Finite Group Databasebeta

← #11788687

Subgroups — #11788687

Order 1152.

705 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
1C2×#63831C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic
3C2×#63637C211yesmaximal, characteristic, complemented
4C3×#4966C211yesmaximal, characteristic
5C2×#63561C211yesmaximal, characteristic, complemented
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70304—31nomaximal
9#69007—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3719—21no—
18#63831—22no—
19#63831C414yescomplemented
20C2×#3716—21no—
21C2×#3711—21no—
22#63815—22no—
23#63815—22no—
24C2×D3×C3⋊C8—21no—
25#63637—21no—
26#63637—21no—
27C3×#810—21no—
28C3×#809—21no—
29#63561—22no—
30C2×#951—31no—
31C2×#948—31no—
32C2×#909—31no—
33C2×#907—31no—
34C3×#417—31no—
35C2×#824—31no—
36C2×#824—31no—
37C2×#810—31no—
38C2×#810—31no—
39C2×#810—61no—
40#4966D311yescharacteristic
41C3×#343—31no—
42#4558—31no—
43#4558—31no—
44#4530D311yescharacteristic, complemented
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634C2×C412yes—
54C2×C3×#67—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235C2×C412yes—
58C3×#235D412yes—
59C2×C3×D12D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×Dic6D411yescharacteristic
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)D411yescharacteristic
67C2×C3⋊(C3⋊C8)D411yescharacteristic
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yes—
73C3×#208D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77#3719—24no—
78#3716—24no—
79#3711—24no—
80D3×C3⋊C8—24no—
81#1908—91noSylow
82C2×C3×#41—31no—
83C2×#235C2×D311yescharacteristic
84C22×Dic6—31no—
85C22×Dic6—31no—
86C22×Dic6—61no—
87C2×C3×M16—31no—
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C2×D311yescharacteristic
93#951—34no—
94#951—62no—
95#948—62no—
96#948—62no—
97C2×#216—61no—
98C2×#214—61no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102C2×#208C2×D311yescharacteristic
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106C22×C3⋊C8—61no—
107#909—34no—
108#909—62no—
109#907—62no—
110#907—62no—
111C2×Dic12—61no—
112C2×#204—61no—
113C2×ΓL(1,𝔽25)—61no—
114C2×D3×C8—61no—
115C3×#103—61no—
116C3×#102—61no—
117#824—62no—
118#824—62no—
119#810—21no—
120#810—61no—
121#810—61no—
122#810—61no—
123#810—61no—
124#810—62no—
125#810—62no—
126#809—21no—
127C23×C32#4111yescharacteristic
128C22×C3×D3—21no—
129C2×C32×C4—41no—
130C2×C32×C4—81no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140#634—22no—
141#634—22no—
142#634—41no—
143#634—41no—
144C3×#67—22no—
145C3×#67—22no—
146C2×C3×Dic3—21no—
147C3×D12—21no—
148C3×D12C22⋊C412yes—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3×Dic6—21no—
152C3×Dic6C22⋊C412yes—
153C3⋊(C3⋊C8)—21no—
154C3⋊(C3⋊C8)—21no—
155C3×C3⋊C8—22no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—41no—
158C2×#137—91no—
159C2×#131—91no—
160#417—31no—
161C2×#103—91no—
162C2×#101—91no—
163#343—31no—
164#341—91no—
165C3×#41—32no—
166C3×#41—32no—
167C3×#41—61no—
168C3×#41—61no—
169C2×C3×Q8—31no—
170C2×C3×D4—31no—
171C2×C3×D4—61no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—41no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C2×#67—21no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—121no—
