Finite Group Databasebeta

← #11785326

Subgroups — #11785326

Order 1152.

709 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594954C211yesmaximal, characteristic
2C2×#63632C211yesmaximal, characteristic
3C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#10591115C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#69494—31nomaximal
9#68770—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×Dic3⋊C4—21no—
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63952—21no—
19#63952—21no—
20#63894C411yescharacteristic, complemented
21#63894C411yescharacteristic, complemented
22C4×#624—21no—
23#63874—21no—
24#63844C411yescharacteristic, complemented
25#63844C411yescharacteristic, complemented
26#63632—22no—
27C3×C3⋊#95—21no—
28Dic3⋊(C3⋊C8)—21no—
29Dic3⋊(C3⋊C8)—21no—
30#63570—22no—
31#5522—31no—
32C4×#235—31no—
33C3×C4×C4⋊C4—31no—
34C2×#825—31no—
35#5118—31no—
36C4×Dic3⋊C4D311yescharacteristic, complemented
37C2×#805—31no—
38C2×#805—31no—
39C2×#805—31no—
40C2×#805—61no—
41#4924—31no—
42C3×#339—31no—
43#4532—31no—
44#4523—31no—
45#4523D311yescharacteristic, complemented
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×#638—21no—
49#3828—21no—
50#3828—21no—
51#3828D412yes—
52#3828Q812yes—
53C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×#634C2×C411yescharacteristic
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×#624—21no—
60C2×#624—21no—
61C32×C42—21no—
62C32×C42—21no—
63#3748—21no—
64#3748—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217—21no—
67C3×C4⋊Dic3C2×C411yescharacteristic
68C3×C4⋊Dic3C2×C411yescharacteristic
69C3×Dic3⋊C4—24no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3C2×C411yescharacteristic
74C3×C4×Dic3C2×C411yescharacteristic
75C3×C4×Dic3D411yescharacteristic
76C3×C4×Dic3D411yescharacteristic
77C3×#208—21no—
78C3×#208—21no—
79C2×C3×C3⋊C8—21no—
80#3724—21no—
81#3724—21no—
82#3722—21no—
83#3722—21no—
84Dic32—21no—
85Dic32—21no—
86#1806—91noSylow
87C2×#235—31no—
88C2×#235—31no—
89C2×#235—61no—
90C2×C3×M16—31no—
91C3×#117—31no—
92C2×C3×C4⋊C4—61no—
93C2×C3×C42—21no—
94C2×C3×C42—31no—
95C2×C3×C42—31no—
96C2×C3×C42C2×D311yescharacteristic
97C2×C3×C42C2×D311yescharacteristic
98C4×#67—61no—
99C4×#67—61no—
100#926C2×D311yescharacteristic
101C2×Dic3⋊C4—21no—
102C2×C4×Dic3C2×D311yescharacteristic
103C2×C4×Dic3C2×D311yescharacteristic
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—61no—
107C2×#208C2×D311yescharacteristic
108#893—31no—
109#893—31no—
110#887—31no—
111#887—31no—
112#67⋊C4—61no—
113#67⋊C4—61no—
114C4×D12—31no—
115C4×D12—31no—
116#872—61no—
117#872—61no—
118C42×D3—61no—
119C42×D3—61no—
120C4×Dic6—31no—
121C4×Dic6—31no—
122C3×#95—61no—
123C3⋊#95—21no—
124#825—62no—
125Dic3⋊C8—61no—
126Dic3⋊C8—61no—
127#805—62no—
128#805—62no—
129#805—62no—
130#805—64no—
131C4⋊(C3⋊C8)—61no—
132C4⋊(C3⋊C8)—61no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—21no—
135C2×C32×C4—22no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×Q811yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144#638—22no—
145#638—22no—
146C2×C3⋊Dic3—21no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)C4⋊C412yescomplemented
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151#634—21no—
152#634C4⋊C412yescomplemented
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3C22⋊C411yescharacteristic
161C2×C3×Dic3C22⋊C411yescharacteristic
162C2×C3×Dic3C22⋊C411yescharacteristic
163C2×C3×Dic3C22⋊C411yescharacteristic
164#624—42no—
165#624—42no—
166C3⋊(C3⋊C8)—41no—
167C3×C3⋊C8—41no—
168C4×#41—91no—
169#423—91no—
170C2×#104—91no—
171C2×#104—91no—
172C4×C4⋊C4—31no—
173#339—31no—
174#339—91no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—41no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—61no—
185C2×#67—61no—
186C2×#67—121no—
187C22×Dic3—21no—
188C22×Dic3#6711yescharacteristic
