Finite Group Databasebeta

← #11775396

Subgroups — #11775396

Order 1152.

689 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 689 conjugacy classes of subgroups — too many to draw. Only its 92 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#10594922C211yesmaximal, characteristic
2#10592366C211yesmaximal, characteristic, complemented
3#10591159C211yesmaximal, characteristic, complemented
4C3×#4452C211yesmaximal, characteristic, complemented
5C3×#4451C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#68337—31nomaximal
9#68305—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×#3796C411yescharacteristic, complemented
12C2×#3752—21no—
13C2×#3750—21no—
14C3×#930C2211yescharacteristic
15C3×#924C2211yescharacteristic
16#63981—21no—
17#67⋊Dic3—21no—
18#63916C411yescharacteristic, complemented
19#63881—21no—
20#63871C411yescharacteristic, complemented
21#63853—21no—
22#63849C411yescharacteristic, complemented
23C2×#3712—21no—
24C32×#95C2211yescharacteristic
25#63658C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#830C2211yescharacteristic
28#63557—21no—
29#5627—31no—
30#5606—31no—
31#4726—31no—
32#4726—31no—
33#4667—31no—
34#4667—31no—
35#4667—61no—
36C3×#328—31no—
37C3×#327—31no—
38#4538—31no—
39#4537—31no—
40#4470—31no—
41#4467—31no—
42#4452D311yescharacteristic, complemented
43#4451D311yescharacteristic, complemented
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—42no—
50C2×C4×C3⋊D3C2×C411yescharacteristic
51C2×C4×C3⋊D3C2×C411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C3×#67—21no—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×Dic6C2×C411yescharacteristic
57C2×#626—21no—
58C2×#626—21no—
59C2×D3×Dic3—21no—
60#3796—42no—
61#3752—42no—
62#3750—42no—
63C3×#217—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×C4⋊Dic3C2×C411yescharacteristic
67C3×Dic3⋊C4—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72#3722—21no—
73(C2×D3)⋊Dic3—21no—
74Dic32—21no—
75#3712—42no—
76#1513—91noSylow
77C2×#239—31no—
78C2×#237—31no—
79C22×C4×D3—31no—
80C22×C4×D3—31no—
81C22×C4×D3—61no—
82C3×C22⋊Q8—31no—
83C3×#121—31no—
84#946—31no—
85#938—31no—
86#937—61no—
87D4×Dic3—61no—
88#930C2×D311yescharacteristic
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4—61no—
91C2×(C2×D3)⋊C4—62no—
92#924C2×D311yescharacteristic
93C2×Dic3⋊C4—61no—
94C2×Dic3⋊C4—61no—
95C2×Dic3⋊C4—62no—
96C2×ΓL(1,𝔽25)—61no—
97C2×ΓL(1,𝔽25)—61no—
98#897—31no—
99#895—31no—
100#894—61no—
101#893—61no—
102#892—31no—
103#892—31no—
104#883—61no—
105#882—61no—
106#67⋊C4—61no—
107#67⋊C4—61no—
108C3×C22⋊C8—31no—
109C3×C22⋊C8—31no—
110C3×#95—21no—
111C3×#95C2×D311yescharacteristic
112C3×#95C2×D311yescharacteristic
113C3⋊#95—31no—
114C3⋊#95—31no—
115C3⋊#95—61no—
116#830C2×D311yescharacteristic
117#830C2×D311yescharacteristic
118(C2×D3)⋊C8—61no—
119(C2×D3)⋊C8—61no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3C22⋊C411yescharacteristic
126C22×C3⋊D3C22⋊C411yescharacteristic
127C22×C3×D3—21no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3C22⋊C411yescharacteristic
139C2×C3⋊Dic3C22⋊C411yescharacteristic
140C4×C3⋊D3—22no—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—41no—
143C4×C3⋊D3—41no—
144C3×#67—41no—
145C3×#67—41no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C3×D12—41no—
150C3×Dic6—41no—
151#626—42no—
152#626—42no—
153D3×Dic3—42no—
154C3×C3⋊C8—41no—
155C3×C3⋊C8—41no—
156#525—91no—
157#407—91no—
158#380—91no—
159#328—31no—
160#328—91no—
161#327—31no—
162#327—91no—
163C23×D3—31no—
164C23×D3—31no—
165C23×D3—61no—
166C2×C3×Q8—31no—
167C2×C3×D4—31no—
168C2×C3×D4—61no—
