Finite Group Databasebeta

← #11778023

Subgroups — #11778023

Order 1152.

726 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594971C211yesmaximal, characteristic, complemented
2#10592917C211yesmaximal, characteristic, complemented
3C3×#5223C211yesmaximal, characteristic
4C3×#5218C211yesmaximal, characteristic, complemented
5#10589154C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#70976—31nomaximal
9#69698—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—21no—
12C2×#3754—21no—
13#64133C2211yescharacteristic
14C2×C3×#217—21no—
15C2×C3×#214—21no—
16C2×C3×(C2×D3)⋊C4C2211yescharacteristic
17C3×#924C2211yescharacteristic
18D3×#217—21no—
19#63964—21no—
20#63899—21no—
21#63896—21no—
22#63893—21no—
23#63887—21no—
24#63659—21no—
25#63657C2211yescharacteristic
26C3×#832—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5634—31no—
30#5483—31no—
31C3×#450—31no—
32C3×#392—31no—
33#5223D311yescharacteristic
34#5218—31no—
35#5218—31no—
36#5218—61no—
37#5218D311yescharacteristic, complemented
38#4538—31no—
39#4525—31no—
40#4468—31no—
41#4467—31no—
42#4452—31no—
43#4452—31no—
44C24×C32—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—42no—
49C22×C32×C4C2311yescharacteristic
50C2×#634D411yescharacteristic, complemented
51C2×C3×#67—42no—
52C2×C3×#67—42no—
53C2×C3×#67—42no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D411yescharacteristic
56C2×C3×Dic6D411yescharacteristic, complemented
57C2×#627—21no—
58C2×D3×Dic3—21no—
59C2×D3×Dic3—21no—
60#3757—21no—
61#3754—42no—
62C4⋊(C3⋊Dic3)D411yescharacteristic, complemented
63#3750—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×#217—21no—
66C3×#217—42no—
67C3×#214—42no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×C4⋊Dic3D411yescharacteristic, complemented
71C3×Dic3⋊C4—21no—
72C2×C3×C3⋊C8—21no—
73#3724—21no—
74Dic3⋊Dic3—21no—
75Dic3⋊Dic3—21no—
76(C2×D3)⋊Dic3—21no—
77(C2×D3)⋊Dic3—21no—
78#1596—91noSylow
79C22×C3×D4—21no—
80C22×C3×D4—61no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C2×D311yescharacteristic
83C22×#67—21no—
84C2×C3×SD16—61no—
85C3×C22⋊Q8—31no—
86C2×C3×C22⋊C4—31no—
87C2×C3×C22⋊C4—61no—
88C2×#217—21no—
89C2×#217—61no—
90#946—61no—
91C2×#214—21no—
92C2×#214—61no—
93C2×#214—61no—
94C2×#214—62no—
95C2×(C2×D3)⋊C4C2×D311yescharacteristic
96#924—31no—
97#924—31no—
98#924—61no—
99#924—61no—
100#924C2×D311yescharacteristic
101#897—61no—
102#896—61no—
103#896—61no—
104D3×C22⋊C4—61no—
105#878—61no—
106#878—61no—
107#878—61no—
108#878—61no—
109#878—61no—
110C3×#102—61no—
111C3×C22⋊C8—31no—
112C3×#95—31no—
113#832—21no—
114#832—61no—
115#832—61no—
116#832—62no—
117C3⋊#95C2×D311yescharacteristic
118#830—31no—
119#830—31no—
120#830—61no—
121#830C2×D311yescharacteristic
122C23×C32—22no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32C2×D411yescharacteristic
130C22×C3×D3—21no—
131C22×C3×D3—21no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3SD1612yescomplemented
135C32×D4—22no—
136C32×D4—22no—
137C32×D4—41no—
138C32×D4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144#634—41no—
145C3×#67—48no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C3×Dic6—41no—
154#627—81no—
155D3×Dic3—81no—
156D3×Dic3—81no—
157C3⋊(C3⋊C8)—41no—
158C3×C3⋊C8—41no—
159#543—91no—
160#450—31no—
161#450—91no—
162#392—31no—
163#328—91no—
164#328—91no—
165#323—91no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—31no—
169C24×C3—41no—
170C23×D3#6711yescharacteristic
171C2×C3×Q8—31no—
172C2×C3×D4—22no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—41no—
178C2×C3×D4—42no—
179C2×C3×D4—42no—
180C2×C3×D4—44no—
181C2×C3×D4—122no—
