Finite Group Databasebeta

← #11778081

Subgroups — #11778081

Order 1152.

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

normal subgroups only

This group has 583 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
2C3×#4731C211yesmaximal, characteristic, complemented
3#10591302C211yesmaximal, characteristic, complemented
4#10591160C211yesmaximal, characteristic
5#10589335C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7#10589153C211yesmaximal, characteristic, complemented
8#70978—31nomaximal
9#68292—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×#3750C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×#204—21no—
15#67⋊Dic3—21no—
16#63962—21no—
17C2×(C2×D3)⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19#63887—21no—
20#63884—21no—
21#63858—21no—
22#63846—21no—
23C2×#3713—21no—
24C32×C22⋊C8C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#821—21no—
28#63562—21no—
29#5645—31no—
30#5602—31no—
31C3×#450—31no—
32#5222—31no—
33#5217—31no—
34#5036—31no—
35#4731D311yescharacteristic, complemented
36#4672—31no—
37C3×#327—31no—
38#4538—31no—
39#4470D311yescharacteristic, complemented
40#4469—31no—
41#4469—31no—
42#4469—61no—
43#4452—31no—
44C23×C3×D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—42no—
53C2×C3×D12D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×D3×Dic3—21no—
56C2×C32×C8—21no—
57#3750—21no—
58#3750—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×#204—42no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—42no—
73(C2×D3)⋊Dic3—42no—
74Dic32—21no—
75#3713—42no—
76#1597—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C2×C3×SD16—61no—
80C3×C22⋊Q8—31no—
81C3×#121—31no—
82C2×#217—61no—
83C2×#217—61no—
84#946—61no—
85#935—61no—
86#935—61no—
87D4×Dic3—61no—
88C2×#213—61no—
89C2×#213—61no—
90#930C2×D311yescharacteristic
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93#924C2×D311yescharacteristic
94C2×Dic3⋊C4—31no—
95C2×Dic3⋊C4—31no—
96C2×Dic3⋊C4—61no—
97C2×#204—21no—
98#898—61no—
99#894—61no—
100#890—61no—
101#889—61no—
102#886—61no—
103#67⋊C4—61no—
104#879—61no—
105#878—61no—
106C3×#102—61no—
107C3×C22⋊C8—21no—
108C3×C22⋊C8C2×D311yescharacteristic
109C3×C22⋊C8C2×D311yescharacteristic
110C3×#95—31no—
111#832—61no—
112C3⋊#95C2×D311yescharacteristic
113#830—31no—
114#830—31no—
115#830—61no—
116#821—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—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—41no—
135C3×#67—41no—
136C3×#67—41no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C3×D12—22no—
144C3×D12—22no—
145C3×D12—41no—
146C3×D12—41no—
147C3×D12—41no—
148C3×Dic6—41no—
149D3×Dic3—81no—
150C32×C8—41no—
151C3⋊(C3⋊C8)—41no—
152#539—91no—
153#450—31no—
154#447—91no—
155#394—91no—
156#328—91no—
157#327—31no—
158#324—91no—
159C24×C3—61no—
160C23×D3—21no—
161C2×C3×Q8—31no—
162C2×C3×D4—31no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—122no—
167C22×C3×C4—21no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C2×#67—21no—
172C22×Dic3—21no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—42no—
183C2×D12D1211yescharacteristic
184C2×C4×D3—61no—
185C2×Dic6#6711yescharacteristic
186C3×SD16—122no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—41no—
190C3×C4⋊C4—31no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195#217—21no—
196#217—61no—
197#217—61no—
198#217—61no—
199#217—122no—
200#217—122no—
201#213—122no—
202#213—122no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—122no—
208(C2×D3)⋊C4—122no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3D1211yescharacteristic
213C4⋊Dic3#6711yescharacteristic
214Dic3⋊C4—21no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—121no—
223Dic3⋊C4—121no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229#204—42no—
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—
247C3⋊Dic3—41no—
248C3⋊Dic3—41no—
249C3×Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—81no—
253C22×D4—31no—
254C2×SD16—61no—
255C2×D8—181no—
256#126—181no—
257#125—181no—
258#123—181no—
259#123—181no—
260C22⋊Q8—31no—
261C22⋊Q8—181no—
262#121—31no—
263C4×D4—181no—
264C2×C4⋊C4—91no—
