Finite Group Databasebeta

← #11777991

Subgroups — #11777991

Order 1152.

835 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 835 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595072C211yesmaximal, characteristic, complemented
2#10592916C211yesmaximal, characteristic, complemented
3C3×#5223C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic, complemented
5#10589151C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#70968—31nomaximal
9#69696—31nomaximal
10C22×C32×D4C2211yescharacteristic, complemented
11C22×C3×#67—21no—
12C2×D3×#67—21no—
13C2×#3753—21no—
14#64139C2211yescharacteristic
15C2×C3×#217—21no—
16C2×C3×#213—21no—
17C3×#930C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2211yescharacteristic
19#63978—21no—
20#63923—21no—
21#63922—21no—
22#63891—21no—
23#63890—21no—
24#63659—21no—
25#63657C2211yescharacteristic, complemented
26C3×#832—21no—
27C3×C3⋊#95C2211yescharacteristic, complemented
28C3×#830C2211yescharacteristic, complemented
29#5605—31no—
30#5493—31no—
31C3×#447—31no—
32C3×#392—31no—
33#5223D311yescharacteristic, complemented
34#5217—31no—
35#5217—31no—
36#5217—61no—
37#5217D311yescharacteristic, complemented
38#4537—31no—
39#4525—31no—
40#4470—31no—
41#4468—31no—
42#4451—31no—
43#4451—31no—
44C24×C32—21no—
45C23×C3×D3D411yescharacteristic
46C22×D32—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—42no—
50C22×C32×C4C2311yescharacteristic
51C2×#638—21no—
52C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
53C2×C3×#67—21no—
54C2×C3×#67—42no—
55C2×C3×#67—42no—
56C2×C3×#67—42no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C2×C3×D12D411yescharacteristic, complemented
60D3×#67—42no—
61D3×#67—42no—
62C2×#626—21no—
63C2×#626—21no—
64C2×#625—21no—
65C2×D3×Dic3—21no—
66#3753—42no—
67#3752—21no—
68C4⋊(C3⋊Dic3)D411yescharacteristic, complemented
69C2×C3⋊(C3⋊C8)—21no—
70C3×#217—42no—
71C3×#213—42no—
72C3×(C2×D3)⋊C4—21no—
73C3×(C2×D3)⋊C4—21no—
74C3×(C2×D3)⋊C4—21no—
75C3×C4⋊Dic3D411yescharacteristic, complemented
76C2×C3×C3⋊C8—21no—
77Dic3⋊Dic3—21no—
78#3722—21no—
79(C2×D3)⋊Dic3—21no—
80#1595—91noSylow
81C22×C3×D4—21no—
82C22×C3×D4—61no—
83C22×C3×D4C2×D311yescharacteristic, complemented
84C22×C3×D4C2×D311yescharacteristic, complemented
85C22×#67—21no—
86C22×#67—61no—
87C2×D3×D4—61no—
88C2×C3×D8—61no—
89C3×#121—31no—
90C2×C3×C22⋊C4—31no—
91C2×C3×C22⋊C4—61no—
92C2×#217—21no—
93#939—61no—
94#937—61no—
95C2×#213—21no—
96C2×#213—61no—
97C2×#213—61no—
98C2×#213—62no—
99#930—31no—
100#930—31no—
101#930—61no—
102#930—61no—
103#930C2×D311yescharacteristic
104C2×(C2×D3)⋊C4C2×D311yescharacteristic
105#894—61no—
106#886—61no—
107#886—61no—
108#883—61no—
109#882—61no—
110#882—61no—
111#882—61no—
112C3×#102—61no—
113C3×C22⋊C8—31no—
114C3×#95—31no—
115#832—21no—
116#832—61no—
117#832—61no—
118#832—62no—
119C3⋊#95C2×D311yescharacteristic, complemented
120#830—31no—
121#830—31no—
122#830—61no—
123#830C2×D311yescharacteristic, complemented
124C23×C32—22no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32—41no—
130C23×C32—41no—
131C23×C32C2×D411yescharacteristic
132C22×C3⋊D3—21no—
133C22×C3×D3—21no—
134C22×C3×D3—21no—
135C22×C3×D3—21no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C22×C3×D3D812yescomplemented
