Finite Group Databasebeta

← #11788634

Subgroups — #11788634

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3C2×C3×#833C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591106C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70218—31nomaximal
9#70088—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C2×#3754—21no—
13#64141—22no—
14#64141C414yescomplemented
15C2×#3753—21no—
16C2×#3748C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3712—21no—
22#63817—22no—
23#63817—22no—
24C2×#3710—21no—
25C3×#833—22no—
26C3×#832—21no—
27C3×#832—21no—
28#63567—21no—
29#63564—21no—
30C2×#932—31no—
31C2×#932—31no—
32C2×#932—61no—
33C2×#907—31no—
34C2×#901—31no—
35C2×C3×#102—31no—
36C2×C3×#100—31no—
37C2×#833D311yescharacteristic, complemented
38C2×#832D311yescharacteristic, complemented
39#5133—31no—
40#4966—31no—
41#4558—31no—
42#4554—31no—
43#4552—31no—
44#4530—31no—
45C24×C32—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4C2×C412yes—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—21no—
55#3828—21no—
56#3828C2×C412yes—
57#3828D412yes—
58C2×C4⋊(C3⋊D3)D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634D411yescharacteristic
61C22×C3×Dic3—21no—
62#3754—24no—
63#3753—24no—
64#3748—21no—
65#3748C2×C412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208D412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D411yescharacteristic
78C2×C3×C3⋊C8D411yescharacteristic
79#3712—24no—
80#3710—24no—
81#1907—91noSylow
82C22×C3×D4—21no—
83C22×C3×D4C2×D311yescharacteristic
84C22×C3×D4C2×D311yescharacteristic
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C22×C3×C8—31no—
91C2×C3×C4⋊C4—31no—
92C2×#214—61no—
93C2×#214—61no—
94C2×#214—62no—
95#932—34no—
96#932—34no—
97#932—64no—
98#932—62no—
99#932—62no—
100#932—64no—
101C2×#213—61no—
102C2×#213—61no—
103C2×#213—62no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109C2×#208C2×D311yescharacteristic
110C22×C3⋊C8C2×D311yescharacteristic
111#907—62no—
112#907—62no—
113#901—62no—
114#901—62no—
115C2×ΓL(1,𝔽25)—61no—
116C2×ΓL(1,𝔽25)—61no—
117C2×D3×C8—61no—
118C2×D3×C8—61no—
119C3×#102—61no—
120C3×#102—61no—
121C3×#100—62no—
122#833—22no—
123#832—21no—
124#832—21no—
125#821—61no—
126#816—61no—
127#810—61no—
128#809—61no—
129C23×C32—22no—
130C23×C32—41no—
131C23×C32—41no—
132C23×C32—81no—
133C23×C32—81no—
134C23×C32#4111yescharacteristic
135C22×C3⋊D3—21no—
136C32×D4—22no—
137C32×D4—22no—
138C32×D4—41no—
139C32×D4—41no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4111yescharacteristic
146#638—22no—
147#638—22no—
148C2×C3⋊Dic3—21no—
149C4⋊(C3⋊D3)—21no—
150C4⋊(C3⋊D3)C22⋊C412yes—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153#634—21no—
154#634C22⋊C412yes—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—81no—
157C3⋊(C3⋊C8)—22no—
158C3×C3⋊C8—21no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—21no—
161C3×C3⋊C8—41no—
162C2×AGL(1,ℤ/8)—91no—
163C2×#131—91no—
164#417—91no—
165C2×#102—31no—
166C2×#100—31no—
167#343—91no—
168#341—91no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—41no—
172C2×C3×D4—22no—
173C2×C3×D4—22no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—22no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4C4×D312yes—
189C2×C3×D4C4×D312yes—
190C22×C3×C4—21no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—61no—
195C2×#67—61no—
196C2×#67—121no—
197C22×Dic3—21no—
198#235—32no—
199#235—32no—
200#235—32no—
201#235—32no—
202#235—62no—
203#235—62no—
204#235—61no—