265C2×C22⋊C4—181no—
266C2×C22⋊C4—181no—
267#102—61no—
268#102—181no—
269C22⋊C8—91no—
270C22⋊C8D3211yescharacteristic
271#95—31no—
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×C3D3×D411yescharacteristic
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—121no—
292C3×D4—62no—
293C3×D4—62no—
294C3×D4—121no—
295C3×D4—121no—
296C3×D4—121no—
297C3×D4—121no—
298C3×D4—121no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—81no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4C2×D1211yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314#67—41no—
315#67—41no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—21no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—62no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—241no—
337C2×Dic3—241no—
338D12—22no—
339D12—22no—
340D12—41no—
341D12—41no—
342D12—41no—
343C4×D3—241no—
344Dic6—41no—
345C3×C8—41no—
346C3×C8—41no—
347C3×C8—81no—
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—31no—
360C2×D4—31no—
361C2×D4—61no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—122no—
365C22×C4—61no—
366C22×C4—91no—
367C22×C4—91no—
368C22×C4—181no—
369C22×C4C2×D3211yescharacteristic
370SD16—122no—
371D8—362no—
372C2×C8—21no—
373C2×C8—181no—
374C4⋊C4—31no—
375C4⋊C4—31no—
376C4⋊C4—61no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C22⋊C4—61no—
383C22⋊C4—61no—
384C22⋊C4—181no—
385C22⋊C4—181no—
386C22⋊C4—181no—
387C22⋊C4—362no—
388C22⋊C4—362no—
389C42—181no—
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#88211yescharacteristic
410C22×C3#91111yescharacteristic
411C22×C3#91411yescharacteristic
412C22×C3#91611yescharacteristic
413C22×C3#91611yescharacteristic
414C22×C3#93711yescharacteristic
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—41no—
418C2×D3—42no—
419C2×D3—41no—
420C2×D3—41no—
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—121no—
432C3×C4—121no—
433C3×C4—121no—
434C3×C4—241no—
435Dic3—41no—
436Dic3—41no—
437Dic3—41no—
438Dic3—81no—
439Dic3—122no—
440Dic3—121no—
441Dic3—121no—
442Dic3—121no—
443Dic3—121no—
444Dic3—241no—
445C32#159711yescharacteristic, complemented, Sylow
446C23—62no—
447C23—61no—
448C23—121no—
449C23—121no—
450C23—121no—
451C23—121no—
452C23—121no—
453C23—121no—
454C23#380211yescharacteristic
455Q8—121no—
456D4—62no—
457D4—62no—
458D4—121no—
459D4—121no—
460D4—121no—
461D4—121no—
462D4—121no—
463C2×C4—41no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—121no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—361no—
475C2×C4—721no—
476C2×C4D3×D1211yescharacteristic
477C2×C4D3×#6711yescharacteristic
478C8—41no—
479C8—361no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—241no—
490C2×C3—242no—
491C2×C3#474111yescharacteristic
492C2×C3#478111yescharacteristic
493C2×C3#482711yescharacteristic
494C2×C3#503211yescharacteristic
495C2×C3#517211yescharacteristic
496C2×C3#520111yescharacteristic
497D3—82no—
498D3—81no—
499C22—21no—
500C22—21no—
501C22—122no—
502C22—122no—
503C22—121no—
504C22—121no—
505C22—122no—
506C22—121no—
507C22—241no—
508C22—241no—
509C22—241no—
510C22—241no—
511C22#6379811yescharacteristic
512C22#6380911yescharacteristic
513C22#6392211yescharacteristic
514C4—21no—
515C4—21no—
516C4—121no—
517C4—121no—
518C4—121no—
519C4—241no—
520C4—361no—
521C4—361no—
522C3—21no—
523C3#6829211yescharacteristic, complemented
524C3#7097811yescharacteristic, complemented
525C2—21no—
526C2—21no—
527C2—242no—
528C2—241no—
529C2#1059040711yescharacteristic
530C2#1059096411yescharacteristic
531C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10591160C2
hypercenterC22⋊C8D32
hypocenterC32#1597
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. #10594974C2semidirect
2. C3×#4731C2semidirect
3. #10591302C2semidirect
5. #10589335C2semidirect
6. C3×#4470C2semidirect
7. #10589153C2semidirect
35. #4731D3semidirect
39. #4470D3semidirect
445. C32#1597semidirect
523. C3#68292semidirect
524. C3#70978semidirect

Maximal subgroups

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

subgroupindex
#105949742
C3×#47312
#105913022
#105911602
#105893352
C3×#44702
#105891532
#709783
#682923