139C2×D32—42no—
140C2×D32—81no—
141C2×D32—81no—
142C32×D4—22no—
143C32×D4—22no—
144C32×D4—41no—
145C32×D4—41no—
146C2×C32×C4—41no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149#638—41no—
150#638—41no—
151C2×C3⋊Dic3—21no—
152C4⋊(C3⋊D3)—41no—
153C3×#67—48no—
154C3×#67—41no—
155C3×#67—41no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—41no—
162C3×D12—41no—
163#626—42no—
164#626—81no—
165#625—42no—
166D3×Dic3—42no—
167C3⋊(C3⋊C8)—41no—
168C3×C3⋊C8—41no—
169#534—91no—
170#447—31no—
171#447—91no—
172#392—31no—
173#327—91no—
174#327—91no—
175#323—91no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3—31no—
179C24×C3—41no—
180C23×D3—61no—
181C23×D3—61no—
182C23×D3#6711yescharacteristic
183C2×C3×D4—22no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—31no—
189C2×C3×D4—41no—
190C2×C3×D4—42no—
191C2×C3×D4—42no—
192C2×C3×D4—44no—
193C2×C3×D4—61no—
194C2×C3×D4—122no—
195C2×C3×D4—122no—
196C2×C3×D4—122no—
197C22×C3×C4—21no—
198C22×C3×C4—31no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C2×#67—21no—
203C2×#67—42no—
204C2×#67—42no—
205C2×#67—42no—
206C2×#67—61no—
207C2×#67—61no—
208C2×#67—61no—
209C2×#67—61no—
210C2×#67—61no—
211C2×#67—61no—
212C2×#67—121no—
213C2×#67—122no—
214C2×#67—122no—
215C22×Dic3—21no—
216C22×Dic3—61no—
217C22×Dic3#6711yescharacteristic
218D3×D4—122no—
219D3×D4—122no—
220C2×D12—31no—
221C2×D12—31no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—61no—
225C2×D12#6711yescharacteristic, complemented
226C2×C4×D3—61no—
227C3×D8—122no—
228C2×C3×C8—61no—
229C3×C4⋊C4—31no—
230C3×C22⋊C4—61no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—61no—
233C3×C22⋊C4—122no—
234#217—42no—
235#217—61no—
236#213—42no—
237#213—122no—
238#213—122no—
239#213—124no—
240(C2×D3)⋊C4—21no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—61no—
244(C2×D3)⋊C4—61no—
245(C2×D3)⋊C4—61no—
246(C2×D3)⋊C4—61no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—121no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3#6711yescharacteristic, complemented
254Dic3⋊C4—61no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C22×C32—21no—
260C22×C32—21no—
261C22×C32—42no—
262C22×C32—42no—
263C22×C32—42no—
264C22×C32—81no—
265C22×C32—81no—
266C22×C32—81no—
267C22×C32—81no—
268C22×C32#12011yescharacteristic
269C22×C32C2×D811yescharacteristic
270C22×C32AGL(1,ℤ/8)11yescharacteristic
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C2×C3⋊D3—41no—
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—42no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—81no—
282D32—84no—
283C32×C4—21no—
284C32×C4—21no—
285C3⋊Dic3—41no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C3×Dic3—41no—
289C22×D4—61no—
290C22×D4—181no—
291C22×D4D3211yescharacteristic, complemented
292C2×D8—61no—
293C2×D8—181no—
294#123—181no—
295#123—181no—
296#121—31no—
297#121—91no—
298#121—181no—
299#120—181no—
300#120—181no—
301C2×C22⋊C4—31no—
302C2×C22⋊C4—61no—
303#102—61no—
304#102—181no—
305C22⋊C8—31no—
306C22⋊C8—91no—
307#95—31no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—21no—
311C23×C3—32no—
