Finite Group Databasebeta

← #11792610

Subgroups — #11792610

Order 1152.

839 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
1C2×C3×#875C211yesmaximal, characteristic
2C22×#3718C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic
4C3×#4929C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7#10589390C211yesmaximal, characteristic, complemented
8#71729—31nomaximal
9#69689—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C3×#875—22no—
19C3×#875—22no—
20C2×#3718—22no—
21C2×#3718—22no—
22C2×#3718—22no—
23C2×#3715—22no—
24C2×#3715—22no—
25C2×#3715—22no—
26C3×C3⋊#95—22no—
27#63565—22no—
28#63562—22no—
29C2×C3×#124—31no—
30C22×#216—31no—
31C22×#216—31no—
32C22×#215—31no—
33C22×#214—31no—
34C2×#875D311yescharacteristic
35C3×#391—31no—
36C2×#835—31no—
37C2×#832—31no—
38C2×#810—31no—
39C2×#809—31no—
40#4929D311yescharacteristic, complemented
41#4524—31no—
42#4524—31no—
43#4524—61no—
44C23×C3×D3—21no—
45C22×C32×C4D412yes—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12D412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D412yes—
67C2×C3×Dic6D412yes—
68C32×C42—21no—
69C32×C42—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)D412yes—
75C2×C3⋊(C3⋊C8)D412yes—
76C3×(C2×D3)⋊C4—28no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79#3718—28no—
80#3715—28no—
81#2015—91noSylow
82C22×C3×Q8—31no—
83C22×C3×Q8—31no—
84C22×C3×D4—31no—
85C22×D12C2×D311yescharacteristic
86C22×Dic6C2×D311yescharacteristic
87C22×Dic6C2×D311yescharacteristic
88C3×#124—62no—
89C3×#124—62no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C22⋊C4—62no—
92C2×C3×C42—21no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C2×D311yescharacteristic
95C2×#216—62no—
96C2×#216—62no—
97C2×#216—62no—
98C2×#216—62no—
99C2×#216—62no—
100C2×#216—62no—
101C2×#215—62no—
102C2×#215—62no—
103C2×#215—62no—
104C2×#214—62no—
105C2×#214—62no—
106C2×#214—62no—
107C2×(C2×D3)⋊C4—22no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C22×C3⋊C8—31no—
110C22×C3⋊C8—31no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114C22×C3⋊C8—61no—
115#875—22no—
116#875—22no—
117C3×#95—62no—
118#835—62no—
119#832—62no—
120C3⋊#95—22no—
121#810—62no—
122#809—62no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—42no—
128C22×C3×D3—42no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—42no—
146C3×D12—22no—
147C3×D12—22no—
148C3×D12—41no—
149C3×D12—41no—
150C3×Dic6—22no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—41no—
155C3×Dic6—41no—
156C3×Dic6—41no—
157C3×Dic6—41no—
158C3⋊(C3⋊C8)—22no—
159C3⋊(C3⋊C8)—22no—
160C22×Q16—91no—
161C22×SD16—91no—
162C2×#124—31no—
163C2×#103—91no—
164C2×#102—91no—
165#391—31no—
166#336—91no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×Q8—32no—
170C2×C3×Q8—32no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×D4—32no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4#6712yes—
193C22×C3×C4#6712yes—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12#6712yes—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6D1212yes—
216C2×Dic6#6712yes—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C22⋊C4—68no—
220C3×C42—21no—
221C3×C42—21no—
222C3×C42—21no—
223C3×C42—21no—
224C3×C42—41no—
225C3×C42—41no—
226#216—68no—
227#216—68no—
228#215—68no—
229#214—68no—
230(C2×D3)⋊C4—28no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—121no—
248C2×C3⋊C8—121no—
249C2×C3⋊C8—121no—
250C2×C3⋊C8—121no—
251C22×C32#12011yescharacteristic
252C22×C32#12111yescharacteristic
253C22×C32#12711yescharacteristic
254C22×C32#13512yes—
255C22×C32#13712yes—
256C2×C3×D3—42no—
257C2×C3×D3—44no—
258C2×C3×D3—82no—
259C2×C3×D3—81no—
260C2×C3×D3—81no—
261C32×C4—42no—
262C32×C4#12011yescharacteristic
263C32×C4#12011yescharacteristic
264C32×C4#12111yescharacteristic
265C32×C4#12111yescharacteristic
266C3×Dic3—42no—
267C3×Dic3—42no—
268C3×Dic3—81no—
269C22×Q8—31no—
270C22×Q8—31no—
271C22×D4—31no—
272C2×Q16—182no—
273C2×Q16—182no—
274C2×Q16—182no—
275C2×SD16—182no—
276C2×SD16—182no—
277C2×SD16—182no—
278C22×C8—91no—
279C22×C8—91no—
280#124—62no—
281#124—62no—
282C2×C4⋊C4—31no—
283C2×C22⋊C4—62no—
284C2×C42D3211yescharacteristic
285#103—182no—
286#102—182no—
287#95—62no—
288C23×C3—21no—
289C23×C3—62no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—122no—
293C23×C3—122no—
294C23×C3C2×#6711yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C22×D3—22no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—42no—
