Finite Group Databasebeta

← #11791192

Subgroups — #11791192

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic
2C2×C3×#837C211yesmaximal, characteristic, complemented
3C3×#5234C211yesmaximal, characteristic, complemented
4C2×#63578C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#70373—31nomaximal
9#69999—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12#64159—22no—
13#64159—22no—
14C2×#3756C411yescharacteristic, complemented
15C2×#3755C411yescharacteristic, complemented
16C2×#3754C411yescharacteristic, complemented
17C2×#3753C411yescharacteristic, complemented
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C3×#837—22no—
24C3×#830—22no—
25#63578—22no—
26#63570—22no—
27#63557—22no—
28Dic3×C3⋊C8—22no—
29C2×#950—31no—
30C2×#950—31no—
31C2×#950—61no—
32C2×C3×#104—31no—
33C3×#408—31no—
34C2×#837D311yescharacteristic, complemented
35#5234D311yescharacteristic, complemented
36C2×#825—31no—
37#5129—31no—
38C2×#822—31no—
39C2×#822—31no—
40#5110—31no—
41C2×C8×Dic3—31no—
42C2×#805—31no—
43C2×C4×C3⋊C8—31no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41—21no—
48C2×C32×Q8C2×C411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4C2×C411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—21no—
55#3828—21no—
56#3828—21no—
57#3828—21no—
58C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634C2×C411yescharacteristic
61C22×C3×Dic3—21no—
62#3756—22no—
63#3755—22no—
64#3754—22no—
65#3753—22no—
66C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
67C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
68C2×C3⋊(C3⋊C8)D412yes—
69C2×C3⋊(C3⋊C8)D412yes—
70C3×C4×Dic3—21no—
71C3×C4×Dic3D412yes—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8D412yes—
81#1974—91noSylow
82C2×C3×#41—21no—
83C2×C3×#41C2×D311yescharacteristic
84C2×C3×#41C2×D311yescharacteristic
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C22×C3×C8—31no—
91C2×C3×C42—31no—
92#950—62no—
93#950—62no—
94#950—62no—
95#950—62no—
96#950—64no—
97#950—64no—
98C2×#216—31no—
99C2×#216—31no—
100C2×#216—61no—
101C2×#215—31no—
102C2×#215—31no—
103C2×#215—61no—
104C2×#214—31no—
105C2×#214—31no—
106C2×#214—61no—
107C2×#213—31no—
108C2×#213—31no—
109C2×#213—61no—
110C2×C4×Dic3C2×D311yescharacteristic
111C2×#208C2×D311yescharacteristic
112C2×#208C2×D311yescharacteristic
113C22×C3⋊C8—31no—
114C22×C3⋊C8—31no—
115C22×C3⋊C8—61no—
116C22×C3⋊C8C2×D311yescharacteristic
117C3×#104—62no—
118C3×C22⋊C8—62no—
119#837—22no—
120#830—22no—
121#825—62no—
122#822—62no—
123#822—62no—
124(C2×D3)⋊C8—62no—
125(C2×D3)⋊C8—62no—
126C8×Dic3—62no—
127#805—62no—
128C4×C3⋊C8—62no—
129C23×C32—21no—
130C23×C32#4111yescharacteristic
131C22×C3⋊D3—21no—
132C32×Q8—21no—
133C32×Q8—21no—
134C32×D4—21no—
135C32×D4—21no—
136C32×D4—41no—
137C32×D4—41no—
138C2×C32×C4—21no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147#638—41no—
148#638—41no—
149C2×C3⋊Dic3—21no—
150C4⋊(C3⋊D3)—21no—
151C4⋊(C3⋊D3)—21no—
152C4×C3⋊D3—41no—
153C4×C3⋊D3—41no—
154#634—21no—
155#634—21no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—22no—
158C3⋊(C3⋊C8)C22⋊C412yes—
159C3⋊(C3⋊C8)C22⋊C412yes—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C3×C3⋊C8—41no—
163C2×#135—91no—
164C2×#108—91no—
165C2×#104—31no—
166C2×#104—91no—
167#408—31no—
168#408—91no—
169C2×C4×C8—91no—
170C3×#41—22no—
171C3×#41—22no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—41no—
181C3×#41—41no—
182C2×C3×Q8—21no—
183C2×C3×Q8C4×D311yescharacteristic
184C2×C3×Q8C4×D311yescharacteristic
