Finite Group Databasebeta

← #11787403

Subgroups — #11787403

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63829C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3C2×#63652C211yesmaximal, characteristic, complemented
4C3×#5129C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70011—31nomaximal
9#68946—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3719C411yescharacteristic, complemented
18C2×#3717C411yescharacteristic, complemented
19#63829—22no—
20#63829—22no—
21C2×#3716C411yescharacteristic, complemented
22C2×#3714C411yescharacteristic, complemented
23C2×#3712—21no—
24#63817—22no—
25#63817—22no—
26C2×#3710—21no—
27#63652—22no—
28C3×(C2×D3)⋊C8—21no—
29C3×(C2×D3)⋊C8—21no—
30#63568—22no—
31C2×#950—31no—
32C2×#907—31no—
33C2×#904—31no—
34C2×#901—31no—
35C3×#408—31no—
36C2×#837—31no—
37C2×#825—31no—
38C2×#825—31no—
39C2×#825—31no—
40C2×#825—61no—
41#5129D311yescharacteristic, complemented
42C3×#341—31no—
43#4558D311yescharacteristic, complemented
44#4550—31no—
45#4550—31no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C22×C3⋊Dic3—21no—
49#3828—21no—
50#3828—21no—
51#3828D412yes—
52#3828D412yes—
53C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×#634C2×C411yescharacteristic
56C2×C3×#67—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
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C3×#208—21no—
70C3×#208D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8C2×C411yescharacteristic
77C2×C3×C3⋊C8C2×C411yescharacteristic
78C2×C3×C3⋊C8D411yescharacteristic
79C2×C3×C3⋊C8D411yescharacteristic
80#3719—22no—
81#3717—22no—
82#3716—22no—
83#3714—22no—
84#3712—24no—
85#3710—24no—
86#1876—91noSylow
87C2×C3×#41—31no—
88C2×#235—31no—
89C2×#235—31no—
90C2×#235—61no—
91C2×#235C2×D311yescharacteristic
92C2×C3×M16—21no—
93C2×C3×M16—31no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C22×C3×C8—31no—
97C22×C3×C8—31no—
98#950—62no—
99#950—62no—
100C2×#216—31no—
101C2×#215—31no—
102C2×#214—31no—
103C2×#213—31no—
104C2×C4×Dic3—31no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—61no—
107C2×#208C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110#907—62no—
111#907—62no—
112C2×Dic12—31no—
113#904—62no—
114#904—62no—
115C2×D24—31no—
116C2×#204—31no—
117C2×#204—31no—
118#901—62no—
119#901—62no—
120C2×ΓL(1,𝔽25)—61no—
121C2×ΓL(1,𝔽25)—61no—
122C2×D3×C8—61no—
123C2×D3×C8—61no—
124C3×C22⋊C8—61no—
125C3×C22⋊C8—61no—
126#837—62no—
127#825—62no—
128#825—62no—
129#825—64no—
130#825—62no—
131(C2×D3)⋊C8—21no—
132(C2×D3)⋊C8—21no—
133C23×C32#4111yescharacteristic
134C22×C3⋊D3—21no—
135C22×C3×D3—21no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142#638—22no—
143#638—22no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—41no—
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—21no—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—41no—
160C3×C4×D3—41no—
161C3×Dic6—21no—
162C3×Dic6—21no—
163C32×C8—41no—
164C3×C3⋊C8—21no—
165C3×C3⋊C8—21no—
166C3×C3⋊C8—21no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—21no—
169C2×#135—91no—
170C2×#131—91no—
171C2×#104—91no—
172C2×#104—91no—
173#408—31no—
174#341—31no—
175#336—91no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—31no—
181C2×C3×D4—31no—
182C2×C3×D4—61no—
183C22×C3×C4—21no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—21no—
188C2×#67—61no—
189C2×#67—61no—
190C2×#67—121no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—121no—
194#235—21no—
195#235—21no—
196#235—21no—
197#235—21no—
198#235—32no—
199#235—32no—
200#235—32no—
201#235—32no—
202#235—62no—
203#235—62no—
204#235—61no—
205#235—61no—
206#235—61no—
207#235—61no—
208#235—121no—
