Finite Group Databasebeta

← #11793135

Subgroups — #11793135

Order 1152.

661 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5483C211yesmaximal, characteristic, complemented
2C2×#63633C211yesmaximal, characteristic
3C2×#63581C211yesmaximal, characteristic
4C2×#63581C211yesmaximal, characteristic
5C3×#4527C211yesmaximal, characteristic, complemented
6#10589187C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#71896—31nomaximal
9#68967—31nomaximal
10C22×#638C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×C3×#217C2211yescharacteristic
14C2×C3×#217C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C3×#924—22no—
18C3×#878—22no—
19C3×#878—22no—
20#63633—22no—
21#63581—22no—
22#63581—22no—
23C3×#543—31no—
24#5483D311yescharacteristic, complemented
25C2×#806—31no—
26C2×#806—31no—
27C2×#806—31no—
28C2×#806—31no—
29C2×#806—31no—
30C2×#806—31no—
31C2×#806—61no—
32C3×#342—31no—
33#4527—31no—
34#4527—31no—
35#4527—31no—
36#4527D311yescharacteristic, complemented
37#4526—31no—
38C24×C32C2311yescharacteristic
39C23×C3⋊D3Q811yescharacteristic, complemented
40C22×C32×C4—21no—
41C2×#638—21no—
42C2×#638—21no—
43C2×#638—21no—
44C2×#638—21no—
45C2×#638—21no—
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3Q811yescharacteristic, complemented
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C2×C3×Dic6—22no—
54C32×C22⋊C4—21no—
55C32×C22⋊C4D412yes—
56#3757—21no—
57#3757—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×#217D412yes—
65C3×#217D412yes—
66C3×C4⋊Dic3—22no—
67C3×Dic3⋊C4—24no—
68#2032—91noSylow
69C22×#67—31no—
70C22×#67—31no—
71C22×#67—61no—
72C3×C22⋊Q8—62no—
73C3×C22⋊Q8—62no—
74C3×C22⋊Q8—62no—
75C2×C3×C22⋊C4—21no—
76C2×C3×C22⋊C4—31no—
77C2×C3×C22⋊C4—31no—
78C2×C3×C22⋊C4—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4C2×D311yescharacteristic
81C2×C3×C22⋊C4C2×D311yescharacteristic
82C2×#217—31no—
83C2×#217—31no—
84C2×#217—61no—
85C2×#217C2×D311yescharacteristic
86C2×#217C2×D311yescharacteristic
87C2×#217C2×D311yescharacteristic
88C2×#217C2×D311yescharacteristic
89#924—22no—
90#878—22no—
91#878—22no—
92#806—62no—
93#806—62no—
94#806—64no—
95#806—62no—
96#806—62no—
97#806—62no—
98#806—62no—
99C23×C32—81no—
100C23×C32C2×D411yescharacteristic
101C23×C32C2×D411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×Q811yescharacteristic
104C23×C32#4111yescharacteristic
105C23×C32#4111yescharacteristic
106C23×C32#4111yescharacteristic
107C22×C3⋊D3—21no—
108C22×C3⋊D3—21no—
109C22×C3⋊D3—21no—
110C22×C3⋊D3—81no—
111C2×C32×C4—22no—
112C2×C32×C4—81no—
113#638—41no—
114#638—41no—
115#638—41no—
116#638—41no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—81no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—81no—
127C2×C3×Dic3—81no—
128C2×C3×Dic3—81no—
129C2×C3×Dic3—81no—
130C3×Dic6—82no—
131#543—31no—
132C2×#99—91no—
133C2×#99—91no—
134C2×#99—91no—
135#342—31no—
136#342—91no—
137#342—91no—
138C24×C3—21no—
139C24×C3C22×D311yescharacteristic
140C24×C3C22×D311yescharacteristic
141C23×D3—31no—
142C23×D3—31no—
143C23×D3—61no—
144C2×C3×Q8—62no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—41no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C2×#67—62no—
153C2×#67—62no—
154C2×#67—61no—
155C2×#67—61no—
156C2×#67—61no—
157C2×#67—61no—
158C2×#67—61no—
159C2×#67—61no—
160C2×#67—61no—
161C2×#67—61no—
162C2×#67—61no—
163C2×#67—61no—
164C2×#67—61no—
165C2×#67—61no—