182C2×C3×D4—122no—
183C2×C3×D4—122no—
184C22×C3×C4—21no—
185C22×C3×C4—31no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C2×#67—42no—
190C2×#67—42no—
191C2×#67—42no—
192C22×Dic3—21no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3#6711yescharacteristic
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×Dic6—31no—
199C2×Dic6—31no—
200C2×Dic6—61no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6#6711yescharacteristic, complemented
204C3×SD16—122no—
205C2×C3×C8—61no—
206C3×C4⋊C4—31no—
207C3×C4⋊C4—61no—
208C3×C22⋊C4—61no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—122no—
212#217—21no—
213#217—42no—
214#217—61no—
215#217—61no—
216#217—61no—
217#217—61no—
218#217—121no—
219#214—42no—
220#214—122no—
221#214—122no—
222#214—124no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—21no—
225(C2×D3)⋊C4—61no—
226(C2×D3)⋊C4—61no—
227C4⋊Dic3—31no—
228C4⋊Dic3—31no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3#6711yescharacteristic, complemented
233Dic3⋊C4—21no—
234Dic3⋊C4—61no—
235Dic3⋊C4—61no—
236Dic3⋊C4—61no—
237Dic3⋊C4—61no—
238Dic3⋊C4—61no—
239Dic3⋊C4—61no—
240Dic3⋊C4—121no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32—42no—
250C22×C32—81no—
251C22×C32—81no—
252C22×C32—81no—
253C22×C32—81no—
254C22×C32#12011yescharacteristic
255C22×C32C2×SD1611yescharacteristic
256C22×C32#13711yescharacteristic
257C2×C3×D3—22no—
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C2×C3×D3—42no—
261C2×C3×D3—81no—
262C32×C4—21no—
263C32×C4—21no—
264C3⋊Dic3—41no—
265C3⋊Dic3—41no—
266C3×Dic3—42no—
267C3×Dic3—41no—
268C3×Dic3—41no—
269C3×Dic3—41no—
270C22×D4—61no—
271C22×D4D3211yescharacteristic
272C2×SD16—61no—
273C2×SD16—181no—
274C22⋊Q8—31no—
275C22⋊Q8—91no—
276C22⋊Q8—181no—
277C22⋊Q8—181no—
278C22⋊Q8—181no—
279C22⋊Q8—181no—
280C22⋊Q8—181no—
281C2×C22⋊C4—31no—
282C2×C22⋊C4—61no—
283C2×C22⋊C4—181no—
284#102—61no—
285#102—181no—
286C22⋊C8—31no—
287C22⋊C8—91no—
288#95—31no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—21no—
292C23×C3—32no—
293C23×C3—42no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3—41no—
297C23×C3—42no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—42no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—61no—
309C23×C3—61no—
310C23×C3—81no—
311C23×C3—81no—
312C23×C3—81no—
313C23×C3—81no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3D3×D411yescharacteristic
317C23×C3C2×#6711yescharacteristic
318C22×D3—21no—
319C22×D3—21no—
320C22×D3—41no—
321C22×D3—41no—
322C22×D3#21412yescomplemented
323C3×Q8—121no—
324C3×D4—22no—
325C3×D4—24no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—42no—
330C3×D4—42no—
331C3×D4—41no—
332C3×D4—41no—
333C3×D4—41no—
334C3×D4—41no—
335C3×D4—42no—
336C3×D4—128no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—62no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—121no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353#67—48no—
354C2×Dic3—22no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—241no—
368C2×Dic3—241no—
369C4×D3—241no—
370C4×D3—241no—
371Dic6—41no—
372Dic6—121no—
373Dic6—121no—
374Dic6—122no—
375Dic6—241no—
376Dic6—241no—
377C3×C8—121no—
378C3⋊C8—41no—
379C3⋊C8—122no—
380C3⋊C8—121no—
381C3⋊C8—121no—
382C2×C32—21no—
383C2×C32—21no—
384C2×C32—82no—
385C2×C32#44811yescharacteristic
386C2×C32#45311yescharacteristic
387C2×C32B(4,𝔽2)11yescharacteristic
388C3×D3—42no—
389C24—21no—
390C24—31no—
391C2×Q8—31no—
392C2×Q8—91no—
393C2×Q8—181no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—122no—
398C2×D4—122no—
399C2×D4—122no—
400C22×C4—31no—
