Finite Group Databasebeta

← #11787406

Subgroups — #11787406

Order 1152.

781 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
1C2×#64110C211yesmaximal, characteristic, complemented
2C2×#63829C211yesmaximal, characteristic
3C3×#5110C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70011—31nomaximal
9#68695—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14#64110—22no—
15#64110—22no—
16C2×#3743—21no—
17C2×C8×C3⋊D3—21no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3719C411yescharacteristic, complemented
22C2×#3717C411yescharacteristic, complemented
23#63829—22no—
24#63829—22no—
25C2×#3716C411yescharacteristic, complemented
26C2×#3714C411yescharacteristic, complemented
27C3×(C2×D3)⋊C8—21no—
28C3×(C2×D3)⋊C8—21no—
29#63570—22no—
30#63569—22no—
31C2×#950—31no—
32C2×#904—31no—
33C2×#901—31no—
34C2×#901—31no—
35C2×#901—61no—
36C3×#408—31no—
37C2×#837—31no—
38C2×#825—31no—
39#5110D311yescharacteristic, complemented
40C2×#805—31no—
41C2×#805—31no—
42C3×#336—31no—
43#4558—31no—
44#4552—31no—
45#4550D311yescharacteristic, complemented
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48#3828—21no—
49#3828—21no—
50#3828D412yes—
51#3828D412yes—
52C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×#634C2×C411yescharacteristic
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12C2×C411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6C2×C411yescharacteristic
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8D411yescharacteristic
67C2×C32×C8D411yescharacteristic
68#3748—21no—
69#3748D412yes—
70C2×C3⋊(C3⋊C8)—21no—
71#3743—24no—
72C8×C3⋊D3—24no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8C2×C411yescharacteristic
81C2×C3×C3⋊C8C2×C411yescharacteristic
82#3719—22no—
83#3717—22no—
84#3716—22no—
85#3714—22no—
86#1876—91noSylow
87C2×C3×#41—31no—
88C2×#235—31no—
89C2×#235—31no—
90C2×#235—61no—
91C2×#235C2×D311yescharacteristic
92C2×C3×M16—31no—
93C22×C3×C8—21no—
94C22×C3×C8—31no—
95C22×C3×C8C2×D311yescharacteristic
96C22×C3×C8C2×D311yescharacteristic
97C2×C3×C42—31no—
98#950—62no—
99#950—62no—
100C2×#216—31no—
101C2×#215—31no—
102C2×#214—31no—
103C2×#213—31no—
104C2×C4×Dic3C2×D311yescharacteristic
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110C2×Dic12—31no—
111#904—62no—
112#904—62no—
113C2×D24—31no—
114C2×#204—31no—
115C2×#204—31no—
116#901—62no—
117#901—62no—
118#901—62no—
119#901—62no—
120#901—64no—
121#901—64no—
122C2×ΓL(1,𝔽25)—62no—
123C2×ΓL(1,𝔽25)—61no—
124C2×ΓL(1,𝔽25)—61no—
125C2×D3×C8—62no—
126C2×D3×C8—61no—
127C2×D3×C8—61no—
128C3×C22⋊C8—61no—
129C3×C22⋊C8—61no—
130#837—62no—
131#825—62no—
132(C2×D3)⋊C8—21no—
133(C2×D3)⋊C8—21no—
134#805—62no—
135#805—62no—
136C23×C32#4111yescharacteristic
137C22×C3⋊D3—21no—
138C22×C3×D3—21no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145#638—22no—
146#638—22no—
147C2×C3⋊Dic3—21no—
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)C22⋊C412yes—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152#634—21no—
153#634C22⋊C412yes—
154C3×#67—41no—
155C3×#67—41no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C3×D12—21no—
161C3×D12—21no—
162C3×C4×D3—41no—
163C3×C4×D3—41no—
164C3×Dic6—21no—
165C3×Dic6—21no—
166C32×C8—21no—
167C32×C8—21no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8—21no—
170C3×C3⋊C8—21no—
171C3×C3⋊C8—41no—
172C2×#135—91no—
173C2×#131—91no—
174C2×#104—91no—
175C2×#104—91no—
176#408—31no—
177#341—91no—
178#336—31no—
179C3×#41—61no—
180C3×#41—61no—
181C3×#41—61no—
182C3×#41—61no—
183C2×C3×Q8—31no—
184C2×C3×D4—31no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—21no—
192C2×#67—62no—
193C2×#67—61no—
194C2×#67—61no—
195C22×Dic3—21no—
196#235—21no—
197#235—21no—
198#235—21no—
199#235—21no—
200#235—32no—
