Finite Group Databasebeta

← #11877035

Subgroups — #11877035

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595374C212yesmaximal
2#10592888C211yesmaximal, characteristic
3C3×#5184C211yesmaximal, characteristic, complemented
4C3×#5183C211yesmaximal, characteristic, complemented
5#10591623C212yesmaximal, complemented
6#10591600C212yesmaximal
7#10591576C212yesmaximal, complemented
8#10590889C211yesmaximal, characteristic, complemented
9#10590858C211yesmaximal, characteristic
10#10590812C211yesmaximal, characteristic, complemented
11#10590664C211yesmaximal, characteristic
12#81794—31nomaximal
13#79838—31nomaximal
14C2×C32×Q16C2211yescharacteristic
15#64155C2212yes—
16C2×#3743C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C3×#944C2212yes—
19C2×C3×#216C2212yes—
20C2×C3×Dic12C2211yescharacteristic
21#63918C2212yes—
22#63895—22no—
23C4×#624C2211yescharacteristic
24#63871C2212yes—
25#63846—22no—
26Dic3×Dic6C2212yes—
27#63837—22no—
28#63836—22no—
29C2×#3712C2211yescharacteristic
30#63662C2212yes—
31#63644C2211yescharacteristic
32C3×#835C2212yes—
33C3×#817C2211yescharacteristic
34C3×#815C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63573C2212yes—
37#63566C2212yes—
38#63565C2212yes—
39#63554C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5728—32no—
42#5578—32no—
43C3×#494—31no—
44C3×#441—31no—
45#5189—31no—
46#5189—31no—
47#5189—32no—
48#5189—31no—
49#5189—61no—
50#5184—32no—
51#5184—31no—
52#5184D311yescharacteristic, complemented
53#5183D311yescharacteristic, complemented
54#5079—32no—
55#5030—32no—
56#4867—31no—
57#4855—31no—
58#4816—32no—
59#4792—32no—
60#4716—31no—
61#4707—31no—
62C4×ΓL(1,𝔽25)—31no—
63#4680—31no—
64C2×C32×Q8C2312yes—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×Dic6C2312yes—
67C2×#627—22no—
68C2×#624D412yes—
69C32×Q16—22no—
70C2×C32×C8C2311yescharacteristic
71#3752—22no—
72C4⋊(C3⋊Dic3)C2312yes—
73#3750—22no—
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75#3743—22no—
76C3×#216—24no—
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82C3×C4×Dic3C2311yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C3×Dic12—22no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90#3722—22no—
91Dic32—22no—
92Dic32D412yes—
93#3712—22no—
94#3185—91noSylow
95C2×C3×Q16—21no—
96C2×C3×Q16—32no—
97C2×C3×Q16—31no—
98C2×C3×Q16C2×D311yescharacteristic
99C2×C3×Q16C2×D311yescharacteristic
100C3×C4⋊Q8—32no—
101C3×C4×Q8—32no—
102#946—32no—
103#946—32no—
104#946—32no—
105#946—62no—
106Q8×Dic3—32no—
107Q8×Dic3C2×D312yes—
108#944C2×D312yes—
109C2×#216C2×D312yes—
110C2×Dic12C2×D311yescharacteristic
111C2×ΓL(1,𝔽25)—31no—
112C2×ΓL(1,𝔽25)—31no—
113C2×ΓL(1,𝔽25)—31no—
114C2×ΓL(1,𝔽25)—31no—
115C2×ΓL(1,𝔽25)—61no—
116#897—32no—
117#897—62no—
118#896—62no—
119#892—62no—
120#890—62no—
121#889—62no—
122#888—32no—
123#887—62no—
124#872—62no—
125C42×D3—31no—
126C42×D3—31no—
127#869—32no—
128C4×Dic6—32no—
129C4×Dic6—62no—
130C3×#106—31no—
131C3×#103—32no—
132C3×#97—31no—
133C3×C4×C8—31no—
134#835—32no—
135#835—32no—
136#835—32no—
137#835—32no—
138#835—62no—
139#835C2×D312yes—
140#817—31no—
141#817—31no—
142#817—32no—
143#817—61no—
144#817C2×D311yescharacteristic
145#816—32no—