166C2×#67—121no—
167C2×#67—121no—
168C2×#67—121no—
169C2×#67—121no—
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—31no—
175C22×Dic3—31no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—121no—
180C2×Dic6—22no—
181C3×C4⋊C4—64no—
182C3×C4⋊C4—62no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—32no—
187C3×C22⋊C4—32no—
188C3×C22⋊C4—41no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4D1212yes—
196C3×C22⋊C4#6712yes—
197#217—21no—
198#217—21no—
199#217—21no—
200#217—21no—
201#217—21no—
202#217—21no—
203#217—62no—
204#217—61no—
205#217—61no—
206#217—61no—
207#217—61no—
208#217—121no—
209#217#6712yes—
210#217#6712yes—
211C4⋊Dic3—22no—
212Dic3⋊C4—24no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32—41no—
220C22×C32#12011yescharacteristic
221C22×C32C22⋊Q811yescharacteristic
222C22×C32C22⋊Q811yescharacteristic
223C22×C32C22⋊Q811yescharacteristic
224C22×C32#12411yescharacteristic
225C22×C32#12411yescharacteristic
226C22×C32#12411yescharacteristic
227C2×C3⋊D3—41no—
228C2×C3⋊D3—81no—
229C2×C3⋊D3—81no—
230C2×C3⋊D3—81no—
231C32×C4—42no—
232C3⋊Dic3—41no—
233C3⋊Dic3—81no—
234C3×Dic3—42no—
235C3×Dic3—42no—
236C3×Dic3—81no—
237C3×Dic3—81no—
238C22×D4—91no—
239C22⋊Q8—62no—
240C22⋊Q8—62no—
241C22⋊Q8—62no—
242C2×C22⋊C4—31no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—31no—
246C2×C22⋊C4—91no—
247C2×C22⋊C4D3211yescharacteristic
248#99—182no—
249#99—182no—
250#99—182no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—81no—
259C23×C3—81no—
260C23×C3—82no—
261C23×C3C2×D1211yescharacteristic
262C23×C3#23511yescharacteristic
263C23×C3#23511yescharacteristic
264C23×C3D3×D411yescharacteristic
265C23×C3D3×D411yescharacteristic
266C23×C3#23711yescharacteristic
267C23×C3D3×Q811yescharacteristic
268C23×C3D3×Q811yescharacteristic
269C23×C3#23911yescharacteristic
270C23×C3#23911yescharacteristic
271C23×C3#23911yescharacteristic
272C23×C3C2×#6711yescharacteristic
273C23×C3C2×#6711yescharacteristic
274C23×C3C2×#6711yescharacteristic
275C22×D3—62no—
276C22×D3—61no—
277C22×D3—61no—
278C22×D3—61no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—121no—
283C22×D3—121no—
284C22×D3—242no—
285C22×D3—241no—
286C22×D3—241no—
287C3×Q8—242no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—42no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—81no—
294C2×C3×C4—81no—
295C2×C3×C4—82no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—241no—
299C2×C3×C4—241no—
300C2×C3×C4—241no—
301C2×C3×C4—241no—
302#67—122no—
303#67—122no—
304#67—122no—
305#67—122no—
306#67—121no—
307#67—121no—
308#67—121no—
309#67—121no—
310#67—121no—
311#67—121no—
312#67—121no—
313#67—121no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—62no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—81no—
326C2×Dic3—81no—
327C2×Dic3—81no—
328C2×Dic3—81no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—122no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—242no—
335C2×Dic3—241no—
336C2×Dic3—241no—
337Dic6—82no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32#39311yescharacteristic
346C3⋊D3—81no—
347C24—91no—
348C24C2×D3211yescharacteristic
349C2×Q8—62no—
350C2×D4—181no—
351C2×D4—181no—
352C2×D4—181no—
353C2×D4—181no—
354C2×D4—181no—
355C2×D4—181no—
356C22×C4—21no—
357C22×C4—61no—
358C22×C4—61no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—91no—
362C22×C4—181no—
363C4⋊C4—64no—
364C4⋊C4—62no—
