Finite Group Databasebeta

← #11895549

Subgroups — #11895549

Order 1152.

728 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595422C211yesmaximal, characteristic, complemented
2#10595273C211yesmaximal, characteristic
3#10592865C211yesmaximal, characteristic
4C3×#5166C211yesmaximal, characteristic
5C3×Dic3×SD16C211yesmaximal, characteristic
6#10591625C211yesmaximal, characteristic, complemented
7#10591581C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10591478C211yesmaximal, characteristic
10#10591410C211yesmaximal, characteristic
11#10591403C211yesmaximal, characteristic
12#10590890C211yesmaximal, characteristic, complemented
13#10590820C211yesmaximal, characteristic, complemented
14#10590809C211yesmaximal, characteristic, complemented
15#10590644C211yesmaximal, characteristic, complemented
16#80580—31nomaximal
17#79623—31nomaximal
18C2×C32×SD16C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21#64145C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#936C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27#63964—21no—
28#63956—21no—
29#63956—21no—
30#63955—21no—
31#63918—21no—
32#63918C2211yescharacteristic
33C4×#627—21no—
34C4×#627C2211yescharacteristic
35#63872—21no—
36#63872C2211yescharacteristic
37#63869—21no—
38#63869C2211yescharacteristic
39#63866C2211yescharacteristic
40#63844C2211yescharacteristic
41#63843C2211yescharacteristic
42#63659C2211yescharacteristic
43#63643C2211yescharacteristic
44#63641C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5671—31no—
62#5570—31no—
63#5569—31no—
64#5542—31no—
65C3×#464—31no—
66C3×C4×SD16—31no—
67#5182—31no—
68Dic3×Q16—31no—
69#5166—31no—
70#5166—31no—
71#5166—61no—
72#5166D311yescharacteristic
73Dic3×SD16D311yescharacteristic
74#5056—31no—
75#5031—31no—
76C4×#216—31no—
77#5007—31no—
78#4857—31no—
79#4857—31no—
80#4830—31no—
81#4829—31no—
82#4799—31no—
83#4792—31no—
84#4790—31no—
85#4790—31no—
86#4768—31no—
87#4768—31no—
88#4768—31no—
89#4759—31no—
90#4681—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C22×C3×Dic3—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#627D411yescharacteristic
99C32×SD16—22no—
100C2×C32×C8C2311yescharacteristic
101#3757—21no—
102#3757—21no—
103#3756—22no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4×C3⋊Dic3—21no—
107C4×C3⋊Dic3C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×#217—21no—
110C3×#217—21no—
111C3×#217—21no—
112C3×#216—22no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4×Dic3—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124#3724—21no—
125#3724—21no—
126#3724D411yescharacteristic
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135Dic3⋊Dic3D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138#3364—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—21no—
141C2×C3×SD16C2×D311yescharacteristic
142C2×C3×SD16C2×D311yescharacteristic
143C3×#124—31no—
144C3×C4×Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—31no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150Q8×Dic3—61no—
151Q8×Dic3C2×D311yescharacteristic
152Q8×Dic3C2×D311yescharacteristic
153#944—31no—
154C2×#216—31no—
155C2×#216—31no—
156C2×#216—61no—
157C2×#216C2×D311yescharacteristic
158#936—31no—
159#936—31no—
160#936—61no—
161#936C2×D311yescharacteristic
162D4×Dic3C2×D311yescharacteristic
163#926—61no—
164#924—61no—
165#890—31no—
166#890—31no—
167#890—31no—
168#890—61no—
169#890—61no—
170#890—61no—
171#888—31no—
172#888—61no—
173#887—31no—
174#887—31no—
175#879—61no—
176#879—61no—
177#879—61no—
178#879—61no—
179#878—61no—
180#877—61no—
181#870—31no—
182#870—61no—
183#869—31no—
184#869—31no—
185#869—61no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—61no—
190C4×Dic6—61no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×C4×C8—31no—
198#835—31no—
199#835—31no—
200#835C2×D311yescharacteristic
201#832—31no—
202#832—31no—
203#832—61no—
204#832C2×D311yescharacteristic
205#832C2×D311yescharacteristic
206#818—31no—