146#815—31no—
147#815C2×D311yescharacteristic
148C8×Dic3—31no—
149C8×Dic3C2×D311yescharacteristic
150#810—32no—
151#808—32no—
152#803—31no—
153C4×C3⋊C8—31no—
154C22×C3⋊D3C2×D411yescharacteristic
155C32×Q8—22no—
156C32×Q8—22no—
157C2×C32×C4—22no—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3C2×D411yescharacteristic
161C4×C3⋊D3—21no—
162C4×C3⋊D3—21no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D412yes—
166C2×C3×Dic3C2×D412yes—
167C3×Dic6—22no—
168C3×Dic6—22no—
169#627—44no—
170#624—24no—
171C32×C8#4112yes—
172C3⋊(C3⋊C8)—21no—
173C3×C3⋊C8—21no—
174C3×C3⋊C8#4112yes—
175#533—92no—
176#498—91no—
177#494—31no—
178#487—92no—
179#470—92no—
180#470—91no—
181#470—91no—
182#441—31no—
183#441—91no—
184#441—92no—
185C4×M16—91no—
186C2×C3×Q8—22no—
187C2×C3×Q8—32no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C2×C4×D3—31no—
191C2×C4×D3—31no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—61no—
195C2×Dic6—62no—
196C2×Dic6—62no—
197C2×Dic6C22×D312yes—
198C3×Q16—22no—
199C3×Q16—22no—
200C3×Q16—42no—
201C3×Q16—64no—
202C3×Q16—62no—
203C2×C3×C8—21no—
204C2×C3×C8—31no—
205C2×C3×C8—31no—
206C2×C3×C8C22×D311yescharacteristic
207C2×C3×C8C22×D311yescharacteristic
208C3×C4⋊C4—32no—
209C3×C4⋊C4—62no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4—62no—
212C3×C42—31no—
213C3×C42—31no—
214C3×C42—62no—
215#216—24no—
216(C2×D3)⋊C4—62no—
217(C2×D3)⋊C4—62no—
218(C2×D3)⋊C4—62no—
219(C2×D3)⋊C4—62no—
220(C2×D3)⋊C4—122no—
221C4⋊Dic3—22no—
222C4⋊Dic3—32no—
223C4⋊Dic3—32no—
224C4⋊Dic3—62no—
225C4⋊Dic3—62no—
226C4⋊Dic3—62no—
227C4⋊Dic3—62no—
228C4⋊Dic3C22×D312yes—
229Dic3⋊C4—22no—
230Dic3⋊C4—22no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—122no—
237C4×Dic3—22no—
238C4×Dic3—32no—
239C4×Dic3—32no—
240C4×Dic3—62no—
241C4×Dic3—62no—
242C4×Dic3C22×D311yescharacteristic
243C4×Dic3C22×D311yescharacteristic
244C2×C3⋊C8—31no—
245C2×C3⋊C8—31no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8C22×D311yescharacteristic
248C2×C3⋊C8C22×D311yescharacteristic
249Dic12—22no—
250ΓL(1,𝔽25)—62no—
251ΓL(1,𝔽25)—62no—
252ΓL(1,𝔽25)—62no—
253ΓL(1,𝔽25)—62no—
254ΓL(1,𝔽25)—122no—
255C22×C32C22×D411yescharacteristic
256C2×C3⋊D3—21no—
257C2×C3⋊D3—22no—
258C32×C4—42no—
259C32×C4C2×#4111yescharacteristic
260C32×C4C2×#4111yescharacteristic
261C3⋊Dic3—21no—
262C3⋊Dic3—42no—
263C3×Dic3—22no—
264C3×Dic3—42no—
265C3×Dic3—42no—
266C3×Dic3#13714yes—
267C2×Q16—32no—
268C2×Q16—31no—
269C2×Q16D3211yescharacteristic
270C2×M16—91no—
271C2×M16—91no—
272C4⋊Q8—32no—
273C4⋊Q8—92no—
274#125—182no—
275C22⋊Q8—92no—
276C22⋊Q8—92no—
277C22⋊Q8—182no—
278C4×Q8—32no—
279C4×Q8—92no—
280C4×Q8—182no—
281#117—182no—
282C2×C42—91no—
283#106—31no—
284#106—92no—
285#106—91no—
286#103—32no—
287#103—92no—
288#103—92no—
289#103—92no—
290#97—31no—
291#97—91no—
292C4×C8—31no—
293C4×C8—91no—
294C22×D3—31no—
295C22×D3—31no—
296C22×D3—61no—
297C3×Q8—22no—
298C3×Q8—22no—
299C3×Q8—22no—
300C3×Q8—22no—
301C3×Q8—42no—
302C3×Q8—42no—
303C3×Q8—62no—
304C3×Q8—62no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—32no—
309C2×C3×C4—32no—
310C2×C3×C4—42no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—31no—
318C2×Dic3—31no—
