Finite Group Databasebeta

← #11904219

Subgroups — #11904219

Order 1152.

2333 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596302C211yesmaximal, characteristic, complemented
2C3×#5831C211yesmaximal, characteristic, complemented
3C3×Dic3×#41C211yesmaximal, characteristic, complemented
4#10595422C211yesmaximal, characteristic, complemented
5Q8×#626C211yesmaximal, characteristic, complemented
6Q8×#624C211yesmaximal, characteristic, complemented
7D3×Q8×Dic3C211yesmaximal, characteristic, complemented
8#10595273C213yesmaximal, complemented
9#10595191C213yesmaximal, complemented
10#10595172C213yesmaximal, complemented
11#10595136C213yesmaximal, complemented
12#10594970C213yesmaximal, complemented
13#10594939C213yesmaximal, complemented
14C4×#3804C213yesmaximal, complemented
15#10594808C213yesmaximal, complemented
16#86712—31nomaximal
17#85844—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3804C2213yes—
22Q8×C3⋊Dic3C2211yescharacteristic
23#64147C2213yes—
24#64145C2213yes—
25C4×#638C2213yes—
26#64133C2213yes—
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×#938C2213yes—
31C3×#936C2213yes—
32C3×D4×Dic3C2213yes—
33C3×D4×Dic3C2213yes—
34C3×C4×#67C2213yes—
35C3×#926C2213yes—
36C3×#924C2213yes—
37C2×C3×C4×Dic3C2213yes—
38#63975C2216yes—
39Dic3×#67C2213yes—
40#63969C2216yes—
41#63964C2216yes—
42#63956C2216yes—
43#63956C2216yes—
44#63955C2213yes—
45#63955C2216yes—
46#63952C2213yes—
47#63918C2213yes—
48C4×#627C2213yes—
49C4×#626C2213yes—
50#63900C2213yes—
51D3×C4⋊Dic3C2213yes—
52C4×#624C2213yes—
53#63880C2211yescharacteristic
54#63877C2213yes—
55C4×D3×Dic3C2213yes—
56#63872C2213yes—
57#63871C2213yes—
58#63869C2213yes—
59#63867C2216yes—
60#63866C2213yes—
61#63857C2213yes—
62#63844C2213yes—
63#63844C2213yes—
64#63843C2213yes—
65Dic3×Dic6C2213yes—
66#63837C2213yes—
67#63836C2213yes—
68C3×#548—31no—
69C3×C4×#41—31no—
70#5831—31no—
71#5831—31no—
72#5831—61no—
73#5831D311yescharacteristic, complemented
74Dic3×#41D311yescharacteristic, complemented
75Q8×#67—31no—
76C2×Q8×Dic3—31no—
77#5680—33no—
78#5671—33no—
79#5639—33no—
80#5622—33no—
81#5611—33no—
82#5600—33no—
83Q8×D12—31no—
84C4×D3×Q8—31no—
85C4×D3×Q8—31no—
86C4×D3×Q8—31no—
87#5570—31no—
88#5569—31no—
89#5557—33no—
90#5557—33no—
91#5551—33no—
92#5542—33no—
93#5541—33no—
94C4×#237—33no—
95#5529—33no—
96#5529—33no—
97C4×#235—33no—
98#5470—33no—
99C32×#41—24no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2313yes—
102C22×C32×C4C2313yes—
103C2×#638C2313yes—
104Q8×C3⋊D3—24no—
105C2×C4×C3⋊D3C2313yes—
106C2×#634C2313yes—
107C2×C3×#67C2313yes—
108C22×C3×Dic3C2313yes—
109C22×C3×Dic3C2313yes—