169C22×C3×C4—22no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—21no—
176C2×#67—61no—
177C2×#67—61no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—62no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185#239—122no—
186#237—122no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12C4×D311yescharacteristic
190C2×C4×D3—31no—
191C2×C4×D3—31no—
192C2×C4×D3—31no—
193C2×C4×D3—31no—
194C2×C4×D3—31no—
195C2×C4×D3—31no—
196C2×C4×D3—31no—
197C2×C4×D3—31no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×C4×D3—122no—
204C2×C4×D3—122no—
205C2×C4×D3—124no—
206C2×Dic6C4×D311yescharacteristic
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C3×C4⋊C4—31no—
210C3×C4⋊C4—31no—
211C3×C4⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214#217—21no—
215#217—61no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—61no—
222(C2×D3)⋊C4—124no—
223(C2×D3)⋊C4—122no—
224(C2×D3)⋊C4—122no—
225C4⋊Dic3—61no—
226C4⋊Dic3C4×D311yescharacteristic
227C4⋊Dic3C4×D311yescharacteristic
228Dic3⋊C4—21no—
229Dic3⋊C4—61no—
230Dic3⋊C4—122no—
231Dic3⋊C4—122no—
232Dic3⋊C4—124no—
233C4×Dic3—61no—
234C4×Dic3—61no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237ΓL(1,𝔽25)—122no—
238ΓL(1,𝔽25)—122no—
239C22×C32—21no—
240C22×C32—21no—
241C22×C32C2×C22⋊C411yescharacteristic
242C22×C32AGL(1,ℤ/8)11yescharacteristic
243C22×C32#13711yescharacteristic
244C2×C3⋊D3—21no—
245C2×C3⋊D3—21no—
246C2×C3⋊D3—21no—
247C2×C3⋊D3—21no—
248C2×C3⋊D3—21no—
249C2×C3⋊D3—21no—
250C2×C3⋊D3—42no—
251C2×C3⋊D3—42no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C2×C3×D3—41no—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4—81no—
258C3⋊Dic3—21no—
259C3⋊Dic3—81no—
260C3⋊Dic3#9912yes—
261C3×Dic3—41no—
262C3×Dic3—41no—
263C3×Dic3—41no—
264C2×#41—91no—
265C23×C4—91no—
266C2×M16—181no—
267#123—181no—
268C22⋊Q8—31no—
269C22⋊Q8—91no—
270#121—31no—
271#121—91no—
272#120—181no—
273C4×D4—181no—
274C4×D4—181no—
275#117—91no—
276C2×C4⋊C4—181no—
277C2×C22⋊C4—181no—
278C22⋊C8—31no—
279C22⋊C8—31no—
280C22⋊C8—181no—
281#95—91no—
282#95D3211yescharacteristic
283C23×C3—21no—
284C23×C3—61no—
285C23×C3D3×D411yescharacteristic
286C23×C3D3×D411yescharacteristic
287C22×D3—21no—
288C22×D3—31no—
289C22×D3—31no—
290C22×D3—31no—
291C22×D3—31no—
292C22×D3—61no—
293C22×D3—61no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—61no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—61no—
300C22×D3—121no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—122no—
305C22×D3—122no—
306C3×Q8—121no—
307C3×D4—121no—
308C3×D4—121no—
309C3×D4—121no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331#67—41no—
332#67—41no—
333#67—122no—
334#67—122no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—31no—
339C2×Dic3—31no—
340C2×Dic3—31no—
341C2×Dic3—31no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—64no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357D12—41no—
358D12—122no—
359D12—122no—
360C4×D3—62no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—62no—
364C4×D3—122no—
365C4×D3—122no—
366C4×D3—122no—
367C4×D3—121no—
368C4×D3—121no—
369C4×D3—121no—
370C4×D3—121no—
371C4×D3—122no—
372C4×D3—122no—
373Dic6—41no—
374C3×C8—121no—
375C3×C8—121no—
376C3⋊C8—41no—
377C3⋊C8—41no—
378C2×C32—21no—
379C2×C32—21no—
380C2×C32C2×#9911yescharacteristic
381C2×C32#41711yescharacteristic
382C2×C32#42111yescharacteristic
383C3⋊D3—41no—
384C3⋊D3—41no—
385C3×D3—81no—
386C24—91no—
387#41—362no—
388C2×Q8—31no—
389C2×D4—31no—
390C2×D4—61no—
391C2×D4—181no—
392C2×D4—181no—
393C22×C4—21no—
394C22×C4—91no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—362no—