401C22×C4—61no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4C2×D3211yescharacteristic
405SD16—122no—
406SD16—362no—
407C2×C8—61no—
408C2×C8—181no—
409C4⋊C4—31no—
410C4⋊C4—61no—
411C4⋊C4—91no—
412C4⋊C4—181no—
413C4⋊C4—181no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C22⋊C4—61no—
417C22⋊C4—61no—
418C22⋊C4—61no—
419C22⋊C4—122no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—42no—
433C22×C3—44no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—62no—
440C22×C3—82no—
441C22×C3—82no—
442C22×C3—81no—
443C22×C3—81no—
444C22×C3—81no—
445C22×C3—81no—
446C22×C3—82no—
447C22×C3—82no—
448C22×C3—82no—
449C22×C3—82no—
450C22×C3—81no—
451C22×C3—81no—
452C22×C3—81no—
453C22×C3—81no—
454C22×C3—122no—
455C22×C3—121no—
456C22×C3—121no—
457C22×C3—241no—
458C22×C3D3×SD1611yescharacteristic
459C22×C3#91511yescharacteristic
460C22×C3C2×#21411yescharacteristic
461C22×C3#93711yescharacteristic
462C22×C3#93711yescharacteristic
463C22×C3#95111yescharacteristic
464C2×D3—22no—
465C2×D3—41no—
466C2×D3—41no—
467C2×D3—42no—
468C2×D3—81no—
469C3×C4—22no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—41no—
475C3×C4—122no—
476C3×C4—121no—
477C3×C4—121no—
478C3×C4—121no—
479Dic3—42no—
480Dic3—41no—
481Dic3—41no—
482Dic3—41no—
483Dic3—121no—
484Dic3—121no—
485Dic3—121no—
486Dic3—121no—
487Dic3—241no—
488Dic3—241no—
489C32#159611yescharacteristic, complemented, Sylow
490C23—22no—
491C23—32no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—61no—
499C23—61no—
500C23—121no—
501C23—121no—
502C23D3×#6711yescharacteristic
503Q8—121no—
504Q8—361no—
505Q8—721no—
506D4—22no—
507D4—22no—
508D4—41no—
509D4—41no—
510D4—128no—
511C2×C4—41no—
512C2×C4—62no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—121no—
517C2×C4—121no—
518C2×C4—121no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—721no—
522C2×C4—721no—
523C2×C4D3×#6711yescharacteristic
524C2×C4#381111yescharacteristic
525C8—121no—
526C8—361no—
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—122no—
540C2×C3#503211yescharacteristic
541C2×C3#503211yescharacteristic
542C2×C3#504011yescharacteristic
543C2×C3#507711yescharacteristic
544C2×C3#517011yescharacteristic
545C2×C3#519811yescharacteristic
546D3—42no—
547C22—21no—
548C22—21no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—62no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—122no—
558C22—121no—
559C22—121no—
560C22—241no—
561C22D3×#21411yescharacteristic
562C22#6392911yescharacteristic
563C22#6398311yescharacteristic
564C4—21no—
565C4—21no—
566C4—122no—
567C4—121no—
568C4—121no—
569C4—121no—
570C4—361no—
571C4—361no—
572C3—21no—
573C3#6969811yescharacteristic, complemented
574C3#7097611yescharacteristic, complemented
575C2—21no—
576C2—21no—
577C2—82no—
578C2—122no—
579C2#1059151711yescharacteristic
580C2#1059152311yescharacteristic
581C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC3×#5223C2
hypercenterC22×D4D32
hypocenterC32#1596
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10594971C2semidirect
2. #10592917C2semidirect
4. C3×#5218C2semidirect
5. #10589154C2semidirect
6. #10589153C2semidirect
7. #10589145C2semidirect
37. #5218D3semidirect
50. C2×#634D4semidirect
56. C2×C3×Dic6D4semidirect
62. C4⋊(C3⋊Dic3)D4semidirect
70. C3×C4⋊Dic3D4semidirect
134. C22×C3×D3SD16semidirect
203. C2×Dic6#67semidirect
232. C4⋊Dic3#67semidirect
322. C22×D3#214semidirect
489. C32#1596semidirect
573. C3#69698semidirect
574. C3#70976semidirect

Maximal subgroups

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

subgroupindex
#105949712
#105929172
C3×#52232
C3×#52182
#105891542
#105891532
#105891452
#709763
#696983