12—912no—
663D12—912no—
664D12—912no—
665D12—93no—
666D12—91no—
667D12—93no—
668D12—93no—
669D12—912no—
670D12—93no—
671D12—1812no—
672D12C22×C3⋊D313yes—
673C4×D3—34no—
674C4×D3—312no—
675C4×D3—312no—
676C4×D3—312no—
677C4×D3—924no—
678C4×D3—924no—
679C4×D3—96no—
680C4×D3—94no—
681C4×D3—912no—
682C4×D3—912no—
683C4×D3—912no—
684C4×D3—91no—
685C4×D3—93no—
686C4×D3—93no—
687C4×D3—93no—
688C4×D3—96no—
689C4×D3—184no—
690C4×D3—1812no—
691C4×D3—1812no—
692C4×D3—1812no—
693C4×D3C22×C3⋊D313yes—
694C4×D3C22×C3⋊D311yescharacteristic
695C4×D3C22×C3⋊D313yes—
696C4×D3C22×C3⋊D313yes—
697Dic6—312no—
698Dic6—912no—
699Dic6—94no—
700Dic6—912no—
701Dic6—912no—
702Dic6—912no—
703Dic6—93no—
704Dic6—91no—
705Dic6—93no—
706Dic6—93no—
707Dic6—93no—
708Dic6—1812no—
709Dic6C22×C3⋊D313yes—
710C2×C32—23no—
711C2×C32—24no—
712C2×C32—212no—
713C2×C32—412no—
714C2×C32—63no—
715C2×C32—61no—
716C2×C32C24×D314yes—
717C2×C32C24×D311yescharacteristic
718C3⋊D3—21no—
719C3⋊D3—23no—
720C3⋊D3—68no—
721C3⋊D3—64no—
722C3⋊D3—61no—
723C3⋊D3—63no—
724C3⋊D3—612no—
725C3⋊D3—1212no—
726C3×D3—212no—
727C3×D3—24no—
728C3×D3—612no—
729C3×D3—64no—
730#41—31no—
731#41—33no—
732#41—33no—
733#41—91no—
734#41—93no—
735#41—93no—
736#41—271no—
737#41—273no—
738#41—273no—
739#41—273no—
740#41—273no—
741#41—273no—
742#41—273no—
743#41—273no—
744#41—276no—
745#41—273no—
746#41—273no—
747#41—276no—
748#41—273no—
749#41—273no—
750#41—276no—
751#41—273no—
752#41—273no—
753#41—271no—
754#41—273no—
755#41—273no—
756#41D3×C3⋊D311yescharacteristic, complemented
757C2×Q8—31no—
758C2×Q8—91no—
759C2×Q8—273no—
760C2×Q8—273no—
761C2×Q8—273no—
762C2×Q8—273no—
763C2×Q8—271no—
764C2×D4—33no—
765C2×D4—93no—
766C2×D4—273no—
767C2×D4—273no—
768C2×D4—273no—
769C2×D4—273no—
770C2×D4—276no—
771C2×D4—273no—
772C2×D4—276no—
773C2×D4—276no—
774C2×D4—273no—
775C2×D4—273no—
776C22×C4—33no—
777C22×C4—93no—
778C22×C4—276no—
779C22×C4—273no—
780C22×C3—212no—
781C22×C3—312no—
782C22×C3—34no—
783C22×C3—93no—
784C22×C3—91no—
785C22×C3—1212no—
786C22×C3—363no—
787C22×C3C22×D32112yes—
788C22×C3C23×C3⋊D313yes—
789C2×D3—34no—
790C2×D3—312no—
791C2×D3—43no—
792C2×D3—94no—
793C2×D3—912no—
794C2×D3—91no—
795C2×D3—93no—
796C2×D3—1212no—
797C2×D3—184no—
798C2×D3—1812no—
799C2×D3—366no—
800C2×D3—3624no—
801C2×D3—3612no—
802C2×D3—363no—
803C2×D3—3624no—
804C2×D3C23×C3⋊D313yes—
805C2×D3C23×C3⋊D311yescharacteristic
806C3×C4—212no—
807C3×C4—24no—
808C3×C4—34no—
809C3×C4—312no—
810C3×C4—91no—
811C3×C4—93no—