110C3×D3×Q8—24no—
111C2×C3×C4×D3C2313yes—
112C2×C3×Dic6C2313yes—
113C2×#627C2313yes—
114C2×#626C2311yescharacteristic
115C2×#624C2313yes—
116C2×#624C2311yescharacteristic
117#3804—212no—
118C2×D3×Dic3C2313yes—
119C2×D3×Dic3C2311yescharacteristic
120#3757C2316yes—
121#3757C2313yes—
122#3752C2311yescharacteristic
123C4⋊(C3⋊Dic3)C2313yes—
124#3750C2313yes—
125C4×C3⋊Dic3C2313yes—
126C3×#217C2316yes—
127C3×#217C2316yes—
128C3×#217C2313yes—
129C3×(C2×D3)⋊C4C2311yescharacteristic
130C3×C4⋊Dic3C2313yes—
131C3×C4⋊Dic3C2313yes—
132C3×C4⋊Dic3C2313yes—
133C3×Dic3⋊C4C2313yes—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2313yes—
136C3×C4×Dic3C2313yes—
137C3×C4×Dic3C2313yes—
138C3×C4×Dic3C2313yes—
139#3724C2316yes—
140#3724C2313yes—
141Dic3⋊Dic3C2313yes—
142Dic3⋊Dic3C2313yes—
143Dic3⋊Dic3C2316yes—
144Dic3⋊Dic3C2316yes—
145Dic3⋊Dic3C2316yes—
146Dic3⋊Dic3C2311yescharacteristic
147#3722C2313yes—
148(C2×D3)⋊Dic3C2313yes—
149Dic32C2313yes—
150Dic32C2313yes—
151Dic32C2313yes—
152Dic32C2313yes—
153#3482—91noSylow
154C2×C3×#41—21no—
155C2×C3×#41C2×D311yescharacteristic
156C2×C3×#41C2×D311yescharacteristic
157C22×C3×Q8—31no—
158C2×D3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—61no—
161C2×D3×Q8C2×D311yescharacteristic
162C2×#237—33no—
163C2×#235—33no—
164C3×#124—33no—
165C3×C22⋊Q8—33no—
166C3×#121—33no—
167C3×C4×Q8—31no—
168C3×C4×Q8—31no—
169C3×C4×Q8—31no—
170C3×C4×D4—33no—
171C3×C4×D4—33no—
172C3×C4×D4—33no—
173C3×#117—33no—
174C2×C3×C42—33no—
175#946—33no—
176Q8×Dic3—31no—
177Q8×Dic3—31no—
178Q8×Dic3—33no—
179Q8×Dic3—33no—
180Q8×Dic3—61no—
181Q8×Dic3C2×D311yescharacteristic
182Q8×Dic3C2×D311yescharacteristic
183Q8×Dic3C2×D311yescharacteristic
184#944—33no—
185#938—33no—
186#938—33no—
187#938—63no—
188#938C2×D313yes—
189#936—33no—
190#936—33no—
191#936—63no—
192#936C2×D313yes—
193#935—36no—
194D4×Dic3—33no—
195D4×Dic3C2×D313yes—
196D4×Dic3C2×D313yes—
197C4×#67—33no—
198C4×#67—33no—
199C4×#67—33no—
200C4×#67—33no—
201C4×#67—33no—
202C4×#67—63no—
203C4×#67C2×D313yes—
204#926—36no—
205#926—33no—
206#926C2×D313yes—
207C2×C4⋊Dic3—33no—
208#924—33no—
209#924—33no—
210#924—36no—
211#924—33no—
212#924—63no—
213#924C2×D313yes—
214C2×C4×Dic3—33no—
215C2×C4×Dic3C2×D313yes—
216#897—33no—
217#897—33no—
218#892—33no—
219D3×C4⋊C4—33no—
220D3×C4⋊C4—33no—
221D3×C4⋊C4—33no—
222#890—33no—
223#890—33no—
224#890—33no—
225#889—36no—
226#888—33no—
227#887—33no—
228#887—33no—
229#887—33no—
230#887—33no—
231#883—36no—
232#883—36no—
233#883—36no—
234#67⋊C4—33no—
235#67⋊C4—31no—
236#879—36no—
237#879—36no—
238#879—36no—
239#879—36no—
240#878—36no—
241#877—33no—
242#877—36no—
243#877—33no—