189C22×Dic3#6711yescharacteristic
190#235—32no—
191#235—32no—
192#235—32no—
193#235—32no—
194#235—62no—
195#235—62no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—121no—
201#235—121no—
202C2×D12—31no—
203C2×D12—31no—
204C2×D12—61no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—121no—
212C2×Dic6—31no—
213C2×Dic6—31no—
214C2×Dic6—61no—
215C3×M16—61no—
216C3×M16—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—31no—
220C3×C4⋊C4—64no—
221C3×C22⋊C4—61no—
222C3×C42—22no—
223C3×C42—21no—
224C3×C42—21no—
225C3×C42—21no—
226C3×C42—21no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42—31no—
230C3×C42—31no—
231C3×C42—41no—
232C3×C42—61no—
233C3×C42—61no—
234C3×C42—61no—
235#217—21no—
236(C2×D3)⋊C4—61no—
237(C2×D3)⋊C4—61no—
238(C2×D3)⋊C4—61no—
239(C2×D3)⋊C4—61no—
240C4⋊Dic3C4×D311yescharacteristic
241C4⋊Dic3C4×D311yescharacteristic
242Dic3⋊C4—24no—
243Dic3⋊C4—61no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246Dic3⋊C4—61no—
247C4×Dic3—21no—
248C4×Dic3—21no—
249C4×Dic3—21no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3C4×D311yescharacteristic
255C4×Dic3C4×D311yescharacteristic
256C4×Dic3D1211yescharacteristic
257C4×Dic3D1211yescharacteristic
258#208—21no—
259#208—21no—
260#208—62no—
261#208—61no—
262#208—61no—
263#208—61no—
264#208—61no—
265#208—121no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—121no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32C2×C22⋊C411yescharacteristic
273C22×C32#12111yescharacteristic
274C22×C32C22⋊Q811yescharacteristic
275C2×C3⋊D3—22no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C32×C4—42no—
279C32×C4C2×C4⋊C411yescharacteristic
280C32×C4#11711yescharacteristic
281C32×C4#12111yescharacteristic
282C32×C4C22⋊Q811yescharacteristic
283C3⋊Dic3—22no—
284C3×Dic3—21no—
285C3×Dic3—21no—
286C3×Dic3—21no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3#10412yescomplemented
291C2×#41—91no—
292C2×M16—31no—
293C2×M16—91no—
294C4×Q8—91no—
295C4×Q8—91no—
296C4×D4—91no—
297C4×D4—91no—
298C4×D4—181no—
299C4×D4—181no—
300#117—31no—
301#117—181no—
302C2×C4⋊C4—61no—
303C2×C42—31no—
304C2×C42—31no—
305C2×C42—181no—
306C2×C42D3211yescharacteristic
307C4⋊C8—181no—
308C4⋊C8—181no—
309#104—182no—
310#104—182no—
311#95—61no—
312C23×C3—21no—
313C23×C3D3×D411yescharacteristic
314C23×C3C2×#6711yescharacteristic
315C22×D3—61no—
316C22×D3—61no—
317C22×D3—121no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
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—31no—
327C2×C3×C4—31no—
328C2×C3×C4—31no—
329C2×C3×C4—31no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—42no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4D3×Q811yescharacteristic
354C2×C3×C4D3×Q811yescharacteristic
355C2×C3×C4#23911yescharacteristic
356#67—62no—
357#67—62no—
358#67—62no—
359#67—62no—
360#67—122no—
361#67—122no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—41no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—121no—
372C2×Dic3(C2×D3)⋊C411yescharacteristic
373C2×Dic3(C2×D3)⋊C411yescharacteristic
374C2×Dic3(C2×D3)⋊C411yescharacteristic
375C2×Dic3(C2×D3)⋊C411yescharacteristic
376D12—32no—
377D12—32no—
378D12—62no—
379D12—61no—
380D12—61no—
381D12—121no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—62no—
385C4×D3—62no—
386C4×D3—122no—
387C4×D3—122no—
388C4×D3—122no—
389C4×D3—122no—
390C4×D3—122no—
391C4×D3—122no—
392Dic6—32no—
393Dic6—32no—
394Dic6—62no—
395Dic6—61no—
396Dic6—61no—
397Dic6—121no—
398C3×C8—121no—
399C3⋊C8—41no—
400C3⋊C8—122no—
401C3⋊C8—121no—
402C3⋊C8—121no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32#38011yescharacteristic
406C2×C32C2×#10411yescharacteristic
407C2×C32#42111yescharacteristic
408C3⋊D3—42no—
409#41—92no—
410#41—92no—
411#41—181no—
412#41—181no—
413C2×Q8—91no—
414C2×D4—91no—
415C2×D4—181no—
