Finite Group Databasebeta

← #11792731

Subgroups — #11792731

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic, complemented
4C2×C3×#833C211yesmaximal, characteristic, complemented
5C2×#63560C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72059—31nomaximal
9#70091—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×#3754—21no—
14#64141—22no—
15#64141—22no—
16C2×#3753—21no—
17C2×#3748C2211yescharacteristic
18C2×C3×#214—22no—
19C2×C3×#214—22no—
20C2×C3×#214—22no—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3719—21no—
25#63833—22no—
26#63833—22no—
27C2×#3717—21no—
28C3×#833—22no—
29#63560—22no—
30#63557—22no—
31C22×C3×SD16—31no—
32C2×#942—31no—
33C22×#214D311yescharacteristic, complemented
34C2×#932—31no—
35C2×#932—31no—
36C2×#932—61no—
37C2×#909—31no—
38C2×C3×#100—31no—
39C2×#836—31no—
40C2×#833D311yescharacteristic, complemented
41C2×#824—31no—
42#5129—31no—
43#5110—31no—
44#4558—31no—
45#4552—31no—
46C24×C32—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4D412yes—
53C22×C32×C4C2311yescharacteristic
54C2×#638—21no—
55#3828—21no—
56#3828—21no—
57#3828—21no—
58#3828—21no—
59C2×C4⋊(C3⋊D3)D411yescharacteristic
60C2×C4×C3⋊D3—21no—
61C2×#634D411yescharacteristic
62C22×C3×Dic3—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6D412yes—
69#3754—24no—
70#3753—24no—
71#3748—21no—
72#3748D412yes—
73C2×C3⋊(C3⋊C8)—21no—
74C3×#214—28no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208D412yes—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8D412yes—
84#3719—24no—
85#3717—24no—
86#2019—91noSylow
87C22×C3×Q8—31no—
88C22×C3×D4—21no—
89C22×C3×D4C2×D311yescharacteristic
90C22×C3×D4C2×D311yescharacteristic
91C2×#235—31no—
92C2×#235—31no—
93C2×#235—61no—
94C22×Dic6C2×D311yescharacteristic
95C2×C3×SD16—62no—
96C2×C3×SD16—62no—
97C2×C3×SD16—62no—
98C2×C3×M16—31no—
99C2×C3×M16—31no—
100C22×C3×C8—31no—
101C2×#216—61no—
102#942—62no—
103#942—62no—
104C2×#215—61no—
105C2×#214—22no—
106C2×#214—22no—
107C2×#214—22no—
108C2×#214—61no—
109C2×#214—61no—
110C2×#214—62no—
111#932—62no—
112#932—62no—
113#932—64no—
114#932—64no—
115#932—62no—
116#932—62no—
117C2×#213—61no—
118C2×#213—61no—
119C2×#213—62no—
120C2×#208—31no—
121C2×#208—31no—
122C2×#208—61no—
123C2×#208C2×D311yescharacteristic
124C2×#208C2×D311yescharacteristic
125C22×C3⋊C8C2×D311yescharacteristic
126#909—62no—
127#909—62no—
128C2×Dic12—61no—
129C2×#204—61no—
130C3×#100—62no—
131#836—62no—
132#833—22no—
133#824—62no—
134(C2×D3)⋊C8—62no—
135(C2×D3)⋊C8—62no—
136C23×C32—22no—
137C23×C32—41no—
138C23×C32—41no—
139C23×C32—82no—
140C23×C32#4111yescharacteristic
141C22×C3⋊D3—21no—
142C32×D4—22no—
143C32×D4—22no—
144C32×D4—41no—
145C32×D4—41no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152#638—41no—
153#638—41no—
154C2×C3⋊Dic3—21no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)—21no—
157C4×C3⋊D3—41no—
158C4×C3⋊D3—41no—
159#634—21no—
160#634—21no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—41no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—41no—
167C3×Dic6—41no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—22no—
171C3×C3⋊C8—41no—
172C2×#137—91no—
173C2×AGL(1,ℤ/8)—91no—
174C22×SD16—31no—
175C2×#101—91no—
176C2×#100—31no—
177#408—91no—
178#341—91no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—41no—
182C2×C3×Q8—32no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—22no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4—41no—
204C2×C3×D4D1212yes—
205C2×C3×D4#6712yes—