205#235—61no—
206#235—61no—
207#235—61no—
208#235—121no—
209#235—121no—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—121no—
216C2×Dic6—31no—
217C2×Dic6—31no—
218C2×Dic6—61no—
219C3×M16—32no—
220C3×M16—61no—
221C3×M16—61no—
222C3×M16—61no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231#214—64no—
232#214—64no—
233#214—68no—
234#213—64no—
235#213—64no—
236#213—68no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239#208—21no—
240#208—21no—
241#208—21no—
242#208—32no—
243#208—32no—
244#208—62no—
245#208—62no—
246#208—61no—
247#208—61no—
248#208#6712yes—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8#6711yescharacteristic
257C2×C3⋊C8#6711yescharacteristic
258ΓL(1,𝔽25)—64no—
259ΓL(1,𝔽25)—64no—
260D3×C8—64no—
261D3×C8—64no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—42no—
265C22×C32—82no—
266C22×C32—82no—
267C22×C32—81no—
268C22×C32—81no—
269C22×C32C4×D411yescharacteristic
270C22×C32#12111yescharacteristic
271C22×C32#12311yescharacteristic
272C2×C3⋊D3—22no—
273C2×C3⋊D3—41no—
274C2×C3⋊D3—41no—
275C32×C4C2×C22⋊C411yescharacteristic
276C32×C4C4×D411yescharacteristic
277C32×C4#12011yescharacteristic
278C32×C4#12111yescharacteristic
279C3⋊Dic3—22no—
280C3×Dic3—81no—
281C2×#41—91no—
282C22×D4D3211yescharacteristic
283AGL(1,ℤ/8)—94no—
284AGL(1,ℤ/8)—182no—
285C2×SD16—181no—
286C2×D8—181no—
287#131—182no—
288#131—182no—
289C2×M16—31no—
290C2×M16—31no—
291C2×M16—91no—
292C2×M16—181no—
293C22×C8—31no—
294C22×C8—181no—
295C2×C4⋊C4—31no—
296#103—181no—
297#102—61no—
298#102—61no—
299#102—181no—
300#100—62no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—21no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—42no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—81no—
312C23×C3—81no—
313C23×C3—81no—
314C23×C3—81no—
315C23×C3—82no—
316C23×C3—82no—
317C23×C3#23511yescharacteristic
318C23×C3#23711yescharacteristic
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—121no—
322C3×D4—24no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—42no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—41no—
331C3×D4—41no—
332C3×D4—41no—
333C3×D4—41no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—121no—
341C2×C3×C4—241no—
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4#23511yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4#23711yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354#67—62no—
355#67—62no—
356#67—62no—
357#67—62no—
358#67—122no—
359#67—122no—
360C2×Dic3—41no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—81no—
364C2×Dic3—121no—
365D12—32no—
366D12—32no—
367D12—62no—
368D12—61no—
369D12—61no—
370D12—121no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—122no—
376C4×D3—122no—
377Dic6—32no—
378Dic6—32no—
379Dic6—62no—
380Dic6—61no—
381Dic6—61no—
382Dic6—121no—
383C3×C8—61no—
384C3×C8—62no—
385C3×C8—61no—
386C3×C8—121no—
387C3⋊C8—21no—
388C3⋊C8—22no—
389C3⋊C8—21no—
390C3⋊C8—41no—
391C3⋊C8—64no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32—82no—
397C2×C32#38611yescharacteristic
398C2×C32#47111yescharacteristic
399C2×C32#47211yescharacteristic
400C3⋊D3—42no—
401C24—21no—
402#41—92no—
403#41—92no—
404#41—181no—
405#41—181no—
406C2×Q8—91no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—91no—
413C2×D4—181no—
414C2×D4#62412yes—
415C22×C4—61no—
416C22×C4—181no—
417C22×C4C2×D3211yescharacteristic
418SD16—184no—
419D8—184no—
420M16—32no—
421M16—61no—
422M16—61no—
423M16—61no—
424M16—92no—
