Finite Group Databasebeta

← #11787395

Subgroups — #11787395

Order 1152.

693 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic, complemented
2C2×#63822C211yesmaximal, characteristic
3C2×C3×#825C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic, complemented
5#10591070C211yesmaximal, characteristic, complemented
6#10589424C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72010—31nomaximal
9#70390—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#907—22no—
18C3×#907—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C2×#3718C411yescharacteristic, complemented
22C2×#3715C411yescharacteristic, complemented
23C2×#3715C411yescharacteristic, complemented
24#63822—22no—
25#63822—22no—
26C2×#3713C411yescharacteristic, complemented
27C3×#825—22no—
28#63569—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C2×C3×#131—31no—
32C2×#950—31no—
33C2×#950—31no—
34C2×#907D311yescharacteristic, complemented
35C2×C3×#104—31no—
36C2×#837—31no—
37#5234—31no—
38C2×#825D311yescharacteristic, complemented
39#5110—31no—
40C2×#805—31no—
41#4558—31no—
42#4558—31no—
43#4558—61no—
44#4550—31no—
45#4524—31no—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235D412yes—
57C3×#235D412yes—
58C2×C3×D12C2×C411yescharacteristic
59C2×C3×D12C2×C411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×Dic6C2×C411yescharacteristic
63C2×C3×Dic6C2×C411yescharacteristic
64C32×M16—21no—
65C32×M16D412yes—
66C2×C32×C8—21no—
67#3748—21no—
68#3748—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
73C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8D411yescharacteristic
79C2×C3×C3⋊C8D411yescharacteristic
80C3×ΓL(1,𝔽25)—24no—
81C3×D3×C8—24no—
82#3718—22no—
83#3715—22no—
84#3715—22no—
85#3713—22no—
86#1876—91noSylow
87C2×C3×#41—31no—
88C2×C3×#41—31no—
89C2×#235C2×D311yescharacteristic
90C2×#235C2×D311yescharacteristic
91C3×#131—62no—
92C3×#131—62no—
93C2×C3×M16—21no—
94C2×C3×M16—61no—
95C2×C3×M16C2×D311yescharacteristic
96C2×C3×M16C2×D311yescharacteristic
97C22×C3×C8—31no—
98C22×C3×C8—61no—
99C2×C3×C42—31no—
100#950—62no—
101#950—62no—
102#950—62no—
103#950—62no—
104C2×#216—31no—
105C2×#216—31no—
106C2×#215—31no—
107C2×#215—31no—
108C2×#214—31no—
109C2×#214—31no—
110C2×#213—31no—
111C2×#213—31no—
112C2×C4×Dic3C2×D311yescharacteristic
113C2×#208—31no—
114C2×#208—31no—
115C2×#208—61no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—61no—
119C22×C3⋊C8C2×D311yescharacteristic
120#907—22no—
121#907—22no—
122C2×ΓL(1,𝔽25)—21no—
123C2×D3×C8—21no—
124C3×#104—62no—
125#837—62no—
126#830—61no—
127#830—61no—
128#825—22no—
129(C2×D3)⋊C8—61no—
130(C2×D3)⋊C8—61no—
131#805—62no—
132C23×C32#4111yescharacteristic
133C22×C3×D3—21no—
134C22×C3×D3—21no—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C3×#67—22no—
142C3×#67—22no—
143C3×#67—41no—
144C3×#67—41no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×D12—21no—
151C3×D12—21no—
152C3×D12—21no—
153C3×D12C22⋊C412yes—
154C3×C4×D3—22no—
155C3×C4×D3—22no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C3×Dic6—21no—
159C3×Dic6—21no—
160C3×Dic6—21no—
161C3×Dic6C22⋊C412yes—
162C32×C8—22no—
163C3⋊(C3⋊C8)—21no—
164C3⋊(C3⋊C8)—21no—
165C3⋊(C3⋊C8)—41no—
166C3×C3⋊C8—21no—
167C3×C3⋊C8—21no—
168C2×#135—91no—
169C2×#131—31no—
170C2×#104—31no—
171C2×#104—91no—
172#408—91no—
173#341—91no—
174#336—91no—
175C3×#41—32no—
176C3×#41—32no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C3×#41—61no—
181C3×#41—61no—
182C3×#41—61no—
183C2×C3×Q8—31no—
184C2×C3×Q8—31no—
185C2×C3×D4—31no—
