Finite Group Databasebeta

← #11787408

Subgroups — #11787408

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×#904C211yesmaximal, characteristic
2C2×#63814C211yesmaximal, characteristic, complemented
3C2×#63569C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic, complemented
5#10591070C211yesmaximal, characteristic, complemented
6#10589418C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#72087—31nomaximal
9#68695—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×C3×Dic12C411yescharacteristic, complemented
18C3×#904—22no—
19C3×#904—22no—
20C2×C3×D24C411yescharacteristic, complemented
21C2×C3×#204C411yescharacteristic, complemented
22C2×C3×#204C411yescharacteristic, complemented
23C2×#3711—21no—
24#63814—22no—
25#63814—22no—
26C2×D3×C3⋊C8—21no—
27#63569—22no—
28#63569—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C2×C3×#135—31no—
32C2×#948—31no—
33C2×#904D311yescharacteristic
34C2×#901—31no—
35C2×#837—31no—
36C2×#837—31no—
37#5234—31no—
38#5110—31no—
39C2×#805—31no—
40C2×#805—31no—
41C3×#336—31no—
42#4552—31no—
43#4552—31no—
44#4552—61no—
45#4550D311yescharacteristic, complemented
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
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8C2×C411yescharacteristic
67C2×C32×C8C2×C411yescharacteristic
68#3748—21no—
69#3748—21no—
70#3748—21no—
71#3748D412yes—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)—21no—
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×Dic12—22no—
81C3×D24—22no—
82C3×#204—22no—
83C3×#204—22no—
84#3711—24no—
85D3×C3⋊C8—24no—
86#1876—91noSylow
87C2×C3×#41—31no—
88C2×C3×#41—31no—
89C2×#235C2×D311yescharacteristic
90C2×#235C2×D311yescharacteristic
91C3×#135—62no—
92C3×#135—62no—
93C2×C3×Q16—31no—
94C2×C3×SD16—31no—
95C2×C3×SD16—31no—
96C2×C3×D8—31no—
97C22×C3×C8—21no—
98C22×C3×C8—31no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C2×C3×C42—31no—
102#948—62no—
103#948—62no—
104C2×C4×Dic3C2×D311yescharacteristic
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—31no—
108C2×#208—31no—
109C2×#208—61no—
110C2×#208—61no—
111C2×#208—61no—
112C22×C3⋊C8—61no—
113C22×C3⋊C8C2×D311yescharacteristic
114C2×Dic12Dic311yescharacteristic, complemented
115#904—22no—
116#904—22no—
117C2×D24Dic311yescharacteristic, complemented
118C2×#204Dic311yescharacteristic, complemented
119C2×#204Dic311yescharacteristic, complemented
120#901—62no—
121#901—62no—
122C2×ΓL(1,𝔽25)—61no—
123C2×D3×C8—61no—
124#837—62no—
125#837—62no—
126#830—61no—
127#830—61no—
128(C2×D3)⋊C8—61no—
129(C2×D3)⋊C8—61no—
130#805—62no—
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—21no—
163C32×C8—21no—
164C3⋊(C3⋊C8)—22no—
165C3⋊(C3⋊C8)—41no—
166C3×C3⋊C8—21no—
167C3×C3⋊C8—21no—
168C2×#135—31no—
169C2×#131—91no—
170C2×#104—91no—
171C2×#104—91no—
172#408—91no—
173#341—91no—
174#336—31no—
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#235#6712yes—
205#235#6712yes—
206C2×D12C2×Dic311yescharacteristic
207C2×D12C2×Dic311yescharacteristic
208C2×C4×D3—21no—
209C2×C4×D3—21no—
210C2×Dic6C2×Dic311yescharacteristic
211C2×Dic6C2×Dic311yescharacteristic
212C3×Q16—62no—
213C3×SD16—62no—
214C3×SD16—62no—
215C3×D8—62no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8—41no—
225C2×C3×C8—41no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8C4×D311yescharacteristic
229C2×C3×C8C4×D311yescharacteristic
230C2×C3×C8C2×Dic311yescharacteristic
231C2×C3×C8C2×Dic311yescharacteristic
232C3×C42—61no—
233C3×C42—61no—
234C4×Dic3—21no—
235C4×Dic3—21no—
236#208—32no—
237#208—32no—
238#208—62no—
239#208—64no—
240#208—61no—
241#208—61no—
242#208—62no—
243#208—61no—
244#208—61no—
245#208—61no—
246#208—61no—
247#208—121no—
248#208—121no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—64no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—121no—
257C2×C3⋊C8—121no—
258C2×C3⋊C8D1211yescharacteristic