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—41no—
189C2×C3×D4C4×D311yescharacteristic
190C2×C3×D4C4×D311yescharacteristic
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—41no—
195C22×C3×C4—61no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—61no—
199C2×#67—61no—
200C2×#67—121no—
201C22×Dic3—21no—
202#235—62no—
203#235—62no—
204#235—61no—
205#235—61no—
206#235—61no—
207#235—61no—
208#235—61no—
209#235—61no—
210#235—61no—
211#235—61no—
212#235—121no—
213#235—121no—
214C2×D12—31no—
215C2×D12—31no—
216C2×D12—61no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—121no—
220C2×Dic6—31no—
221C2×Dic6—31no—
222C2×Dic6—61no—
223C3×M16—61no—
224C3×M16—61no—
225C3×M16—61no—
226C3×M16—61no—
227C2×C3×C8—32no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C3×C42—32no—
233C3×C42—61no—
234#216—62no—
235#216—62no—
236#216—64no—
237#215—62no—
238#215—62no—
239#215—64no—
240#214—62no—
241#214—62no—
242#214—64no—
243#213—62no—
244#213—62no—
245#213—64no—
246C4×Dic3—21no—
247C4×Dic3#6712yes—
248#208—21no—
249#208—21no—
250#208—21no—
251#208—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—32no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—62no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8#6712yes—
269C22×C32—22no—
270C22×C32—41no—
271C22×C32—42no—
272C22×C32C4×D411yescharacteristic
273C22×C32#12111yescharacteristic
274C22×C32#12411yescharacteristic
275C2×C3⋊D3—41no—
276C2×C3⋊D3—42no—
277C32×C4—41no—
278C32×C4C2×C22⋊C411yescharacteristic
279C32×C4C4×D411yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4#12711yescharacteristic
282C3⋊Dic3—41no—
283C3×Dic3—24no—
284C2×#41—91no—
285C2×#41D3211yescharacteristic
286#135—182no—
287#135—182no—
288C2×Q16—91no—
289C2×SD16—91no—
290C2×SD16—91no—
291C2×D8—91no—
292C2×M16—31no—
293C2×M16—31no—
294C22×C8—31no—
295C22×C8—91no—
296C2×C42—31no—
297#108—182no—
298#104—62no—
299#104—182no—
300C22⋊C8—62no—
301C22⋊C8—182no—
302C4×C8—182no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—41no—
307C23×C3#23511yescharacteristic
308C23×C3#23711yescharacteristic
309C22×D3—61no—
310C22×D3—61no—
311C22×D3—121no—
312C3×Q8—22no—
313C3×Q8—21no—
314C3×Q8—21no—
315C3×Q8—21no—
316C3×Q8—21no—
317C3×Q8—41no—
318C3×D4—22no—
319C3×D4—21no—
320C3×D4—21no—
321C3×D4—21no—
322C3×D4—21no—
323C3×D4—41no—
324C3×D4—42no—
325C3×D4—42no—
326C3×D4—41no—
327C3×D4—41no—
328C3×D4—41no—
329C3×D4—41no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—41no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—64no—
346C2×C3×C4—62no—
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C2×C4×D311yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359#67—122no—
360#67—122no—
361#67—121no—
362#67—121no—
363#67—121no—
364#67—121no—
365C2×Dic3—24no—
366C2×Dic3—22no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—121no—
370D12—62no—
371D12—61no—
372D12—61no—
373D12—61no—
374D12—61no—
375D12—121no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—121no—
379C4×D3—121no—
380C4×D3—121no—
381C4×D3—121no—
382Dic6—62no—
383Dic6—61no—
384Dic6—61no—
385Dic6—61no—
386Dic6—61no—
387Dic6—121no—
388C3×C8—62no—
389C3×C8—121no—
390C3×C8—121no—
391C3⋊C8—22no—
392C3⋊C8—32no—
393C3⋊C8—32no—
394C3⋊C8—32no—
395C3⋊C8—32no—
396C3⋊C8—41no—
397C3⋊C8—41no—
398C3⋊C8—62no—
399C3⋊C8—62no—
400C2×C32—21no—
401C2×C32—21no—
402C2×C32—81no—
403C2×C32#39011yescharacteristic
404C2×C32#44312yes—
405C3⋊D3—81no—
406#41—21no—
407#41—21no—
408#41—21no—
409#41—21no—
