Finite Group Databasebeta

← #11778079

Subgroups — #11778079

Order 1152.

584 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#5645C211yesmaximal, characteristic, complemented
2C3×#5046C211yesmaximal, characteristic, complemented
3#10591300C211yesmaximal, characteristic, complemented
4#10591160C211yesmaximal, characteristic
5#10589404C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71888—31nomaximal
9#70978—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12C3×#946—21no—
13C2×C3×#215—21no—
14C3×#930C2211yescharacteristic
15C2×C3×Dic3⋊C4C2211yescharacteristic
16C3×#898—21no—
17C3×#894—21no—
18C3×#890—21no—
19C3×#886—21no—
20C3×#67⋊C4—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×#3713—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#809—21no—
28#63562—21no—
29C3×#539—31no—
30#5645D311yescharacteristic, complemented
31C3×#450—31no—
32#5222—31no—
33#5217—31no—
34#5046D311yescharacteristic, complemented
35#5036—31no—
36#4991—31no—
37#4538—31no—
38#4538—31no—
39#4538—61no—
40#4537—31no—
41#4528—31no—
42#4470—31no—
43#4469—31no—
44C23×C3×D3—21no—
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—42no—
54C2×C3×D12D411yescharacteristic
55C2×C3×C4×D3—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#215—42no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3D411yescharacteristic
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—42no—
74(C2×D3)⋊Dic3—42no—
75#3713—42no—
76#1597—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C2×C3×SD16—61no—
80C3×#126—61no—
81C3×#125—61no—
82C3×#123—61no—
83C3×#123—61no—
84C3×C22⋊Q8—21no—
85C3×C22⋊Q8—61no—
86C3×C22⋊Q8C2×D311yescharacteristic
87C3×C22⋊Q8C2×D311yescharacteristic
88C3×#121—31no—
89C3×C4×D4—61no—
90C2×C3×C4⋊C4—31no—
91C2×#217—61no—
92C2×#217—61no—
93#946—21no—
94C2×#215—21no—
95C2×#213—61no—
96C2×#213—61no—
97#930C2×D311yescharacteristic
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×Dic3⋊C4C2×D311yescharacteristic
101#898—21no—
102#894—21no—
103#890—21no—
104#886—21no—
105#67⋊C4—21no—
106C3×#102—61no—
107C3×C22⋊C8—31no—
108#832—61no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—61no—
112#830—31no—
113#830—31no—
114#830—61no—
115#830C2×D311yescharacteristic
116#809—21no—
117#809—61no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—22no—
120C22×C3×D3—21no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C32×Q8—41no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C3×#67—41no—
137C3×#67—41no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C3×D12—22no—
145C3×D12—22no—
146C3×D12—41no—
147C3×D12—41no—
148C3×D12—41no—
149C3×C4×D3—81no—
150C3⋊(C3⋊C8)—41no—
151C3×C3⋊C8—41no—
152#539—31no—
153#450—31no—
154#447—91no—
155#394—91no—
156#328—91no—
157#327—91no—
158#324—91no—
159C24×C3—61no—
160C23×D3—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8#6711yescharacteristic
163C2×C3×Q8#6711yescharacteristic
164C2×C3×D4—31no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—122no—
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—21no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—121no—
179C22×Dic3#6711yescharacteristic
180C22×Dic3#6711yescharacteristic
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—42no—
184C2×D12#6711yescharacteristic
185C2×C4×D3—21no—
186C3×SD16—122no—
187C2×C3×C8—61no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—41no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4#6711yescharacteristic
199C3×C4⋊C4#6711yescharacteristic
200C3×C22⋊C4—21no—
201C3×C22⋊C4—21no—
202C3×C22⋊C4—41no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C42—61no—
208#217—122no—
209#217—122no—
210#215—42no—
211#213—122no—
212#213—122no—
213(C2×D3)⋊C4—21no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—122no—
218(C2×D3)⋊C4—122no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3#6711yescharacteristic
222Dic3⋊C4—21no—
223Dic3⋊C4—21no—
224Dic3⋊C4—21no—
225C4×Dic3—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—121no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32#12011yescharacteristic
233C22×C32#13511yescharacteristic
234C22×C32AGL(1,ℤ/8)11yescharacteristic
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C2×C3×D3—41no—
240C2×C3×D3—42no—
241C2×C3×D3—81no—
242C2×C3×D3—81no—
243C2×C3×D3—81no—
244C2×C3×D3—81no—
245C32×C4—21no—
246C32×C4—21no—
247C32×C4—41no—
248C32×C4—41no—
249C3⋊Dic3—81no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C22×D4—31no—
254C2×SD16—61no—
255C2×D8—181no—
256#126—61no—
257#125—61no—
258#123—61no—
259#123—61no—
260C22⋊Q8—61no—
261C22⋊Q8D3211yescharacteristic
262#121—31no—
263C4×D4—61no—
264C2×C4⋊C4—31no—
