Finite Group Databasebeta

← #11785318

Subgroups — #11785318

Order 1152.

709 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594954C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic
3C3×#5118C211yesmaximal, characteristic, complemented
4C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70529—31nomaximal
9#68770—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×Dic3⋊Dic3—21no—
18#63952—21no—
19#63952—21no—
20#63894C411yescharacteristic, complemented
21#63894C411yescharacteristic, complemented
22C4×#624—21no—
23#63874—21no—
24#63844C411yescharacteristic, complemented
25#63844C411yescharacteristic, complemented
26#63652—22no—
27C3×Dic3⋊C8—21no—
28C3×Dic3⋊C8—21no—
29#63579—21no—
30#63570—22no—
31#5522—31no—
32C4×#235—31no—
33C3×#423—31no—
34C2×#825—31no—
35C2×#825—31no—
36C2×#825—31no—
37C2×#825—61no—
38#5118D311yescharacteristic, complemented
39C4×C4⋊Dic3—31no—
40C4×Dic3⋊C4—31no—
41C2×#805—31no—
42C3×#339—31no—
43#4555—31no—
44#4555D311yescharacteristic, complemented
45#4532—31no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C22×C3⋊Dic3—21no—
49#3828—21no—
50#3828—21no—
51#3828D412yes—
52#3828Q812yes—
53C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×#634C2×C411yescharacteristic
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×#624—21no—
60C2×#624—21no—
61C32×M16—21no—
62C32×M16—21no—
63C2×C32×C8—21no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—21no—
66C3×#217—21no—
67C3×C4⋊Dic3C2×C411yescharacteristic
68C3×C4⋊Dic3C2×C411yescharacteristic
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3C2×C411yescharacteristic
73C3×C4×Dic3C2×C411yescharacteristic
74C3×C4×Dic3D411yescharacteristic
75C3×C4×Dic3D411yescharacteristic
76C3×#208—21no—
77C3×#208—21no—
78C2×C3×C3⋊C8—21no—
79#3724—21no—
80#3724—21no—
81Dic3⋊Dic3—24no—
82#3722—21no—
83#3722—21no—
84Dic32—21no—
85Dic32—21no—
86#1806—91noSylow
87C2×#235—31no—
88C2×#235—31no—
89C2×#235—61no—
90C2×C3×M16—21no—
91C2×C3×M16—31no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C3×#117—31no—
95C2×C3×C42—31no—
96C2×C3×C42—31no—
97C4×#67—61no—
98C4×#67—61no—
99#926C2×D311yescharacteristic
100C2×C4⋊Dic3—61no—
101C2×Dic3⋊C4—61no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3C2×D311yescharacteristic
106C2×C4×Dic3C2×D311yescharacteristic
107C2×#208C2×D311yescharacteristic
108#893—31no—
109#893—31no—
110#887—31no—
111#887—31no—
112#67⋊C4—61no—
113#67⋊C4—61no—
114C4×D12—31no—
115C4×D12—31no—
116#872—61no—
117#872—61no—
118C42×D3—61no—
119C42×D3—61no—
120C4×Dic6—31no—
121C4×Dic6—31no—
122C3×C4⋊C8—61no—
123C3×C4⋊C8—61no—
124C3⋊#95—61no—
125C3⋊#95—61no—
126#825—62no—
127#825—62no—
128#825—62no—
129#825—64no—
130Dic3⋊C8—21no—
131Dic3⋊C8—21no—
132#805—62no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—21no—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×Q811yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141#638—22no—
142#638—22no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—41no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)C4⋊C412yescomplemented
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151#634—21no—
152#634C4⋊C412yescomplemented
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3C22⋊C411yescharacteristic
161C2×C3×Dic3C22⋊C411yescharacteristic
162C2×C3×Dic3C22⋊C411yescharacteristic
163C2×C3×Dic3C22⋊C411yescharacteristic
164#624—42no—
165#624—42no—
166C32×C8—41no—
167C3×C3⋊C8—41no—
168C4×#41—91no—
169#423—31no—
170C2×#104—91no—
171C2×#104—91no—
172C4×C4⋊C4—91no—
173#339—31no—
174#339—91no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—61no—
182C2×#67—61no—
183C2×#67—121no—
184C22×Dic3—21no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—121no—
188C22×Dic3D1211yescharacteristic
189C22×Dic3D1211yescharacteristic
190#235—32no—
191#235—32no—
192#235—32no—
193#235—32no—