410#41—181no—
411#41—181no—
412#41—181no—
413#41—181no—
414C2×Q8—91no—
415C2×Q8#62411yescharacteristic
416C2×D4—21no—
417C2×D4—91no—
418C2×D4—181no—
419C2×D4#62411yescharacteristic
420C22×C4—21no—
421C22×C4—61no—
422C22×C4—181no—
423C22×C4C2×D3211yescharacteristic
424Q16—182no—
425SD16—182no—
426SD16—182no—
427D8—182no—
428M16—61no—
429M16—61no—
430M16—61no—
431M16—61no—
432C2×C8—32no—
433C2×C8—61no—
434C2×C8—61no—
435C2×C8—61no—
436C2×C8—61no—
437C2×C8—91no—
438C2×C8—91no—
439C2×C8—92no—
440C2×C8—92no—
441C42—32no—
442C42—61no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—42no—
454C22×C3—82no—
455C22×C3#67⋊C411yescharacteristic
456C22×C3#88411yescharacteristic
457C22×C3#88511yescharacteristic
458C22×C3#88511yescharacteristic
459C22×C3C4×#6711yescharacteristic
460C22×C3#93911yescharacteristic
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—122no—
466C2×D3—242no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—42no—
472C3×C4—41no—
473C3×C4—41no—
474C3×C4—64no—
475C3×C4D3×C22⋊C411yescharacteristic
476C3×C4D3×C22⋊C411yescharacteristic
477C3×C4#67⋊C411yescharacteristic
478C3×C4#88411yescharacteristic
479C3×C4C4×#6711yescharacteristic
480C3×C4#93911yescharacteristic
481C3×C4#94011yescharacteristic
482C3×C4#94011yescharacteristic
483Dic3—24no—
484Dic3—122no—
485Dic3—121no—
486Dic3—121no—
487C32#197411yescharacteristic, complemented, Sylow
488C23—21no—
489C23—181no—
490C23#380411yescharacteristic
491Q8—21no—
492Q8—21no—
493Q8—181no—
494Q8—181no—
495D4—21no—
496D4—21no—
497D4—41no—
498D4—41no—
499D4—181no—
500D4—181no—
501D4—361no—
502D4—361no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—64no—
507C2×C4—62no—
508C2×C4—181no—
509C2×C4—361no—
510C2×C4—361no—
511C2×C4#380411yescharacteristic
512C2×C4C2×#62411yescharacteristic
513C2×C4D3×#6711yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C2×C4#381111yescharacteristic
516C2×C4#381111yescharacteristic
517C8—62no—
518C8—92no—
519C8—92no—
520C8—121no—
521C8—121no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—41no—
529C2×C3—41no—
530C2×C3—82no—
531C2×C3—81no—
532C2×C3—81no—
533C2×C3#482412yes—
534C2×C3#495711yescharacteristic
535C2×C3#495711yescharacteristic
536C2×C3#514412yes—
537D3—242no—
538D3—241no—
539D3—241no—
540C22—22no—
541C22—42no—
542C22—41no—
543C22—362no—
544C22—361no—
545C22#6395211yescharacteristic
546C22#6395311yescharacteristic
547C22#6397111yescharacteristic
548C4—41no—
549C4—64no—
550C4—361no—
551C4#6395211yescharacteristic
552C4#6397111yescharacteristic
553C4#6397411yescharacteristic
554C4#6397911yescharacteristic
555C3—21no—
556C3#6999911yescharacteristic, complemented
557C3#7037311yescharacteristic, complemented
558C2—21no—
559C2—21no—
560C2—81no—
561C2—721no—
562C2#1059166212yes—
563C2#1059170411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C4×D4
prime radicalC2×#64159C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1974
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#837C2semidirect
3. C3×#5234C2semidirect
4. C2×#63578C2semidirect
5. C2×#63570C2semidirect
6. #10591073C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
14. C2×#3756C4semidirect
15. C2×#3755C4semidirect
16. C2×#3754C4semidirect
17. C2×#3753C4semidirect
34. C2×#837D3semidirect
35. #5234D3semidirect
487. C32#1974semidirect
556. C3#69999semidirect
557. C3#70373semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C2×C3×#8372
C3×#52342
C2×#635782
C2×#635702
#105910732
C2×Dic3×C3⋊C82
#703733
#699993