Finite Group Databasebeta

← #11787410

Subgroups — #11787410

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×#904C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic, complemented
3C2×#63568C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic, complemented
5#10591071C211yesmaximal, characteristic, complemented
6#10589416C211yesmaximal, characteristic, complemented
7C3×#4552C211yesmaximal, characteristic, complemented
8#72087—31nomaximal
9#68946—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
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#63815—22no—
25#63815—22no—
26C2×D3×C3⋊C8—21no—
27#63568—22no—
28#63568—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C2×C3×#135—31no—
32C2×#948—31no—
33C2×#907—31no—
34C2×#904D311yescharacteristic
35C2×#837—31no—
36C2×#837—31no—
37#5234—31no—
38C2×#825—31no—
39C2×#825—31no—
40#5129—31no—
41C3×#341—31no—
42#4552D311yescharacteristic, complemented
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×C8C2×C411yescharacteristic
67C2×C32×C8C2×C411yescharacteristic
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)D411yescharacteristic
73C2×C3⋊(C3⋊C8)D411yescharacteristic
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208D412yes—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
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—
97C2×C3×M16—31no—
98C2×C3×M16—31no—
99C22×C3×C8—21no—
100C22×C3×C8C2×D311yescharacteristic
101C22×C3×C8C2×D311yescharacteristic
102#948—62no—
103#948—62no—
104C2×C4×Dic3—31no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—61no—
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109C2×#208C2×D311yescharacteristic
110C22×C3⋊C8—31no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—61no—
113C22×C3⋊C8—61no—
114#907—62no—
115#907—62no—
116C2×Dic12Dic311yescharacteristic, complemented
117#904—22no—
118#904—22no—
119C2×D24Dic311yescharacteristic, complemented
120C2×#204Dic311yescharacteristic, complemented
121C2×#204Dic311yescharacteristic, complemented
122C2×ΓL(1,𝔽25)—61no—
123C2×D3×C8—61no—
124#837—62no—
125#837—62no—
126#830—61no—
127#830—61no—
128#825—62no—
129#825—62no—
130(C2×D3)⋊C8—61no—
131(C2×D3)⋊C8—61no—
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—31no—
169C2×#131—91no—
170C2×#104—91no—
171C2×#104—91no—
172#408—91no—
173#341—31no—
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#235#6712yes—
206#235#6712yes—
207C2×D12C2×Dic311yescharacteristic
208C2×D12C2×Dic311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—21no—
211C2×Dic6C2×Dic311yescharacteristic
212C2×Dic6C2×Dic311yescharacteristic
213C3×Q16—62no—
214C3×SD16—62no—
215C3×SD16—62no—
216C3×D8—62no—
217C3×M16—32no—
218C3×M16—61no—
219C3×M16—61no—
220C3×M16—61no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—41no—
228C2×C3×C8—41no—
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231C2×C3×C8C4×D311yescharacteristic
232C2×C3×C8C4×D311yescharacteristic
233C2×C3×C8C2×Dic311yescharacteristic
234C2×C3×C8C2×Dic311yescharacteristic
235C4×Dic3—61no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238C4×Dic3—61no—
239C4×Dic3—121no—
240C4×Dic3—121no—
241#208—21no—
242#208—21no—
243#208—21no—
244#208—64no—
245#208D1212yes—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—31no—
249C2×C3⋊C8—31no—
250C2×C3⋊C8—31no—
251C2×C3⋊C8—31no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—64no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—121no—
260C2×C3⋊C8—121no—
261Dic12—22no—
262D24—22no—
263#204—22no—
264#204—22no—
265ΓL(1,𝔽25)—64no—
266D3×C8—64no—
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—62no—
288#135—62no—