183#235—21no—
184#235—21no—
185#235C4×D312yes—
186#235D1212yes—
187C2×D12#6711yescharacteristic
188C2×C4×D3—21no—
189C2×Dic6—32no—
190C2×Dic6—32no—
191C2×Dic6—62no—
192C2×Dic6—62no—
193C2×Dic6—62no—
194C2×Dic6—61no—
195C2×Dic6—61no—
196C2×Dic6—61no—
197C2×Dic6—61no—
198C2×Dic6—61no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—121no—
205C2×Dic6—121no—
206C2×Dic6—121no—
207C2×Dic6#6711yescharacteristic
208C3×M16—32no—
209C3×M16—32no—
210C3×M16—61no—
211C3×M16—61no—
212C3×M16—61no—
213C3×M16—61no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—41no—
223#216—64no—
224#214—64no—
225#208—21no—
226#208—21no—
227#208—21no—
228#208—21no—
229#208—64no—
230#208C4×D312yes—
231#208D1212yes—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—31no—
236C2×C3⋊C8—31no—
237C2×C3⋊C8—31no—
238C2×C3⋊C8—31no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—64no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—121no—
247C2×C3⋊C8—121no—
248Dic12—64no—
249#204—64no—
250ΓL(1,𝔽25)—64no—
251D3×C8—64no—
252C22×C32—21no—
253C22×C32—21no—
254C22×C32C4×D411yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32#12311yescharacteristic
257C2×C3×D3—22no—
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C32×C4—81no—
261C32×C4C2×C22⋊C411yescharacteristic
262C32×C4C4×D411yescharacteristic
263C32×C4#12011yescharacteristic
264C32×C4#12111yescharacteristic
265C3⋊Dic3—42no—
266C3×Dic3—22no—
267C2×#41—31no—
268C22×Q8—91no—
269#137—94no—
270#137—182no—
271C2×Q16—181no—
272C2×SD16—181no—
273#131—182no—
274#131—182no—
275C2×M16—31no—
276C2×M16—31no—
277C2×M16—31no—
278C2×M16—181no—
279C22×C8—91no—
280C22×C8—181no—
281C2×C4⋊C4D3211yescharacteristic
282#103—61no—
283#103—181no—
284#103—181no—
285#102—61no—
286#101—182no—
287C23×C3—21no—
288C23×C3—61no—
289C23×C3#23511yescharacteristic
290C23×C3#23711yescharacteristic
291C22×D3—21no—
292C3×Q8—32no—
293C3×Q8—61no—
294C3×D4—32no—
295C3×D4—62no—
296C3×D4—62no—
297C3×D4—61no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—42no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—61no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—82no—
311C2×C3×C4—81no—
312C2×C3×C4—81no—
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4C2×D1211yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4#23911yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325#67—22no—
326#67—22no—
327C2×Dic3—21no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337D12—21no—
338D12(C2×D3)⋊C412yes—
339C4×D3—22no—
340C4×D3—22no—
341Dic6—21no—
342Dic6—64no—
343Dic6—62no—
344Dic6—62no—
345Dic6—62no—
346Dic6—62no—
347Dic6—122no—
348Dic6—122no—
349Dic6—122no—
350Dic6—121no—
351Dic6—121no—
352Dic6—121no—
353Dic6—121no—
354Dic6(C2×D3)⋊C412yes—
355C3×C8—62no—
356C3×C8—62no—
357C3×C8—121no—
358C3⋊C8—22no—
359C3⋊C8—22no—
360C3⋊C8—41no—
361C3⋊C8—61no—
362C3⋊C8—61no—
363C3⋊C8—61no—
364C3⋊C8—61no—
365C3⋊C8—121no—
366C3⋊C8—121no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32#38611yescharacteristic
370C2×C32#47111yescharacteristic
371C2×C32#47311yescharacteristic
372C3×D3—42no—
373#41—32no—
374#41—32no—
375#41—61no—
376#41—61no—
377C2×Q8—31no—
378C2×Q8—92no—
