Finite Group Databasebeta

← #11778403

Subgroups — #11778403

Order 1152.

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

normal subgroups only

This group has 594 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#10594977C211yesmaximal, characteristic
2#10592927C211yesmaximal, characteristic, complemented
3C3×#5231C211yesmaximal, characteristic, complemented
4C3×#5227C211yesmaximal, characteristic, complemented
5#10589154C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#70973—31nomaximal
9#69700—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3756—21no—
12#64133C2211yescharacteristic
13C2×C3×#215—21no—
14C3×#930C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4C2211yescharacteristic
17#63976—21no—
18Dic3×#67—21no—
19#63913—21no—
20#63891—21no—
21#63885—21no—
22#63858—21no—
23#63662—21no—
24#63657C2211yescharacteristic
25C3×#835—21no—
26C3×C3⋊#95—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5617—31no—
30#5494—31no—
31C3×#448—31no—
32C3×#393—31no—
33#5231D311yescharacteristic, complemented
34#5228—31no—
35#5228—31no—
36#5228—61no—
37#5227D311yescharacteristic, complemented
38#4537—31no—
39#4525—31no—
40#4468—31no—
41#4467—31no—
42#4452—31no—
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—42no—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×#634D411yescharacteristic
51C2×C3×#67—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C2×C3×D12D411yescharacteristic
55C2×#625—21no—
56C2×#625—21no—
57C2×D3×Dic3—21no—
58#3757—21no—
59#3756—42no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61#3750—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C3×#215—42no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—42no—
68C3×C4⋊Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70Dic3⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74Dic32—21no—
75#1606—91noSylow
76C22×C3×Q8—21no—
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×Q8C2×D311yescharacteristic
79C2×C3×SD16—61no—
80C3×#121—31no—
81C2×C3×C22⋊C4—31no—
82C2×C3×C22⋊C4—61no—
83#953—61no—
84C2×#216—61no—
85C2×#216—61no—
86C2×#216—62no—
87C2×#215—21no—
88#939—61no—
89#937—61no—
90D4×Dic3—61no—
91#930C2×D311yescharacteristic
92C4×#67—61no—
93C2×(C2×D3)⋊C4—21no—
94C2×(C2×D3)⋊C4C2×D311yescharacteristic
95#924—31no—
96#924—31no—
97#924—61no—
98#898—61no—
99#886—61no—
100#885—61no—
101#885—61no—
102#884—61no—
103#883—61no—
104#879—61no—
105C3×#103—61no—
106C3×C22⋊C8—31no—
107C3×#95—31no—
108C3×#95—61no—
109#835—21no—
110#835—61no—
111#835—61no—
112#835—62no—
113C3⋊#95—21no—
114C3⋊#95C2×D311yescharacteristic
115#830—31no—
116#830—31no—
117#830—61no—
118#830C2×D311yescharacteristic
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C32×Q8—22no—
127C32×Q8—22no—
128C32×Q8—41no—
129C32×Q8—41no—
130C2×C32×C4—22no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138#634—41no—
139C3×#67—41no—
140C3×#67—41no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×D12—41no—
148#625—81no—
149#625—81no—
150D3×Dic3—81no—
151C3⋊(C3⋊C8)—41no—
152C3×C3⋊C8—41no—
153#538—91no—
154#451—91no—
155#448—31no—
156#393—31no—
157#328—91no—
158#327—91no—
159#323—91no—
160C24×C3—31no—
161C23×D3#6711yescharacteristic
162C2×C3×Q8—22no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—41no—
168C2×C3×Q8—42no—
169C2×C3×Q8—42no—
170C2×C3×Q8—44no—
171C2×C3×D4—31no—
172C2×C3×D4—61no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—41no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—21no—
182C2×#67—61no—
183C2×#67—61no—
184C2×#67—61no—
185C2×#67—61no—
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3#6711yescharacteristic
189C2×D12#6711yescharacteristic
190C2×C4×D3—61no—
191C2×Dic6—31no—
192C2×Dic6—31no—
193C2×Dic6—61no—
194C3×SD16—122no—
195C2×C3×C8—61no—
196C3×C4⋊C4—31no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—122no—
201#217—61no—
202#217—61no—
203#217—61no—
204#217—61no—
205#217—61no—
206#217—121no—
207#216—122no—
208#216—122no—
209#216—124no—
210#215—42no—
211(C2×D3)⋊C4—21no—
212(C2×D3)⋊C4—21no—
213(C2×D3)⋊C4—21no—
214(C2×D3)⋊C4—42no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218C4⋊Dic3—31no—
219C4⋊Dic3—31no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3#6711yescharacteristic
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—121no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32#12011yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32#13711yescharacteristic
238C2×C3×D3—42no—
239C2×C3×D3—41no—
240C2×C3×D3—41no—
241C2×C3×D3—41no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—81no—
246C32×C4—21no—
247C32×C4—21no—
248C32×C4—42no—
249C3⋊Dic3—41no—
250C3⋊Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—81no—