201#235—32no—
202#235—32no—
203#235—32no—
204#235—62no—
205#235—62no—
206#235—62no—
207#235—62no—
208#235—61no—
209#235—61no—
210#235—61no—
211#235—61no—
212C2×D12—31no—
213C2×D12—31no—
214C2×D12—61no—
215C2×D12C4×D311yescharacteristic
216C2×C4×D3—21no—
217C2×C4×D3—62no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×Dic6—31no—
221C2×Dic6—31no—
222C2×Dic6—61no—
223C2×Dic6C4×D311yescharacteristic
224C3×M16—61no—
225C3×M16—61no—
226C2×C3×C8—22no—
227C2×C3×C8—22no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—31no—
235C2×C3×C8—31no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C2×C3×C8D1211yescharacteristic
240C2×C3×C8D1211yescharacteristic
241C2×C3×C8#6711yescharacteristic
242C2×C3×C8#6711yescharacteristic
243C3×C42—61no—
244C3×C42—61no—
245#216—62no—
246#215—62no—
247#214—62no—
248#213—62no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251#208—21no—
252#208—21no—
253#208—32no—
254#208—32no—
255#208—62no—
256#208—62no—
257#208—61no—
258#208—61no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—62no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8C4×D311yescharacteristic
266C2×C3⋊C8C4×D311yescharacteristic
267Dic12—62no—
268D24—62no—
269#204—62no—
270#204—62no—
271ΓL(1,𝔽25)—68no—
272ΓL(1,𝔽25)—64no—
273ΓL(1,𝔽25)—64no—
274D3×C8—68no—
275D3×C8—64no—
276D3×C8—64no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32C4×D411yescharacteristic
280C22×C32#12111yescharacteristic
281C22×C32#12311yescharacteristic
282C2×C3⋊D3—22no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4C2×C22⋊C411yescharacteristic
289C32×C4C4×D411yescharacteristic
290C32×C4#12011yescharacteristic
291C32×C4#12111yescharacteristic
292C3⋊Dic3—22no—
293C3×Dic3—42no—
294C3×Dic3—41no—
295C2×#41—31no—
296C2×#41—91no—
297#135—182no—
298#135—182no—
299C2×Q16—91no—
300C2×SD16—91no—
301C2×SD16—91no—
302C2×D8—91no—
303#131—182no—
304#131—182no—
305C2×M16—31no—
306C2×M16—91no—
307C2×M16—181no—
308C22×C8—31no—
309C22×C8—181no—
310C22×C8D3211yescharacteristic
311C2×C42—31no—
312#104—182no—
313#104—182no—
314C22⋊C8—61no—
315C22⋊C8—61no—
316C23×C3—21no—
317C23×C3—61no—
318C23×C3#23511yescharacteristic
319C23×C3#23511yescharacteristic
320C22×D3—21no—
321C22×D3—62no—
322C22×D3—61no—
323C22×D3—61no—
324C3×Q8—61no—
325C3×Q8—61no—
326C3×D4—61no—
327C3×D4—61no—
328C3×D4—121no—
329C3×D4—121no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—62no—
337C2×C3×C4—61no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4#23711yescharacteristic
352C2×C3×C4#23911yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354#67—41no—
355#67—41no—
356#67—64no—
357#67—64no—
358#67—62no—
359#67—62no—
360#67—62no—
361#67—62no—
362C2×Dic3—22no—
363C2×Dic3—21no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—62no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369D12—21no—
370D12—21no—
371D12—32no—
372D12—32no—
373D12—62no—
374D12—62no—
375D12—61no—
376D12—61no—
377C4×D3—41no—
378C4×D3—41no—
379C4×D3—64no—
380C4×D3—64no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—62no—
385Dic6—21no—
386Dic6—21no—
387Dic6—32no—
388Dic6—32no—
389Dic6—62no—
390Dic6—62no—
391Dic6—61no—
392Dic6—61no—
393C3×C8—22no—
394C3×C8—22no—
395C3×C8—21no—
396C3×C8—21no—
397C3×C8—21no—
398C3×C8—21no—
399C3×C8—61no—
400C3×C8—61no—
401C3×C8—121no—
402C3⋊C8—21no—
403C3⋊C8—21no—
404C3⋊C8—41no—
405C3⋊C8—64no—
406C3⋊C8—62no—
407C3⋊C8—62no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32#38611yescharacteristic
411C2×C32#44311yescharacteristic
412C2×C32#44411yescharacteristic
413C3⋊D3—42no—
414C3×D3—81no—
415#41—61no—
416#41—61no—
417#41—61no—
418#41—61no—
419#41—92no—
420#41—92no—
421#41—181no—
422#41—181no—
423C2×Q8—31no—
424C2×Q8—91no—
425C2×D4—31no—
426C2×D4—61no—
427C2×D4—91no—
