Finite Group Databasebeta

← #11787405

Subgroups — #11787405

Order 1152.

707 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic, complemented
2C2×#63822C211yesmaximal, characteristic
3C3×#5110C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6#10589416C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#72010—31nomaximal
9#70011—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#901—22no—
18C3×#901—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×(C2×D3)⋊C8—21no—
28C3×(C2×D3)⋊C8—21no—
29#63568—22no—
30#63568—22no—
31C2×C3×#131—31no—
32C2×#950—31no—
33C2×#950—31no—
34C2×#901D311yescharacteristic, complemented
35C3×#408—31no—
36C2×#837—31no—
37C2×#837—31no—
38C2×#825—31no—
39C2×#825—31no—
40#5110D311yescharacteristic, complemented
41#4558—31no—
42#4558—31no—
43#4550—31no—
44#4550—31no—
45#4550—61no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C2×C3×#67—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
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8D411yescharacteristic
67C2×C32×C8D411yescharacteristic
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
73C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208D412yes—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
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—31no—
94C2×C3×M16—31no—
95C2×C3×M16—61no—
96C22×C3×C8—21no—
97C22×C3×C8—61no—
98C22×C3×C8C2×D311yescharacteristic
99C22×C3×C8C2×D311yescharacteristic
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×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C2×#208C2×D311yescharacteristic
116C2×#208C2×D311yescharacteristic
117C22×C3⋊C8—31no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—61no—
120#901—22no—
121#901—22no—
122C2×ΓL(1,𝔽25)—21no—
123C2×D3×C8—21no—
124C3×C22⋊C8—61no—
125C3×C22⋊C8—61no—
126#837—62no—
127#837—62no—
128#825—62no—
129#825—62no—
130(C2×D3)⋊C8—21no—
131(C2×D3)⋊C8—21no—
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
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C3×#67—22no—
145C3×#67—22no—
146C3×#67—41no—
147C3×#67—41no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
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—21no—
163C32×C8—21no—
164C3⋊(C3⋊C8)—21no—
165C3⋊(C3⋊C8)—21no—
166C3×C3⋊C8—22no—
167C3×C3⋊C8—41no—
168C2×#135—91no—
169C2×#131—31no—
170C2×#104—91no—
171C2×#104—91no—
172#408—31no—
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×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—21no—
195C2×#67—21no—
196C22×Dic3—62no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199#235—21no—
200#235—21no—
201#235—21no—
202#235—21no—
203#235—21no—
204#235—21no—
205#235D1212yes—
206#235#6712yes—
207C2×D12C4×D311yescharacteristic
208C2×D12C4×D311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—21no—
211C2×Dic6C4×D311yescharacteristic
212C2×Dic6C4×D311yescharacteristic
213C3×M16—32no—
214C3×M16—64no—
215C3×M16—61no—
216C3×M16—61no—
217C3×M16—61no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—41no—
225C2×C3×C8—41no—
226C2×C3×C8—64no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8#6711yescharacteristic
230C2×C3×C8#6711yescharacteristic
231C2×C3×C8#6711yescharacteristic
232C2×C3×C8#6711yescharacteristic
233#216—62no—
234#216—62no—
235#215—62no—
236#215—62no—
237#214—62no—
238#214—62no—
239#213—62no—
240#213—62no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—121no—
246C4×Dic3—121no—
247#208—21no—
248#208—21no—
249#208—21no—
250#208#6712yes—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—31no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—121no—
264C2×C3⋊C8—121no—
265ΓL(1,𝔽25)—24no—
266D3×C8—24no—
267C22×C32—21no—
268C22×C32—21no—
269C22×C32C4×D411yescharacteristic
270C22×C32#12111yescharacteristic
271C22×C32#12311yescharacteristic
272C2×C3×D3—22no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4C2×C22⋊C411yescharacteristic
279C32×C4C4×D411yescharacteristic
280C32×C4#12011yescharacteristic
281C32×C4#12111yescharacteristic
282C3⋊Dic3—42no—
283C3×Dic3—22no—
284C3×Dic3—41no—
285C2×#41—31no—
286C2×#41—31no—
287#135—182no—
288#135—182no—
289C2×Q16—91no—
290C2×SD16—91no—
291C2×SD16—91no—
292C2×D8—91no—
293#131—62no—
294#131—62no—
295C2×M16—31no—
296C2×M16—31no—
297C2×M16—61no—
298C22×C8—61no—
299C22×C8—91no—
300C22×C8D3211yescharacteristic
301C2×C42—91no—
302#104—182no—
303#104—182no—
304C22⋊C8—61no—
305C22⋊C8—61no—
306C23×C3—21no—
307C23×C3—61no—
308C23×C3—61no—
309C23×C3#23511yescharacteristic
310C23×C3#23511yescharacteristic
311C22×D3—21no—
312C22×D3—21no—
313C3×Q8—32no—
314C3×Q8—61no—
315C3×Q8—61no—
316C3×Q8—61no—
317C3×D4—32no—
318C3×D4—62no—
319C3×D4—62no—
320C3×D4—61no—
321C3×D4—61no—
322C3×D4—61no—
323C3×D4—121no—
324C3×D4—121no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—61no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—61no—
