Finite Group Databasebeta

← #11868715

Subgroups — #11868715

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596159C211yesmaximal, characteristic
2C4×Q8×C3⋊D3C211yesmaximal, characteristic
3C32×#479C211yesmaximal, characteristic, complemented
4#10592762C211yesmaximal, characteristic, complemented
5#10592721C211yesmaximal, characteristic, complemented
6#10592580C211yesmaximal, characteristic
7#10592574C211yesmaximal, characteristic, complemented
8#10592560C211yesmaximal, characteristic
9#10592553C211yesmaximal, characteristic, complemented
10#10592536C211yesmaximal, characteristic
11#10592528C211yesmaximal, characteristic, complemented
12#10592501C211yesmaximal, characteristic
13#10592501C211yesmaximal, characteristic
14#10592492C211yesmaximal, characteristic, complemented
15#10592490C211yesmaximal, characteristic, complemented
16#81230—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C32×#125C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23#64105—21no—
24#64105—21no—
25#64101C2211yescharacteristic
26#64101C2211yescharacteristic
27C4⋊C4×C3⋊D3—21no—
28C4⋊C4×C3⋊D3C2211yescharacteristic
29#64097C2211yescharacteristic
30#64097C2211yescharacteristic
31#64096—21no—
32#64096—21no—
33#64096—21no—
34#64096C2211yescharacteristic
35C42×C3⋊D3—21no—
36C42×C3⋊D3C2211yescharacteristic
37#64079C2211yescharacteristic
38C4×#634—21no—
39C4×#634C2211yescharacteristic
40C32×#107C2211yescharacteristic
41C32×#106C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63645C2211yescharacteristic
48#63644C2211yescharacteristic
49#63643C2211yescharacteristic
50#63643C2211yescharacteristic
51#63641C2211yescharacteristic
52#63641C2211yescharacteristic
53#63637C2211yescharacteristic
54#63637C2211yescharacteristic
55#63635C2211yescharacteristic
56#63635C2211yescharacteristic
57#63634C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5688—34no—
61C4×D3×Q8—34no—
62C3×#479D314yescomplemented
63#5063—34no—
64#5022—34no—
65#4881—34no—
66#4875—34no—
67#4861—34no—
68#4854—34no—
69#4837—34no—
70#4829—34no—
71#4802—34no—
72#4802—34no—
73#4793—34no—
74#4791—34no—
75C2×C32×Q8C2311yescharacteristic
76Q8×C3⋊D3—22no—
77Q8×C3⋊D3Q814yescomplemented
78C2×C4×C3⋊D3—21no—
79C2×C4×C3⋊D3—21no—
80C2×C4×C3⋊D3D411yescharacteristic
81C2×C4×C3⋊D3D411yescharacteristic
82C2×C4×C3⋊D3C2311yescharacteristic
83C2×#634—21no—
84C2×#634—21no—
85C2×#634—21no—
86C2×#634C2311yescharacteristic
87C2×C32×C8C2311yescharacteristic
88C2×C32×C8C2311yescharacteristic
89C32×C4⋊C4—21no—
90C32×C4⋊C4—21no—
91C32×C4⋊C4—21no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C4⋊C4C2311yescharacteristic
95C32×C42—21no—
96C32×C42C2311yescharacteristic
97#3752—21no—
98#3752—21no—
99C4⋊(C3⋊Dic3)—21no—
100C4⋊(C3⋊Dic3)C2311yescharacteristic
101C4⋊(C3⋊Dic3)C2311yescharacteristic
102C4⋊(C3⋊Dic3)C2311yescharacteristic
103#3750—21no—
104#3750—21no—
105#3750—21no—
106#3750—21no—
107#3750—21no—
108#3750—21no—
109#3750—21no—
110C4×C3⋊Dic3—21no—
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3—21no—
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3D411yescharacteristic
116C4×C3⋊Dic3D411yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3743—22no—
121#3743—22no—
122#3078—91noSylow