209#235—121no—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×D12C4×D311yescharacteristic
214C2×C4×D3—21no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—121no—
218C2×Dic6—31no—
219C2×Dic6—31no—
220C2×Dic6—61no—
221C2×Dic6C4×D311yescharacteristic
222C3×M16—22no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—21no—
226C3×M16—21no—
227C3×M16—32no—
228C3×M16—41no—
229C3×M16—61no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—31no—
233C2×C3×C8—31no—
234C2×C3×C8—31no—
235C2×C3×C8—31no—
236C2×C3×C8—41no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C2×C3×C8—61no—
241C2×C3×C8—61no—
242#216—62no—
243#215—62no—
244#214—62no—
245#213—62no—
246C4×Dic3—62no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—121no—
252#208—21no—
253#208D1212yes—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8C4×D311yescharacteristic
260C2×C3⋊C8C4×D311yescharacteristic
261C2×C3⋊C8#6711yescharacteristic
262C2×C3⋊C8#6711yescharacteristic
263Dic12—62no—
264D24—62no—
265#204—62no—
266#204—62no—
267ΓL(1,𝔽25)—64no—
268ΓL(1,𝔽25)—64no—
269D3×C8—64no—
270D3×C8—64no—
271C22×C32—21no—
272C22×C32—21no—
273C22×C32C4×D411yescharacteristic
274C22×C32#12111yescharacteristic
275C22×C32#12311yescharacteristic
276C2×C3⋊D3—22no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C32×C4C2×C22⋊C411yescharacteristic
283C32×C4C4×D411yescharacteristic
284C32×C4#12011yescharacteristic
285C32×C4#12111yescharacteristic
286C3⋊Dic3—22no—
287C3⋊Dic3—42no—
288C3×Dic3—41no—
289C2×#41—31no—
290C2×#41—91no—
291#135—182no—
292#135—182no—
293C2×Q16—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×D8—91no—
297#131—182no—
298#131—182no—
299C2×M16—31no—
300C2×M16—181no—
301C2×M16D3211yescharacteristic
302C22×C8—31no—
303C22×C8—31no—
304C22×C8—181no—
305C2×C42—91no—
306#104—182no—
307#104—182no—
308C22⋊C8—61no—
309C22⋊C8—61no—
310C23×C3—21no—
311C23×C3—61no—
312C23×C3#23511yescharacteristic
313C23×C3#23911yescharacteristic
314C22×D3—21no—
315C22×D3—61no—
316C22×D3—61no—
317C22×D3—121no—
318C3×Q8—61no—
319C3×Q8—61no—
320C3×D4—61no—
321C3×D4—61no—
322C3×D4—121no—
323C3×D4—121no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—61no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4#23511yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4#23711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345#67—41no—
346#67—41no—
347#67—62no—
348#67—62no—
349#67—62no—
350#67—62no—
351#67—122no—
352#67—122no—
353C2×Dic3—21no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—121no—
359C2×Dic3—122no—
360C2×Dic3—122no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—122no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366D12—21no—
367D12—21no—
368D12—32no—
369D12—32no—
370D12—62no—
371D12—61no—
372D12—61no—
373D12—121no—
374C4×D3—41no—
375C4×D3—41no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—122no—
381C4×D3—122no—
382Dic6—21no—
383Dic6—21no—
384Dic6—32no—
385Dic6—32no—
386Dic6—62no—
387Dic6—61no—
388Dic6—61no—
389Dic6—121no—
390C3×C8—42no—
391C3×C8—41no—
392C3×C8—41no—
393C3×C8—61no—
394C3×C8—61no—
395C3×C8—61no—
396C3×C8—61no—
397C3×C8—62no—
398C3⋊C8—21no—
399C3⋊C8—21no—
400C3⋊C8—22no—
401C3⋊C8—21no—
402C3⋊C8—21no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32#38611yescharacteristic
406C2×C32#44311yescharacteristic
407C2×C32#44411yescharacteristic
408C3⋊D3—42no—
409C3×D3—81no—
410#41—61no—
411#41—61no—
412#41—61no—
413#41—61no—
414#41—92no—
415#41—92no—
416#41—181no—
417#41—181no—
418C2×Q8—31no—
419C2×Q8—91no—
420C2×D4—31no—
421C2×D4—61no—
422C2×D4—91no—
423C2×D4—181no—
424C22×C4—61no—
425C22×C4—181no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428Q16—182no—