207#817C2×D311yescharacteristic
208#816—31no—
209#816—31no—
210#816—31no—
211#816—31no—
212#816—31no—
213#816—61no—
214#816C2×D311yescharacteristic
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—61no—
219Dic3⋊C8C2×D311yescharacteristic
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3C2×D311yescharacteristic
224#810—31no—
225#810—31no—
226#810—31no—
227#807—31no—
228#807—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C23×C32—21no—
233C32×Q8—21no—
234C32×Q8#4112yes—
235C32×D4—21no—
236C32×D4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243#634—21no—
244#634—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—42no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×Dic6—21no—
255C3×Dic6—21no—
256#627—22no—
257#627—42no—
258C32×C8—21no—
259C3⋊(C3⋊C8)—21no—
260C3×C3⋊C8—21no—
261C3×C3⋊C8—21no—
262#557—91no—
263#556—91no—
264#488—91no—
265#488—91no—
266#487—91no—
267#479—91no—
268#479—91no—
269#474—91no—
270#464—31no—
271#464—91no—
272#462—91no—
273C8×Q8—91no—
274C4×Q16—91no—
275C4×Q16—91no—
276C4×SD16—31no—
277C2×C3×Q8—21no—
278C2×C3×Q8—31no—
279C2×C3×Q8C22×D311yescharacteristic
280C2×C3×Q8C22×D311yescharacteristic
281C2×C3×D4—21no—
282C2×C3×D4C22×D311yescharacteristic
283C2×C3×D4C22×D311yescharacteristic
284C22×C3×C4—61no—
285C22×Dic3—21no—
286C2×Dic6—31no—
287C2×Dic6—31no—
288C2×Dic6—31no—
289C2×Dic6—31no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6C22×D311yescharacteristic
294C3×Q16—62no—
295C3×SD16—22no—
296C3×SD16—22no—
297C3×SD16—42no—
298C2×C3×C8—21no—
299C2×C3×C8—31no—
300C2×C3×C8—31no—
301C2×C3×C8C22×D311yescharacteristic
302C2×C3×C8C22×D311yescharacteristic
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—61no—
307C3×C4⋊C4—61no—
308C3×C22⋊C4—61no—
309C3×C22⋊C4—61no—
310C3×C22⋊C4—61no—
311C3×C42—31no—
312C3×C42—31no—
313C3×C42—61no—
314C3×C42—61no—
315#217—21no—
316#217—21no—
317#217—21no—
318#217—61no—
319#217—61no—
320#217—61no—
321#217—61no—
322#217—121no—
323#217—121no—
324#216—22no—
325#216—62no—
326#216—62no—
327#216—122no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—31no—
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—61no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—121no—
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363C4×Dic3—21no—
364C4×Dic3—21no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—121no—
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32C22×D411yescharacteristic
386C32×C4—22no—
387C32×C4C2×#4111yescharacteristic
388C32×C42−1+411yescharacteristic
389C3⋊Dic3—21no—
390C3⋊Dic3—21no—
391C3⋊Dic3—41no—
392C3⋊Dic3—41no—
393C3×Dic3—21no—
394C3×Dic3—21no—
395C3×Dic3—21no—
396C3×Dic3—41no—
397C3×Dic3—41no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3#13512yes—
401C2×Q16—31no—
402C2×Q16—91no—
403C2×SD16D3211yescharacteristic
404C4⋊Q8—91no—
405C4⋊Q8—91no—
406C4⋊Q8—181no—
407#126—181no—
408#126—181no—
409#125—91no—
410#125—91no—
411#125—181no—
412#125—181no—
413#124—31no—
414#124—91no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—181no—
423C4×D4—31no—
424#117—181no—
425#107—91no—
426#107—91no—
427#106—31no—
428C4⋊C8—31no—
429C4⋊C8—91no—
430C4⋊C8—91no—
431#103—31no—
432#103—31no—
433#103—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—31no—
440#102—91no—
441C4×C8—31no—
442C4×C8—91no—
443C4×C8—91no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—41no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—22no—
450C3×Q8—41no—
451C3×Q8—61no—
452C3×Q8—61no—
453C3×Q8#23512yes—
454C3×Q8#23712yes—
455C3×D4—21no—
456C3×D4—21no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—41no—
460C3×D4—41no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—41no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—122no—
474C2×C3×C4C23×D311yescharacteristic
475C2×C3×C4C23×D311yescharacteristic
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—42no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—121no—
492C2×Dic3—121no—