206C22×C3×C4—21no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—61no—
211C2×#67—61no—
212C2×#67—121no—
213C22×Dic3—21no—
214#235—62no—
215#235—62no—
216#235—61no—
217#235—61no—
218#235—61no—
219#235—61no—
220#235—61no—
221#235—61no—
222#235—61no—
223#235—61no—
224#235—121no—
225#235—121no—
226C2×D12—31no—
227C2×D12—31no—
228C2×D12—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—121no—
232C2×Dic6—21no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6—21no—
237C2×Dic6—31no—
238C2×Dic6—31no—
239C2×Dic6—61no—
240C2×Dic6#6712yes—
241C3×SD16—68no—
242C3×M16—32no—
243C3×M16—61no—
244C3×M16—61no—
245C3×M16—61no—
246C2×C3×C8—32no—
247C2×C3×C8—61no—
248C2×C3×C8—61no—
249C2×C3×C8—61no—
250C2×C3×C8—61no—
251#216—64no—
252#215—64no—
253#214—28no—
254#214—68no—
255#214—64no—
256#214—64no—
257#213—68no—
258#213—64no—
259#213—64no—
260#208—21no—
261#208—21no—
262#208—21no—
263#208—32no—
264#208—32no—
265#208—62no—
266#208—62no—
267#208—61no—
268#208—61no—
269#208#6712yes—
270C2×C3⋊C8—21no—
271C2×C3⋊C8—21no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—21no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8#6712yes—
278Dic12—64no—
279#204—64no—
280C22×C32—22no—
281C22×C32—42no—
282C22×C32—82no—
283C22×C32—82no—
284C22×C32—82no—
285C22×C32#12111yescharacteristic
286C22×C32#12111yescharacteristic
287C22×C32#12111yescharacteristic
288C2×C3⋊D3—41no—
289C2×C3⋊D3—42no—
290C32×C4#12011yescharacteristic
291C32×C4#12011yescharacteristic
292C32×C4#12011yescharacteristic
293C32×C4#12711yescharacteristic
294C3⋊Dic3—41no—
295C3×Dic3—42no—
296C2×#41—91no—
297C22×Q8—31no—
298C22×D4D3211yescharacteristic
299#137—182no—
300#137—182no—
301AGL(1,ℤ/8)—182no—
302AGL(1,ℤ/8)—182no—
303C2×Q16—181no—
304C2×SD16—62no—
305C2×SD16—62no—
306C2×SD16—62no—
307C2×SD16—181no—
308C2×SD16—181no—
309C2×D8—181no—
310C2×M16—31no—
311C2×M16—31no—
312C2×M16—91no—
313C22×C8—31no—
314#101—182no—
315#100—62no—
316C22⋊C8—182no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—21no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—82no—
328C23×C3—82no—
329C23×C3—84no—
330C23×C3#23511yescharacteristic
331C23×C3#23711yescharacteristic
332C22×D3—61no—
333C22×D3—61no—
334C22×D3—121no—
335C3×Q8—62no—
336C3×Q8—62no—
337C3×Q8—121no—
338C3×Q8—121no—
339C3×D4—24no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—22no—
344C3×D4—42no—
345C3×D4—42no—
346C3×D4—42no—
347C3×D4—41no—
348C3×D4—41no—
349C3×D4—41no—
350C3×D4—41no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—62no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4C2×D1211yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372#67—122no—
373#67—122no—
374#67—121no—
375#67—121no—
376#67—121no—
377#67—121no—
378C2×Dic3—22no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—121no—
384D12—62no—
385D12—61no—
386D12—61no—
387D12—61no—
388D12—61no—
389D12—121no—
390C4×D3—122no—
391C4×D3—122no—
392C4×D3—121no—
393C4×D3—121no—
394C4×D3—121no—
395C4×D3—121no—
396Dic6—22no—
397Dic6—22no—
398Dic6—41no—
399Dic6—41no—
400Dic6—62no—
401Dic6—61no—
402Dic6—61no—
403Dic6—61no—
404Dic6—61no—
405Dic6—121no—
406C3×C8—62no—
407C3×C8—62no—
408C3×C8—121no—
409C3⋊C8—22no—
410C3⋊C8—22no—
411C3⋊C8—41no—
412C3⋊C8—64no—
413C3⋊C8—62no—
414C3⋊C8—62no—
415C2×C32—21no—
416C2×C32—21no—
417C2×C32—82no—
418C2×C32#39211yescharacteristic
419C2×C32#47112yes—
420C3⋊D3—81no—
421C24—21no—
422#41—181no—
423#41—181no—
424#41—181no—
425#41—181no—
426C2×Q8—32no—
427C2×Q8—61no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—61no—
