Finite Group Databasebeta

← #11785327

Subgroups — #11785327

Order 1152.

679 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
1Dic3×#235C211yesmaximal, characteristic
2C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#805C211yesmaximal, characteristic
4#10591115C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic
6#10589389C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70355—31nomaximal
9#69494—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×Dic3⋊C4—21no—
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18Dic3×#67—21no—
19Dic3×#67—21no—
20Dic3×D12C411yescharacteristic, complemented
21Dic3×D12C411yescharacteristic, complemented
22C4×D3×Dic3—21no—
23#63855—21no—
24Dic3×Dic6C411yescharacteristic, complemented
25Dic3×Dic6C411yescharacteristic, complemented
26C3×C3⋊#95—21no—
27C3×#805—22no—
28Dic3⋊(C3⋊C8)—21no—
29Dic3⋊(C3⋊C8)—21no—
30#63569—22no—
31Dic3×#41—31no—
32C4×#235—31no—
33C2×C3×#104—31no—
34C3×C4×C4⋊C4—31no—
35C2×#837—31no—
36#5118—31no—
37C4×Dic3⋊C4D311yescharacteristic, complemented
38C2×#805—31no—
39C2×#805D311yescharacteristic
40#4924—31no—
41#4555—31no—
42#4523—31no—
43#4523—31no—
44#4523—31no—
45#4523—61no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C3×#235—21no—
53C3×#235—21no—
54C3×#235D412yes—
55C3×#235Q812yes—
56C2×C3×D12C2×C411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×Dic6C2×C411yescharacteristic
59C2×D3×Dic3—21no—
60C2×D3×Dic3—21no—
61C32×C42—21no—
62C32×C42—21no—
63#3757—21no—
64C4⋊(C3⋊Dic3)C2×C411yescharacteristic
65C4⋊(C3⋊Dic3)C2×C411yescharacteristic
66C4×C3⋊Dic3—21no—
67#3748—21no—
68#3748—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×Dic3⋊C4—24no—
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—
80Dic3⋊Dic3—21no—
81Dic3⋊Dic3—21no—
82(C2×D3)⋊Dic3—21no—
83(C2×D3)⋊Dic3—21no—
84Dic32—21no—
85Dic32—21no—
86#1806—91noSylow
87C2×C3×#41—31no—
88C2×#235C2×D311yescharacteristic
89C2×C3×M16—31no—
90C2×C3×C4⋊C4—61no—
91C2×C3×C42—21no—
92C2×C3×C42—31no—
93C2×C3×C42—31no—
94C2×C3×C42C2×D311yescharacteristic
95C2×C3×C42C2×D311yescharacteristic
96Q8×Dic3—31no—
97Q8×Dic3—31no—
98D4×Dic3—31no—
99D4×Dic3—31no—
100D4×Dic3—61no—
101D4×Dic3—61no—
102C4×#67—61no—
103C4×#67—61no—
104#926—31no—
105#926—31no—
106#926—61no—
107#926—61no—
108C2×Dic3⋊C4—21no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3C2×D311yescharacteristic
111C2×C4×Dic3C2×D311yescharacteristic
112C2×#208—31no—
113C2×#208—31no—
114C2×#208—61no—
115C2×#208C2×D311yescharacteristic
116C4×D12—31no—
117C4×D12—31no—
118#872—61no—
119C42×D3—61no—
120C4×Dic6—31no—
121C4×Dic6—31no—
122C3×#104—62no—
123C3×#95—61no—
124#837—62no—
125C3⋊#95—21no—
126Dic3⋊C8—61no—
127Dic3⋊C8—61no—
128#805—22no—
129#805—62no—
130C4⋊(C3⋊C8)—61no—
131C4⋊(C3⋊C8)—61no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—21no—
134C2×C32×C4—22no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×Q811yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C3×#67—22no—
146C3×#67—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3C22⋊C411yescharacteristic
154C2×C3×Dic3C22⋊C411yescharacteristic
155C2×C3×Dic3C22⋊C411yescharacteristic
156C2×C3×Dic3C22⋊C411yescharacteristic
157C3×D12—21no—
158C3×D12C4⋊C412yescomplemented
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×Dic6—21no—
162C3×Dic6C4⋊C412yescomplemented
163D3×Dic3—42no—
164D3×Dic3—42no—
165C3⋊(C3⋊C8)—41no—
166C3×C3⋊C8—41no—
167C4×#41—91no—
168#423—91no—
169C2×#104—31no—
170C2×#104—91no—
171C4×C4⋊C4—31no—
172#339—91no—
173#339—91no—
174C3×#41—32no—
175C3×#41—32no—
176C3×#41—61no—
177C3×#41—61no—
178C2×C3×Q8—31no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—31no—
185C22×C3×C4—31no—
186C22×C3×C4—41no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—21no—