244C4×D12—33no—
245C4×D12—31no—
246#872—33no—
247#872—33no—
248C42×D3—33no—
249C42×D3—33no—
250C42×D3—33no—
251#870—33no—
252#870—36no—
253#869—33no—
254#869—33no—
255C4×Dic6—33no—
256C4×Dic6—33no—
257C4×Dic6—33no—
258C4×Dic6—33no—
259C4×Dic6—33no—
260C4×Dic6—33no—
261C23×C32C2413yes—
262C22×C3⋊D3C2411yescharacteristic
263C22×C3×D3C2411yescharacteristic
264C32×Q8#4114yescomplemented
265C32×D4—26no—
266C2×C32×C4—26no—
267C2×C32×C4C2411yescharacteristic
268C2×C32×C4C2413yes—
269#638—26no—
270C2×C3⋊Dic3C2411yescharacteristic
271C2×C3⋊Dic3C2413yes—
272C2×C3⋊Dic3C2413yes—
273C4×C3⋊D3—26no—
274#634—26no—
275C3×#67—26no—
276C2×C3×Dic3—26no—
277C2×C3×Dic3—26no—
278C2×C3×Dic3C2411yescharacteristic
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2413yes—
281C2×C3×Dic3C2413yes—
282C2×C3×Dic3C2413yes—
283C2×C3×Dic3C2411yescharacteristic
284C2×C3×Dic3C2411yescharacteristic
285C3×C4×D3—26no—
286C3×Dic6—26no—
287#627—26no—
288#626#4114yescomplemented
289#624—26no—
290#624—22no—
291D3×Dic3—26no—
292D3×Dic3—22no—
293#557—91no—
294#556—93no—
295#552—93no—
296#552—93no—
297D4×Q8—91no—
298#548—31no—
299#548—91no—
300#547—93no—
301#533—93no—
302#529—93no—
303#529—93no—
304C4×#41—31no—
305C4×#41—93no—
306C2×C4×Q8—91no—
307C2×C4×Q8—91no—
308C3×#41—24no—
309C3×#41—24no—
310C3×#41—44no—
311C2×C3×Q8—21no—
312C2×C3×Q8—33no—
313C2×C3×Q8—64no—
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×D4—23no—
317C2×C3×D4—33no—
318C2×C3×D4C22×D313yes—
319C2×C3×D4C22×D313yes—
320C22×C3×C4—23no—
321C22×C3×C4—33no—
322C22×C3×C4—33no—
323C22×C3×C4—33no—
324C22×C3×C4C22×D313yes—
325C22×C3×C4C22×D313yes—
326C2×#67—33no—
327C2×#67—33no—
328C2×#67—31no—
329C2×#67—63no—
330C2×#67C22×D313yes—
331C22×Dic3—33no—
332C22×Dic3—31no—
333C22×Dic3C22×D313yes—
334C22×Dic3C22×D313yes—
335D3×Q8—24no—
336D3×Q8—64no—
337D3×Q8—64no—
338D3×Q8—124no—
339#237—612no—
340#235—612no—
341C2×D12—31no—
342C2×C4×D3—31no—
343C2×C4×D3—33no—
344C2×C4×D3—33no—
345C2×C4×D3—33no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—33no—
349C2×C4×D3—33no—
350C2×C4×D3—63no—
351C2×C4×D3C22×D313yes—
352C2×Dic6—33no—
353C2×Dic6—33no—
354C2×Dic6—33no—
355C2×Dic6—33no—
356C2×Dic6—63no—
357C2×Dic6C22×D313yes—
358C3×C4⋊C4—33no—
359C3×C4⋊C4—33no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—33no—
362C3×C22⋊C4—36no—
363C3×C22⋊C4—33no—
364C3×C22⋊C4—36no—
365C3×C22⋊C4—31no—
366C3×C42—31no—
367C3×C42—33no—
368C3×C42—33no—
369C3×C42—33no—
370C3×C42—33no—
371#217—36no—
372#217—33no—
373#217—33no—
374#217—36no—
375#217—33no—
376#217—66no—
377#217—63no—
378#217C22×D316yes—
379#217C22×D313yes—
380#217C22×D316yes—
