Finite Group Databasebeta

← #11778063

Subgroups — #11778063

Order 1152.

663 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 663 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594974C211yesmaximal, characteristic, complemented
2#10592921C211yesmaximal, characteristic, complemented
3C3×#5218C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic
5#10589152C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589148C211yesmaximal, characteristic, complemented
8#70978—31nomaximal
9#70970—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3757—21no—
12C2×#3757—21no—
13C2×#3750C2211yescharacteristic
14C2×C3×#214—21no—
15C2×C3×#213—21no—
16C3×#930C2211yescharacteristic
17C3×#924C2211yescharacteristic
18#67⋊Dic3—21no—
19#63962—21no—
20#63887—21no—
21#63884—21no—
22#63858—21no—
23#63846—21no—
24#63658C2211yescharacteristic
25C3×#832—21no—
26C3×#832—21no—
27C3×#830C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5645—31no—
30#5602—31no—
31C3×#450—31no—
32C3×#447—31no—
33#5222—31no—
34#5222—31no—
35#5222—61no—
36#5218D311yescharacteristic, complemented
37#5217D311yescharacteristic
38#4538—31no—
39#4537—31no—
40#4470—31no—
41#4469—31no—
42#4469—31no—
43#4467—31no—
44C24×C32—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—42no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C2×C3×#67—21no—
53C2×C3×D12D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×D3×Dic3—21no—
56#3757—42no—
57#3757—42no—
58#3750—21no—
59#3750—21no—
60C3×#217—21no—
61C3×#214—42no—
62C3×#213—42no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71Dic3⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74(C2×D3)⋊Dic3—21no—
75Dic32—21no—
76#1597—91noSylow
77C22×C3×D4—21no—
78C22×C3×D4C2×D311yescharacteristic
79C22×C3×D4C2×D311yescharacteristic
80C2×C3×SD16—61no—
81C2×C3×D8—61no—
82C3×C22⋊Q8—31no—
83C3×#121—31no—
84C2×#217—61no—
85C2×#217—61no—
86C2×#217—61no—
87C2×#217—61no—
88C2×#217—62no—
89C2×#217—62no—
90#946—61no—
91#935—61no—
92#935—61no—
93D4×Dic3—61no—
94C2×#214—21no—
95C2×#213—21no—
96#930C2×D311yescharacteristic
97#924C2×D311yescharacteristic
98C2×Dic3⋊C4—31no—
99C2×Dic3⋊C4—31no—
100C2×Dic3⋊C4—61no—
101#898—61no—
102#894—61no—
103#890—61no—
104#889—61no—
105#886—61no—
106#67⋊C4—61no—
107#879—61no—
108#878—61no—
109C3×#102—61no—
110C3×#102—61no—
111C3×C22⋊C8—31no—
112C3×C22⋊C8—31no—
113#832—21no—
114#832—21no—
115C3⋊#95—31no—
116C3⋊#95—31no—
117C3⋊#95—61no—
118#830C2×D311yescharacteristic
119#830C2×D311yescharacteristic
120C23×C32—22no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—21no—
129C32×D4—22no—
130C32×D4—22no—
131C32×D4—41no—
132C32×D4—41no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C3×#67—41no—
145C3×#67—41no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C3×D12—41no—
150C3×Dic6—41no—
151D3×Dic3—81no—
152C3×C3⋊C8—41no—
153C3×C3⋊C8—41no—
154#539—91no—
155#450—31no—
156#447—31no—
157#394—91no—
158#328—91no—
159#327—91no—
160#324—91no—
161C24×C3—22no—
162C24×C3—21no—
163C24×C3—21no—
164C2×C3×Q8—31no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—31no—
170C2×C3×D4—41no—
171C2×C3×D4—41no—
172C2×C3×D4—42no—
173C2×C3×D4—42no—
174C2×C3×D4—44no—
175C2×C3×D4—61no—
176C22×C3×C4—21no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C2×#67—21no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—62no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C2×D12#6711yescharacteristic
191C2×C4×D3—61no—
192C2×Dic6#6711yescharacteristic
193C3×SD16—122no—
194C3×D8—122no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—31no—
199C3×C4⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202#217—21no—
203#217—61no—
204#217—61no—
205#217—61no—
206#217—124no—
207#217—122no—
208#217—122no—
209#217—122no—
210#217—122no—
211#217—124no—
212#214—42no—
213#213—42no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3#6711yescharacteristic
222C4⋊Dic3#6711yescharacteristic
223Dic3⋊C4—21no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229Dic3⋊C4—61no—
230Dic3⋊C4—61no—
231Dic3⋊C4—121no—
232Dic3⋊C4—121no—
233C4×Dic3—61no—
234C4×Dic3—61no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C22×C32—21no—
238C22×C32—21no—
239C22×C32—42no—
240C22×C32—42no—
241C22×C32—42no—
242C22×C32—81no—
243C22×C32—81no—
244C22×C32—81no—
245C22×C32—81no—
246C22×C32#12011yescharacteristic
247C22×C32#13511yescharacteristic
248C22×C32AGL(1,ℤ/8)11yescharacteristic
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C32×C4—21no—
253C32×C4—21no—
254C3⋊Dic3—41no—
255C3⋊Dic3—41no—
256C3⋊Dic3—81no—
257C3×Dic3—41no—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C22×D4D3211yescharacteristic
261C2×SD16—61no—
262C2×D8—61no—
263#126—181no—
264#125—181no—
265#123—181no—
266#123—181no—
267C22⋊Q8—31no—
268C22⋊Q8—181no—
269#121—31no—
270C4×D4—181no—
