Finite Group Databasebeta

← #11897611

Subgroups — #11897611

Order 1152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596193C211yesmaximal, characteristic, complemented
2#10596161C211yesmaximal, characteristic
3C32×#501C211yesmaximal, characteristic, complemented
4#10592786C211yesmaximal, characteristic
5#10592762C211yesmaximal, characteristic, complemented
6#10592589C211yesmaximal, characteristic
7#10592588C211yesmaximal, characteristic
8#10592574C211yesmaximal, characteristic, complemented
9#10592573C211yesmaximal, characteristic, complemented
10#10592569C211yesmaximal, characteristic
11#10592556C211yesmaximal, characteristic, complemented
12#10592555C211yesmaximal, characteristic, complemented
13#10592551C211yesmaximal, characteristic
14#10592409C211yesmaximal, characteristic
15#10592400C211yesmaximal, characteristic, complemented
16#81965—34nomaximal
17C32×C4⋊Q8C2211yescharacteristic
18C32×#125C2211yescharacteristic
19#64153—21no—
20#64153—21no—
21C2×#3744C2211yescharacteristic
22#64106—21no—
23#64105—21no—
24#64105—21no—
25#64102C2211yescharacteristic
26#64102C2211yescharacteristic
27C4⋊C4×C3⋊D3—21no—
28#64099C2211yescharacteristic
29#64097—21no—
30#64097C2211yescharacteristic
31#64097C2211yescharacteristic
32#64097C2211yescharacteristic
33#64096—21no—
34#64096C2211yescharacteristic
35#64096C2211yescharacteristic
36C4×C4⋊(C3⋊D3)C2211yescharacteristic
37C4×#634C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C32×#107C2211yescharacteristic
40C32×#107C2211yescharacteristic
41C32×#106C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C32×#97C2211yescharacteristic
44#63648C2211yescharacteristic
45#63645C2211yescharacteristic
46#63643C2211yescharacteristic
47#63642C2211yescharacteristic
48#63641C2211yescharacteristic
49#63641C2211yescharacteristic
50C8×C3⋊Dic3C2211yescharacteristic
51#63637C2211yescharacteristic
52#63637C2211yescharacteristic
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic
55#63635C2211yescharacteristic
56#63634C2211yescharacteristic
57#63634C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5722—34no—
61#5690—34no—
62C3×#501D314yescomplemented
63#5087—34no—
64#5063—34no—
65#4890—34no—
66#4889—34no—
67#4875—34no—
68#4874—34no—
69#4870—34no—
70#4857—34no—
71#4856—34no—
72#4852—34no—
73#4710—34no—
74#4701—34no—
75C2×C32×Q8—21no—
76C2×C4⋊(C3⋊D3)C2311yescharacteristic
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×C4×C3⋊D3—21no—
80C2×#634—21no—
81C2×#634—21no—
82C2×#634—21no—
83C2×#634D411yescharacteristic
84C2×#634C2311yescharacteristic
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C4⋊C4—21no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4—21no—
90C32×C4⋊C4C2311yescharacteristic
91C32×C4⋊C4C2311yescharacteristic
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C42C2311yescharacteristic
95#3752—21no—
96#3752—21no—
97#3752—21no—
98C4⋊(C3⋊Dic3)—21no—
99C4⋊(C3⋊Dic3)D411yescharacteristic
100C4⋊(C3⋊Dic3)C2311yescharacteristic
101C4⋊(C3⋊Dic3)C2311yescharacteristic
102#3750—21no—
103#3750—21no—
104#3750—21no—
105#3750—21no—
106#3750—21no—
107#3750—21no—
108#3750—21no—
109#3750D411yescharacteristic
110#3750D411yescharacteristic
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3—21no—
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3C2311yescharacteristic
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3744Q814yescomplemented
119#3385—91noSylow
120C3×C4⋊Q8C2×D314yes—
121C3×#125C2×D314yes—
122#944—64no—