192C22×Dic3—21no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3#6711yescharacteristic
196C22×Dic3#6711yescharacteristic
197#235—21no—
198#235—21no—
199#235Dic612yes—
200#235#6712yes—
201C2×D12C4×D311yescharacteristic
202C2×C4×D3—21no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×Dic6C4×D311yescharacteristic
206C3×M16—61no—
207C3×M16—61no—
208C2×C3×C8—61no—
209C3×C4⋊C4—64no—
210C3×C42—22no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—31no—
216C3×C42—31no—
217C3×C42—31no—
218C3×C42—31no—
219C3×C42—41no—
220C3×C42—61no—
221C3×C42—61no—
222#217—61no—
223#217—61no—
224#217—61no—
225#217—61no—
226#217—121no—
227(C2×D3)⋊C4—61no—
228(C2×D3)⋊C4—61no—
229C4⋊Dic3—31no—
230C4⋊Dic3—31no—
231C4⋊Dic3—31no—
232C4⋊Dic3—31no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237Dic3⋊C4—24no—
238Dic3⋊C4—61no—
239Dic3⋊C4—61no—
240C4×Dic3—21no—
241C4×Dic3—21no—
242C4×Dic3—61no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249C4×Dic3C4×D311yescharacteristic
250C4×Dic3C4×D311yescharacteristic
251C4×Dic3D1211yescharacteristic
252C4×Dic3D1211yescharacteristic
253#208—21no—
254#208—21no—
255#208—62no—
256#208—61no—
257#208—61no—
258#208—61no—
259#208—61no—
260#208—121no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—121no—
265C22×C32—21no—
266C22×C32—21no—
267C22×C32C2×C22⋊C411yescharacteristic
268C22×C32#12111yescharacteristic
269C22×C32C22⋊Q811yescharacteristic
270C2×C3×D3—22no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C32×C4—42no—
274C32×C4C2×C4⋊C411yescharacteristic
275C32×C4#11711yescharacteristic
276C32×C4#12111yescharacteristic
277C32×C4C22⋊Q811yescharacteristic
278C3⋊Dic3—41no—
279C3⋊Dic3—41no—
280C3×Dic3—22no—
281C3×Dic3—21no—
282C3×Dic3—21no—
283C3×Dic3—21no—
284C3×Dic3—42no—
285C3×Dic3#10412yescomplemented
286C2×#41—31no—
287C2×M16—31no—
288C2×M16—91no—
289C4×Q8—91no—
290C4×Q8—91no—
291C4×D4—91no—
292C4×D4—91no—
293C4×D4—181no—
294C4×D4—181no—
295#117—91no—
296#117—181no—
297C2×C4⋊C4—61no—
298C2×C42—31no—
299C2×C42—31no—
300C2×C42—181no—
301C2×C42D3211yescharacteristic
302C4⋊C8—181no—
303C4⋊C8—181no—
304#104—62no—
305#104—182no—
306#95—61no—
307C23×C3—21no—
308C23×C3—61no—
309C23×C3D3×D411yescharacteristic
310C23×C3C2×#6711yescharacteristic
311C22×D3—21no—
312C3×Q8—32no—
313C3×Q8—61no—
314C3×D4—32no—
315C3×D4—62no—
316C3×D4—62no—
317C3×D4—61no—
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—61no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4—121no—
345C2×C3×C4C2×Dic611yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4#23711yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4#23711yescharacteristic
354C2×C3×C4D3×Q811yescharacteristic
355C2×C3×C4#23911yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357#67—22no—
358#67—22no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—121no—
370C2×Dic3—121no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3(C2×D3)⋊C411yescharacteristic
374C2×Dic3(C2×D3)⋊C411yescharacteristic
375C2×Dic3(C2×D3)⋊C411yescharacteristic
376C2×Dic3(C2×D3)⋊C411yescharacteristic
377D12—21no—
378D12Dic3⋊C412yescomplemented
379C4×D3—22no—
380C4×D3—22no—
381C4×D3—122no—
382C4×D3—122no—
383Dic6—21no—
384Dic6Dic3⋊C412yescomplemented
385C3×C8—121no—
386C3⋊C8—41no—
387C3⋊C8—122no—
388C3⋊C8—121no—
389C3⋊C8—121no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32#38011yescharacteristic
393C2×C32C2×#10411yescharacteristic
394C2×C32#42111yescharacteristic
395C3×D3—42no—
396#41—32no—
397#41—32no—
398#41—61no—
399#41—61no—
400C2×Q8—31no—
401C2×D4—31no—
402C2×D4—61no—
403C22×C4—21no—
404C22×C4—31no—
405C22×C4—31no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4C2×D3211yescharacteristic