335C2×C3×C4—121no—
336C2×C3×C4—121no—
337C2×C3×C4C2×C4×D311yescharacteristic
338C2×C3×C4C2×C4×D311yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4#23511yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4#23711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349#67—22no—
350#67—22no—
351#67—41no—
352#67—41no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—64no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364D12—21no—
365D12—21no—
366D12—21no—
367D12(C2×D3)⋊C412yes—
368C4×D3—22no—
369C4×D3—22no—
370C4×D3—41no—
371C4×D3—41no—
372Dic6—21no—
373Dic6—21no—
374Dic6—21no—
375Dic6(C2×D3)⋊C412yes—
376C3×C8—21no—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—21no—
380C3×C8—41no—
381C3×C8—41no—
382C3×C8—62no—
383C3×C8—121no—
384C3⋊C8—22no—
385C3⋊C8—41no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C3⋊C8—61no—
390C3⋊C8—121no—
391C3⋊C8—121no—
392C2×C32—21no—
393C2×C32—21no—
394C2×C32#38611yescharacteristic
395C2×C32#44311yescharacteristic
396C2×C32#44411yescharacteristic
397C3×D3—42no—
398C3×D3—81no—
399#41—32no—
400#41—32no—
401#41—61no—
402#41—61no—
403#41—61no—
404#41—61no—
405#41—61no—
406#41—61no—
407C2×Q8—31no—
408C2×Q8—31no—
409C2×D4—31no—
410C2×D4—31no—
411C2×D4—61no—
412C2×D4—61no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417Q16—182no—
418SD16—182no—
419SD16—182no—
420D8—182no—
421M16—32no—
422M16—64no—
423M16—61no—
424M16—61no—
425M16—61no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—64no—
429C2×C8—61no—
430C2×C8—61no—
431C2×C8—91no—
432C2×C8—91no—
433C2×C8—181no—
434C2×C8—181no—
435C2×C8#62511yescharacteristic
436C2×C8#62511yescharacteristic
437C42—181no—
438C42—181no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—62no—
449C22×C3—121no—
450C22×C3—121no—
451C22×C3—121no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3#88311yescharacteristic
455C22×C3#88411yescharacteristic
456C22×C3C4×#6711yescharacteristic
457C22×C3C4×#6711yescharacteristic
458C22×C3#92911yescharacteristic
459C22×C3#93011yescharacteristic
460C2×D3—22no—
461C2×D3—41no—
462C2×D3—41no—
463C2×D3—41no—
464C2×D3—41no—
465C2×D3—41no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—62no—
471C3×C4—121no—
472C3×C4D3×C22⋊C411yescharacteristic
473C3×C4#67⋊C411yescharacteristic
474C3×C4C2×(C2×D3)⋊C411yescharacteristic
475C3×C4C4×#6711yescharacteristic
476C3×C4#93011yescharacteristic
477C3×C4#93711yescharacteristic
478C3×C4#93811yescharacteristic
479C3×C4#95311yescharacteristic
480Dic3—22no—
481Dic3—41no—
482Dic3—124no—
483Dic3—122no—
484Dic3—122no—
485C32#187611yescharacteristic, complemented, Sylow
486C23—61no—
487C23—61no—
488C23#379811yescharacteristic
489Q8—32no—
490Q8—61no—
491Q8—61no—
492Q8—61no—
493D4—32no—
494D4—62no—
495D4—62no—
496D4—61no—
497D4—61no—
498D4—61no—
499D4—121no—
500D4—121no—
501C2×C4—61no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—61no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4—182no—
508C2×C4—361no—
509C2×C4—361no—
510C2×C4#379511yescharacteristic
511C2×C4C4×D3211yescharacteristic
512C2×C4D3×D1211yescharacteristic
513C2×C4C2×#62511yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C2×C4D3×#6711yescharacteristic
516C8—21no—
517C8—21no—
518C8—62no—
519C8—121no—
520C8—181no—
521C8—181no—
522C2×C3—22no—
523C2×C3—22no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—122no—
532C2×C3—241no—
533C2×C3#495611yescharacteristic
534C2×C3#514411yescharacteristic
535C2×C3#514411yescharacteristic
536C2×C3#514511yescharacteristic
537C2×C3#514511yescharacteristic
538C2×C3#521311yescharacteristic
539D3—42no—
540D3—81no—
541C22—21no—
542C22—21no—
543C22—62no—
544C22—121no—
545C22—121no—
546C22—121no—
547C22—121no—
548C22—121no—
549C22C4×#62511yescharacteristic
550C22#6390511yescharacteristic
551C22#6390611yescharacteristic
552C4—62no—
553C4—121no—
554C4—362no—
555C4#6387911yescharacteristic
556C4#6390811yescharacteristic
557C4D3×(C2×D3)⋊C411yescharacteristic
558C4#6397611yescharacteristic
559C3—21no—
560C3#7001111yescharacteristic, complemented
561C3#7201011yescharacteristic, complemented
562C2—21no—
563C2—21no—
564C2—122no—
565C2—241no—
566C2#1059092111yescharacteristic
567C2#1059092211yescharacteristic
568C2#1059138111yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×#63822C2
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×C3×#901C2semidirect
3. C3×#5110C2semidirect
4. C2×#63568C2semidirect
5. C2×#63568C2semidirect
6. #10589416C2semidirect
7. #10589165C2semidirect
21. C2×#3718C4semidirect
22. C2×#3715C4semidirect
23. C2×#3715C4semidirect
26. C2×#3713C4semidirect
34. C2×#901D3semidirect
40. #5110D3semidirect
485. C32#1876semidirect
560. C3#70011semidirect
561. C3#72010semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
C2×#638222
C3×#51102
C2×#635682
#105894162
#105891652
#720103
#700113