812C3×C4C22×D32112yes—
813C3×C4C22×D3214yes—
814C3×C4C23×C3⋊D313yes—
815C3×C4C23×C3⋊D311yescharacteristic
816Dic3—312no—
817Dic3—34no—
818Dic3—94no—
819Dic3—912no—
820Dic3—93no—
821Dic3—91no—
822Dic3—1812no—
823Dic3—184no—
824Dic3C23×C3⋊D311yescharacteristic
825Dic3C23×C3⋊D313yes—
826C32—24no—
827C32#596414yescomplemented
828C32#596411yescharacteristic, complemented
829C23—33no—
830C23—93no—
831C23—276no—
832C23—273no—
833Q8—33no—
834Q8—93no—
835Q8—271no—
836Q8—273no—
837Q8—273no—
838Q8—273no—
839Q8—273no—
840Q8C2×D3×C3⋊D311yescharacteristic
841D4—36no—
842D4—33no—
843D4—96no—
844D4—93no—
845D4—271no—
846D4—273no—
847D4—273no—
848D4—273no—
849D4—271no—
850D4—273no—
851D4—273no—
852D4—273no—
853D4—271no—
854D4—273no—
855D4—273no—
856D4—273no—
857D4—276no—
858D4—273no—
859D4C2×D3×C3⋊D313yes—
860C2×C4—33no—
861C2×C4—33no—
862C2×C4—33no—
863C2×C4—31no—
864C2×C4—33no—
865C2×C4—93no—
866C2×C4—93no—
867C2×C4—93no—
868C2×C4—91no—
869C2×C4—93no—
870C2×C4—276no—
871C2×C4—276no—
872C2×C4—276no—
873C2×C4—273no—
874C2×C4—273no—
875C2×C4—273no—
876C2×C4—273no—
877C2×C4—271no—
878C2×C4C2×D3×C3⋊D313yes—
879C2×C3—212no—
880C2×C3—23no—
881C2×C3—24no—
882C2×C3—412no—
883C2×C3—612no—
884C2×C3—64no—
885C2×C3—183no—
886C2×C3—181no—
887C2×C3C23×D3214yes—
888C2×C3C24×C3⋊D311yescharacteristic
889D3—21no—
890D3—23no—
891D3—64no—
892D3—612no—
893D3—188no—
894D3—184no—
895D3—1812no—
896D3—181no—
897D3—183no—
898D3—3612no—
899C22—31no—
900C22—33no—
901C22—91no—
902C22—93no—
903C22—123no—
904C22—271no—
905C22—273no—
906C22—363no—
907C22—1083no—
908C22—1086no—
909C22C22×D3×C3⋊D313yes—
910C4—31no—
911C4—33no—
912C4—91no—
913C4—93no—
914C4—273no—
915C4—271no—
916C4C22×D3×C3⋊D313yes—
917C4C22×D3×C3⋊D311yescharacteristic
918C3—24no—
919C3#1059669514yescomplemented
920C3#1059675611yescharacteristic, complemented
921C2—23no—
922C2—61no—
923C2—63no—
924C2—181no—
925C2—183no—
926C2—541no—
927C2—543no—
928C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC4C22×D3×C3⋊D3
commutator, socle, cosocleC2×C33C25
FrattiniC2C23×D3×C3⋊D3
FittingC33×#41C22
hypercenter#41D3×C3⋊D3
hypocenterC33#585
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊(C3⋊D3)C2semidirect
2. C3×#41×C3⋊D3C2semidirect
3. C32×D3×#41C2semidirect
4. #11724597C2semidirect
5. #11724592C2semidirect
6. #11724591C2semidirect
7. #11724590C2semidirect
8. #11724589C2semidirect
9. #11724588C2semidirect
10. #11724587C2semidirect
11. #11724582C2semidirect
12. #11724578C2semidirect
13. C3⋊D3×#235C2semidirect
