Finite Group Databasebeta

← #11778032

Subgroups — #11778032

Order 1152.

681 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 681 conjugacy classes of subgroups — too many to draw. Only its 80 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#10594981C211yesmaximal, characteristic, complemented
2C3×#4731C211yesmaximal, characteristic, complemented
3#10591391C211yesmaximal, characteristic
4#10591169C211yesmaximal, characteristic, complemented
5#10589334C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589153C211yesmaximal, characteristic, complemented
8#70976—31nomaximal
9#68316—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×#626—21no—
12C2×#3752C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C3×#924C2211yescharacteristic
15C2×C3×#204—21no—
16#63982—21no—
17#63974—21no—
18C2×(C2×D3)⋊Dic3—21no—
19#63895—21no—
20#63895—21no—
21#63888—21no—
22#63888—21no—
23C2×#3715—21no—
24C32×C22⋊C8C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#821—21no—
28#63562—21no—
29#5634—31no—
30#5634—31no—
31C3×#450—31no—
32#5223—31no—
33#5218—31no—
34#5046—31no—
35#4731D311yescharacteristic, complemented
36#4671—31no—
37C3×#328—31no—
38#4538—31no—
39#4468—31no—
40#4468—31no—
41#4468—61no—
42#4467D311yescharacteristic, complemented
43#4452—31no—
44C23×C3⋊D3D411yescharacteristic
45C23×C3×D3—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3×Dic3—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—42no—
52C2×C3×Dic6D411yescharacteristic, complemented
53C2×C3×Dic6D411yescharacteristic, complemented
54C2×#627—21no—
55C2×#626—42no—
56C2×#626—42no—
57C2×#626—42no—
58C2×#624—21no—
59C2×#624—21no—
60C2×C32×C8—21no—
61#3752—21no—
62#3752—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×#217—21no—
66C3×C4⋊Dic3D411yescharacteristic, complemented
67C3×C4⋊Dic3D411yescharacteristic, complemented
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×#204—42no—
71#3724—21no—
72Dic3⋊Dic3—21no—
73Dic3⋊Dic3—21no—
74#3722—21no—
75#3722—21no—
76(C2×D3)⋊Dic3—42no—
77#3715—42no—
78#1596—91noSylow
79C22×C3×D4—31no—
80C22×#67—61no—
81C22×D12—61no—
82C22×D12C2×D311yescharacteristic
83C2×C3×SD16—61no—
84C3×C22⋊Q8—31no—
85C3×C22⋊Q8—31no—
86C2×#217—61no—
87#946—61no—
88#946—61no—
89C2×#215—61no—
90C2×#214—61no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—31no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95#924C2×D311yescharacteristic
96#924C2×D311yescharacteristic
97C2×#204—21no—
98#897—61no—
99#897—61no—
100#896—61no—
101#896—61no—
102#896—61no—
103#896—61no—
104D3×C22⋊C4—61no—
105D3×C22⋊C4—61no—
106#878—61no—
107#878—61no—
108C3×#102—61no—
109C3×C22⋊C8—21no—
110C3×C22⋊C8C2×D311yescharacteristic
111C3×C22⋊C8C2×D311yescharacteristic
112C3×#95—31no—
113#832—61no—
114C3⋊#95C2×D311yescharacteristic
115#830—31no—
116#830—31no—
117#830—61no—
118#821—21no—
119#809—61no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3SD1612yescomplemented
126C22×C3×D3—22no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—41no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C3×D12—22no—
146C3×D12—22no—
147C3×D12—41no—
148C3×D12—41no—
149C3×Dic6—41no—
150C3×Dic6—41no—
151#627—81no—
152#626—48no—
153#624—81no—
154#624—81no—
155C32×C8—41no—
156C3⋊(C3⋊C8)—41no—
157#543—91no—
158#450—31no—
159#450—91no—
160#392—91no—
161#328—31no—
162#328—91no—
163#323—91no—
164C24×C3—61no—
165C23×D3—21no—
166C23×D3—31no—
167C23×D3—31no—
168C23×D3—61no—
169C2×C3×Q8—31no—
170C2×C3×Q8—31no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—122no—
174C22×C3×C4—21no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C2×#67—122no—