416C22×C4—21no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—61no—
420C22×C4—181no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4C2×D3211yescharacteristic
424M16—61no—
425M16—61no—
426M16—181no—
427M16—181no—
428C2×C8—61no—
429C2×C8—181no—
430C4⋊C4—31no—
431C4⋊C4—31no—
432C4⋊C4—64no—
433C4⋊C4—181no—
434C4⋊C4—181no—
435C22⋊C4—61no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C42—21no—
439C42—21no—
440C42—31no—
441C42—31no—
442C42—31no—
443C42—31no—
444C42—61no—
445C42—61no—
446C42—61no—
447C42—181no—
448C42—181no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3D3×C22⋊C411yescharacteristic
459C22×C3#88411yescharacteristic
460C22×C3#89611yescharacteristic
461C22×C3C2×(C2×D3)⋊C411yescharacteristic
462C22×C3#93811yescharacteristic
463C22×C3#94611yescharacteristic
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—122no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—241no—
472C2×D3—241no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—32no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—44no—
481C3×C4—61no—
482C3×C4—61no—
483C3×C4—61no—
484C3×C4—122no—
485C3×C4—121no—
486C3×C4—121no—
487C3×C4#87211yescharacteristic
488C3×C4#88411yescharacteristic
489C3×C4D3×C4⋊C411yescharacteristic
490C3×C4D3×C4⋊C411yescharacteristic
491C3×C4#89211yescharacteristic
492C3×C4#89511yescharacteristic
493C3×C4#89611yescharacteristic
494C3×C4#89711yescharacteristic
495Dic3—21no—
496Dic3—21no—
497Dic3—21no—
498Dic3—42no—
499Dic3—41no—
500Dic3—41no—
501Dic3—62no—
502Dic3—62no—
503Dic3—122no—
504Dic3#80512yescomplemented
505C32#180611yescharacteristic, complemented, Sylow
506C23—181no—
507C23D3×#6711yescharacteristic
508Q8—92no—
509Q8—181no—
510D4—92no—
511D4—182no—
512D4—182no—
513D4—181no—
514C2×C4—22no—
515C2×C4—31no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—31no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—181no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4—362no—
532C2×C4—362no—
533C2×C4#379711yescharacteristic
534C2×C4#379911yescharacteristic
535C2×C4C4×D3211yescharacteristic
536C2×C4D3×D1211yescharacteristic
537C2×C4#380411yescharacteristic
538C2×C4#381111yescharacteristic
539C8—121no—
540C8—361no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—41no—
549C2×C3—41no—
550C2×C3#466711yescharacteristic
551C2×C3D3×#10411yescharacteristic
552C2×C3#482111yescharacteristic
553C2×C3C2×#80511yescharacteristic
554C2×C3#498711yescharacteristic
555C2×C3#500511yescharacteristic
556D3—122no—
557D3—122no—
558D3—242no—
559C22—21no—
560C22—21no—
561C22—182no—
562C22—361no—
563C22—361no—
564C22#6388811yescharacteristic
565C22D3×(C2×D3)⋊C411yescharacteristic
566C22#6395811yescharacteristic
567C4—32no—
568C4—42no—
569C4—61no—
570C4—61no—
571C4—61no—
572C4—122no—
573C4—121no—
574C4—121no—
575C4—182no—
576C4#6383611yescharacteristic
577C4#6388311yescharacteristic
578C4#6389511yescharacteristic
579C4#6391011yescharacteristic
580C3—21no—
581C3#6877011yescharacteristic, complemented
582C3#6949411yescharacteristic, complemented
583C2—21no—
584C2—21no—
585C2—362no—
586C2D3×#80511yescharacteristic
587C2#1059039211yescharacteristic
588C2#1059136711yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C4×Dic3⋊C4C2semidirect
4. #10591115C2semidirect
6. C3×#4523C2semidirect
7. #10589161C2semidirect
20. #63894C4semidirect
21. #63894C4semidirect
24. #63844C4semidirect
25. #63844C4semidirect
36. C4×Dic3⋊C4D3semidirect
45. #4523D3semidirect
148. C4⋊(C3⋊D3)C4⋊C4semidirect
152. #634C4⋊C4semidirect
290. C3×Dic3#104semidirect
504. Dic3#805semidirect
505. C32#1806semidirect
581. C3#68770semidirect
582. C3#69494semidirect

Maximal subgroups

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

subgroupindex
#105949542
C2×#636322
C3×C4×Dic3⋊C42
#105911152
C2×#635702
C3×#45232
#105891612
#694943
#687703