300C22×D3—42no—
301C3×Q8—62no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—121no—
306C3×Q8—121no—
307C3×Q8—121no—
308C3×Q8—121no—
309C3×D4—62no—
310C3×D4—62no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
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—42no—
327C2×C3×C4—42no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—122no—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
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×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—42no—
356D12—22no—
357D12—22no—
358D12—41no—
359D12—41no—
360Dic6—22no—
361Dic6—22no—
362Dic6—22no—
363Dic6—22no—
364Dic6—41no—
365Dic6—41no—
366Dic6—41no—
367Dic6—41no—
368C3⋊C8—62no—
369C3⋊C8—62no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C3⋊C8—122no—
373C3⋊C8—122no—
374C2×C32#39211yescharacteristic
375C2×C32#45212yes—
376C2×C32#46412yes—
377C2×C32#49511yescharacteristic
378C2×C32#49711yescharacteristic
379C3×D3—82no—
380C24—61no—
381C2×Q8—32no—
382C2×Q8—32no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×Q8—61no—
392C2×Q8—61no—
393C2×D4—32no—
394C2×D4—61no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4#62512yes—
403C22×C4C2×D3211yescharacteristic
404Q16—188no—
405SD16—188no—
406C2×C8—92no—
407C2×C8—92no—
408C2×C8—181no—
409C2×C8—181no—
410C2×C8—181no—
411C2×C8—181no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C22⋊C4—68no—
415C42—21no—
416C42—21no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—122no—
423C22×C3—124no—
424C22×C3—242no—
425C22×C3—241no—
426C22×C3—241no—
427C22×C3#93011yescharacteristic
428C22×C3#93711yescharacteristic
429C22×C3#93811yescharacteristic
430C22×C3#94011yescharacteristic
431C22×C3#94011yescharacteristic
432C22×C3#94212yes—
433C22×C3#95012yes—
434C22×C3#95012yes—
435C22×C3#95112yes—
436C22×C3#95311yescharacteristic
437C2×D3—42no—
438C2×D3—44no—
439C2×D3—82no—
440C2×D3—81no—
441C2×D3—81no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—44no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—122no—
450C3×C4—122no—
451C3×C4—241no—
452C3×C4#88211yescharacteristic
453C3×C4#88211yescharacteristic
454C3×C4#88411yescharacteristic
455C3×C4#88411yescharacteristic
456C3×C4#93711yescharacteristic
457C3×C4#93711yescharacteristic
458C3×C4#93911yescharacteristic
459C3×C4#93911yescharacteristic
460Dic3—42no—
461Dic3—42no—
462Dic3—81no—
463C32#201511yescharacteristic, complemented, Sylow
464C23—62no—
465C23—122no—
466C23—122no—
467C23—121no—
468C23—121no—
469C23C2×#62511yescharacteristic
470Q8—62no—
471Q8—62no—
472Q8—62no—
473Q8—62no—
474Q8—121no—
475Q8—121no—
476Q8—121no—
477Q8—121no—
478D4—62no—
479D4—62no—
480D4—121no—
481D4—121no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—122no—
492C2×C4—121no—
493C2×C4#379511yescharacteristic
494C2×C4D3×D1211yescharacteristic
495C2×C4#380211yescharacteristic
496C2×C4#380211yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C2×C4D3×#6711yescharacteristic
499C8—182no—
500C8—182no—
501C2×C3—22no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—22no—
506C2×C3—242no—
507C2×C3#496011yescharacteristic
508C2×C3#502812yes—
509C2×C3#504712yes—
510C2×C3#505412yes—
511C2×C3#505911yescharacteristic
512C2×C3#505911yescharacteristic
513C2×C3#506011yescharacteristic
514C2×C3#508611yescharacteristic
515C2×C3#522311yescharacteristic
516C2×C3#523912yes—
517D3—82no—
518C22—122no—
519C22—124no—
520C22—242no—
521C22—241no—
522C22—241no—
523C22#6382212yes—
524C22#6382712yes—
525C22#6390811yescharacteristic
526C22#6391411yescharacteristic
527C22#6397611yescharacteristic
528C4—42no—
529C4—122no—
530C4—122no—
531C4—241no—
532C4#6388511yescharacteristic
533C4#6388511yescharacteristic
534C4#6392211yescharacteristic
535C4#6392211yescharacteristic
536C3—21no—
537C3#6968911yescharacteristic, complemented
538C3#7172911yescharacteristic, complemented
539C2—242no—
540C2#1059026712yes—
541C2#1059035311yescharacteristic
542C2#1059037611yescharacteristic
543C2#1059117012yes—
544C2#1059138911yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C22×#3718C2semidirect
4. C3×#4929C2semidirect
5. C2×#63565C2semidirect
7. #10589390C2semidirect
40. #4929D3semidirect
463. C32#2015semidirect
537. C3#69689semidirect
538. C3#71729semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8752
C22×#37182
C22×#37152
C3×#49292
C2×#635652
C2×#635622
#105893902
#717293
#696893