179C2×#67—122no—
180C2×#67—122no—
181C22×Dic3—21no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—61no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—42no—
188C2×D12—122no—
189C2×D12—122no—
190C2×D12—122no—
191C2×C4×D3—61no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C4×D3—61no—
195C2×Dic6—61no—
196C2×Dic6—61no—
197C2×Dic6D1211yescharacteristic, complemented
198C2×Dic6#6711yescharacteristic, complemented
199C3×SD16—122no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—41no—
203C3×C4⋊C4—31no—
204C3×C4⋊C4—31no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—61no—
209#217—21no—
210#217—21no—
211#217—122no—
212#215—122no—
213#214—122no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—61no—
222(C2×D3)⋊C4—121no—
223(C2×D3)⋊C4—121no—
224(C2×D3)⋊C4—122no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3D1211yescharacteristic, complemented
228C4⋊Dic3#6711yescharacteristic, complemented
229Dic3⋊C4—21no—
230Dic3⋊C4—21no—
231Dic3⋊C4—61no—
232Dic3⋊C4—61no—
233Dic3⋊C4—61no—
234Dic3⋊C4—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—121no—
238#204—42no—
239C22×C32—21no—
240C22×C32—21no—
241C22×C32#12011yescharacteristic
242C22×C32C2×SD1611yescharacteristic
243C22×C32#13711yescharacteristic
244C2×C3⋊D3—22no—
245C2×C3⋊D3—41no—
246C2×C3⋊D3—41no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3—81no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—81no—
253C2×C3×D3—81no—
254C2×C3×D3—81no—
255C2×C3×D3—81no—
256C32×C4—21no—
257C32×C4—21no—
258C3⋊Dic3—41no—
259C3×Dic3—42no—
260C3×Dic3—41no—
261C3×Dic3—41no—
262C3×Dic3—41no—
263C3×Dic3—41no—
264C22×D4—31no—
265C22×D4—181no—
266C2×SD16—61no—
267C2×SD16—181no—
268C22⋊Q8—31no—
269C22⋊Q8—31no—
270C22⋊Q8—181no—
271C22⋊Q8—181no—
272C22⋊Q8—181no—
273C22⋊Q8—181no—
274C22⋊Q8—181no—
275C2×C22⋊C4—91no—
276C2×C22⋊C4—181no—
277C2×C22⋊C4—181no—
278#102—61no—
279#102—181no—
280C22⋊C8—91no—
281C22⋊C8D3211yescharacteristic
282#95—31no—
283C23×C3—21no—
284C23×C3—62no—
285C23×C3—121no—
286C23×C3—121no—
287C23×C3—121no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3D3×D411yescharacteristic
292C23×C3D3×D411yescharacteristic
293C22×D3—22no—
294C22×D3—32no—
295C22×D3—32no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—62no—
303C22×D3—61no—
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—61no—
307C22×D3—121no—
308C22×D3—121no—
309C22×D3—121no—
310C22×D3—121no—
311C22×D3—121no—
312C22×D3—121no—
313C22×D3—241no—
314C22×D3—241no—
315C3×Q8—121no—
316C3×Q8—121no—
317C3×D4—62no—
318C3×D4—62no—
319C3×D4—121no—
320C3×D4—121no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—62no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—81no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337#67—128no—
338C2×Dic3—22no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—241no—
351D12—22no—
352D12—22no—
353D12—41no—
354D12—41no—
355D12—128no—
356C4×D3—241no—
357C4×D3—241no—
358C4×D3—241no—
359C4×D3—241no—
360Dic6—41no—
361Dic6—41no—
362Dic6—241no—
363Dic6—241no—
364C3×C8—41no—
365C3×C8—41no—
366C3×C8—81no—
367C3⋊C8—121no—
368C3⋊C8—121no—
369C3⋊C8—241no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32#44811yescharacteristic
373C2×C32#45311yescharacteristic
374C2×C32B(4,𝔽2)11yescharacteristic
375C3⋊D3—42no—
376C3×D3—82no—
377C24—61no—
378C24—91no—
379C2×Q8—31no—
380C2×Q8—31no—
381C2×Q8—181no—
382C2×D4—61no—
383C2×D4—61no—
384C2×D4—122no—
385C2×D4—362no—
386C2×D4—362no—
387C2×D4—362no—
388C22×C4—61no—
389C22×C4—91no—
390C22×C4—181no—
391C22×C4—181no—
392C22×C4C2×D3211yescharacteristic
