Finite Group Databasebeta

← #11778339

Subgroups — #11778339

Order 1152.

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

normal subgroups only

This group has 603 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#10594930C211yesmaximal, characteristic
2C3×#4738C211yesmaximal, characteristic, complemented
3#10591346C211yesmaximal, characteristic, complemented
4#10591171C211yesmaximal, characteristic, complemented
5#10589335C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#70975—31nomaximal
9#68295—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×#3805—21no—
12C2×#3750C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C3×#930C2211yescharacteristic
15C2×C3×#204—21no—
16#63980—21no—
17C2×Dic3⋊Dic3—21no—
18#63899—21no—
19#63899—21no—
20#63885—21no—
21#63885—21no—
22C2×#3715—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#816—21no—
27#63579—21no—
28#63565—21no—
29#5597—31no—
30#5597—31no—
31C3×#448—31no—
32#5230—31no—
33#5227—31no—
34#5040—31no—
35#4738D311yescharacteristic, complemented
36#4656—31no—
37C3×#327—31no—
38#4537—31no—
39#4470D311yescharacteristic, complemented
40#4469—31no—
41#4469—31no—
42#4469—61no—
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C2×C3×D12D411yescharacteristic
52C2×C3×D12D411yescharacteristic
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—42no—
56C2×#627—21no—
57C2×#625—21no—
58C2×#625—21no—
59#3805—42no—
60#3805—42no—
61C2×D3×Dic3—21no—
62C2×D3×Dic3—21no—
63C2×C32×C8—21no—
64#3750—21no—
65#3750—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×C4⋊Dic3D411yescharacteristic
70C3×C4⋊Dic3D411yescharacteristic
71C3×#204—42no—
72#3724—21no—
73Dic3⋊Dic3—42no—
74(C2×D3)⋊Dic3—21no—
75(C2×D3)⋊Dic3—21no—
76#3715—42no—
77#1604—91noSylow
78C22×C3×Q8—31no—
79C2×#237—61no—
80C2×#237—61no—
81C22×Dic6C2×D311yescharacteristic
82C2×C3×SD16—61no—
83C3×#121—31no—
84C3×#121—31no—
85C2×#215—61no—
86#939—61no—
87#939—61no—
88#939—61no—
89#939—61no—
90C2×#214—61no—
91#930C2×D311yescharacteristic
92#930C2×D311yescharacteristic
93C2×C4⋊Dic3—61no—
94C2×Dic3⋊C4—31no—
95C2×Dic3⋊C4—31no—
96C2×Dic3⋊C4—61no—
97C2×Dic3⋊C4—61no—
98C2×#204—21no—
99#896—61no—
100#896—61no—
101#884—61no—
102#884—61no—
103#878—61no—
104#878—61no—
105C3×#103—61no—
106C3×C22⋊C8—21no—
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C22⋊C8C2×D311yescharacteristic
109C3×#95—31no—
110#835—61no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113C3⋊#95C2×D311yescharacteristic
114#830—31no—
115#830—31no—
116#830—61no—
117#816—21no—
118#810—61no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3SD1612yescomplemented
130C3×#67—41no—
131C3×#67—41no—
132C3×#67—41no—
133C3×#67—41no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×D12—41no—
143C3×D12—41no—
144C3×Dic6—22no—
145C3×Dic6—22no—
146C3×Dic6—41no—
147C3×Dic6—41no—
148#627—42no—
149#625—42no—
150#625—81no—
151D3×Dic3—42no—
152D3×Dic3—42no—
153C32×C8—41no—
154C3⋊(C3⋊C8)—41no—
155#537—91no—
156#448—31no—
157#448—91no—
158#395—91no—
159#327—31no—
160#327—91no—
161#324—91no—
162C2×C3×Q8—61no—
163C2×C3×Q8—61no—
164C2×C3×Q8—122no—
165C2×C3×D4—31no—
166C2×C3×D4—31no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C22×C3×C4—21no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C2×#67—21no—
175C2×#67—21no—
176C2×#67—61no—
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—61no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190#237—122no—
191#237—122no—
192#237—122no—
193#237—122no—
194C2×D12D1211yescharacteristic
195C2×D12#6711yescharacteristic
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×Dic6—21no—
199C2×Dic6—21no—
200C2×Dic6—42no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C3×SD16—122no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—41no—
207C3×C4⋊C4—31no—
208C3×C4⋊C4—31no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211#217—61no—
212#217—61no—
213#215—122no—
214#214—122no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219C4⋊Dic3—122no—
220C4⋊Dic3D1211yescharacteristic
221C4⋊Dic3#6711yescharacteristic
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—121no—
229Dic3⋊C4—121no—
230Dic3⋊C4—122no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—121no—
234#204—42no—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32#12011yescharacteristic
238C22×C32C2×SD1611yescharacteristic
239C22×C32AGL(1,ℤ/8)11yescharacteristic
240C2×C3×D3—41no—
241C2×C3×D3—41no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—41no—
246C32×C4—21no—
247C32×C4—21no—
248C3⋊Dic3—22no—
249C3⋊Dic3—41no—
250C3×Dic3—42no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—42no—
254C2×#41—181no—
255C22×Q8—31no—