123C2×D3×Q8—34no—
124C3×#125C2×D314yes—
125C3×C4×Q8C2×D314yes—
126Q8×Dic3—34no—
127C2×ΓL(1,𝔽25)—34no—
128C2×ΓL(1,𝔽25)—34no—
129#896—64no—
130#896—64no—
131#892—34no—
132#892—34no—
133D3×C4⋊C4—34no—
134D3×C4⋊C4—64no—
135#888—34no—
136#888—34no—
137#887—34no—
138#887—64no—
139#887—64no—
140#887—64no—
141C42×D3—34no—
142C42×D3—64no—
143#870—34no—
144C4×Dic6—34no—
145C4×Dic6—64no—
146C3×#107C2×D314yes—
147C3×#106C2×D314yes—
148C3×C4⋊C8C2×D314yes—
149C3×#103C2×D314yes—
150C3×#103C2×D314yes—
151#835—34no—
152#835—34no—
153#818—34no—
154#817—34no—
155#816—34no—
156#816—34no—
157Dic3⋊C8—34no—
158Dic3⋊C8—34no—
159#810—34no—
160#810—34no—
161#808—34no—
162#808—34no—
163#807—34no—
164#807—34no—
165C4⋊(C3⋊C8)—34no—
166C22×C3⋊D3C2×D411yescharacteristic
167C32×Q8—21no—
168C32×Q8C2×Q812yes—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3C2×D411yescharacteristic
181C2×C3⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C4×C3⋊D3—24no—
184C4×C3⋊D3—22no—
185C4×C3⋊D3—41no—
186C4×C3⋊D3—42no—
187C4×C3⋊D3C2×Q812yes—
188C4×C3⋊D3#4112yes—
189#634—21no—
190#634—24no—
191#634—42no—
192#634—42no—
193#634C2×Q812yes—
194C32×C8—21no—
195C32×C8—21no—
196C3⋊(C3⋊C8)—21no—
197C3⋊(C3⋊C8)—21no—
198#533—91no—
199C2×C4×Q8—91no—
200#479—91no—
201#479—91no—
202#479—91no—
203#479C3⋊D311yescharacteristic, complemented
204#477—91no—
205#477—91no—
206#475—91no—
207#475—91no—
208#428—91no—
209#428—91no—
210#423—91no—
211#419—91no—
212#419—91no—
213C2×C3×Q8C22×D314yes—
214D3×Q8—316no—
215D3×Q8—68no—
216C2×C4×D3—34no—
217C2×C4×D3—34no—
218C2×C4×D3—34no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×Dic6—34no—
222C2×Dic6—64no—
223C2×Dic6—64no—
224C2×Dic6—64no—
225C2×C3×C8C22×D314yes—
226C2×C3×C8C22×D314yes—
227C3×C4⋊C4—24no—
228C3×C4⋊C4—24no—
229C3×C4⋊C4—24no—
230C3×C4⋊C4C22×D314yes—
231C3×C4⋊C4C22×D314yes—
232C3×C4⋊C4C22×D314yes—
233C3×C42—24no—
234C3×C42C22×D314yes—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237C4⋊Dic3—34no—
238C4⋊Dic3—34no—
239C4⋊Dic3—34no—
240C4⋊Dic3—64no—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247Dic3⋊C4—64no—
248C4×Dic3—34no—
249C4×Dic3—34no—
250C4×Dic3—34no—
251C4×Dic3—64no—
252C4×Dic3—64no—
253C4×Dic3—64no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C2×C3⋊C8—34no—
257C2×C3⋊C8—34no—
258ΓL(1,𝔽25)—68no—
259ΓL(1,𝔽25)—68no—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—21no—
262C2×C3⋊D3—21no—
263C2×C3⋊D3C22⋊Q812yes—
264C32×C4—22no—
265C32×C4—21no—
266C32×C4—21no—
267C32×C4—41no—
268C32×C4—41no—
269C32×C4—41no—
270C32×C4C22×Q811yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3⋊Dic3—22no—
273C3⋊Dic3—21no—
274C3⋊Dic3—41no—
275C3⋊Dic3—41no—
276C3⋊Dic3—41no—
277C3⋊Dic3C22⋊Q812yes—
278C3⋊Dic3#13712yes—
279C22×Q8—91no—
280C2×M16—91no—
281C2×M16—91no—
282C4⋊Q8—91no—
283C4⋊Q8—91no—
284#125—91no—
285#125C2×C3⋊D311yescharacteristic
286C22⋊Q8—181no—
287C22⋊Q8—181no—
288C4×Q8—91no—
289C4×Q8—91no—
290C4×Q8—91no—
291C4×Q8—181no—
292C4×Q8—181no—
293C4×Q8—181no—
294C4×Q8—181no—
295C4×Q8C2×C3⋊D311yescharacteristic
296#117—91no—
297#117—91no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—181no—
300C2×C42—91no—
301C2×C42—181no—
302#107—91no—
303#107—91no—
304#107—91no—
305#107C2×C3⋊D311yescharacteristic
306#106—91no—