123#944—64no—
124C2×#204—34no—
125#897—64no—
126#896—64no—
127#896—64no—
128#893—34no—
129#893—34no—
130D3×C4⋊C4—64no—
131#890—34no—
132#888—34no—
133#888—34no—
134#888—34no—
135#888—64no—
136#887—34no—
137#887—34no—
138#887—64no—
139C4×D12—34no—
140C4×Dic6—34no—
141C4×Dic6—34no—
142C3×#107C2×D314yes—
143C3×#107C2×D314yes—
144C3×#106C2×D314yes—
145C3×#106C2×D314yes—
146C3×#97C2×D314yes—
147#821—34no—
148#818—34no—
149#816—34no—
150#815—34no—
151Dic3⋊C8—34no—
152Dic3⋊C8—34no—
153C8×Dic3—34no—
154#810—34no—
155#810—34no—
156#809—34no—
157#809—34no—
158#808—34no—
159#807—34no—
160#807—34no—
161#807—34no—
162C4⋊(C3⋊C8)—34no—
163C22×C3⋊D3—21no—
164C32×Q8—81no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C2×D411yescharacteristic
176C2×C3⋊Dic3C2×D411yescharacteristic
177C2×C3⋊Dic3C2×D411yescharacteristic
178C2×C3⋊Dic3C2×D411yescharacteristic
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)C2×Q812yes—
181C4×C3⋊D3—42no—
182C4×C3⋊D3—81no—
183C4×C3⋊D3—81no—
184#634—21no—
185#634—22no—
186#634—81no—
187#634—81no—
188#634—81no—
189#634C2×Q812yes—
190C32×C8—21no—
191C32×C8C2×Q812yes—
192C3⋊(C3⋊C8)—21no—
193C3⋊(C3⋊C8)—21no—
194Q82—91no—
195#554—91no—
196#501—91no—
197#501C3⋊D311yescharacteristic, complemented
198#500—91no—
199#479—91no—
200#479—91no—
201#477—91no—
202#476—91no—
203#474—91no—
204#474—91no—
205#446—91no—
206#440—91no—
207#440—91no—
208C4×SD16—91no—
209C2×C3×Q8—24no—
210C2×D12—34no—
211C2×C4×D3—64no—
212C2×C4×D3—64no—
213C2×C4×D3—64no—
214C2×Dic6—34no—
215C2×Dic6—34no—
216C2×Dic6—64no—
217C2×Dic6—64no—
218C2×Dic6—64no—
219C2×C3×C8C22×D314yes—
220C2×C3×C8C22×D314yes—
221C3×C4⋊C4—24no—
222C3×C4⋊C4—24no—
223C3×C4⋊C4—24no—
224C3×C4⋊C4C22×D314yes—
225C3×C4⋊C4C22×D314yes—
226C3×C4⋊C4C22×D314yes—
227C3×C4⋊C4C22×D314yes—
228C3×C42C22×D314yes—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232C4⋊Dic3—34no—
233C4⋊Dic3—34no—
234C4⋊Dic3—34no—
235C4⋊Dic3—64no—
236Dic3⋊C4—34no—
237Dic3⋊C4—34no—
238Dic3⋊C4—64no—
239Dic3⋊C4—64no—
240Dic3⋊C4—64no—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245C4×Dic3—34no—
246C4×Dic3—34no—
247C4×Dic3—64no—
248C4×Dic3—64no—
249C4×Dic3—64no—
250C2×C3⋊C8—34no—
251C2×C3⋊C8—34no—
252#204—316no—
253C22×C32C22×D411yescharacteristic
254C2×C3⋊D3—22no—
255C2×C3⋊D3—41no—
256C2×C3⋊D3—41no—
257C32×C4—21no—
258C32×C4—21no—
259C32×C4—41no—
260C32×C4—41no—
261C32×C4—41no—
262C32×C4—41no—
263C32×C4C22×Q811yescharacteristic
264C32×C42−1+411yescharacteristic
265C3⋊Dic3—22no—
266C3⋊Dic3—21no—
267C3⋊Dic3—21no—
268C3⋊Dic3—21no—
269C3⋊Dic3—41no—
270C3⋊Dic3—41no—
271C3⋊Dic3#13712yes—
272C2×SD16—91no—
273C4⋊Q8—91no—
274C4⋊Q8—91no—
275C4⋊Q8—91no—
276C4⋊Q8—181no—
277C4⋊Q8—181no—
278C4⋊Q8—181no—
279C4⋊Q8C2×C3⋊D311yescharacteristic
280#125—91no—
281#125C2×C3⋊D311yescharacteristic
282C22⋊Q8—181no—
283C22⋊Q8—181no—
284C22⋊Q8—181no—
285C4×Q8—91no—
286C4×Q8—91no—
287C4×Q8—91no—
288C4×Q8—91no—
289C4×Q8—181no—
290C4×D4—91no—
291C4×D4—91no—
292C4×D4—91no—
293C2×C4⋊C4—181no—
294#107—91no—
295#107—91no—
296#107—91no—
297#107—91no—
298#107C2×C3⋊D311yescharacteristic
299#107C2×C3⋊D311yescharacteristic
300#106—91no—
301#106C2×C3⋊D311yescharacteristic
302#106C2×C3⋊D311yescharacteristic
303C4⋊C8—91no—
304C4⋊C8—91no—
305C4⋊C8—91no—
306#103—91no—
307#103—91no—
308#103—91no—
309#102—91no—
310#102—91no—
311#102—91no—
312#97—91no—
313#97C2×C3⋊D311yescharacteristic
314C4×C8—91no—
315C22×D3—64no—
316C3×Q8—84no—
317C2×C3×C4—24no—
318C2×C3×C4—24no—
319C2×C3×C4—24no—
320C2×C3×C4—24no—