186C2×C3×D4—31no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—21no—
196C2×#67—21no—
197C22×Dic3—21no—
198#235—21no—
199#235—21no—
200#235—21no—
201#235—21no—
202#235—21no—
203#235—21no—
204#235D1212yes—
205#235#6712yes—
206C2×D12C4×D311yescharacteristic
207C2×D12C4×D311yescharacteristic
208C2×C4×D3—21no—
209C2×C4×D3—21no—
210C2×Dic6C4×D311yescharacteristic
211C2×Dic6C4×D311yescharacteristic
212C3×M16—21no—
213C3×M16—21no—
214C3×M16—22no—
215C3×M16—41no—
216C3×M16—64no—
217C3×M16#6712yes—
218C3×M16#6712yes—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—31no—
222C2×C3×C8—31no—
223C2×C3×C8—41no—
224C2×C3×C8—64no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C3×C42—61no—
228C3×C42—61no—
229#216—62no—
230#216—62no—
231#215—62no—
232#215—62no—
233#214—62no—
234#214—62no—
235#213—62no—
236#213—62no—
237C4×Dic3—21no—
238C4×Dic3—21no—
239#208—62no—
240#208—61no—
241#208—61no—
242#208—61no—
243#208—61no—
244#208—121no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—31no—
248C2×C3⋊C8—31no—
249C2×C3⋊C8—31no—
250C2×C3⋊C8—31no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—121no—
260C2×C3⋊C8—121no—
261C2×C3⋊C8—121no—
262C2×C3⋊C8#6711yescharacteristic
263C2×C3⋊C8#6711yescharacteristic
264ΓL(1,𝔽25)—24no—
265D3×C8—24no—
266C22×C32—21no—
267C22×C32—21no—
268C22×C32C4×D411yescharacteristic
269C22×C32#12111yescharacteristic
270C22×C32#12311yescharacteristic
271C2×C3×D3—22no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C32×C4C2×C22⋊C411yescharacteristic
278C32×C4C4×D411yescharacteristic
279C32×C4#12011yescharacteristic
280C32×C4#12111yescharacteristic
281C3×Dic3—22no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C2×#41—31no—
285C2×#41—31no—
286#135—182no—
287#135—182no—
288C2×Q16—91no—
289C2×SD16—91no—
290C2×SD16—91no—
291C2×D8—91no—
292#131—62no—
293#131—62no—
294C2×M16—61no—
295C2×M16—91no—
296C2×M16D3211yescharacteristic
297C22×C8—31no—
298C22×C8—61no—
299C22×C8—91no—
300C2×C42—31no—
301#104—62no—
302#104—182no—
303C22⋊C8—181no—
304C22⋊C8—181no—
305C23×C3—21no—
306C23×C3—61no—
307C23×C3—61no—
308C23×C3#23511yescharacteristic
309C23×C3#23711yescharacteristic
310C22×D3—21no—
311C22×D3—21no—
312C3×Q8—32no—
313C3×Q8—61no—
314C3×Q8—61no—
315C3×Q8—61no—
316C3×D4—32no—
317C3×D4—62no—
318C3×D4—62no—
319C3×D4—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—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—61no—
335C2×C3×C4—121no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4C2×C4×D311yescharacteristic
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4#23511yescharacteristic
343C2×C3×C4#23511yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351#67—22no—
352#67—22no—
353#67—41no—
354#67—41no—
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—21no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360D12—21no—
361D12—21no—
362D12—21no—
363D12(C2×D3)⋊C412yes—
364C4×D3—22no—
365C4×D3—22no—
366C4×D3—41no—
367C4×D3—41no—
368Dic6—21no—
369Dic6—21no—
370Dic6—21no—
371Dic6(C2×D3)⋊C412yes—
372C3×C8—22no—
373C3×C8—22no—
374C3×C8—42no—
375C3×C8—61no—
376C3×C8—61no—
377C3⋊C8—21no—
378C3⋊C8—21no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C3⋊C8—121no—
384C3⋊C8—121no—
385C3⋊C8—122no—
386C3⋊C8—121no—
387C3⋊C8—121no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32#38611yescharacteristic
391C2×C32#44311yescharacteristic
392C2×C32#44411yescharacteristic
393C3×D3—42no—
394C3×D3—81no—
395#41—32no—
396#41—32no—
397#41—61no—
398#41—61no—
399#41—61no—
400#41—61no—
401#41—61no—
402#41—61no—
403C2×Q8—31no—
404C2×Q8—31no—