365C22⋊C4—21no—
366C22⋊C4—32no—
367C22⋊C4—32no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—181no—
375C22⋊C4—181no—
376C22⋊C4#62612yes—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—81no—
402C22×C3—81no—
403C22×C3—81no—
404C22×C3—81no—
405C22×C3#87511yescharacteristic
406C22×C3#88211yescharacteristic
407C22×C3#88511yescharacteristic
408C22×C3#88511yescharacteristic
409C22×C3#89611yescharacteristic
410C22×C3#89611yescharacteristic
411C22×C3#89711yescharacteristic
412C22×C3#94611yescharacteristic
413C22×C3#94611yescharacteristic
414C22×C3#94611yescharacteristic
415C22×C3#94711yescharacteristic
416C22×C3#94711yescharacteristic
417C22×C3#94711yescharacteristic
418C22×C3#95311yescharacteristic
419C2×D3—122no—
420C2×D3—121no—
421C2×D3—121no—
422C2×D3—242no—
423C2×D3—242no—
424C2×D3—241no—
425C2×D3—241no—
426C2×D3—241no—
427C2×D3—241no—
428C2×D3—241no—
429C2×D3—241no—
430C2×D3—242no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—82no—
434C3×C4—122no—
435C3×C4—122no—
436C3×C4—241no—
437C3×C4—241no—
438Dic3—42no—
439Dic3—42no—
440Dic3—81no—
441Dic3—81no—
442Dic3—122no—
443Dic3—121no—
444Dic3—121no—
445Dic3—241no—
446Dic3—241no—
447Dic3—242no—
448C32#203211yescharacteristic, complemented, Sylow
449C23—81no—
450C23—181no—
451C23—181no—
452C23—181no—
453C23—721no—
454C23#379611yescharacteristic
455C23#379711yescharacteristic
456C23#379911yescharacteristic
457C23#379911yescharacteristic
458C23C2×#62611yescharacteristic
459C23D3×#6711yescharacteristic
460C23D3×#6711yescharacteristic
461Q8—242no—
462D4—361no—
463D4—361no—
464D4—361no—
465D4—361no—
466C2×C4—22no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—81no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—241no—
476C2×C4—241no—
477C2×C4—241no—
478C2×C4—241no—
479C2×C4—361no—
480C2×C4—721no—
481C2×C3—22no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—41no—
498C2×C3—41no—
499C2×C3—41no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3—41no—
503C2×C3#467311yescharacteristic
504C2×C3#523111yescharacteristic
505D3—242no—
506D3—241no—
507D3—241no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—361no—
516C22—721no—
517C22—721no—
518C22—721no—
519C22#6386411yescharacteristic
520C22#6387111yescharacteristic
521C22#6388811yescharacteristic
522C22#6388811yescharacteristic
523C22#6390711yescharacteristic
524C22#6390711yescharacteristic
525C22#6397711yescharacteristic
526C4—42no—
527C4—122no—
528C4—122no—
529C4—241no—
530C4—241no—
531C4—361no—
532C4—721no—
533C3—21no—
534C3#6896711yescharacteristic, complemented
535C3#7189611yescharacteristic, complemented
536C2—21no—
537C2—21no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—721no—
544C2#1059131011yescharacteristic
subgroupG/H
centerC2#10591310
commutator, cosocleC24×C32C23
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC2×C32#393
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2032
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5483C2semidirect
5. C3×#4527C2semidirect
6. #10589187C2semidirect
7. #10589186C2semidirect
24. #5483D3semidirect
36. #4527D3semidirect
39. C23×C3⋊D3Q8semidirect
48. C22×C3⋊Dic3Q8semidirect
448. C32#2032semidirect
534. C3#68967semidirect
535. C3#71896semidirect

Maximal subgroups

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

subgroupindex
C3×#54832
C2×#636332
C2×#635812
C3×#45272
#105891872
#105891862
#718963
#689673