321C2×C3×C4D3×D414yes—
322C2×C3×C4D3×D414yes—
323C2×C3×C4C23×D314yes—
324C2×Dic3—34no—
325C2×Dic3—34no—
326C2×Dic3—34no—
327C2×Dic3—34no—
328C2×Dic3—64no—
329C2×Dic3—64no—
330C2×Dic3—64no—
331D12—38no—
332D12—64no—
333C4×D3—128no—
334C4×D3—244no—
335C4×D3—244no—
336Dic6—38no—
337Dic6—68no—
338Dic6—64no—
339Dic6—244no—
340Dic6—244no—
341Dic6—244no—
342C3×C8—24no—
343C3×C8D3×Q818yes—
344C3⋊C8—64no—
345C3⋊C8—64no—
346C2×C32D4×Q811yescharacteristic
347C2×C32C2×#13711yescharacteristic
348C2×C32#57611yescharacteristic
349C3⋊D3—42no—
350C2×Q8—21no—
351C2×Q8—91no—
352C2×Q8—91no—
353C2×Q8—181no—
354C2×Q8—181no—
355C2×Q8—181no—
356C2×D4—91no—
357C22×C4—181no—
358C22×C4—181no—
359C22×C4—181no—
360SD16—94no—
361C2×C8—91no—
362C2×C8—91no—
363C2×C8C22×C3⋊D311yescharacteristic
364C2×C8C22×C3⋊D311yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—91no—
369C4⋊C4—91no—
370C4⋊C4—91no—
371C4⋊C4—91no—
372C4⋊C4—91no—
373C4⋊C4—181no—
374C4⋊C4—181no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C4⋊C4C22×C3⋊D311yescharacteristic
382C4⋊C4C22×C3⋊D311yescharacteristic
383C4⋊C4C22×C3⋊D311yescharacteristic
384C4⋊C4C22×C3⋊D311yescharacteristic
385C22⋊C4—181no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C42—91no—
389C42—91no—
390C42—181no—
391C42—181no—
392C42—181no—
393C42C22×C3⋊D311yescharacteristic
394C22×C3C2×D3×D414yes—
395C2×D3—68no—
396C2×D3—124no—
397C2×D3—124no—
398C3×C4—24no—
399C3×C4—24no—
400C3×C4—44no—
401C3×C4—44no—
402C3×C4—44no—
403C3×C4—44no—
404C3×C4C2×D3×Q814yes—
405C3×C4#100714yes—
406Dic3—38no—
407Dic3—68no—
408Dic3—64no—
409Dic3—64no—
410Dic3—64no—
411Dic3—124no—
412Dic3—124no—
413C32#338511yescharacteristic, complemented, Sylow
414C23—181no—
415Q8—81no—
416Q8—92no—
417Q8—182no—
418Q8—181no—
419Q8—721no—
420Q8—721no—
421Q8—721no—
422D4—92no—
423D4—181no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—91no—
429C2×C4—91no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—181no—
433C2×C4—181no—
434C2×C4—181no—
435C2×C4—362no—
436C2×C4—721no—
437C2×C4—721no—
438C2×C4D4×C3⋊D311yescharacteristic
439C2×C4D4×C3⋊D311yescharacteristic
440C2×C4C23×C3⋊D311yescharacteristic
441C8—21no—
442C8—181no—
443C8—181no—
444C8Q8×C3⋊D312yes—
445C2×C3#572714yes—
446C2×C3#577414yes—
447C2×C3D3×#13714yes—
448D3—128no—
449C22—182no—
450C22—361no—
451C22—361no—
452C22C2×D4×C3⋊D311yescharacteristic
453C4—21no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—41no—
459C4—92no—
460C4—182no—
461C4—181no—
462C4—181no—
463C4—181no—
464C4—361no—
465C4—361no—
466C4C2×Q8×C3⋊D311yescharacteristic
467C4#6436411yescharacteristic
468C3#8196514yescomplemented
469C2—362no—
470C2#1059619811yescharacteristic
471C2#1059624511yescharacteristic
472C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#501C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenter#501C3⋊D3
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #10596193C2semidirect
3. C32×#501C2semidirect
5. #10592762C2semidirect
8. #10592574C2semidirect
9. #10592573C2semidirect
11. #10592556C2semidirect
12. #10592555C2semidirect
15. #10592400C2semidirect
62. C3×#501D3semidirect
118. #3744Q8semidirect
197. #501C3⋊D3semidirect
413. C32#3385semidirect
468. C3#81965semidirect

Maximal subgroups

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

subgroupindex
#105961932
#105961612
C32×#5012
#105927862
#105927622
#105925892
#105925882
#105925742
#105925732
#105925692
#105925562
#105925552
#105925512
#105924092
#105924002
#819653