Finite Group Databasebeta

← #11787685

Subgroups — #11787685

Order 1152.

815 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic
2C2×#63833C211yesmaximal, characteristic
3C3×#5004C211yesmaximal, characteristic, complemented
4#10591220C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70348—31nomaximal
9#68775—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14#64101—21no—
15C4⋊C4×C3⋊D3—21no—
16#64090—22no—
17C4×C4⋊(C3⋊D3)—21no—
18C4×#634—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×#3719—21no—
23#63833—22no—
24#63833C414yescomplemented
25C2×#3717—21no—
26C3×#810—21no—
27C3×#810—21no—
28#63579—22no—
29#63570—22no—
30C2×#942—31no—
31C2×#909—31no—
32#5523—31no—
33#5523—31no—
34#5523—61no—
35C3×#419—31no—
36#5229—31no—
37C2×#825—31no—
38#5004D311yescharacteristic, complemented
39#4929—31no—
40C2×#805—31no—
41C3×#339—31no—
42#4554—31no—
43#4554—31no—
44#4532D311yescharacteristic, complemented
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3D412yes—
48#3828—21no—
49#3828—21no—
50#3828C2×C412yes—
51#3828D412yes—
52C2×C4⋊(C3⋊D3)D411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3—22no—
55C2×#634D411yescharacteristic
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6C2×C412yescomplemented
64C32×C4⋊C4D411yescharacteristic
65C32×C4⋊C4D411yescharacteristic
66C32×C22⋊C4—21no—
67C32×C42—21no—
68#3752—22no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—21no—
71#3750—22no—
72C4×C3⋊Dic3—22no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208C2×C412yescomplemented
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81#3719—24no—
82#3717—24no—
83#1882—91noSylow
84C22×C3×Q8—31no—
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C22×Dic6C2×D311yescharacteristic
89C2×C3×M16—31no—
90C2×C3×M16—31no—
91C3×#117—21no—
92C3×#117C2×D311yescharacteristic
93C3×#117C2×D311yescharacteristic
94C2×C3×C42—31no—
95C2×#216—61no—
96#942—34no—
97#942—62no—
98C2×#215—61no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—61no—
102C2×C4×Dic3C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104C2×#208C2×D311yescharacteristic
105#909—34no—
106#909—62no—
107C2×Dic12—61no—
108C2×#204—61no—
109#892—62no—
110#892—61no—
111#892—61no—
112D3×C4⋊C4—62no—
113D3×C4⋊C4—61no—
114D3×C4⋊C4—61no—
115#67⋊C4—62no—
116#67⋊C4—62no—
117#67⋊C4—64no—
118C4×D12—61no—
119C4×D12—61no—
120C4×D12—62no—
121C4×Dic6—61no—
122C4×Dic6—61no—
123C4×Dic6—62no—
124C3×#103—61no—
125C3×#103—61no—
126C3⋊#95—62no—
127C3⋊#95—62no—
128#825—62no—
129#810—21no—
130#810—21no—
131#805—62no—
132C23×C32C2×D411yescharacteristic
133C22×C3⋊D3—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142#638—22no—
143#638—22no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—42no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)C22⋊C412yes—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—82no—
152#634—21no—
153#634C22⋊C412yes—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—41no—
163C3×Dic6—41no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—41no—
166C2×#137—91no—
167#520—91no—
168C2×#104—91no—
169#419—31no—
170#391—91no—
171#343—91no—
172#339—31no—
173C2×C3×Q8—32no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C22×C3×C4—21no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—62no—
185C2×#67—61no—
186C2×#67—61no—
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—32no—
190C22×Dic3—32no—
191C22×Dic3—62no—
192#235—32no—
193#235—32no—
194#235—32no—
195#235—32no—
196#235—62no—
197#235—62no—
198#235—62no—
199#235—62no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—61no—
207C2×C4×D3—62no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—64no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—31no—
219C2×Dic6—31no—
220C2×Dic6—61no—
221C2×Dic6C4×D312yescomplemented
222C3×M16—32no—
223C3×M16—61no—
224C3×M16—61no—
225C3×M16—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4D1211yescharacteristic
231C3×C4⋊C4D1211yescharacteristic
232C3×C4⋊C4#6711yescharacteristic
233C3×C4⋊C4#6711yescharacteristic
234C3×C22⋊C4—22no—
235C3×C22⋊C4—21no—
236C3×C22⋊C4—21no—
237C3×C42—22no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—61no—
241C3×C42—61no—
242#216—64no—
243#215—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253Dic3⋊C4—64no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256C4×Dic3—21no—
257C4×Dic3—21no—
258C4×Dic3—64no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261#208—21no—
262#208—21no—
263#208—21no—
264#208C4×D312yescomplemented
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267Dic12—64no—
268#204—64no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32C4×D411yescharacteristic
272C22×C32#12011yescharacteristic
273C22×C32#12111yescharacteristic
274C2×C3⋊D3—22no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C32×C4—41no—
278C32×C4—41no—
279C32×C4C2×C22⋊C411yescharacteristic
280C32×C4C4×D411yescharacteristic
281C32×C4#12111yescharacteristic
282C32×C4#12311yescharacteristic
283C3⋊Dic3—22no—
284C3⋊Dic3—42no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C2×#41—91no—
288C22×Q8—31no—
289#137—94no—
290#137—182no—
291C2×Q16—181no—
292C2×SD16—181no—
293C2×M16—31no—
