Finite Group Databasebeta

← #11791148

Subgroups — #11791148

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×C3×#818C211yesmaximal, characteristic, complemented
3C2×C3×#815C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic
5#10591213C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#70629—31nomaximal
9#69826—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×#3744—22no—
14C2×#3744—22no—
15C2×#3744C414yescomplemented
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3722—22no—
21C3×#818—22no—
22C3×#815—22no—
23#63579—22no—
24#63567—22no—
25#63564—22no—
26C22×#204—31no—
27C22×#204—31no—
28C22×#204—61no—
29C2×C3×#107—31no—
30C2×C3×#97—31no—
31C2×#821—31no—
32C2×#818D311yescharacteristic, complemented
33C2×#816—31no—
34C2×#815D311yescharacteristic, complemented
35#4988—31no—
36#4973—31no—
37C2×#810—31no—
38C2×#809—31no—
39#4939—31no—
40#4929—31no—
41C23×C3⋊D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634C2×C412yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D412yes—
59C2×C32×C8C2×C412yes—
60C2×C32×C8D412yes—
61C2×C32×C8D412yes—
62#3744—28no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8D412yes—
72#3722—44no—
73#1973—91noSylow
74C22×D12—31no—
75C22×D12—31no—
76C22×D12—61no—
77C22×Dic6—31no—
78C22×Dic6—31no—
79C22×Dic6—61no—
80C22×C3×C8—21no—
81C22×C3×C8—31no—
82C22×C3×C8C2×D311yescharacteristic
83C22×C3×C8C2×D311yescharacteristic
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C42—31no—
87C2×(C2×D3)⋊C4—62no—
88C2×(C2×D3)⋊C4—62no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4×Dic3C2×D311yescharacteristic
92C22×C3⋊C8C2×D311yescharacteristic
93C2×#204—34no—
94C2×#204—34no—
95C2×#204—64no—
96C2×#204—64no—
97C2×#204—64no—
98C2×#204—62no—
99C2×#204—62no—
100C2×#204—62no—
101C2×#204—62no—
102C3×#107—62no—
103C3×#97—62no—
104C3⋊#95—62no—
105C3⋊#95—62no—
106#821—62no—
107#818—22no—
108#816—62no—
109#815—22no—
110#810—62no—
111#809—62no—
112C23×C32C2×D411yescharacteristic
113C22×C3⋊D3—22no—
114C22×C3⋊D3—41no—
115C22×C3⋊D3—41no—
116C22×C3⋊D3—42no—
117C22×C3⋊D3—42no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—41no—
130C4⋊(C3⋊D3)—41no—
131#634—22no—
132#634—22no—
133#634—41no—
134#634—41no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C32×C8C22⋊C414yescomplemented
143C3×C3⋊C8—22no—
144C22×SD16—91no—
145C2×#107—31no—
146C2×#103—91no—
147C2×#102—91no—
148C2×#97—31no—
149#391—91no—
150#390—91no—
151C23×D3—61no—
152C23×D3—61no—
153C23×D3—121no—
154C22×C3×C4—21no—
155C22×C3×C4—32no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—21no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—121no—
165C22×Dic3D1212yes—
166C2×D12—32no—
167C2×D12—32no—
168C2×D12—62no—
169C2×D12—62no—
170C2×D12—62no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—61no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—121no—
182C2×D12—121no—
183C2×D12—121no—
184C2×Dic6—32no—
185C2×Dic6—32no—
186C2×Dic6—62no—
187C2×Dic6—62no—
188C2×Dic6—62no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×Dic6—61no—
192C2×Dic6—61no—
193C2×Dic6—61no—
194C2×Dic6—61no—
195C2×Dic6—61no—
196C2×Dic6—61no—
197C2×Dic6—61no—
198C2×Dic6—61no—
199C2×Dic6—121no—
200C2×Dic6—121no—
201C2×Dic6—121no—
202C2×C3×C8—22no—
203C2×C3×C8—22no—