379C2×Q8—181no—
380C2×Q8—181no—
381C2×Q8—181no—
382C2×Q8—181no—
383C2×Q8—181no—
384C2×D4—31no—
385C2×D4—61no—
386C22×C4—21no—
387C22×C4—61no—
388C22×C4—181no—
389C22×C4C2×D3211yescharacteristic
390Q16—184no—
391SD16—184no—
392M16—32no—
393M16—32no—
394M16—61no—
395M16—61no—
396M16—61no—
397M16—61no—
398M16—184no—
399C2×C8—61no—
400C2×C8—61no—
401C2×C8—61no—
402C2×C8—91no—
403C2×C8—91no—
404C2×C8—184no—
405C2×C8—181no—
406C2×C8—181no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—62no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3C4×D1211yescharacteristic
422C22×C3#67⋊C411yescharacteristic
423C22×C3#88411yescharacteristic
424C22×C3#88611yescharacteristic
425C22×C3#89411yescharacteristic
426C22×C3#93911yescharacteristic
427C2×D3—22no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—62no—
435C3×C4—82no—
436C3×C4—81no—
437C3×C4—81no—
438C3×C4D3×C22⋊C411yescharacteristic
439C3×C4#67⋊C411yescharacteristic
440C3×C4#88211yescharacteristic
441C3×C4#88211yescharacteristic
442C3×C4#89311yescharacteristic
443C3×C4#89511yescharacteristic
444C3×C4C2×(C2×D3)⋊C411yescharacteristic
445C3×C4#93911yescharacteristic
446Dic3—22no—
447Dic3—124no—
448Dic3—122no—
449Dic3—122no—
450C32#190811yescharacteristic, complemented, Sylow
451C23—61no—
452C23#380411yescharacteristic
453Q8—32no—
454Q8—61no—
455Q8—182no—
456Q8—182no—
457Q8—361no—
458Q8—361no—
459D4—32no—
460D4—62no—
461D4—62no—
462D4—61no—
463C2×C4—41no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—81no—
468C2×C4—182no—
469C2×C4—361no—
470C2×C4—361no—
471C2×C4#379611yescharacteristic
472C2×C4C4×D3211yescharacteristic
473C2×C4D3×D1211yescharacteristic
474C2×C4D3×D1211yescharacteristic
475C2×C4D3×#6711yescharacteristic
476C2×C4#381111yescharacteristic
477C8—62no—
478C8—62no—
479C8—121no—
480C8—181no—
481C8—181no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—122no—
492C2×C3#466511yescharacteristic
493C2×C3#474811yescharacteristic
494C2×C3#475511yescharacteristic
495C2×C3#495811yescharacteristic
496C2×C3#520011yescharacteristic
497C2×C3#520411yescharacteristic
498D3—42no—
499C22—21no—
500C22—21no—
501C22—62no—
502C22—121no—
503C22—121no—
504C22#6388011yescharacteristic
505C22#6389011yescharacteristic
506C22#6397111yescharacteristic
507C4—62no—
508C4—81no—
509C4—362no—
510C4#6388111yescharacteristic
511C4#6388611yescharacteristic
512C4D3×(C2×D3)⋊C411yescharacteristic
513C4#6392311yescharacteristic
514C3—21no—
515C3#6900711yescharacteristic, complemented
516C3#7030411yescharacteristic, complemented
517C2—21no—
518C2—21no—
519C2—122no—
520C2#1059136411yescharacteristic
521C2#1059150711yescharacteristic
522C2#1059164411yescharacteristic
subgroupG/H
centerC22#63971
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1908
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63637C2semidirect
5. C2×#63561C2semidirect
6. C3×#4530C2semidirect
7. #10589165C2semidirect
19. #63831C4semidirect
44. #4530D3semidirect
450. C32#1908semidirect
515. C3#69007semidirect
516. C3#70304semidirect

Maximal subgroups

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

subgroupindex
C2×#638312
C2×#638152
C2×#636372
C3×#49662
C2×#635612
C3×#45302
#105891652
#703043
#690073