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497Dic6—21no—
498Dic6—21no—
499Dic6—62no—
500Dic6—62no—
501Dic6—61no—
502Dic6—61no—
503Dic6—61no—
504Dic6—61no—
505Dic6—121no—
506Dic6—121no—
507Dic6—122no—
508Dic6—122no—
509C3×C8—21no—
510C3×C8—21no—
511C3×C8—41no—
512C3×C8—61no—
513C3×C8—61no—
514C3⋊C8—21no—
515C3⋊C8—21no—
516C3⋊C8—61no—
517C3⋊C8—61no—
518C3⋊C8—121no—
519C2×C32—81no—
520C2×C32#54811yescharacteristic
521C2×C32C2×#13511yescharacteristic
522C2×C32#57811yescharacteristic
523C2×Q8—31no—
524C2×Q8—91no—
525C2×Q8—91no—
526C2×Q8—181no—
527C2×Q8C2×D3211yescharacteristic
528C2×D4C2×D3211yescharacteristic
529C22×C4—61no—
530Q16—62no—
531Q16—182no—
532SD16—22no—
533C2×C8—31no—
534C2×C8—31no—
535C2×C8—91no—
536C2×C8C2×D3211yescharacteristic
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—91no—
543C4⋊C4—91no—
544C4⋊C4—91no—
545C4⋊C4—91no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C4⋊C4—181no—
549C4⋊C4—181no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C22⋊C4—61no—
557C22⋊C4—61no—
558C22⋊C4—61no—
559C22⋊C4—181no—
560C22⋊C4—181no—
561C42—31no—
562C42—31no—
563C42—61no—
564C42—61no—
565C42—91no—
566C42—181no—
567C42—181no—
568C42—181no—
569C22×C3—21no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—81no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3C2×D3×D411yescharacteristic
580C22×C3C2×D3×D411yescharacteristic
581C3×C4—22no—
582C3×C4—22no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—32no—
586C3×C4—42no—
587C3×C4—61no—
588C3×C4—61no—
589C3×C4—61no—
590C3×C4—121no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4—121no—
594C3×C4C2×#23511yescharacteristic
595C3×C4C2×#23711yescharacteristic
596C3×C4#101011yescharacteristic
597C3×C4#101011yescharacteristic
598Dic3—21no—
599Dic3—21no—
600Dic3—21no—
601Dic3—41no—
602Dic3—41no—
603Dic3—41no—
604Dic3—41no—
605Dic3—61no—
606Dic3—61no—
607Dic3—61no—
608Dic3—61no—
609Dic3—121no—
610Dic3—121no—
611Dic3—121no—
612Dic3—121no—
613Dic3—121no—
614Dic3—121no—
615Dic3—241no—
616Dic3—241no—
617Dic3#91612yes—
618C32#336411yescharacteristic, complemented, Sylow
619C23—21no—
620Q8—21no—
621Q8—61no—
622Q8—61no—
623Q8—182no—
624Q8—181no—
625Q8—181no—
626Q8—362no—
627Q8#380412yes—
628D4—21no—
629D4—21no—
630C2×C4—21no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—91no—
640C2×C4—91no—
641C2×C4—122no—
642C2×C4—181no—
643C2×C4—181no—
644C2×C4C22×D3211yescharacteristic
645C8—21no—
646C8—61no—
647C8—61no—
648C8—181no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—81no—
653C2×C3—81no—
654C2×C3—161no—
655C2×C3#555211yescharacteristic
656C2×C3#559811yescharacteristic
657C2×C3C2×#91611yescharacteristic
658C2×C3D3×#13511yescharacteristic
659C2×C3#577111yescharacteristic
660C2×C3#577911yescharacteristic
661C22—41no—
662C22—41no—
663C22—41no—
664C22D32×D411yescharacteristic
665C4—22no—
666C4—32no—
667C4—61no—
668C4—61no—
669C4—61no—
670C4—121no—
671C4—121no—
672C4—121no—
673C4—121no—
674C4—181no—
675C4—181no—
676C4—361no—
677C4—361no—
678C4#6430911yescharacteristic
679C4C2×#380411yescharacteristic
680C3—21no—
681C3#7962311yescharacteristic, complemented
682C3#8058011yescharacteristic, complemented
683C2—81no—
684C2D3×#91611yescharacteristic
685C2#1059475611yescharacteristic
686C2#1059514111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC2×SD16D32
hypocenterC32#3364
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595422C2semidirect
6. #10591625C2semidirect
7. #10591581C2semidirect
8. #10591537C2semidirect
12. #10590890C2semidirect
13. #10590820C2semidirect
14. #10590809C2semidirect
15. #10590644C2semidirect
618. C32#3364semidirect
681. C3#79623semidirect
682. C3#80580semidirect

Maximal subgroups

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

subgroupindex
#105954222
#105952732
#105928652
C3×#51662
C3×Dic3×SD162
#105916252
#105915812
#105915372
#105914782
#105914102
#105914032
#105908902
#105908202
#105908092
#105906442
#805803
#796233