319C2×Dic3—61no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—122no—
323C2×Dic3D3×D412yes—
324C2×Dic3D3×D412yes—
325C4×D3—64no—
326C4×D3—61no—
327C4×D3—61no—
328C4×D3—61no—
329C4×D3—61no—
330C4×D3—64no—
331C4×D3—121no—
332C4×D3—121no—
333Dic6—22no—
334Dic6—22no—
335Dic6—124no—
336Dic6—124no—
337C3×C8—22no—
338C3×C8—32no—
339C3×C8—61no—
340C3×C8#23512yes—
341C3×C8#23712yes—
342C3⋊C8—21no—
343C3⋊C8—61no—
344C3⋊C8—61no—
345C3⋊C8—121no—
346C3⋊C8#23712yes—
347C2×C32#53211yescharacteristic
348C2×C32C2×#13712yes—
349C3⋊D3—41no—
350C2×Q8—32no—
351C2×Q8—182no—
352C2×Q8C2×D3212yes—
353C22×C4—92no—
354C22×C4—91no—
355Q16—22no—
356Q16—64no—
357Q16—62no—
358M16—182no—
359M16—182no—
360C2×C8—31no—
361C2×C8—31no—
362C2×C8—91no—
363C2×C8C2×D3211yescharacteristic
364C4⋊C4—32no—
365C4⋊C4—62no—
366C4⋊C4—62no—
367C4⋊C4—62no—
368C4⋊C4—92no—
369C4⋊C4—182no—
370C4⋊C4—182no—
371C4⋊C4—182no—
372C4⋊C4—182no—
373C22⋊C4—182no—
374C22⋊C4—182no—
375C42—31no—
376C42—31no—
377C42—62no—
378C42—92no—
379C42—182no—
380C22×C3—21no—
381C22×C3C2×D3×D411yescharacteristic
382C22×C3C2×D3×D411yescharacteristic
383C2×D3—61no—
384C2×D3—62no—
385C2×D3—62no—
386C2×D3—61no—
387C2×D3—121no—
388C2×D3—122no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—34no—
392C3×C4—42no—
393C3×C4—42no—
394C3×C4—62no—
395C3×C4—82no—
396C3×C4—122no—
397C3×C4—122no—
398C3×C4C2×#23511yescharacteristic
399C3×C4C2×#23711yescharacteristic
400C3×C4C2×#23711yescharacteristic
401C3×C4D3×#4111yescharacteristic
402Dic3—22no—
403Dic3—42no—
404Dic3—42no—
405Dic3—61no—
406Dic3—61no—
407Dic3—121no—
408Dic3—122no—
409Dic3—122no—
410Dic3—242no—
411Dic3#91814yes—
412C32#318511yescharacteristic, complemented, Sylow
413C23—91no—
414Q8—22no—
415Q8—22no—
416Q8—62no—
417Q8—62no—
418Q8—364no—
419C2×C4—22no—
420C2×C4—32no—
421C2×C4—32no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—91no—
425C2×C4—184no—
426C2×C4—181no—
427C2×C4—181no—
428C2×C4—182no—
429C2×C4C22×D3211yescharacteristic
430C8—32no—
431C8—61no—
432C8—181no—
433C8#380412yes—
434C2×C3—21no—
435C2×C3—22no—
436C2×C3#554811yescharacteristic
437C2×C3#571611yescharacteristic
438C2×C3C2×#91812yes—
439C2×C3D3×#13712yes—
440D3—121no—
441D3—121no—
442D3—241no—
443C22—181no—
444C22—182no—
445C22D32×D411yescharacteristic
446C4—34no—
447C4—42no—
448C4—62no—
449C4—122no—
450C4—122no—
451C4—181no—
452C4—362no—
453C4D3×#23711yescharacteristic
454C4C2×#380411yescharacteristic
455C3—21no—
456C3#7983811yescharacteristic, complemented
457C3#8179411yescharacteristic, complemented
458C2—361no—
459C2D3×#91812yes—
460C2#1059513911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC2×Q16D32
hypocenterC32#3185
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. C3×#5184C2semidirect
4. C3×#5183C2semidirect
5. #10591623C2semidirect
7. #10591576C2semidirect
8. #10590889C2semidirect
10. #10590812C2semidirect
52. #5184D3semidirect
53. #5183D3semidirect
412. C32#3185semidirect
456. C3#79838semidirect
457. C3#81794semidirect

Maximal subgroups

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

subgroupindex
#105953742
#105928882
C3×#51842
C3×#51832
#105916232
#105916002
#105915762
#105908892
#105908582
#105908122
#105906642
#817943
#798383