204C2×C3×C8—22no—
205C2×C3×C8—32no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C2×C3×C8C4×D312yes—
209C2×C3×C8C4×D312yes—
210C2×C3×C8D1212yes—
211C2×C3×C8D1212yes—
212C2×C3×C8#6712yes—
213C2×C3×C8#6712yes—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C42—61no—
219C3×C42—61no—
220(C2×D3)⋊C4—124no—
221(C2×D3)⋊C4—124no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226C4×Dic3—21no—
227C4×Dic3—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8D1212yes—
231#204—616no—
232#204—68no—
233#204—68no—
234C22×C32C4×D411yescharacteristic
235C22×C32#12111yescharacteristic
236C22×C32#12711yescharacteristic
237C22×C32AGL(1,ℤ/8)12yes—
238C22×C32#13712yes—
239C2×C3⋊D3—42no—
240C2×C3⋊D3—44no—
241C2×C3⋊D3—82no—
242C2×C3⋊D3—81no—
243C2×C3⋊D3—81no—
244C32×C4C2×C22⋊C411yescharacteristic
245C32×C4C4×D411yescharacteristic
246C32×C4#12111yescharacteristic
247C32×C4#12411yescharacteristic
248C3⋊Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—81no—
251C3×Dic3—81no—
252C22×Q8—91no—
253C22×D4—91no—
254C2×SD16—94no—
255C2×SD16—182no—
256C2×SD16—182no—
257C22×C8—31no—
258C22×C8D3211yescharacteristic
259C2×C4⋊C4—31no—
260C2×C4⋊C4—31no—
261C2×C22⋊C4—182no—
262C2×C42—31no—
263#107—62no—
264#103—182no—
265#102—182no—
266#97—62no—
267#95—182no—
268C23×C3—21no—
269C23×C3C2×D1211yescharacteristic
270C23×C3D3×D411yescharacteristic
271C22×D3—62no—
272C22×D3—62no—
273C22×D3—122no—
274C22×D3—122no—
275C22×D3—122no—
276C22×D3—121no—
277C22×D3—121no—
278C22×D3—122no—
279C22×D3—122no—
280C22×D3—122no—
281C22×D3—122no—
282C22×D3—121no—
283C22×D3—121no—
284C22×D3—242no—
285C22×D3—242no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—122no—
298C2×C3×C4—122no—
299C2×C3×C4C2×C4×D311yescharacteristic
300C2×C3×C4C2×C4×D311yescharacteristic
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4#23911yescharacteristic
308C2×C3×C4#23911yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—42no—
315C2×Dic3—42no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327D12—64no—
328D12—62no—
329D12—62no—
330D12—62no—
331D12—62no—
332D12—122no—
333D12—122no—
334D12—122no—
335D12—121no—
336D12—121no—
337D12—121no—
338D12—121no—
339Dic6—64no—
340Dic6—62no—
341Dic6—62no—
342Dic6—62no—
343Dic6—62no—
344Dic6—122no—
345Dic6—122no—
346Dic6—122no—
347Dic6—121no—
348Dic6—121no—
349Dic6—121no—
350Dic6—121no—
351C3×C8—24no—
352C3×C8—62no—
353C3×C8(C2×D3)⋊C414yescomplemented
354C3×C8(C2×D3)⋊C414yescomplemented
355C3⋊C8—22no—
356C2×C32#39011yescharacteristic
357C2×C32#44012yes—
358C2×C32#46812yes—
359C2×C32#49611yescharacteristic
360C2×C32#49711yescharacteristic
361C3⋊D3—82no—
362C24—181no—
363C2×Q8—92no—
364C2×Q8—181no—
365C2×Q8—181no—
366C2×Q8—181no—
367C2×Q8—181no—
368C2×Q8—181no—
369C2×D4—92no—
370C2×D4—181no—
371C2×D4—181no—
372C2×D4—181no—
373C2×D4—181no—
374C2×D4—181no—
375C22×C4—32no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—181no—
379C22×C4C2×D3211yescharacteristic
380SD16—188no—
381C2×C8—32no—
382C2×C8—61no—
383C2×C8—61no—
384C2×C8#62412yes—
385C2×C8#62612yes—
386C2×C8#62612yes—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C22⋊C4—364no—
392C42—61no—
393C42—61no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3C4×D1211yescharacteristic
400C22×C3#87411yescharacteristic