312C23×C3—42no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—42no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—42no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3—61no—
330C23×C3—81no—
331C23×C3—81no—
332C23×C3—81no—
333C23×C3—81no—
334C23×C3—121no—
335C23×C3—121no—
336C23×C3D3×D411yescharacteristic
337C23×C3C2×#6711yescharacteristic
338C22×D3—21no—
339C22×D3—21no—
340C22×D3—21no—
341C22×D3—41no—
342C22×D3—41no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—121no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—241no—
349C22×D3—241no—
350C22×D3—241no—
351C22×D3—241no—
352C22×D3#21312yescomplemented
353C3×D4—22no—
354C3×D4—24no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—42no—
359C3×D4—42no—
360C3×D4—41no—
361C3×D4—41no—
362C3×D4—41no—
363C3×D4—41no—
364C3×D4—42no—
365C3×D4—121no—
366C3×D4—128no—
367C3×D4—121no—
368C3×D4—121no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—42no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4C2×#6711yescharacteristic
384#67—48no—
385#67—41no—
386#67—41no—
387#67—122no—
388#67—122no—
389#67—122no—
390#67—121no—
391#67—121no—
392#67—121no—
393#67—121no—
394#67—241no—
395#67—241no—
396#67—241no—
397C2×Dic3—22no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—41no—
401C2×Dic3—41no—
402C2×Dic3—41no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—121no—
406C2×Dic3—122no—
407D12—41no—
408D12—121no—
409D12—121no—
410D12—122no—
411D12—122no—
412D12—241no—
413C4×D3—122no—
414C3×C8—121no—
415C3⋊C8—41no—
416C3⋊C8—122no—
417C3⋊C8—121no—
418C3⋊C8—121no—
419C2×C32—21no—
420C2×C32—21no—
421C2×C32—82no—
422C2×C32#44711yescharacteristic
423C2×C32#45311yescharacteristic
424C2×C32B(4,𝔽2)11yescharacteristic
425C3⋊D3—81no—
426C3×D3—42no—
427C3×D3—81no—
428C24—21no—
429C24—31no—
430C24—181no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—31no—
434C2×D4—42no—
435C2×D4—61no—
436C2×D4—91no—
437C2×D4—122no—
438C2×D4—122no—
439C2×D4—122no—
440C2×D4—181no—
441C2×D4—181no—
442C2×D4—181no—
443C2×D4—181no—
444C2×D4—362no—
445C2×D4—362no—
446C22×C4—31no—
447C22×C4—61no—
448C22×C4—181no—
449C22×C4C2×D3211yescharacteristic
450D8—122no—
451D8—362no—
452C2×C8—61no—
453C2×C8—181no—
454C4⋊C4—31no—
455C4⋊C4—91no—
456C4⋊C4—181no—
457C22⋊C4—61no—
458C22⋊C4—61no—
459C22⋊C4—61no—
460C22⋊C4—122no—
461C22⋊C4—181no—
462C22⋊C4—181no—
463C22⋊C4—181no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—42no—
474C22×C3—44no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—62no—
481C22×C3—82no—
482C22×C3—82no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3—81no—
486C22×C3—81no—
487C22×C3—82no—
488C22×C3—82no—
489C22×C3—82no—
490C22×C3—82no—
491C22×C3—81no—
492C22×C3—81no—
493C22×C3—81no—
494C22×C3—81no—
495C22×C3—122no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3—121no—
499C22×C3—121no—
500C22×C3—121no—
501C22×C3—241no—
502C22×C3D3×D811yescharacteristic
503C22×C3#91111yescharacteristic
504C22×C3C2×#21311yescharacteristic
505C22×C3#93711yescharacteristic
506C22×C3#93711yescharacteristic
507C22×C3#94911yescharacteristic
508C2×D3—22no—
509C2×D3—41no—
510C2×D3—41no—
511C2×D3—42no—
512C2×D3—41no—
513C2×D3—41no—
514C2×D3—41no—
515C2×D3—81no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—241no—