259C2×C3⋊C8D1211yescharacteristic
260Dic12—22no—
261D24—22no—
262#204—22no—
263#204—22no—
264ΓL(1,𝔽25)—64no—
265D3×C8—64no—
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—62no—
287#135—62no—
288C2×Q16—31no—
289C2×SD16—31no—
290C2×SD16—31no—
291C2×D8—31no—
292#131—182no—
293#131—182no—
294C2×M16—91no—
295C2×M16—91no—
296C2×M16—181no—
297C22×C8—31no—
298C22×C8—181no—
299C22×C8D3211yescharacteristic
300C2×C42—31no—
301#104—182no—
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×D1211yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4#23911yescharacteristic
348C2×C3×C4C22×Dic311yescharacteristic
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#21712yes—
364C4×D3—22no—
365C4×D3—22no—
366C4×D3—41no—
367C4×D3—41no—
368Dic6—21no—
369Dic6—21no—
370Dic6—21no—
371Dic6#21712yes—
372C3×C8—21no—
373C3×C8—21no—
374C3×C8—21no—
375C3×C8—21no—
376C3×C8—41no—
377C3×C8—41no—
378C3×C8—61no—
379C3×C8—61no—
380C3⋊C8—21no—
381C3⋊C8—21no—
382C3⋊C8—62no—
383C3⋊C8—62no—
384C3⋊C8—122no—
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—62no—
414SD16—62no—
415SD16—62no—
416D8—62no—
417M16—92no—
418M16—184no—
419M16—181no—
420M16—181no—
421M16—181no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—31no—
425C2×C8—31no—
426C2×C8—61no—
427C2×C8—61no—
428C2×C8—184no—
429C2×C8—181no—
430C2×C8—181no—
431C2×C8D3×Dic311yescharacteristic
432C2×C8D3×Dic311yescharacteristic
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×C3C4×D1211yescharacteristic
451C22×C3#88411yescharacteristic
452C22×C3#89411yescharacteristic
453C22×C3D4×Dic311yescharacteristic
454C22×C3#93511yescharacteristic
455C22×C3#93911yescharacteristic
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#88211yescharacteristic
471C3×C4#89311yescharacteristic
472C3×C4#89511yescharacteristic
473C3×C4D4×Dic311yescharacteristic
474C3×C4#93711yescharacteristic
475C3×C4#93911yescharacteristic
476C3×C4C2×#21711yescharacteristic
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#379611yescharacteristic
506C2×C4D3×D1211yescharacteristic
507C2×C4#380211yescharacteristic
508C2×C4C2×D3×Dic311yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C2×C4D3×#6711yescharacteristic
511C8—21no—
512C8—21no—
513C8—61no—
514C8—61no—
515C8—182no—
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#466511yescharacteristic
529C2×C3#470011yescharacteristic
530C2×C3#471711yescharacteristic
531C2×C3#519611yescharacteristic
532C2×C3#519711yescharacteristic
533C2×C3#522011yescharacteristic
534D3—42no—
535D3—81no—
536C22—21no—
537C22—21no—
538C22—62no—
539C22—121no—
540C22—121no—
541C22—121no—
542C22—121no—
543C22—121no—
544C22#6388411yescharacteristic
545C22#6388511yescharacteristic
546C22Dic3×D1211yescharacteristic
547C4—62no—
548C4—122no—
549C4—121no—
550C4#6388611yescharacteristic
551C4#6389811yescharacteristic
552C4#6392211yescharacteristic
553C4D3×#21711yescharacteristic
554C3—21no—
555C3#6869511yescharacteristic, complemented
556C3#7208711yescharacteristic, complemented
557C2—21no—
558C2—21no—
559C2—122no—
560C2—241no—
561C2#1059091511yescharacteristic
562C2#1059091611yescharacteristic
563C2#1059137611yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×C3×#904C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1876
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63814C2semidirect
3. C2×#63569C2semidirect
4. C2×#63569C2semidirect
5. #10591070C2semidirect
6. #10589418C2semidirect
7. C3×#4550C2semidirect
17. C2×C3×Dic12C4semidirect
20. C2×C3×D24C4semidirect
21. C2×C3×#204C4semidirect
22. C2×C3×#204C4semidirect
45. #4550D3semidirect
114. C2×Dic12Dic3semidirect
117. C2×D24Dic3semidirect
118. C2×#204Dic3semidirect
119. C2×#204Dic3semidirect
480. C32#1876semidirect
555. C3#68695semidirect
556. C3#72087semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
C2×#638142
C2×#635692
#105910702
#105894182
C3×#45502
#720873
#686953