294C2×M16—31no—
295C4×Q8—181no—
296C4×D4—181no—
297C4×D4—182no—
298#117—181no—
299#117D3211yescharacteristic
300C2×C4⋊C4—91no—
301C2×C4⋊C4—181no—
302C2×C42—31no—
303#104—182no—
304#103—61no—
305#103—61no—
306#95—182no—
307C23×C3—21no—
308C23×C3D3×D411yescharacteristic
309C23×C3D3×D411yescharacteristic
310C22×D3—62no—
311C22×D3—61no—
312C22×D3—61no—
313C3×Q8—62no—
314C3×Q8—62no—
315C3×Q8—121no—
316C3×Q8—121no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4#23511yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4#23711yescharacteristic
345C2×C3×C4#23911yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347#67—64no—
348#67—64no—
349#67—62no—
350#67—62no—
351#67—62no—
352#67—62no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—62no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—64no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—242no—
368D12—32no—
369D12—32no—
370D12—62no—
371D12—62no—
372D12—61no—
373D12—61no—
374C4×D3—64no—
375C4×D3—64no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—244no—
381C4×D3—242no—
382C4×D3—242no—
383Dic6—22no—
384Dic6—22no—
385Dic6—32no—
386Dic6—32no—
387Dic6—41no—
388Dic6—41no—
389Dic6—62no—
390Dic6—62no—
391Dic6—61no—
392Dic6—61no—
393C3×C8—62no—
394C3×C8—121no—
395C3⋊C8—22no—
396C3⋊C8—41no—
397C2×C32—21no—
398C2×C32—21no—
399C2×C32#38611yescharacteristic
400C2×C32#45511yescharacteristic
401C2×C32#45611yescharacteristic
402C3⋊D3—42no—
403#41—92no—
404#41—92no—
405#41—181no—
406#41—181no—
407C2×Q8—32no—
408C2×Q8—61no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—91no—
414C2×D4—91no—
415C2×D4—181no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—92no—
419C22×C4—182no—
420C22×C4—181no—
421C22×C4C2×D3211yescharacteristic
422Q16—184no—
423SD16—184no—
424M16—32no—
425M16—61no—
426M16—61no—
427M16—61no—
428C2×C8—61no—
429C2×C8—61no—
430C4⋊C4—182no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4#62611yescharacteristic
434C4⋊C4#62611yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—182no—
437C42—21no—
438C42—61no—
439C42—61no—
440C42—182no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3#67⋊C411yescharacteristic
451C22×C3#88211yescharacteristic
452C22×C3#88411yescharacteristic
453C22×C3#88411yescharacteristic
454C22×C3#89311yescharacteristic
455C22×C3#93711yescharacteristic
456C2×D3—64no—
457C2×D3—62no—
458C2×D3—62no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—121no—
462C2×D3—121no—
463C2×D3—121no—
464C2×D3—121no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—42no—
470C3×C4—42no—
471C3×C4—41no—
472C3×C4—41no—
473C3×C4—41no—
474C3×C4—41no—
475C3×C4—122no—
476C3×C4—122no—
477C3×C4C4×D1211yescharacteristic
478C3×C4D3×C22⋊C411yescharacteristic
479C3×C4D3×C22⋊C411yescharacteristic
480C3×C4#88311yescharacteristic
481C3×C4#89411yescharacteristic
482C3×C4#89511yescharacteristic
483C3×C4C4×#6711yescharacteristic
484C3×C4#93811yescharacteristic
485Dic3—42no—
486Dic3—42no—
487Dic3—64no—
488Dic3—62no—
489Dic3—62no—
490Dic3—124no—
491Dic3—122no—
492Dic3—122no—
493C32#188211yescharacteristic, complemented, Sylow
494C23—181no—
495C23#381111yescharacteristic
496Q8—62no—
497Q8—62no—
498Q8—92no—
499Q8—121no—
500Q8—121no—
501Q8—181no—
502D4—92no—
503D4—182no—
504D4—182no—
505D4—181no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—181no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—362no—
519C2×C4—722no—
520C2×C4#379611yescharacteristic
521C2×C4#379811yescharacteristic
522C2×C4C4×D3211yescharacteristic
523C2×C4#380211yescharacteristic
524C2×C4C2×#62611yescharacteristic
525C2×C4#381111yescharacteristic
526C8—62no—
527C8—121no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—41no—
536C2×C3—41no—
537C2×C3#466511yescharacteristic
538C2×C3#482511yescharacteristic
539C2×C3#482611yescharacteristic
540C2×C3#495611yescharacteristic
541C2×C3#520211yescharacteristic
542C2×C3#520511yescharacteristic
543D3—124no—
544D3—122no—
545D3—122no—
546C22—21no—
547C22—21no—
548C22—182no—
549C22—361no—
550C22—361no—
551C22#6388111yescharacteristic
552C22#6391211yescharacteristic
553C22#6398111yescharacteristic
554C4—41no—
555C4—41no—
556C4—122no—
557C4—122no—
558C4—182no—
559C4—362no—
560C4#6385311yescharacteristic
561C4C4×#62611yescharacteristic
562C4#6391611yescharacteristic
563C4#6392111yescharacteristic
564C3—21no—
565C3#6877511yescharacteristic, complemented
566C3#7034811yescharacteristic, complemented
567C2—21no—
568C2—21no—
569C2—362no—
570C2#1059138711yescharacteristic
571C2#1059166811yescharacteristic
572C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1882
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. C3×#5004C2semidirect
4. #10591220C2semidirect
6. C3×#4532C2semidirect
7. #10589168C2semidirect
24. #63833C4semidirect
38. #5004D3semidirect
44. #4532D3semidirect
63. C2×C3×Dic6C2×C4semidirect
78. C3×#208C2×C4semidirect
221. C2×Dic6C4×D3semidirect
264. #208C4×D3semidirect
493. C32#1882semidirect
565. C3#68775semidirect
566. C3#70348semidirect

Maximal subgroups

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

subgroupindex
#105959942
C2×#638332
C3×#50042
#105912202
C2×#635702
C3×#45322
#105891682
#703483
#687753