Finite Group Databasebeta

← #11778288

Subgroups — #11778288

Order 1152.

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

normal subgroups only

This group has 567 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#10594980C211yesmaximal, characteristic
2#10592926C211yesmaximal, characteristic
3C3×#5230C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5#10589153C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#70982—31nomaximal
9#69705—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3755—21no—
12#64139C2211yescharacteristic
13C2×C3×#216—21no—
14C3×#924C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16C2×C3×Dic3⋊C4C2211yescharacteristic
17#63966—21no—
18#63952—21no—
19#63897—21no—
20#63888—21no—
21#63848—21no—
22#63845—21no—
23#63662—21no—
24#63657C2211yescharacteristic
25C3×#835—21no—
26C3×C3⋊#95—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5645—31no—
30#5515—31no—
31C3×#451—31no—
32C3×#395—31no—
33#5230D311yescharacteristic, complemented
34#5228D311yescharacteristic, complemented
35#5227—31no—
36#5227—31no—
37#5227—61no—
38#4538—31no—
39#4528—31no—
40#4470—31no—
41#4469—31no—
42#4452—31no—
43#4451—31no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—42no—
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C2×#638—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×#624—21no—
56#3755—42no—
57#3752—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#216—42no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—42no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72#3722—21no—
73#3722—21no—
74Dic32—21no—
75#1603—91noSylow
76C22×C3×Q8—21no—
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×Q8C2×D311yescharacteristic
79C2×C3×Q16—61no—
80C3×C22⋊Q8—31no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—61no—
83#946—61no—
84C2×#216—21no—
85C2×#215—61no—
86C2×#215—61no—
87C2×#215—62no—
88#930—31no—
89#930—31no—
90#930—61no—
91#929—61no—
92C4×#67—61no—
93#924C2×D311yescharacteristic
94C2×Dic3⋊C4—21no—
95C2×Dic3⋊C4C2×D311yescharacteristic
96#898—61no—
97#898—61no—
98#896—61no—
99#894—61no—
100#894—61no—
101#890—61no—
102#889—61no—
103#886—61no—
104#67⋊C4—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—
121C32×Q8—22no—
122C32×Q8—22no—
123C32×Q8—41no—
124C32×Q8—41no—
125C2×C32×C4—22no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131#638—41no—
132#638—41no—
133C2×C3⋊Dic3—21no—
134C4⋊(C3⋊D3)—41no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C3×Dic6—41no—
146#624—81no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—41no—
149#539—91no—
150#451—31no—
151#448—91no—
152#395—31no—
153#328—91no—
154#327—91no—
155#324—91no—
156C2×C3×Q8—22no—
157C2×C3×Q8—21no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—31no—
162C2×C3×Q8—41no—
163C2×C3×Q8—42no—
164C2×C3×Q8—42no—
165C2×C3×Q8—44no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—41no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—121no—
178C22×Dic3—21no—
179C22×Dic3#6711yescharacteristic
180C22×Dic3#6711yescharacteristic
181C2×D12—31no—
182C2×D12—31no—
183C2×D12—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×Dic6#6711yescharacteristic
187C3×Q16—122no—
188C2×C3×C8—61no—
189C3×C4⋊C4—31no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—122no—
194C3×C22⋊C4—61no—
195#217—21no—
196#216—42no—
197#215—122no—
198#215—122no—
199#215—124no—
200(C2×D3)⋊C4—61no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—121no—
209C4⋊Dic3—31no—
210C4⋊Dic3—31no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3#6711yescharacteristic
215Dic3⋊C4—21no—
216Dic3⋊C4—21no—
217Dic3⋊C4—21no—
218Dic3⋊C4—42no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32#12011yescharacteristic
232C22×C32#13511yescharacteristic
233C22×C32#13711yescharacteristic
234C2×C3⋊D3—41no—
235C2×C3⋊D3—41no—
236C2×C3⋊D3—41no—
237C32×C4—21no—
238C32×C4—21no—
239C32×C4—42no—
240C3⋊Dic3—41no—
241C3×Dic3—42no—
242C3×Dic3—41no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C22×Q8D3211yescharacteristic
247C2×Q16—61no—
248C2×SD16—181no—
249#126—181no—
250#125—181no—
251#123—181no—
252#123—181no—
253C22⋊Q8—31no—
254C22⋊Q8—181no—
255#121—91no—
256C4×D4—181no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—61no—
259#103—61no—
260#103—181no—