271C2×C4⋊C4—91no—
272C2×C22⋊C4—181no—
273C2×C22⋊C4—181no—
274#102—61no—
275#102—61no—
276C22⋊C8—31no—
277C22⋊C8—31no—
278#95—91no—
279C23×C3—24no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—21no—
283C23×C3—42no—
284C23×C3—42no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—42no—
288C23×C3—42no—
289C23×C3—42no—
290C23×C3—41no—
291C23×C3—41no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—42no—
295C23×C3—41no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—61no—
302C23×C3D3×D411yescharacteristic
303C23×C3D3×D411yescharacteristic
304C22×D3—21no—
305C3×Q8—121no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—42no—
311C3×D4—42no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—41no—
315C3×D4—41no—
316C3×D4—42no—
317C3×D4—42no—
318C3×D4—121no—
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—42no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333#67—41no—
334#67—41no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—62no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—122no—
357C2×Dic3—122no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—241no—
363D12—41no—
364C4×D3—241no—
365Dic6—41no—
366C3×C8—121no—
367C3×C8—121no—
368C3⋊C8—41no—
369C3⋊C8—41no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32—82no—
373C2×C32#44911yescharacteristic
374C2×C32#45411yescharacteristic
375C2×C32B(4,𝔽2)11yescharacteristic
376C3×D3—81no—
377C24—21no—
378C2×Q8—31no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—31no—
382C2×D4—42no—
383C2×D4—61no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—181no—
387C22×C4—181no—
388C22×C4C2×D3211yescharacteristic
389SD16—122no—
390D8—122no—
391C2×C8—61no—
392C2×C8—61no—
393C4⋊C4—31no—
394C4⋊C4—31no—
395C4⋊C4—61no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C22⋊C4—61no—
402C22⋊C4—61no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C22⋊C4—181no—
406C22⋊C4—362no—
407C22⋊C4—362no—
408C42—181no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—44no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—82no—
428C22×C3—82no—
429C22×C3—81no—
430C22×C3—81no—
431C22×C3—81no—
432C22×C3—81no—
433C22×C3—82no—
434C22×C3—82no—
435C22×C3—81no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3—81no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3#91111yescharacteristic
443C22×C3#91211yescharacteristic
444C22×C3#91411yescharacteristic
445C22×C3#91611yescharacteristic
446C22×C3#93711yescharacteristic
447C22×C3#93711yescharacteristic
448C2×D3—41no—
449C2×D3—41no—
450C2×D3—41no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—121no—
458C3×C4—121no—
459C3×C4—121no—
460Dic3—41no—
461Dic3—41no—
462Dic3—41no—
463Dic3—122no—
464Dic3—121no—
465Dic3—121no—
466Dic3—121no—
467Dic3—121no—
468Dic3—241no—
469Dic3—242no—
470Dic3—241no—
471Dic3—241no—
472C32#159711yescharacteristic, complemented, Sylow
473C23—22no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—61no—
481C23#381111yescharacteristic
482Q8—121no—
483D4—22no—
484D4—22no—
485D4—41no—
486D4—41no—
487D4—121no—
488D4—121no—
489D4—121no—
490C2×C4—41no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—361no—
499C2×C4—361no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4—721no—
503C2×C4D3×#6711yescharacteristic
504C2×C4D3×#6711yescharacteristic
505C8—121no—
506C8—121no—
507C2×C3—22no—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—84no—
517C2×C3—82no—
518C2×C3—82no—
519C2×C3—241no—
520C2×C3#503211yescharacteristic
521C2×C3#503211yescharacteristic
522C2×C3#515811yescharacteristic
523C2×C3#517211yescharacteristic
524C2×C3#520111yescharacteristic
525C2×C3#520111yescharacteristic
526D3—81no—
527C22—21no—
528C22—21no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—121no—
537C22—121no—
538C22—121no—
539C22#6393611yescharacteristic
540C22#6393711yescharacteristic
541C22#6398311yescharacteristic
542C4—21no—
543C4—21no—
544C4—121no—
545C4—121no—
546C4—121no—
547C4—361no—
548C4—361no—
549C4—721no—
550C3—21no—
551C3#7097011yescharacteristic, complemented
552C3#7097811yescharacteristic, complemented
553C2—21no—
554C2—21no—
555C2—82no—
556C2—241no—
557C2#1059152011yescharacteristic
558C2#1059152411yescharacteristic
559C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC3×#5217C2
hypercenterC22×D4D32
hypocenterC32#1597
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. #10594974C2semidirect
2. #10592921C2semidirect
3. C3×#5218C2semidirect
5. #10589152C2semidirect
6. #10589150C2semidirect
7. #10589148C2semidirect
36. #5218D3semidirect
472. C32#1597semidirect
551. C3#70970semidirect
552. C3#70978semidirect

Maximal subgroups

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

subgroupindex
#105949742
#105929212
C3×#52182
C3×#52172
#105891522
#105891502
#105891482
#709783
#709703