429SD16—182no—
430SD16—182no—
431D8—182no—
432M16—21no—
433M16—21no—
434M16—32no—
435M16—61no—
436M16—184no—
437C2×C8—21no—
438C2×C8—31no—
439C2×C8—31no—
440C2×C8—31no—
441C2×C8—31no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8—61no—
447C2×C8—184no—
448C42—181no—
449C42—181no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—121no—
460C22×C3—121no—
461C22×C3—121no—
462C22×C3#88311yescharacteristic
463C22×C3#88411yescharacteristic
464C22×C3#89311yescharacteristic
465C22×C3#89411yescharacteristic
466C22×C3#89511yescharacteristic
467C22×C3C4×#6711yescharacteristic
468C2×D3—41no—
469C2×D3—41no—
470C2×D3—41no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—122no—
474C2×D3—121no—
475C2×D3—121no—
476C2×D3—121no—
477C2×D3—121no—
478C2×D3—241no—
479C2×D3—241no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—121no—
485C3×C4C4×D1211yescharacteristic
486C3×C4D3×C22⋊C411yescharacteristic
487C3×C4D3×C22⋊C411yescharacteristic
488C3×C4#67⋊C411yescharacteristic
489C3×C4#88211yescharacteristic
490C3×C4#88411yescharacteristic
491C3×C4#93711yescharacteristic
492C3×C4#93811yescharacteristic
493Dic3—41no—
494Dic3—62no—
495Dic3—62no—
496Dic3—122no—
497Dic3—122no—
498Dic3—122no—
499Dic3—124no—
500C32#187611yescharacteristic, complemented, Sylow
501C23—61no—
502C23—181no—
503C23#379911yescharacteristic
504Q8—61no—
505Q8—61no—
506Q8—92no—
507Q8—181no—
508D4—61no—
509D4—61no—
510D4—92no—
511D4—121no—
512D4—121no—
513D4—182no—
514D4—182no—
515D4—181no—
516C2×C4—61no—
517C2×C4—121no—
518C2×C4—121no—
519C2×C4—181no—
520C2×C4—182no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4—361no—
524C2×C4—361no—
525C2×C4C4×D3211yescharacteristic
526C2×C4D3×D1211yescharacteristic
527C2×C4#380211yescharacteristic
528C2×C4#380411yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4#381111yescharacteristic
531C8—41no—
532C8—61no—
533C8—61no—
534C8—61no—
535C8—61no—
536C8—62no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—41no—
545C2×C3—41no—
546C2×C3—241no—
547C2×C3#466511yescharacteristic
548C2×C3#489411yescharacteristic
549C2×C3#489511yescharacteristic
550C2×C3#495611yescharacteristic
551C2×C3#514411yescharacteristic
552C2×C3#514511yescharacteristic
553D3—81no—
554D3—122no—
555D3—122no—
556D3—242no—
557C22—21no—
558C22—21no—
559C22—121no—
560C22—121no—
561C22—121no—
562C22—182no—
563C22—361no—
564C22—361no—
565C22#6385411yescharacteristic
566C22#6390411yescharacteristic
567C22#6391011yescharacteristic
568C4—121no—
569C4—182no—
570C4—362no—
571C4#6388011yescharacteristic
572C4#6392111yescharacteristic
573C4#6392211yescharacteristic
574C4#6395811yescharacteristic
575C3—21no—
576C3#6894611yescharacteristic, complemented
577C3#7001111yescharacteristic, complemented
578C2—21no—
579C2—21no—
580C2—241no—
581C2—362no—
582C2#1059099411yescharacteristic
583C2#1059099511yescharacteristic
584C2#1059127511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×#63829C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1876
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
2. C2×#63817C2semidirect
3. C2×#63652C2semidirect
4. C3×#5129C2semidirect
5. C2×#63568C2semidirect
6. C3×#4558C2semidirect
7. #10589156C2semidirect
17. C2×#3719C4semidirect
18. C2×#3717C4semidirect
21. C2×#3716C4semidirect
22. C2×#3714C4semidirect
41. #5129D3semidirect
43. #4558D3semidirect
500. C32#1876semidirect
576. C3#68946semidirect
577. C3#70011semidirect

Maximal subgroups

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

subgroupindex
C2×#638292
C2×#638172
C2×#636522
C3×#51292
C2×#635682
C3×#45582
#105891562
#700113
#689463