261C22⋊C8—31no—
262C22⋊C8—91no—
263#95—31no—
264#95—61no—
265C23×C3—21no—
266C23×C3D3×D411yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C22×D3—61no—
269C22×D3—61no—
270C22×D3—121no—
271C3×Q8—24no—
272C3×Q8—22no—
273C3×Q8—22no—
274C3×Q8—22no—
275C3×Q8—22no—
276C3×Q8—42no—
277C3×Q8—42no—
278C3×Q8—41no—
279C3×Q8—41no—
280C3×Q8—41no—
281C3×Q8—41no—
282C3×Q8—42no—
283C3×Q8—121no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—42no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—42no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—62no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312#67—121no—
313#67—121no—
314#67—121no—
315#67—121no—
316#67—241no—
317#67—241no—
318C2×Dic3—22no—
319C2×Dic3—21no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—121no—
331D12—121no—
332D12—121no—
333D12—122no—
334C4×D3—241no—
335C4×D3—241no—
336Dic6—41no—
337C3×C8—121no—
338C3⋊C8—41no—
339C3⋊C8—122no—
340C3⋊C8—121no—
341C3⋊C8—121no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32#45211yescharacteristic
345C2×C32#45611yescharacteristic
346C2×C32B(4,𝔽2)11yescharacteristic
347C3⋊D3—81no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—31no—
351C2×Q8—42no—
352C2×D4—91no—
353C2×D4—181no—
354C22×C4—21no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—61no—
358C22×C4—181no—
359C22×C4C2×D3211yescharacteristic
360Q16—122no—
361SD16—362no—
362C2×C8—61no—
363C2×C8—181no—
364C4⋊C4—31no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—91no—
369C4⋊C4—122no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C4⋊C4—181no—
373C22⋊C4—61no—
374C22⋊C4—181no—
375C22⋊C4—181no—
376C22⋊C4—181no—
377C22⋊C4—181no—
378C42—181no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3#91811yescharacteristic
389C22×C3#91911yescharacteristic
390C22×C3#93711yescharacteristic
391C22×C3#93711yescharacteristic
392C22×C3#94211yescharacteristic
393C22×C3#95011yescharacteristic
394C2×D3—121no—
395C2×D3—121no—
396C2×D3—121no—
397C2×D3—121no—
398C2×D3—121no—
399C2×D3—121no—
400C2×D3—241no—
401C2×D3—241no—
402C2×D3—241no—
403C3×C4—22no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—41no—
409C3×C4—44no—
410C3×C4—42no—
411C3×C4—42no—
412C3×C4—122no—
413C3×C4—121no—
414C3×C4—121no—
415C3×C4—121no—
416C3×C4—121no—
417Dic3—42no—
418Dic3—41no—
419Dic3—41no—
420Dic3—41no—
421Dic3—41no—
422Dic3—121no—
423Dic3—121no—
424Dic3—241no—
425C32#160311yescharacteristic, complemented, Sylow
426C23—181no—
427C23D3×#6711yescharacteristic
428Q8—22no—
429Q8—22no—
430Q8—41no—
431Q8—41no—
432Q8—121no—
433D4—361no—
434D4—361no—
435D4—361no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—62no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—121no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4—181no—
451C2×C4—721no—
452C2×C4D3×#6711yescharacteristic
453C2×C4#381111yescharacteristic
454C8—121no—
455C8—361no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—41no—
464C2×C3—41no—
465C2×C3#503211yescharacteristic
466C2×C3#503211yescharacteristic
467C2×C3#504711yescharacteristic
468C2×C3#509511yescharacteristic
469C2×C3#518711yescharacteristic
470C2×C3#520511yescharacteristic
471D3—241no—
472D3—241no—
473D3—481no—
474C22—21no—
475C22—21no—
476C22—361no—
477C22—361no—
478C22—361no—
479C22#6394811yescharacteristic
480C22#6394911yescharacteristic
481C22#6398311yescharacteristic
482C4—21no—
483C4—21no—
484C4—42no—
485C4—122no—
486C4—121no—
487C4—121no—
488C4—121no—
489C4—121no—
490C4—361no—
491C3—21no—
492C3#6970511yescharacteristic, complemented
493C3#7098211yescharacteristic, complemented
494C2—21no—
495C2—21no—
496C2—721no—
497C2#1059165711yescharacteristic
498C2#1059166111yescharacteristic
499C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radical#64139C22
hypercenterC22×Q8D32
hypocenterC32#1603
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
3. C3×#5230C2semidirect
4. C3×#5228C2semidirect
5. #10589153C2semidirect
7. #10589147C2semidirect
33. #5230D3semidirect
34. #5228D3semidirect
425. C32#1603semidirect
492. C3#69705semidirect
493. C3#70982semidirect

Maximal subgroups

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

subgroupindex
#105949802
#105929262
C3×#52302
C3×#52282
#105891532
#105891512
#105891472
#709823
#697053