405C2×D4—31no—
406C2×D4—31no—
407C2×D4—61no—
408C2×D4—61no—
409C22×C4—61no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4C2×D3211yescharacteristic
413Q16—182no—
414SD16—182no—
415SD16—182no—
416D8—182no—
417M16—21no—
418M16—64no—
419M16—181no—
420M16—181no—
421M16#62512yes—
422C2×C8—21no—
423C2×C8—31no—
424C2×C8—31no—
425C2×C8—64no—
426C2×C8—61no—
427C2×C8—61no—
428C2×C8—91no—
429C2×C8—91no—
430C2×C8—181no—
431C2×C8—181no—
432C2×C8—181no—
433C42—61no—
434C42—61no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—62no—
445C22×C3—121no—
446C22×C3—121no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3#67⋊C411yescharacteristic
451C22×C3#88311yescharacteristic
452C22×C3C4×#6711yescharacteristic
453C22×C3#92911yescharacteristic
454C22×C3#93011yescharacteristic
455C22×C3#93811yescharacteristic
456C2×D3—22no—
457C2×D3—41no—
458C2×D3—41no—
459C2×D3—41no—
460C2×D3—41no—
461C2×D3—41no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—62no—
467C3×C4—122no—
468C3×C4—121no—
469C3×C4D3×C22⋊C411yescharacteristic
470C3×C4#88411yescharacteristic
471C3×C4C2×(C2×D3)⋊C411yescharacteristic
472C3×C4C4×#6711yescharacteristic
473C3×C4C4×#6711yescharacteristic
474C3×C4#93011yescharacteristic
475C3×C4#93711yescharacteristic
476C3×C4#95311yescharacteristic
477Dic3—22no—
478Dic3—42no—
479Dic3—41no—
480C32#187611yescharacteristic, complemented, Sylow
481C23—61no—
482C23—61no—
483C23#379511yescharacteristic
484Q8—32no—
485Q8—61no—
486Q8—61no—
487Q8—61no—
488D4—32no—
489D4—62no—
490D4—62no—
491D4—61no—
492D4—61no—
493D4—61no—
494D4—121no—
495D4—121no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—61no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4#379811yescharacteristic
506C2×C4C4×D3211yescharacteristic
507C2×C4D3×D1211yescharacteristic
508C2×C4C2×#62511yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C2×C4D3×#6711yescharacteristic
511C8—22no—
512C8—61no—
513C8—61no—
514C8—181no—
515C8—181no—
516C8—361no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—41no—
525C2×C3—41no—
526C2×C3—122no—
527C2×C3—241no—
528C2×C3#482311yescharacteristic
529C2×C3#482411yescharacteristic
530C2×C3#495611yescharacteristic
531C2×C3#514411yescharacteristic
532C2×C3#514511yescharacteristic
533C2×C3#521311yescharacteristic
534D3—42no—
535D3—81no—
536C22—21no—
537C22—21no—
538C22—62no—
539C22—121no—
540C22—121no—
541C22—121no—
542C22—121no—
543C22—121no—
544C22#6387911yescharacteristic
545C22#6390511yescharacteristic
546C22#6390811yescharacteristic
547C4—62no—
548C4—122no—
549C4—121no—
550C4C4×#62511yescharacteristic
551C4#6390611yescharacteristic
552C4D3×(C2×D3)⋊C411yescharacteristic
553C4#6397611yescharacteristic
554C3—21no—
555C3#7039011yescharacteristic, complemented
556C3#7201011yescharacteristic, complemented
557C2—21no—
558C2—21no—
559C2—122no—
560C2—241no—
561C2#1059097511yescharacteristic
562C2#1059097611yescharacteristic
563C2#1059138111yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×#63822C2
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
1. C2×C3×#907C2semidirect
3. C2×C3×#825C2semidirect
4. C2×#63569C2semidirect
5. #10591070C2semidirect
6. #10589424C2semidirect
7. #10589155C2semidirect
21. C2×#3718C4semidirect
22. C2×#3715C4semidirect
23. C2×#3715C4semidirect
26. C2×#3713C4semidirect
34. C2×#907D3semidirect
38. C2×#825D3semidirect
480. C32#1876semidirect
555. C3#70390semidirect
556. C3#72010semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
C2×#638222
C2×C3×#8252
C2×#635692
#105910702
#105894242
#105891552
#720103
#703903