381(C2×D3)⋊C4—33no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—33no—
385(C2×D3)⋊C4—33no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4C22×D311yescharacteristic
388C4⋊Dic3—33no—
389C4⋊Dic3—33no—
390C4⋊Dic3—31no—
391C4⋊Dic3—33no—
392C4⋊Dic3—33no—
393C4⋊Dic3—36no—
394C4⋊Dic3—36no—
395C4⋊Dic3—36no—
396C4⋊Dic3—63no—
397C4⋊Dic3C22×D313yes—
398C4⋊Dic3C22×D313yes—
399C4⋊Dic3C22×D313yes—
400Dic3⋊C4—33no—
401Dic3⋊C4—33no—
402Dic3⋊C4—31no—
403Dic3⋊C4—33no—
404Dic3⋊C4—36no—
405Dic3⋊C4—36no—
406Dic3⋊C4—33no—
407Dic3⋊C4—33no—
408Dic3⋊C4—36no—
409Dic3⋊C4—36no—
410Dic3⋊C4—33no—
411Dic3⋊C4—36no—
412Dic3⋊C4—63no—
413Dic3⋊C4C22×D313yes—
414C4×Dic3—33no—
415C4×Dic3—33no—
416C4×Dic3—33no—
417C4×Dic3—33no—
418C4×Dic3—33no—
419C4×Dic3—33no—
420C4×Dic3—33no—
421C4×Dic3—33no—
422C4×Dic3—33no—
423C4×Dic3—33no—
424C4×Dic3—63no—
425C4×Dic3C22×D313yes—
426C4×Dic3C22×D313yes—
427C4×Dic3C22×D313yes—
428C4×Dic3C22×D313yes—
429C4×Dic3C22×D311yescharacteristic
430C22×C32—23no—
431C22×C32—23no—
432C22×C32—23no—
433C22×C32C2511yescharacteristic
434C2×C3⋊D3—21no—
435C2×C3⋊D3—21no—
436C2×C3⋊D3C2×#4112yes—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3C2×#4112yes—
440C32×C4—21no—
441C32×C4C2×#4116yes—
442C3⋊Dic3—23no—
443C3⋊Dic3—23no—
444C3⋊Dic3—21no—
445C3×Dic3—23no—
446C3×Dic3—23no—
447C3×Dic3—23no—
448C3×Dic3—21no—
449C3×Dic3—23no—
450C3×Dic3C2×#4112yes—
451C3×Dic32−1+412yes—
452C2×#41—93no—
453C2×#41D3211yescharacteristic
454C22×Q8—31no—
455C22×Q8—91no—
456C4⋊Q8—93no—
457C4⋊Q8—93no—
458#126—96no—
459#126—96no—
460#125—93no—
461#125—96no—
462#125—93no—
463#124—33no—
464#124—93no—
465#123—96no—
466#123—96no—
467C22⋊Q8—33no—
468C22⋊Q8—96no—
469C22⋊Q8—93no—
470C22⋊Q8—93no—
471C22⋊Q8—93no—
472#121—33no—
473#121—93no—
474C4×Q8—31no—
475C4×Q8—31no—
476C4×Q8—31no—
477C4×Q8—93no—
478C4×Q8—93no—
479C4×Q8—93no—
480C4×Q8—93no—
481C4×Q8—93no—
482C4×Q8—93no—
483C4×Q8—91no—
484C4×D4—33no—
485C4×D4—33no—
486C4×D4—33no—
487C4×D4—91no—
488C4×D4—93no—
489C4×D4—93no—
490C4×D4—93no—
491C4×D4—93no—
492#117—33no—
493#117—93no—
494#117—93no—
495#117—93no—
496#117—96no—
497C2×C4⋊C4—93no—
498C2×C4⋊C4—93no—
499C2×C42—33no—
500C2×C42—93no—
501C2×C42—93no—
502C23×C3—23no—
503C23×C3—31no—
504C23×C3C23×D313yes—
505C23×C3C23×D313yes—
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—61no—
509C22×D3C23×D311yescharacteristic
510C3×Q8—24no—
511C3×Q8—66no—
512C3×Q8#23514yescomplemented
513C3×Q8#23714yescomplemented
514C3×D4—26no—
515C3×D4—26no—
516C3×D4—46no—
517C3×D4—66no—
518C2×C3×C4—26no—
519C2×C3×C4—26no—
520C2×C3×C4—23no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—33no—
526C2×C3×C4—33no—
527C2×C3×C4—33no—