265C2×C22⋊C4—181no—
266C2×C22⋊C4—181no—
267#102—61no—
268#102—181no—
269C22⋊C8—31no—
270C22⋊C8—91no—
271#95—91no—
272C23×C3—21no—
273C23×C3—62no—
274C23×C3—61no—
275C23×C3—121no—
276C23×C3—121no—
277C23×C3—121no—
278C23×C3—121no—
279C23×C3—121no—
280C23×C3—121no—
281C23×C3D3×D411yescharacteristic
282C23×C3C2×#6711yescharacteristic
283C22×D3—22no—
284C22×D3—21no—
285C22×D3—41no—
286C22×D3—41no—
287C22×D3—41no—
288C22×D3—41no—
289C22×D3—41no—
290C22×D3—41no—
291C3×Q8—41no—
292C3×Q8—41no—
293C3×Q8—81no—
294C3×D4—62no—
295C3×D4—62no—
296C3×D4—121no—
297C3×D4—121no—
298C3×D4—121no—
299C3×D4—121no—
300C3×D4—121no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—81no—
317C2×C3×C4—121no—
318C2×C3×C4—241no—
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323#67—41no—
324#67—41no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—41no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—122no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—241no—
339C2×Dic3—241no—
340D12—22no—
341D12—22no—
342D12—41no—
343D12—41no—
344D12—41no—
345C4×D3—81no—
346C3×C8—121no—
347C3⋊C8—41no—
348C3⋊C8—121no—
349C3⋊C8—121no—
350C3⋊C8—241no—
351C2×C32—21no—
352C2×C32—21no—
353C2×C32#44911yescharacteristic
354C2×C32#45411yescharacteristic
355C2×C32B(4,𝔽2)11yescharacteristic
356C3×D3—81no—
357C3×D3—82no—
358C24—61no—
359C2×Q8#62511yescharacteristic
360C2×D4—31no—
361C2×D4—61no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—122no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—61no—
368C22×C4—181no—
369C22×C4C2×D3211yescharacteristic
370SD16—122no—
371D8—362no—
372C2×C8—61no—
373C2×C8—181no—
374C4⋊C4—21no—
375C4⋊C4—31no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4#62511yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—362no—
388C22⋊C4—362no—
389C42—61no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—122no—
400C22×C3—122no—
401C22×C3—121no—
402C22×C3—121no—
403C22×C3—122no—
404C22×C3—121no—
405C22×C3—241no—
406C22×C3—241no—
407C22×C3—241no—
408C22×C3—241no—
409C22×C3#91411yescharacteristic
410C22×C3#91611yescharacteristic
411C22×C3#93711yescharacteristic
412C22×C3#94911yescharacteristic
413C22×C3#95011yescharacteristic
414C22×C3#95311yescharacteristic
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—41no—
418C2×D3—41no—
419C2×D3—41no—
420C2×D3—42no—
421C2×D3—81no—
422C2×D3—81no—
423C2×D3—81no—
424C2×D3—81no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—41no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—81no—
436C3×C4—81no—
437C3×C4—121no—
438C3×C4—121no—
439C3×C4—121no—
440Dic3—41no—
441Dic3—41no—
442Dic3—41no—
443Dic3—241no—
444Dic3—241no—
445Dic3—242no—
446C32#159711yescharacteristic, complemented, Sylow
447C23—62no—
448C23—61no—
449C23—121no—
450C23—121no—
451C23—121no—
452C23—121no—
453C23—121no—
454C23—121no—
455C23D3×#6711yescharacteristic
456Q8—41no—
457D4—62no—
458D4—62no—
459D4—121no—
460D4—121no—
461D4—121no—
462D4—121no—
463D4—121no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—121no—
473C2×C4—241no—
474C2×C4—361no—
475C2×C4—361no—
476C2×C4—361no—
477C2×C4C2×#62511yescharacteristic
478C2×C4D3×#6711yescharacteristic
479C8—121no—
480C8—361no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—241no—
491C2×C3—242no—
492C2×C3#503211yescharacteristic
493C2×C3#517211yescharacteristic
494C2×C3#520111yescharacteristic
495C2×C3#523811yescharacteristic
496C2×C3#524411yescharacteristic
497C2×C3#524511yescharacteristic
498D3—82no—
499D3—81no—
500C22—21no—
501C22—21no—
502C22—122no—
503C22—122no—
504C22—121no—
505C22—122no—
506C22—121no—
507C22—121no—
508C22—241no—
509C22—241no—
510C22—241no—
511C22—241no—
512C22#6393911yescharacteristic
513C22#6394711yescharacteristic
514C22#6397611yescharacteristic
515C4—21no—
516C4—21no—
517C4—41no—
518C4—41no—
519C4—121no—
520C4—121no—
521C4—121no—
522C4—721no—
523C3—21no—
524C3#7097811yescharacteristic, complemented
525C3#7188811yescharacteristic, complemented
526C2—21no—
527C2—21no—
528C2—242no—
529C2—241no—
530C2#1059153011yescharacteristic
531C2#1059158611yescharacteristic
532C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radical#10591160C2
hypercenterC22⋊Q8D32
hypocenterC32#1597
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5645C2semidirect
2. C3×#5046C2semidirect
3. #10591300C2semidirect
5. #10589404C2semidirect
6. #10589150C2semidirect
7. #10589147C2semidirect
30. #5645D3semidirect
34. #5046D3semidirect
446. C32#1597semidirect
524. C3#70978semidirect
525. C3#71888semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
C3×#50462
#105913002
#105911602
#105894042
#105891502
#105891472
#718883
#709783