14. D3×#3828C2semidirect
15. C2×#89020C2semidirect
18. C33×#41C22semidirect
19. #89080C22semidirect
20. Q8×C3⋊(C3⋊D3)C22semidirect
21. #89078C22semidirect
22. D4×C3⋊(C3⋊D3)C22semidirect
23. #89076C22semidirect
24. C2×C4×C3⋊(C3⋊D3)C22semidirect
25. C3×#3832C22semidirect
26. C3×Q8×C3⋊D3C22semidirect
27. C3×#3830C22semidirect
28. C3×D4×C3⋊D3C22semidirect
29. C3×#3828C22semidirect
30. C2×C3×C4×C3⋊D3C22semidirect
31. C32×#239C22semidirect
32. C32×D3×Q8C22semidirect
33. C32×#237C22semidirect
34. C32×D3×D4C22semidirect
35. C32×#235C22semidirect
36. C2×C32×C4×D3C22semidirect
37. #89039C22semidirect
38. C3⋊D3×#67C22semidirect
39. D3×#638C22semidirect
40. C2×#6293C22semidirect
41. C2×#6292C22semidirect
42. C2×#6291C22semidirect
43. C2×#6290C22semidirect
44. #89031C22semidirect
45. #89029C22semidirect
46. #89028C22semidirect
47. #89026C22semidirect
48. C3⋊D3×D12C22semidirect
49. D3×C4⋊(C3⋊D3)C22semidirect
50. C4×D3×C3⋊D3C22semidirect
51. #89022C22semidirect
52. #89021C22semidirect
53. #89020C22semidirect
54. #89020C22semidirect
55. #89020C22semidirect
56. #89020C22semidirect
57. #89020C22semidirect
58. #89020C22semidirect
59. #89020C22semidirect
60. #89020C22semidirect
61. #89019C22semidirect
62. #89018C22semidirect
63. #89017C22semidirect
64. C3⋊D3×Dic6C22semidirect
65. #89015C22semidirect
66. #89014C22semidirect
67. D3×#634C22semidirect
78. #41×C3⋊D3D3semidirect
86. C3×D3×#41D3semidirect
155. C32×#41C2×D3semidirect
156. C32×#41C2×D3semidirect
168. #3832C2×D3semidirect
174. Q8×C3⋊D3C2×D3semidirect
182. #3830C2×D3semidirect
190. D4×C3⋊D3C2×D3semidirect
205. #3828C2×D3semidirect
212. C2×C4×C3⋊D3C2×D3semidirect
216. C3×#239C2×D3semidirect
218. C3×D3×Q8C2×D3semidirect
220. C3×#237C2×D3semidirect
222. C3×D3×D4C2×D3semidirect
224. C3×#235C2×D3semidirect
226. C2×C3×C4×D3C2×D3semidirect
295. D3×#41C3⋊D3semidirect
436. C3×#41D32semidirect
437. C3×#41C2×C3⋊D3semidirect
458. #239C2×C3⋊D3semidirect
467. D3×Q8C2×C3⋊D3semidirect
480. #237C2×C3⋊D3semidirect
493. D3×D4C2×C3⋊D3semidirect
520. #235C2×C3⋊D3semidirect
531. C2×C4×D3C2×C3⋊D3semidirect
597. C33#585semidirect
756. #41D3×C3⋊D3semidirect
827. C32#5964semidirect
828. C32#5964semidirect
919. C3#10596695semidirect
920. C3#10596756semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊(C3⋊D3)2
C3×#41×C3⋊D32
C32×D3×#412
#117245972
#117245922
#117245912
#117245902
#117245892
#117245882
#117245872
#117245822
#117245782
C3⋊D3×#2352
D3×#38282
C2×#890202
#105967563
#105966953