528C2×C3×C4—33no—
529C2×C3×C4—46no—
530C2×C3×C4—66no—
531C2×C3×C4—66no—
532C2×C3×C4—66no—
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D313yes—
536C2×C3×C4C23×D313yes—
537#67—26no—
538#67—34no—
539#67—66no—
540#67—66no—
541#67—126no—
542C2×Dic3—26no—
543C2×Dic3—26no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—33no—
547C2×Dic3—33no—
548C2×Dic3—33no—
549C2×Dic3—33no—
550C2×Dic3—61no—
551C2×Dic3—63no—
552C2×Dic3—63no—
553C2×Dic3—66no—
554C2×Dic3—62no—
555C2×Dic3C23×D311yescharacteristic
556C2×Dic3C23×D313yes—
557C2×Dic3C23×D313yes—
558C2×Dic3C23×D313yes—
559C2×Dic3C23×D313yes—
560C2×Dic3C23×D311yescharacteristic
561C2×Dic3C23×D311yescharacteristic
562D12—34no—
563C4×D3—26no—
564C4×D3—62no—
565C4×D3—66no—
566C4×D3—66no—
567C4×D3—62no—
568C4×D3—66no—
569C4×D3—66no—
570C4×D3—66no—
571C4×D3—62no—
572C4×D3—126no—
573Dic6—26no—
574Dic6—66no—
575Dic6—66no—
576Dic6—66no—
577Dic6—66no—
578Dic6—126no—
579C2×C32—43no—
580C2×C32C22×#4111yescharacteristic
581C2×C32C22×#4111yescharacteristic
582C2×C32C2×2−1+411yescharacteristic
583C3⋊D3—22no—
584C3×D3—22no—
585#41—24no—
586#41—1812no—
587C2×Q8—33no—
588C2×Q8—64no—
589C2×Q8—93no—
590C2×Q8—93no—
591C2×Q8—184no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—33no—
594C2×D4—91no—
595C2×D4—93no—
596C2×D4C2×D3213yes—
597C22×C4—33no—
598C22×C4—33no—
599C22×C4—33no—
600C22×C4—91no—
601C22×C4—93no—
602C22×C4—91no—
603C22×C4—93no—
604C22×C4—93no—
605C22×C4C2×D3213yes—
606C4⋊C4—33no—
607C4⋊C4—33no—
608C4⋊C4—33no—
609C4⋊C4—33no—
610C4⋊C4—96no—
611C4⋊C4—96no—
612C4⋊C4—91no—
613C4⋊C4—93no—
614C4⋊C4—93no—
615C4⋊C4—93no—
616C4⋊C4—96no—
617C4⋊C4—96no—
618C4⋊C4—93no—
619C4⋊C4—93no—
620C22⋊C4—36no—
621C22⋊C4—33no—
622C22⋊C4—36no—
623C22⋊C4—31no—
624C22⋊C4—93no—
625C22⋊C4—93no—
626C22⋊C4—93no—
627C22⋊C4—96no—
628C22⋊C4—91no—
629C42—31no—
630C42—33no—
631C42—33no—
632C42—33no—
633C42—33no—
634C42—93no—
635C42—93no—
636C42—93no—
637C42—93no—
638C42—93no—
639C22×C3—23no—
640C22×C3—23no—
641C22×C3—23no—
642C22×C3—23no—
643C22×C3—23no—
644C22×C3—23no—
645C22×C3—21no—
646C22×C3—32no—
647C22×C3—43no—
648C22×C3—43no—
649C22×C3—43no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3C24×D311yescharacteristic
653C22×C3C24×D311yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—32no—
657C2×D3—32no—
658C2×D3—62no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3D3×#4112yes—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—26no—
669C3×C4—32no—
670C3×C4—32no—
671C3×C4—41no—
672C3×C4—63no—
673C3×C4—63no—
674C3×C4—63no—
675C3×C4—61no—
676C3×C4—63no—
677C3×C4C2×#23516yes—
678C3×C4C2×#23716yes—
679Dic3—23no—
680Dic3—23no—