523C2×D3—241no—
524C2×D3—241no—
525C2×D3—244no—
526C2×D3—244no—
527C3×C4—22no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—41no—
533C3×C4—122no—
534C3×C4—121no—
535C3×C4—121no—
536Dic3—42no—
537Dic3—41no—
538Dic3—41no—
539Dic3—121no—
540Dic3—121no—
541Dic3—241no—
542C32#159511yescharacteristic, complemented, Sylow
543C23—22no—
544C23—32no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—61no—
552C23—61no—
553C23—61no—
554C23—121no—
555C23—121no—
556C23—181no—
557C23—362no—
558C23—721no—
559C23—721no—
560C23D3×#6711yescharacteristic
561D4—22no—
562D4—22no—
563D4—41no—
564D4—41no—
565D4—121no—
566D4—128no—
567D4—121no—
568D4—121no—
569D4—361no—
570D4—362no—
571D4—362no—
572D4—361no—
573D4—361no—
574D4—721no—
575C2×C4—41no—
576C2×C4—62no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—121no—
580C2×C4—121no—
581C2×C4—121no—
582C2×C4—181no—
583C2×C4—362no—
584C2×C4D3×#6711yescharacteristic
585C2×C4#381111yescharacteristic
586C8—121no—
587C8—361no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—41no—
596C2×C3—41no—
597C2×C3—84no—
598C2×C3—82no—
599C2×C3—82no—
600C2×C3—122no—
601C2×C3—241no—
602C2×C3#503211yescharacteristic
603C2×C3#503211yescharacteristic
604C2×C3#503611yescharacteristic
605C2×C3#507711yescharacteristic
606C2×C3#515611yescharacteristic
607C2×C3#519811yescharacteristic
608D3—42no—
609D3—81no—
610D3—241no—
611D3—241no—
612D3—481no—
613C22—21no—
614C22—21no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—62no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—122no—
624C22—121no—
625C22—121no—
626C22—121no—
627C22—121no—
628C22—121no—
629C22—241no—
630C22—361no—
631C22—361no—
632C22—361no—
633C22—724no—
634C22D3×#21311yescharacteristic
635C22#6392511yescharacteristic
636C22#6398311yescharacteristic
637C4—21no—
638C4—21no—
639C4—122no—
640C4—121no—
641C4—121no—
642C4—361no—
643C3—21no—
644C3#6969611yescharacteristic, complemented
645C3#7096811yescharacteristic, complemented
646C2—21no—
647C2—21no—
648C2—82no—
649C2—122no—
650C2—241no—
651C2—721no—
652C2#1059151511yescharacteristic
653C2#1059152311yescharacteristic
654C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
hypercenterC22×D4D32
hypocenterC32#1595
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10595072C2semidirect
2. #10592916C2semidirect
3. C3×#5223C2semidirect
4. C3×#5217C2semidirect
5. #10589151C2semidirect
6. #10589149C2semidirect
7. #10589145C2semidirect
10. C22×C32×D4C22semidirect
25. #63657C22semidirect
27. C3×C3⋊#95C22semidirect
28. C3×#830C22semidirect
33. #5223D3semidirect
37. #5217D3semidirect
52. C2×C4⋊(C3⋊D3)D4semidirect
59. C2×C3×D12D4semidirect
68. C4⋊(C3⋊Dic3)D4semidirect
75. C3×C4⋊Dic3D4semidirect
83. C22×C3×D4C2×D3semidirect
84. C22×C3×D4C2×D3semidirect
119. C3⋊#95C2×D3semidirect
123. #830C2×D3semidirect
138. C22×C3×D3D8semidirect
225. C2×D12#67semidirect
253. C4⋊Dic3#67semidirect
291. C22×D4D32semidirect
352. C22×D3#213semidirect
542. C32#1595semidirect
644. C3#69696semidirect
645. C3#70968semidirect

Maximal subgroups

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

subgroupindex
#105950722
#105929162
C3×#52232
C3×#52172
#105891512
#105891492
#105891452
#709683
#696963