411M16—61no—
412M16—61no—
413M16—181no—
414M16—181no—
415C2×C8—61no—
416C2×C8—181no—
417C4⋊C4—64no—
418C4⋊C4—91no—
419C4⋊C4—91no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C22⋊C4—181no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C42—21no—
426C42—21no—
427C42—31no—
428C42—31no—
429C42—31no—
430C42—31no—
431C42—61no—
432C42—61no—
433C42—181no—
434C42—181no—
435C42—181no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—62no—
446C22×C3—121no—
447C22×C3—121no—
448C22×C3#87811yescharacteristic
449C22×C3D3×C22⋊C411yescharacteristic
450C22×C3C2×(C2×D3)⋊C411yescharacteristic
451C22×C3#93811yescharacteristic
452C22×C3#93911yescharacteristic
453C22×C3#94611yescharacteristic
454C2×D3—22no—
455C2×D3—41no—
456C2×D3—41no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—32no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—44no—
465C3×C4—62no—
466C3×C4—61no—
467C3×C4—61no—
468C3×C4—61no—
469C3×C4—122no—
470C3×C4#87711yescharacteristic
471C3×C4#87811yescharacteristic
472C3×C4D3×C4⋊C411yescharacteristic
473C3×C4#89211yescharacteristic
474C3×C4#89511yescharacteristic
475C3×C4#89711yescharacteristic
476C3×C4C2×Dic3⋊C411yescharacteristic
477C3×C4#93911yescharacteristic
478Dic3—21no—
479Dic3—22no—
480Dic3—21no—
481Dic3—21no—
482Dic3—42no—
483Dic3—121no—
484Dic3—121no—
485Dic3—121no—
486Dic3—121no—
487Dic3—241no—
488Dic3—241no—
489Dic3#80512yescomplemented
490C32#180611yescharacteristic, complemented, Sylow
491C23—61no—
492C23D3×#6711yescharacteristic
493Q8—32no—
494Q8—61no—
495D4—32no—
496D4—62no—
497D4—62no—
498D4—61no—
499C2×C4—22no—
500C2×C4—31no—
501C2×C4—31no—
502C2×C4—31no—
503C2×C4—31no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—62no—
507C2×C4—61no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—362no—
517C2×C4—362no—
518C2×C4D3×Dic611yescharacteristic
519C2×C4#379611yescharacteristic
520C2×C4C4×D3211yescharacteristic
521C2×C4D3×D1211yescharacteristic
522C2×C4#380511yescharacteristic
523C2×C4D3×#6711yescharacteristic
524C8—121no—
525C8—361no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—41no—
534C2×C3—41no—
535C2×C3—122no—
536C2×C3D3×#10411yescharacteristic
537C2×C3#482111yescharacteristic
538C2×C3C2×#80511yescharacteristic
539C2×C3#494211yescharacteristic
540C2×C3#498711yescharacteristic
541C2×C3#500511yescharacteristic
542D3—42no—
543C22—21no—
544C22—21no—
545C22—62no—
546C22—121no—
547C22—121no—
548C22#6388711yescharacteristic
549C22D3×(C2×D3)⋊C411yescharacteristic
550C22#6397011yescharacteristic
551C4—32no—
552C4—42no—
553C4—62no—
554C4—61no—
555C4—61no—
556C4—61no—
557C4—122no—
558C4—361no—
559C4—361no—
560C4D3×Dic3⋊C411yescharacteristic
561C4#6387811yescharacteristic
562C4#6388611yescharacteristic
563C4#6389311yescharacteristic
564C3—21no—
565C3#6949411yescharacteristic, complemented
566C3#7035511yescharacteristic, complemented
567C2—21no—
568C2—21no—
569C2—122no—
570C2D3×#80511yescharacteristic
571C2#1059039211yescharacteristic
572C2#1059136611yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
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
2. C3×C4×Dic3⋊C4C2semidirect
4. #10591115C2semidirect
6. #10589389C2semidirect
7. #10589162C2semidirect
20. Dic3×D12C4semidirect
21. Dic3×D12C4semidirect
24. Dic3×Dic6C4semidirect
25. Dic3×Dic6C4semidirect
37. C4×Dic3⋊C4D3semidirect
158. C3×D12C4⋊C4semidirect
162. C3×Dic6C4⋊C4semidirect
285. C3×Dic3#104semidirect
378. D12Dic3⋊C4semidirect
384. Dic6Dic3⋊C4semidirect
489. Dic3#805semidirect
490. C32#1806semidirect
565. C3#69494semidirect
566. C3#70355semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2352
C3×C4×Dic3⋊C42
C2×C3×#8052
#105911152
C2×#635692
#105893892
#105891622
#703553
#694943