194#235—62no—
195#235—62no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—121no—
201#235—121no—
202C2×D12—31no—
203C2×D12—31no—
204C2×D12—61no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—121no—
212C2×Dic6—31no—
213C2×Dic6—31no—
214C2×Dic6—61no—
215C3×M16—22no—
216C3×M16—21no—
217C3×M16—21no—
218C3×M16—21no—
219C3×M16—21no—
220C3×M16—41no—
221C3×M16—61no—
222C3×M16—61no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—41no—
226C2×C3×C8—61no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—31no—
229C3×C22⋊C4—61no—
230C3×C42—31no—
231C3×C42—31no—
232C3×C42—31no—
233C3×C42—31no—
234C3×C42—61no—
235C3×C42—61no—
236C3×C42—61no—
237#217—21no—
238(C2×D3)⋊C4—61no—
239(C2×D3)⋊C4—61no—
240(C2×D3)⋊C4—61no—
241(C2×D3)⋊C4—61no—
242C4⋊Dic3—64no—
243C4⋊Dic3C4×D311yescharacteristic
244C4⋊Dic3C4×D311yescharacteristic
245Dic3⋊C4—61no—
246Dic3⋊C4—61no—
247Dic3⋊C4—64no—
248Dic3⋊C4—61no—
249Dic3⋊C4—61no—
250C4×Dic3—21no—
251C4×Dic3—21no—
252C4×Dic3—21no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—62no—
258C4×Dic3—61no—
259C4×Dic3—61no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262C4×Dic3—121no—
263C4×Dic3C4×D311yescharacteristic
264C4×Dic3C4×D311yescharacteristic
265C4×Dic3#6711yescharacteristic
266C4×Dic3#6711yescharacteristic
267#208—21no—
268#208—21no—
269C2×C3⋊C8—21no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32C2×C22⋊C411yescharacteristic
273C22×C32#12111yescharacteristic
274C22×C32C22⋊Q811yescharacteristic
275C2×C3⋊D3—22no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C32×C4C2×C4⋊C411yescharacteristic
279C32×C4#11711yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4C22⋊Q811yescharacteristic
282C3⋊Dic3—22no—
283C3⋊Dic3—42no—
284C3×Dic3—21no—
285C3×Dic3—21no—
286C3×Dic3—21no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3#10412yescomplemented
291C2×#41—91no—
292C2×M16—31no—
293C2×M16D3211yescharacteristic
294C4×Q8—91no—
295C4×Q8—91no—
296C4×D4—91no—
297C4×D4—91no—
298C4×D4—181no—
299C4×D4—181no—
300#117—31no—
301#117—181no—
302C2×C4⋊C4—181no—
303C2×C42—31no—
304C2×C42—31no—
305C2×C42—91no—
306C2×C42—181no—
307C4⋊C8—61no—
308C4⋊C8—61no—
309#104—182no—
310#104—182no—
311#95—181no—
312C23×C3—21no—
313C23×C3C2×D1211yescharacteristic
314C23×C3D3×D411yescharacteristic
315C22×D3—61no—
316C22×D3—61no—
317C22×D3—121no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—31no—
327C2×C3×C4—31no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4#23511yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4#23711yescharacteristic
343C2×C3×C4D3×Q811yescharacteristic
344C2×C3×C4D3×Q811yescharacteristic
345C2×C3×C4#23911yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347#67—62no—
348#67—62no—
349#67—62no—
350#67—62no—
351#67—122no—
352#67—122no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—121no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—121no—
368C2×Dic3—121no—
369C2×Dic3—122no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372C2×Dic3(C2×D3)⋊C411yescharacteristic
373C2×Dic3(C2×D3)⋊C411yescharacteristic
374C2×Dic3(C2×D3)⋊C411yescharacteristic
375C2×Dic3(C2×D3)⋊C411yescharacteristic
376D12—32no—
377D12—32no—
378D12—62no—
379D12—61no—
380D12—61no—
381D12—121no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—62no—
385C4×D3—62no—
386C4×D3—122no—
387C4×D3—122no—
388C4×D3—122no—
389C4×D3—122no—
390C4×D3—122no—
391C4×D3—122no—
392Dic6—32no—
393Dic6—32no—
394Dic6—62no—
395Dic6—61no—
396Dic6—61no—
397Dic6—121no—
398C3×C8—42no—
399C3×C8—41no—
400C3×C8—41no—
401C3×C8—121no—
402C3⋊C8—41no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32#38011yescharacteristic
406C2×C32C2×#10411yescharacteristic
407C2×C32#42111yescharacteristic
408C3⋊D3—42no—
409#41—92no—
410#41—92no—
411#41—181no—
412#41—181no—
413C2×Q8—91no—
414C2×D4—91no—