401C22×C3#89311yescharacteristic
402C22×C3#89511yescharacteristic
403C22×C3#90812yes—
404C22×C3#90912yes—
405C22×C3#91112yes—
406C22×C3#91812yes—
407C22×C3#93011yescharacteristic
408C22×C3#94011yescharacteristic
409C2×D3—124no—
410C2×D3—124no—
411C2×D3—122no—
412C2×D3—124no—
413C2×D3—122no—
414C2×D3—244no—
415C2×D3—244no—
416C2×D3—242no—
417C2×D3—242no—
418C2×D3—242no—
419C2×D3—242no—
420C2×D3—241no—
421C2×D3—241no—
422C2×D3—241no—
423C2×D3—241no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—122no—
429C3×C4—241no—
430C3×C4—241no—
431C3×C4C4×D1211yescharacteristic
432C3×C4#87511yescharacteristic
433C3×C4#89311yescharacteristic
434C3×C4#89511yescharacteristic
435C3×C4C2×(C2×D3)⋊C411yescharacteristic
436C3×C4C2×(C2×D3)⋊C411yescharacteristic
437C3×C4#93011yescharacteristic
438C3×C4#94711yescharacteristic
439Dic3—42no—
440Dic3—81no—
441Dic3—81no—
442Dic3—124no—
443Dic3—122no—
444Dic3—122no—
445C32#197311yescharacteristic, complemented, Sylow
446C23—182no—
447C23—362no—
448C23—362no—
449C23—361no—
450C23—361no—
451C23D3×D1211yescharacteristic
452Q8—182no—
453Q8—182no—
454Q8—361no—
455Q8—361no—
456D4—182no—
457D4—182no—
458D4—361no—
459D4—361no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—122no—
464C2×C4—122no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4—182no—
468C2×C4—361no—
469C2×C4—361no—
470C2×C4#379911yescharacteristic
471C2×C4#379911yescharacteristic
472C2×C4D3×D1211yescharacteristic
473C2×C4C2×#62411yescharacteristic
474C2×C4C2×#62611yescharacteristic
475C2×C4C2×#62611yescharacteristic
476C8—62no—
477C8#372214yescomplemented
478C2×C3—22no—
479C2×C3—21no—
480C2×C3—22no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3#471012yes—
484C2×C3#471211yescharacteristic
485C2×C3#471511yescharacteristic
486C2×C3#488612yes—
487C2×C3#488912yes—
488C2×C3#493911yescharacteristic
489C2×C3#498811yescharacteristic
490C2×C3#513412yes—
491C2×C3#515411yescharacteristic
492C2×C3#519011yescharacteristic
493D3—244no—
494D3—242no—
495D3—242no—
496C22—364no—
497C22—362no—
498C22—722no—
499C22—721no—
500C22—721no—
501C22#6379512yes—
502C22#6380112yes—
503C22#6389411yescharacteristic
504C22#6390911yescharacteristic
505C22#6391111yescharacteristic
506C4—122no—
507C4—241no—
508C4—241no—
509C4—362no—
510C4#6386411yescharacteristic
511C4#6389411yescharacteristic
512C4#6390911yescharacteristic
513C4C2×#372211yescharacteristic
514C3—21no—
515C3#6982611yescharacteristic, complemented
516C3#7062911yescharacteristic, complemented
517C2—722no—
518C2#1059077312yes—
519C2#1059083812yes—
520C2#1059088311yescharacteristic
521C2#1059089911yescharacteristic
522C2#1059132011yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1973
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#818C2semidirect
3. C2×C3×#815C2semidirect
5. #10591213C2semidirect
6. C2×#63567C2semidirect
15. C2×#3744C4semidirect
32. C2×#818D3semidirect
34. C2×#815D3semidirect
142. C32×C8C22⋊C4semidirect
353. C3×C8(C2×D3)⋊C4semidirect
354. C3×C8(C2×D3)⋊C4semidirect
445. C32#1973semidirect
477. C8#3722semidirect
515. C3#69826semidirect
516. C3#70629semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×C3×#8182
C2×C3×#8152
#105913202
#105912132
C2×#635672
C2×#635642
#706293
#698263