425M16—184no—
426M16—181no—
427C2×C8—31no—
428C2×C8—31no—
429C2×C8—61no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—184no—
434C2×C8—181no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—44no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—82no—
450C22×C3—82no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—82no—
454C22×C3—82no—
455C22×C3—84no—
456C22×C3—84no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3#67⋊C411yescharacteristic
462C22×C3#88311yescharacteristic
463C22×C3#88311yescharacteristic
464C22×C3#88411yescharacteristic
465C22×C3C4×#6711yescharacteristic
466C22×C3#93811yescharacteristic
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—122no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—121no—
473C2×D3—121no—
474C2×D3—241no—
475C2×D3—241no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—241no—
481C3×C4D3×C22⋊C411yescharacteristic
482C3×C4D3×C22⋊C411yescharacteristic
483C3×C4#67⋊C411yescharacteristic
484C3×C4#88411yescharacteristic
485C3×C4C4×#6711yescharacteristic
486C3×C4#93711yescharacteristic
487C3×C4#93711yescharacteristic
488C3×C4#93811yescharacteristic
489Dic3—62no—
490Dic3—62no—
491Dic3—81no—
492Dic3—122no—
493C32#190711yescharacteristic, complemented, Sylow
494C23—22no—
495C23—41no—
496C23—41no—
497C23—81no—
498C23—81no—
499C23—181no—
500C23#380411yescharacteristic
501Q8—92no—
502Q8—181no—
503D4—22no—
504D4—22no—
505D4—41no—
506D4—41no—
507D4—92no—
508D4—182no—
509D4—182no—
510D4—181no—
511C2×C4—121no—
512C2×C4—181no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—241no—
516C2×C4#380411yescharacteristic
517C2×C4C2×#62411yescharacteristic
518C2×C4D3×#6711yescharacteristic
519C2×C4D3×#6711yescharacteristic
520C2×C4#381111yescharacteristic
521C2×C4#381111yescharacteristic
522C8—61no—
523C8—61no—
524C8—62no—
525C8—121no—
526C8—182no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—41no—
535C2×C3—41no—
536C2×C3—84no—
537C2×C3—82no—
538C2×C3—82no—
539C2×C3#474811yescharacteristic
540C2×C3#474911yescharacteristic
541C2×C3#495611yescharacteristic
542C2×C3#495611yescharacteristic
543C2×C3#516011yescharacteristic
544C2×C3#517711yescharacteristic
545D3—122no—
546D3—122no—
547D3—242no—
548C22—21no—
549C22—21no—
550C22—42no—
551C22—82no—
552C22—82no—
553C22—81no—
554C22—81no—
555C22—182no—
556C22—361no—
557C22—361no—
558C22#6395211yescharacteristic
559C22#6395811yescharacteristic
560C22#6397511yescharacteristic
561C4—182no—
562C4—241no—
563C4#6395211yescharacteristic
564C4#6395811yescharacteristic
565C4#6397411yescharacteristic
566C4#6398311yescharacteristic
567C3—21no—
568C3#7008811yescharacteristic, complemented
569C3#7021811yescharacteristic, complemented
570C2—21no—
571C2—21no—
572C2—82no—
573C2—362no—
574C2#1059140611yescharacteristic
575C2#1059140711yescharacteristic
576C2#1059172211yescharacteristic
subgroupG/H
centerC22#63958
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#121
prime radicalC2×#64141C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1907
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C2×C3×#833C2semidirect
4. C2×C3×#832C2semidirect
5. #10591106C2semidirect
6. #10589167C2semidirect
7. #10589166C2semidirect
14. #64141C4semidirect
37. C2×#833D3semidirect
38. C2×#832D3semidirect
493. C32#1907semidirect
568. C3#70088semidirect
569. C3#70218semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C2×#638172
C2×C3×#8332
C2×C3×#8322
#105911062
#105891672
#105891662
#702183
#700883