428C2×D4—181no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—181no—
432C22×C4C2×D3211yescharacteristic
433Q16—182no—
434SD16—182no—
435SD16—182no—
436D8—182no—
437M16—61no—
438M16—61no—
439M16—92no—
440M16—184no—
441M16—181no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—31no—
445C2×C8—31no—
446C2×C8—61no—
447C2×C8—61no—
448C2×C8—61no—
449C2×C8—184no—
450C2×C8—181no—
451C2×C8#62611yescharacteristic
452C2×C8#62611yescharacteristic
453C42—61no—
454C42—61no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—121no—
465C22×C3—121no—
466C22×C3—121no—
467C22×C3C4×D1211yescharacteristic
468C22×C3#88311yescharacteristic
469C22×C3#88411yescharacteristic
470C22×C3#88411yescharacteristic
471C22×C3#89411yescharacteristic
472C22×C3C4×#6711yescharacteristic
473C2×D3—41no—
474C2×D3—41no—
475C2×D3—41no—
476C2×D3—64no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—122no—
480C2×D3—122no—
481C2×D3—121no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—121no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—122no—
490C3×C4—121no—
491C3×C4D3×C22⋊C411yescharacteristic
492C3×C4D3×C22⋊C411yescharacteristic
493C3×C4#67⋊C411yescharacteristic
494C3×C4#88211yescharacteristic
495C3×C4#89311yescharacteristic
496C3×C4#89511yescharacteristic
497C3×C4#93711yescharacteristic
498C3×C4#93811yescharacteristic
499Dic3—42no—
500Dic3—41no—
501Dic3—64no—
502Dic3—62no—
503Dic3—62no—
504C32#187611yescharacteristic, complemented, Sylow
505C23—61no—
506C23—181no—
507C23#379811yescharacteristic
508Q8—61no—
509Q8—61no—
510Q8—92no—
511Q8—181no—
512D4—61no—
513D4—61no—
514D4—92no—
515D4—121no—
516D4—121no—
517D4—182no—
518D4—182no—
519D4—181no—
520C2×C4—62no—
521C2×C4—61no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4—181no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4#379611yescharacteristic
530C2×C4C4×D3211yescharacteristic
531C2×C4#380211yescharacteristic
532C2×C4C2×#62611yescharacteristic
533C2×C4#381111yescharacteristic
534C2×C4#381111yescharacteristic
535C8—21no—
536C8—21no—
537C8—61no—
538C8—61no—
539C8—121no—
540C8—182no—
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—241no—
551C2×C3#466511yescharacteristic
552C2×C3#470011yescharacteristic
553C2×C3#471711yescharacteristic
554C2×C3#495611yescharacteristic
555C2×C3#514411yescharacteristic
556C2×C3#514511yescharacteristic
557D3—81no—
558D3—124no—
559D3—122no—
560D3—122no—
561C22—21no—
562C22—21no—
563C22—121no—
564C22—121no—
565C22—121no—
566C22—182no—
567C22—361no—
568C22—361no—
569C22#6385311yescharacteristic
570C22C4×#62611yescharacteristic
571C22#6391211yescharacteristic
572C4—122no—
573C4—121no—
574C4—182no—
575C4#6388111yescharacteristic
576C4#6391611yescharacteristic
577C4#6392111yescharacteristic
578C4#6398111yescharacteristic
579C3—21no—
580C3#6869511yescharacteristic, complemented
581C3#7001111yescharacteristic, complemented
582C2—21no—
583C2—21no—
584C2—241no—
585C2—362no—
586C2#1059092311yescharacteristic
587C2#1059092411yescharacteristic
588C2#1059138711yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×#63829C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1876
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64110C2semidirect
3. C3×#5110C2semidirect
4. C2×#63570C2semidirect
5. C2×#63569C2semidirect
6. C3×#4550C2semidirect
7. #10589166C2semidirect
21. C2×#3719C4semidirect
22. C2×#3717C4semidirect
25. C2×#3716C4semidirect
26. C2×#3714C4semidirect
39. #5110D3semidirect
45. #4550D3semidirect
504. C32#1876semidirect
580. C3#68695semidirect
581. C3#70011semidirect

Maximal subgroups

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

subgroupindex
C2×#641102
C2×#638292
C3×#51102
C2×#635702
C2×#635692
C3×#45502
#105891662
#700113
#686953