431C2×Q8—61no—
432C2×Q8—91no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—91no—
439C2×D4—181no—
440C2×D4#62612yes—
441C22×C4—61no—
442C22×C4—181no—
443C22×C4C2×D3211yescharacteristic
444Q16—184no—
445SD16—68no—
446SD16—184no—
447SD16—184no—
448D8—184no—
449M16—32no—
450M16—61no—
451M16—61no—
452M16—61no—
453M16—92no—
454M16—181no—
455C2×C8—32no—
456C2×C8—61no—
457C2×C8—61no—
458C2×C8—61no—
459C2×C8—61no—
460C2×C8—181no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—42no—
467C22×C3—44no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—82no—
471C22×C3—82no—
472C22×C3—82no—
473C22×C3—82no—
474C22×C3—84no—
475C22×C3—84no—
476C22×C3—84no—
477C22×C3—82no—
478C22×C3—82no—
479C22×C3#88411yescharacteristic
480C22×C3#88411yescharacteristic
481C22×C3#93011yescharacteristic
482C22×C3#93811yescharacteristic
483C22×C3#93911yescharacteristic
484C22×C3#93911yescharacteristic
485C2×D3—122no—
486C2×D3—122no—
487C2×D3—121no—
488C2×D3—121no—
489C2×D3—122no—
490C2×D3—242no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—122no—
496C3×C4#88211yescharacteristic
497C3×C4#88211yescharacteristic
498C3×C4#93711yescharacteristic
499C3×C4#93711yescharacteristic
500C3×C4#93711yescharacteristic
501C3×C4#94011yescharacteristic
502C3×C4#94011yescharacteristic
503C3×C4#95311yescharacteristic
504Dic3—42no—
505Dic3—122no—
506Dic3—121no—
507Dic3—121no—
508C32#201911yescharacteristic, complemented, Sylow
509C23—22no—
510C23—41no—
511C23—41no—
512C23—82no—
513C23—181no—
514C23#380411yescharacteristic
515Q8—62no—
516Q8—62no—
517Q8—121no—
518Q8—121no—
519Q8—181no—
520Q8—181no—
521D4—22no—
522D4—22no—
523D4—41no—
524D4—41no—
525D4—181no—
526D4—181no—
527D4—361no—
528D4—361no—
529C2×C4—62no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—181no—
533C2×C4—361no—
534C2×C4—361no—
535C2×C4C2×#62611yescharacteristic
536C2×C4D3×#6711yescharacteristic
537C2×C4D3×#6711yescharacteristic
538C2×C4D3×#6711yescharacteristic
539C2×C4#381111yescharacteristic
540C2×C4#381111yescharacteristic
541C8—62no—
542C8—62no—
543C8—121no—
544C8—182no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—41no—
552C2×C3—41no—
553C2×C3—84no—
554C2×C3—82no—
555C2×C3—82no—
556C2×C3#474812yes—
557C2×C3#496011yescharacteristic
558C2×C3#517712yes—
559C2×C3#522311yescharacteristic
560D3—242no—
561D3—241no—
562D3—241no—
563C22—22no—
564C22—42no—
565C22—82no—
566C22—82no—
567C22—82no—
568C22—362no—
569C22—361no—
570C22#6395811yescharacteristic
571C22#6397111yescharacteristic
572C22#6397811yescharacteristic
573C4—122no—
574C4—361no—
575C4#6397711yescharacteristic
576C4#6397911yescharacteristic
577C4#6398111yescharacteristic
578C4#6398311yescharacteristic
579C3—21no—
580C3#7009111yescharacteristic, complemented
581C3#7205911yescharacteristic, complemented
582C2—21no—
583C2—21no—
584C2—82no—
585C2—721no—
586C2#1059140712yes—
587C2#1059172411yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#121
prime radicalC2×#64141C2
hypercenterC22×D4D32
hypocenterC32#2019
LCSG ▷ C22×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. C22×C3×#214C2semidirect
3. C2×#63833C2semidirect
4. C2×C3×#833C2semidirect
5. C2×#63560C2semidirect
6. #10591073C2semidirect
7. #10589166C2semidirect
33. C22×#214D3semidirect
40. C2×#833D3semidirect
508. C32#2019semidirect
580. C3#70091semidirect
581. C3#72059semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C22×C3×#2142
C2×#638332
C2×C3×#8332
C2×#635602
#105910732
#105891662
#720593
#700913