256C2×SD16—61no—
257C2×SD16—181no—
258C22⋊Q8—181no—
259C22⋊Q8—181no—
260#121—31no—
261#121—31no—
262#121—181no—
263#121—181no—
264#121—181no—
265C2×C4⋊C4—91no—
266C2×C4⋊C4—181no—
267#103—61no—
268#103—181no—
269C22⋊C8—91no—
270C22⋊C8D3211yescharacteristic
271#95—31no—
272#95—181no—
273C23×C3—21no—
274C23×C3—61no—
275C23×C3—61no—
276C23×C3D3×D411yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—21no—
279C22×D3—21no—
280C3×Q8—62no—
281C3×Q8—62no—
282C3×Q8—121no—
283C3×Q8—121no—
284C3×D4—121no—
285C3×D4—121no—
286C3×D4—121no—
287C3×D4—121no—
288C3×D4—121no—
289C3×D4—121no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—81no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307#67—41no—
308#67—41no—
309#67—41no—
310#67—41no—
311#67—122no—
312#67—122no—
313#67—241no—
314#67—241no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—21no—
318C2×Dic3—21no—
319C2×Dic3—32no—
320C2×Dic3—32no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—62no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—122no—
336C2×Dic3—122no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—241no—
340D12—41no—
341D12—41no—
342C4×D3—122no—
343C4×D3—122no—
344Dic6—22no—
345Dic6—22no—
346Dic6—41no—
347Dic6—41no—
348Dic6—122no—
349Dic6—122no—
350C3×C8—41no—
351C3×C8—41no—
352C3×C8—81no—
353C3⋊C8—121no—
354C3⋊C8—121no—
355C3⋊C8—241no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32#45011yescharacteristic
359C2×C32#45611yescharacteristic
360C2×C32B(4,𝔽2)11yescharacteristic
361C3×D3—81no—
362C3×D3—81no—
363#41—362no—
364#41—362no—
365C2×Q8—61no—
366C2×Q8—61no—
367C2×Q8—122no—
368C2×Q8—181no—
369C2×D4—31no—
370C2×D4—31no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—181no—
374C2×D4—181no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—181no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382SD16—122no—
383SD16—362no—
384C2×C8—21no—
385C2×C8—181no—
386C4⋊C4—31no—
387C4⋊C4—31no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—362no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—181no—
395C22⋊C4—181no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3#88211yescharacteristic
412C22×C3#91111yescharacteristic
413C22×C3D3×SD1611yescharacteristic
414C22×C3D3×SD1611yescharacteristic
415C22×C3#91411yescharacteristic
416C22×C3#93711yescharacteristic
417C2×D3—41no—
418C2×D3—41no—
419C2×D3—41no—
420C2×D3—41no—
421C2×D3—41no—
422C2×D3—41no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—41no—
428C3×C4—41no—
429C3×C4—122no—
430C3×C4—121no—
431C3×C4—122no—
432C3×C4—121no—
433Dic3—42no—
434Dic3—41no—
435Dic3—41no—
436Dic3—42no—
437Dic3—62no—
438Dic3—62no—
439Dic3—122no—
440Dic3—121no—
441Dic3—121no—
442Dic3—241no—
443C32#160411yescharacteristic, complemented, Sylow
444C23—61no—
445C23—61no—
446C23#380211yescharacteristic
447Q8—62no—
448Q8—62no—
449Q8—121no—
450Q8—121no—
451Q8—362no—
452D4—121no—
453D4—121no—
454D4—121no—
455D4—121no—
456D4—121no—
457D4—121no—
458D4—362no—
459D4—721no—
460C2×C4—41no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—92no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—121no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—362no—
474C2×C4—362no—
475C2×C4—361no—
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—241no—
491C2×C3#474111yescharacteristic
492C2×C3#477611yescharacteristic
493C2×C3#482611yescharacteristic
494C2×C3#503211yescharacteristic
495C2×C3#516911yescharacteristic
496C2×C3#520511yescharacteristic
497D3—81no—
498D3—81no—
499C22—21no—
500C22—21no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22#6379611yescharacteristic
508C22#6379811yescharacteristic
509C22#6392211yescharacteristic
510C4—21no—
511C4—21no—
512C4—122no—
513C4—122no—
514C4—121no—
515C4—121no—
516C4—182no—
517C4—361no—
518C3—21no—
519C3#6829511yescharacteristic, complemented
520C3#7097511yescharacteristic, complemented
521C2—21no—
522C2—21no—
523C2—241no—
524C2—241no—
525C2#1059040711yescharacteristic
526C2#1059094311yescharacteristic
527C2#1059101711yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10594930C2
hypercenterC22⋊C8D32
hypocenterC32#1604
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
2. C3×#4738C2semidirect
3. #10591346C2semidirect
4. #10591171C2semidirect
5. #10589335C2semidirect
6. C3×#4470C2semidirect
7. #10589149C2semidirect
35. #4738D3semidirect
39. #4470D3semidirect
129. C2×C3⋊Dic3SD16semidirect
443. C32#1604semidirect
519. C3#68295semidirect
520. C3#70975semidirect

Maximal subgroups

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

subgroupindex
#105949302
C3×#47382
#105913462
#105911712
#105893352
C3×#44702
#105891492
#709753
#682953