402C22×C4C2×D3211yescharacteristic
403M16—362no—
404C2×C8—61no—
405C2×C8—61no—
406C4⋊C4—31no—
407C4⋊C4—31no—
408C4⋊C4—61no—
409C4⋊C4—181no—
410C4⋊C4—362no—
411C22⋊C4—61no—
412C22⋊C4—61no—
413C22⋊C4—181no—
414C22⋊C4—181no—
415C22⋊C4—181no—
416C22⋊C4—362no—
417C42—181no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—121no—
428C22×C3—121no—
429C22×C3—121no—
430C22×C3D3×C22⋊C411yescharacteristic
431C22×C3D3×C22⋊C411yescharacteristic
432C22×C3#91111yescharacteristic
433C22×C3#91411yescharacteristic
434C22×C3#91511yescharacteristic
435C22×C3#91811yescharacteristic
436C2×D3—41no—
437C2×D3—41no—
438C2×D3—41no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—61no—
442C2×D3—61no—
443C2×D3—61no—
444C2×D3—61no—
445C2×D3—61no—
446C2×D3—61no—
447C2×D3—61no—
448C2×D3—61no—
449C2×D3—61no—
450C2×D3—61no—
451C2×D3—61no—
452C2×D3—61no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—124no—
458C2×D3—124no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—82no—
470C3×C4—81no—
471C3×C4—81no—
472C3×C4—121no—
473C3×C4—121no—
474C3×C4—121no—
475Dic3—32no—
476Dic3—32no—
477Dic3—41no—
478Dic3—41no—
479Dic3—41no—
480Dic3—62no—
481Dic3—62no—
482Dic3—61no—
483Dic3—61no—
484Dic3—242no—
485Dic3—241no—
486Dic3—241no—
487C32#151311yescharacteristic, complemented, Sylow
488C23—61no—
489C23—91no—
490C23—91no—
491C23—181no—
492C23—181no—
493C23—361no—
494C23—361no—
495C23#381111yescharacteristic
496Q8—121no—
497D4—121no—
498D4—121no—
499D4—121no—
500D4—362no—
501D4—362no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—91no—
510C2×C4—91no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4—182no—
514C2×C4—361no—
515C2×C4—361no—
516C2×C4—362no—
517C2×C4—361no—
518C2×C4—361no—
519C2×C4—361no—
520C2×C4C4×D3211yescharacteristic
521C2×C4#380211yescharacteristic
522C8—121no—
523C8—121no—
524C2×C3—22no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—241no—
534C2×C3D3×#9911yescharacteristic
535C2×C3D3×#9911yescharacteristic
536C2×C3#477111yescharacteristic
537C2×C3#480311yescharacteristic
538C2×C3#482111yescharacteristic
539C2×C3#482111yescharacteristic
540D3—81no—
541D3—122no—
542D3—122no—
543D3—121no—
544D3—121no—
545D3—121no—
546D3—121no—
547C22—21no—
548C22—21no—
549C22—121no—
550C22—121no—
551C22—121no—
552C22—181no—
553C22—181no—
554C22—181no—
555C22—181no—
556C22—181no—
557C22—181no—
558C22—362no—
559C22—362no—
560C22#6392111yescharacteristic
561C22#6393711yescharacteristic
562C22#6395111yescharacteristic
563C4—21no—
564C4—21no—
565C4—81no—
566C4—92no—
567C4—121no—
568C4—121no—
569C4—121no—
570C4—181no—
571C4—721no—
572C3—21no—
573C3#6830511yescharacteristic, complemented
574C3#6833711yescharacteristic, complemented
575C2—21no—
576C2—21no—
577C2—241no—
578C2—361no—
579C2—361no—
580C2#1059039411yescharacteristic
581C2#1059040411yescharacteristic
582C2#1059061211yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radical#10594922C2
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1513
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592366C2semidirect
3. #10591159C2semidirect
4. C3×#4452C2semidirect
5. C3×#4451C2semidirect
6. #10589152C2semidirect
7. #10589150C2semidirect
11. C2×#3796C4semidirect
18. #63916C4semidirect
20. #63871C4semidirect
22. #63849C4semidirect
42. #4452D3semidirect
43. #4451D3semidirect
487. C32#1513semidirect
573. C3#68305semidirect
574. C3#68337semidirect

Maximal subgroups

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

subgroupindex
#105949222
#105923662
#105911592
C3×#44522
C3×#44512
#105891522
#105891502
#683373
#683053