415C2×D4—181no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—61no—
419C22×C4—181no—
420C22×C4—181no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4C2×D3211yescharacteristic
424M16—21no—
425M16—21no—
426M16—61no—
427M16—61no—
428C2×C8—21no—
429C2×C8—61no—
430C4⋊C4—31no—
431C4⋊C4—31no—
432C4⋊C4—181no—
433C4⋊C4—181no—
434C4⋊C4—184no—
435C22⋊C4—61no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C42—31no—
439C42—31no—
440C42—31no—
441C42—31no—
442C42—61no—
443C42—61no—
444C42—61no—
445C42—181no—
446C42—181no—
447C42—181no—
448C42—181no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3D3×C22⋊C411yescharacteristic
459C22×C3#88411yescharacteristic
460C22×C3#89511yescharacteristic
461C22×C3#89611yescharacteristic
462C22×C3#89711yescharacteristic
463C22×C3C2×(C2×D3)⋊C411yescharacteristic
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—122no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—241no—
472C2×D3—241no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—32no—
478C3×C4—61no—
479C3×C4—61no—
480C3×C4—61no—
481C3×C4—122no—
482C3×C4—121no—
483C3×C4—121no—
484C3×C4#87211yescharacteristic
485C3×C4#88411yescharacteristic
486C3×C4D3×C4⋊C411yescharacteristic
487C3×C4D3×C4⋊C411yescharacteristic
488C3×C4#89211yescharacteristic
489C3×C4#89611yescharacteristic
490C3×C4#93811yescharacteristic
491C3×C4#94611yescharacteristic
492Dic3—21no—
493Dic3—21no—
494Dic3—21no—
495Dic3—42no—
496Dic3—41no—
497Dic3—41no—
498Dic3—62no—
499Dic3—62no—
500Dic3—122no—
501Dic3—122no—
502Dic3—122no—
503Dic3—124no—
504Dic3#82512yescomplemented
505C32#180611yescharacteristic, complemented, Sylow
506C23—181no—
507C23D3×D1211yescharacteristic
508Q8—92no—
509Q8—181no—
510D4—92no—
511D4—182no—
512D4—182no—
513D4—181no—
514C2×C4—31no—
515C2×C4—31no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—121no—
525C2×C4—181no—
526C2×C4—182no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—362no—
530C2×C4—362no—
531C2×C4—361no—
532C2×C4—361no—
533C2×C4#379711yescharacteristic
534C2×C4#379911yescharacteristic
535C2×C4C4×D3211yescharacteristic
536C2×C4#380411yescharacteristic
537C2×C4D3×#6711yescharacteristic
538C2×C4#381111yescharacteristic
539C8—41no—
540C8—121no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—41no—
549C2×C3—41no—
550C2×C3#466711yescharacteristic
551C2×C3D3×#10411yescharacteristic
552C2×C3#482111yescharacteristic
553C2×C3#498711yescharacteristic
554C2×C3C2×#82511yescharacteristic
555C2×C3#513911yescharacteristic
556D3—122no—
557D3—122no—
558D3—242no—
559C22—21no—
560C22—21no—
561C22—182no—
562C22—361no—
563C22—361no—
564C22#6389511yescharacteristic
565C22#6391011yescharacteristic
566C22D3×(C2×D3)⋊C411yescharacteristic
567C4—32no—
568C4—61no—
569C4—61no—
570C4—61no—
571C4—122no—
572C4—121no—
573C4—121no—
574C4—182no—
575C4—362no—
576C4#6383611yescharacteristic
577C4#6388311yescharacteristic
578C4#6388811yescharacteristic
579C4#6395811yescharacteristic
580C3—21no—
581C3#6877011yescharacteristic, complemented
582C3#7052911yescharacteristic, complemented
583C2—21no—
584C2—21no—
585C2—362no—
586C2D3×#82511yescharacteristic
587C2#1059100511yescharacteristic
588C2#1059136711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5118C2semidirect
4. C4×Dic3⋊Dic3C2semidirect
6. C3×#4555C2semidirect
7. #10589160C2semidirect
20. #63894C4semidirect
21. #63894C4semidirect
24. #63844C4semidirect
25. #63844C4semidirect
38. #5118D3semidirect
44. #4555D3semidirect
148. C4⋊(C3⋊D3)C4⋊C4semidirect
152. #634C4⋊C4semidirect
290. C3×Dic3#104semidirect
504. Dic3#825semidirect
505. C32#1806semidirect
581. C3#68770semidirect
582. C3#70529semidirect

Maximal subgroups

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

subgroupindex
#105949542
C2×#636522
C3×#51182
C4×Dic3⋊Dic32
C2×#635702
C3×#45552
#105891602
#705293
#687703