393SD16—122no—
394SD16—362no—
395C2×C8—21no—
396C2×C8—181no—
397C4⋊C4—31no—
398C4⋊C4—31no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4—181no—
404C22⋊C4—61no—
405C22⋊C4—61no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4—181no—
409C22⋊C4—181no—
410C22⋊C4—362no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3—241no—
424C22×C3—241no—
425C22×C3—241no—
426C22×C3—241no—
427C22×C3#88211yescharacteristic
428C22×C3D3×SD1611yescharacteristic
429C22×C3D3×SD1611yescharacteristic
430C22×C3#91511yescharacteristic
431C22×C3#91811yescharacteristic
432C22×C3#93711yescharacteristic
433C2×D3—42no—
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—62no—
437C2×D3—62no—
438C2×D3—81no—
439C2×D3—81no—
440C2×D3—81no—
441C2×D3—81no—
442C2×D3—122no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—241no—
450C2×D3—241no—
451C2×D3—242no—
452C2×D3—241no—
453C2×D3—241no—
454C2×D3—242no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—122no—
462C3×C4—121no—
463C3×C4—121no—
464C3×C4—121no—
465C3×C4—121no—
466Dic3—42no—
467Dic3—41no—
468Dic3—41no—
469Dic3—41no—
470Dic3—41no—
471Dic3—121no—
472Dic3—121no—
473Dic3—241no—
474C32#159611yescharacteristic, complemented, Sylow
475C23—62no—
476C23—92no—
477C23—121no—
478C23—121no—
479C23—121no—
480C23—121no—
481C23—121no—
482C23—121no—
483C23—181no—
484C23—181no—
485C23—361no—
486C23—361no—
487C23#380211yescharacteristic
488Q8—121no—
489Q8—121no—
490Q8—721no—
491D4—62no—
492D4—62no—
493D4—121no—
494D4—121no—
495D4—368no—
496C2×C4—41no—
497C2×C4—62no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—181no—
505C2×C4—361no—
506C2×C4—721no—
507C2×C4—721no—
508C2×C4D3×D1211yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C8—41no—
511C8—361no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—41no—
520C2×C3—41no—
521C2×C3—242no—
522C2×C3#474111yescharacteristic
523C2×C3#480611yescharacteristic
524C2×C3#482211yescharacteristic
525C2×C3#503211yescharacteristic
526C2×C3#517011yescharacteristic
527C2×C3#519811yescharacteristic
528D3—82no—
529D3—122no—
530D3—122no—
531D3—242no—
532C22—21no—
533C22—21no—
534C22—122no—
535C22—122no—
536C22—122no—
537C22—182no—
538C22—241no—
539C22—241no—
540C22—241no—
541C22—241no—
542C22—362no—
543C22—361no—
544C22—361no—
545C22—721no—
546C22#6379611yescharacteristic
547C22#6381111yescharacteristic
548C22#6392211yescharacteristic
549C4—21no—
550C4—21no—
551C4—122no—
552C4—121no—
553C4—121no—
554C4—121no—
555C4—121no—
556C4—361no—
557C3—21no—
558C3#6831611yescharacteristic, complemented
559C3#7097611yescharacteristic, complemented
560C2—21no—
561C2—21no—
562C2—242no—
563C2—362no—
564C2#1059040711yescharacteristic
565C2#1059082411yescharacteristic
566C2#1059101311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10591391C2
hypercenterC22⋊C8D32
hypocenterC32#1596
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594981C2semidirect
2. C3×#4731C2semidirect
4. #10591169C2semidirect
5. #10589334C2semidirect
6. C3×#4467C2semidirect
7. #10589153C2semidirect
35. #4731D3semidirect
42. #4467D3semidirect
52. C2×C3×Dic6D4semidirect
53. C2×C3×Dic6D4semidirect
66. C3×C4⋊Dic3D4semidirect
67. C3×C4⋊Dic3D4semidirect
125. C22×C3⋊D3SD16semidirect
197. C2×Dic6D12semidirect
198. C2×Dic6#67semidirect
227. C4⋊Dic3D12semidirect
228. C4⋊Dic3#67semidirect
474. C32#1596semidirect
558. C3#68316semidirect
559. C3#70976semidirect

Maximal subgroups

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

subgroupindex
#105949812
C3×#47312
#105913912
#105911692
#105893342
C3×#44672
#105891532
#709763
#683163