254C22×Q8D3211yescharacteristic
255C2×Q16—181no—
256C2×SD16—61no—
257#126—181no—
258#124—181no—
259#123—181no—
260C22⋊Q8—91no—
261#121—31no—
262#121—181no—
263#120—181no—
264C4×D4—181no—
265C2×C22⋊C4—31no—
266C2×C22⋊C4—61no—
267#103—61no—
268#103—181no—
269C22⋊C8—31no—
270C22⋊C8—91no—
271#95—31no—
272#95—61no—
273C23×C3—21no—
274C23×C3—61no—
275C23×C3—61no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—121no—
279C23×C3—121no—
280C23×C3D3×D411yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3—21no—
286C22×D3—41no—
287C22×D3—41no—
288C3×Q8—22no—
289C3×Q8—24no—
290C3×Q8—22no—
291C3×Q8—22no—
292C3×Q8—22no—
293C3×Q8—42no—
294C3×Q8—42no—
295C3×Q8—41no—
296C3×Q8—41no—
297C3×Q8—41no—
298C3×Q8—41no—
299C3×Q8—42no—
300C3×D4—121no—
301C3×D4—121no—
302C3×D4—121no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—42no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—42no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—42no—
314C2×C3×C4—42no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327#67—41no—
328#67—41no—
329#67—241no—
330#67—241no—
331#67—241no—
332#67—241no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—241no—
346D12—41no—
347C4×D3—241no—
348Dic6—121no—
349Dic6—121no—
350Dic6—122no—
351C3×C8—121no—
352C3⋊C8—41no—
353C3⋊C8—122no—
354C3⋊C8—121no—
355C3⋊C8—121no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32#45211yescharacteristic
359C2×C32#45511yescharacteristic
360C2×C32B(4,𝔽2)11yescharacteristic
361C3×D3—81no—
362C3×D3—81no—
363C24—31no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—42no—
367C2×Q8—91no—
368C2×D4—31no—
369C2×D4—61no—
370C2×D4—181no—
371C2×D4—181no—
372C22×C4—21no—
373C22×C4—31no—
374C22×C4—61no—
375C22×C4—181no—
376C22×C4C2×D3211yescharacteristic
377Q16—362no—
378SD16—122no—
379C2×C8—61no—
380C2×C8—181no—
381C4⋊C4—31no—
382C4⋊C4—91no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—122no—
389C22⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C22⋊C4—181no—
393C42—181no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—122no—
404C22×C3—121no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—121no—
410C22×C3—241no—
411C22×C3#91511yescharacteristic
412C22×C3#91611yescharacteristic
413C22×C3#93711yescharacteristic
414C22×C3#93711yescharacteristic
415C22×C3#94211yescharacteristic
416C22×C3#95011yescharacteristic
417C2×D3—42no—
418C2×D3—41no—
419C2×D3—41no—
420C2×D3—41no—
421C2×D3—41no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—81no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—41no—
431C3×C4—44no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—121no—
435C3×C4—121no—
436C3×C4—241no—
437Dic3—41no—
438Dic3—41no—
439Dic3—81no—
440Dic3—121no—
441Dic3—121no—
442Dic3—121no—
443Dic3—121no—
444Dic3—241no—
445Dic3—241no—
446C32#160611yescharacteristic, complemented, Sylow
447C23—61no—
448C23—61no—
449C23—61no—
450C23—61no—
451C23—121no—
452C23—121no—
453C23D3×#6711yescharacteristic
454Q8—22no—
455Q8—22no—
456Q8—41no—
457Q8—41no—
458Q8—361no—
459D4—121no—
460D4—121no—
461D4—121no—
462D4—721no—
463D4—721no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—721no—
477C2×C4D3×#6711yescharacteristic
478C2×C4#381111yescharacteristic
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—241no—
492C2×C3#503211yescharacteristic
493C2×C3#503211yescharacteristic
494C2×C3#504711yescharacteristic
495C2×C3#506111yescharacteristic
496C2×C3#517311yescharacteristic
497C2×C3#520211yescharacteristic
498D3—81no—
499D3—81no—
500C22—21no—
501C22—21no—
502C22—122no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22—121no—
509C22—241no—
510C22#6394611yescharacteristic
511C22#6394711yescharacteristic
512C22#6398311yescharacteristic
513C4—21no—
514C4—21no—
515C4—42no—
516C4—121no—
517C4—121no—
518C4—241no—
519C4—361no—
520C4—361no—
521C3—21no—
522C3#6970011yescharacteristic, complemented
523C3#7097311yescharacteristic, complemented
524C2—21no—
525C2—21no—
526C2—241no—
527C2—241no—
528C2#1059165511yescharacteristic
529C2#1059165911yescharacteristic
530C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radical#10594977C2
hypercenterC22×Q8D32
hypocenterC32#1606
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
2. #10592927C2semidirect
3. C3×#5231C2semidirect
4. C3×#5227C2semidirect
5. #10589154C2semidirect
6. #10589149C2semidirect
7. #10589145C2semidirect
33. #5231D3semidirect
37. #5227D3semidirect
446. C32#1606semidirect
522. C3#69700semidirect
523. C3#70973semidirect

Maximal subgroups

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

subgroupindex
#105949772
#105929272
C3×#52312
C3×#52272
#105891542
#105891492
#105891452
#709733
#697003