289C2×Q16—31no—
290C2×SD16—31no—
291C2×SD16—31no—
292C2×D8—31no—
293#131—182no—
294#131—182no—
295C2×M16—31no—
296C2×M16—31no—
297C2×M16—181no—
298C22×C8—91no—
299C22×C8—181no—
300C22×C8D3211yescharacteristic
301C2×C42—91no—
302#104—182no—
303#104—182no—
304C22⋊C8—181no—
305C22⋊C8—181no—
306C23×C3—21no—
307C23×C3—61no—
308C23×C3—61no—
309C23×C3#23711yescharacteristic
310C23×C3#23911yescharacteristic
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×D1211yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4#23711yescharacteristic
346C2×C3×C4C22×Dic311yescharacteristic
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#21712yes—
368C4×D3—22no—
369C4×D3—22no—
370C4×D3—41no—
371C4×D3—41no—
372Dic6—21no—
373Dic6—21no—
374Dic6—21no—
375Dic6#21712yes—
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—62no—
418SD16—62no—
419SD16—62no—
420D8—62no—
421M16—32no—
422M16—61no—
423M16—61no—
424M16—61no—
425M16—184no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—61no—
429C2×C8—61no—
430C2×C8—91no—
431C2×C8—91no—
432C2×C8—184no—
433C2×C8—181no—
434C2×C8—181no—
435C2×C8D3×Dic311yescharacteristic
436C2×C8D3×Dic311yescharacteristic
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#89311yescharacteristic
455C22×C3#89411yescharacteristic
456C22×C3#89511yescharacteristic
457C22×C3D4×Dic311yescharacteristic
458C22×C3#93511yescharacteristic
459C22×C3#93911yescharacteristic
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×C4C4×D1211yescharacteristic
473C3×C4D3×C22⋊C411yescharacteristic
474C3×C4#88211yescharacteristic
475C3×C4#88411yescharacteristic
476C3×C4D4×Dic311yescharacteristic
477C3×C4#93711yescharacteristic
478C3×C4#93911yescharacteristic
479C3×C4C2×#21711yescharacteristic
480Dic3—22no—
481Dic3—41no—
482Dic3—124no—
483Dic3—122no—
484Dic3—122no—
485C32#187611yescharacteristic, complemented, Sylow
486C23—61no—
487C23—61no—
488C23#379611yescharacteristic
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×C4D3×D1211yescharacteristic
512C2×C4#380211yescharacteristic
513C2×C4C2×D3×Dic311yescharacteristic
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#466511yescharacteristic
534C2×C3#489411yescharacteristic
535C2×C3#489511yescharacteristic
536C2×C3#519611yescharacteristic
537C2×C3#519711yescharacteristic
538C2×C3#522011yescharacteristic
539D3—42no—
540D3—81no—
541C22—21no—
542C22—21no—
543C22—62no—
544C22—121no—
545C22—121no—
546C22—121no—
547C22—121no—
548C22—121no—
549C22#6388411yescharacteristic
550C22#6388611yescharacteristic
551C22#6389811yescharacteristic
552C4—62no—
553C4—121no—
554C4—362no—
555C4#6388511yescharacteristic
556C4Dic3×D1211yescharacteristic
557C4#6392211yescharacteristic
558C4D3×#21711yescharacteristic
559C3—21no—
560C3#6894611yescharacteristic, complemented
561C3#7208711yescharacteristic, complemented
562C2—21no—
563C2—21no—
564C2—122no—
565C2—241no—
566C2#1059091911yescharacteristic
567C2#1059092011yescharacteristic
568C2#1059137611yescharacteristic
subgroupG/H
centerC2×C4#3802
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×#63815C2semidirect
3. C2×#63568C2semidirect
4. C2×#63568C2semidirect
5. #10591071C2semidirect
6. #10589416C2semidirect
7. C3×#4552C2semidirect
17. C2×C3×Dic12C4semidirect
20. C2×C3×D24C4semidirect
21. C2×C3×#204C4semidirect
22. C2×C3×#204C4semidirect
42. #4552D3semidirect
116. C2×Dic12Dic3semidirect
119. C2×D24Dic3semidirect
120. C2×#204Dic3semidirect
121. C2×#204Dic3semidirect
485. C32#1876semidirect
560. C3#68946semidirect
561. 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×#638152
C2×#635682
#105910712
#105894162
C3×#45522
#720873
#689463