681Dic3—23no—
682Dic3—23no—
683Dic3—21no—
684Dic3—63no—
685Dic3—63no—
686Dic3—63no—
687Dic3—63no—
688Dic3—61no—
689Dic3—61no—
690Dic3—123no—
691Dic3—123no—
692Dic3—121no—
693Dic3D3×#4112yes—
694Dic3#101012yes—
695C32#348211yescharacteristic, complemented, Sylow
696C23—31no—
697C23—91no—
698C23C22×D3213yes—
699Q8—66no—
700Q8—186no—
701Q8—186no—
702Q8#380414yescomplemented
703D4—26no—
704D4—66no—
705D4—94no—
706D4—186no—
707C2×C4—26no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—33no—
712C2×C4—33no—
713C2×C4—33no—
714C2×C4—33no—
715C2×C4—66no—
716C2×C4—66no—
717C2×C4—66no—
718C2×C4—91no—
719C2×C4—93no—
720C2×C4—93no—
721C2×C4—182no—
722C2×C4—182no—
723C2×C4—186no—
724C2×C4—186no—
725C2×C4—186no—
726C2×C4C22×D3211yescharacteristic
727C2×C4C22×D3213yes—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—43no—
732C2×C3—43no—
733C2×C3—62no—
734C2×C3—83no—
735C2×C3C22×#23511yescharacteristic
736C2×C3C22×#23711yescharacteristic
737C2×C3C2×D3×#4111yescharacteristic
738C2×C3C2×D3×#4111yescharacteristic
739C2×C3C2×#101011yescharacteristic
740C2×C3D3×2−1+411yescharacteristic
741D3—22no—
742D3—62no—
743D3—62no—
744D3—122no—
745C22—23no—
746C22—23no—
747C22—23no—
748C22—32no—
749C22—61no—
750C22—61no—
751C22—92no—
752C22—181no—
753C22—181no—
754C22C23×D3211yescharacteristic
755C4—21no—
756C4—32no—
757C4—32no—
758C4—63no—
759C4—63no—
760C4—63no—
761C4—61no—
762C4—63no—
763C4—183no—
764C4—181no—
765C4—183no—
766C4C2×#380416yes—
767C3—21no—
768C3#8584411yescharacteristic, complemented
769C3#8671211yescharacteristic, complemented
770C2—43no—
771C2—62no—
772C2—182no—
773C2D32×#4111yescharacteristic
774C2D3×#101011yescharacteristic
775C2C22×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596302C2semidirect
2. C3×#5831C2semidirect
3. C3×Dic3×#41C2semidirect
4. #10595422C2semidirect
5. Q8×#626C2semidirect
6. Q8×#624C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10595273C2semidirect
9. #10595191C2semidirect
10. #10595172C2semidirect
11. #10595136C2semidirect
12. #10594970C2semidirect
13. #10594939C2semidirect
14. C4×#3804C2semidirect
15. #10594808C2semidirect
73. #5831D3semidirect
74. Dic3×#41D3semidirect
264. C32×Q8#41semidirect
288. #626#41semidirect
512. C3×Q8#235semidirect
513. C3×Q8#237semidirect
695. C32#3482semidirect
702. Q8#3804semidirect
768. C3#85844semidirect
769. C3#86712semidirect

Maximal subgroups

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

subgroupindex
#105963022
C3×#58312
C3×Dic3×#412
#105954222
Q8×#6262
Q8×#6242
D3×Q8×Dic32
#105952732
#105951912
#105951722
#105951362
#105949702
#105949392
C4×#38042
#105948082
#867123
#858443