307#106—91no—
308#106—91no—
309#106C2×C3⋊D311yescharacteristic
310C4⋊C8—91no—
311C4⋊C8—91no—
312C4⋊C8—91no—
313C4⋊C8C2×C3⋊D311yescharacteristic
314#103—91no—
315#103—91no—
316#103—91no—
317#103—91no—
318#103—91no—
319#103—91no—
320#103C2×C3⋊D311yescharacteristic
321#103C2×C3⋊D311yescharacteristic
322C22×D3—34no—
323C3×Q8—24no—
324C3×Q8D3×Q818yes—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4D3×D414yes—
330C2×C3×C4D3×D414yes—
331C2×C3×C4C23×D314yes—
332C2×Dic3—34no—
333C2×Dic3—34no—
334C2×Dic3—34no—
335C2×Dic3—64no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339C4×D3—38no—
340C4×D3—38no—
341C4×D3—68no—
342C4×D3—616no—
343C4×D3—124no—
344C4×D3—128no—
345Dic6—38no—
346Dic6—616no—
347Dic6—64no—
348Dic6—128no—
349Dic6—128no—
350C3×C8—24no—
351C3×C8—24no—
352C3⋊C8—64no—
353C3⋊C8—64no—
354C2×C32C2×C22⋊Q811yescharacteristic
355C2×C32C2×#13711yescharacteristic
356C2×C32#57511yescharacteristic
357C3⋊D3—22no—
358C2×Q8—94no—
359C2×Q8—91no—
360C2×Q8—181no—
361C2×Q8—181no—
362C2×Q8—181no—
363C2×Q8—182no—
364C2×Q8C22×C3⋊D311yescharacteristic
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—91no—
368C22×C4—181no—
369C22×C4—181no—
370M16—182no—
371M16—182no—
372C2×C8—91no—
373C2×C8—91no—
374C2×C8C22×C3⋊D311yescharacteristic
375C2×C8C22×C3⋊D311yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4C22×C3⋊D311yescharacteristic
391C4⋊C4C22×C3⋊D311yescharacteristic
392C4⋊C4C22×C3⋊D311yescharacteristic
393C22⋊C4—181no—
394C22⋊C4—181no—
395C42—21no—
396C42—91no—
397C42—91no—
398C42—91no—
399C42—181no—
400C42—181no—
401C42—181no—
402C42—181no—
403C42—181no—
404C42C22×C3⋊D311yescharacteristic
405C22×C3C2×D3×D414yes—
406C2×D3—38no—
407C2×D3—64no—
408C2×D3—64no—
409C3×C4—24no—
410C3×C4—24no—
411C3×C4—28no—
412C3×C4—44no—
413C3×C4—44no—
414C3×C4—44no—
415C3×C4C2×D3×Q814yes—
416C3×C4D3×#4114yes—
417Dic3—38no—
418Dic3—38no—
419Dic3—64no—
420Dic3—68no—
421Dic3—124no—
422Dic3—124no—
423Dic3—124no—
424C32#307811yescharacteristic, complemented, Sylow
425C23—91no—
426Q8—21no—
427Q8—92no—
428Q8—184no—
429Q8—181no—
430Q8—362no—
431Q8—362no—
432Q8Q8×C3⋊D312yes—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—91no—
438C2×C4—91no—
439C2×C4—92no—
440C2×C4—92no—
441C2×C4—91no—
442C2×C4—182no—
443C2×C4—184no—
444C2×C4—181no—
445C2×C4—181no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—361no—
449C2×C4—362no—
450C2×C4D4×C3⋊D311yescharacteristic
451C2×C4D4×C3⋊D311yescharacteristic
452C2×C4C23×C3⋊D311yescharacteristic
453C8—21no—
454C8—21no—
455C8—181no—
456C8—181no—
457C2×C3D3×C22⋊Q814yes—
458C2×C3#576814yes—
459C2×C3D3×#13714yes—
460D3—68no—
461C22—92no—
462C22—181no—
463C22—181no—
464C22C2×D4×C3⋊D311yescharacteristic
465C4—22no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—92no—
472C4—92no—
473C4—182no—
474C4—181no—
475C4—361no—
476C4—361no—
477C4—361no—
478C4C2×Q8×C3⋊D311yescharacteristic
479C4#41×C3⋊D311yescharacteristic
480C3#8123014yescomplemented
481C2—182no—
482C2C3⋊D3×C22⋊Q811yescharacteristic
483C2#1059623911yescharacteristic
484C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#479C3⋊D3
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. C32×#479C2semidirect
4. #10592762C2semidirect
5. #10592721C2semidirect
7. #10592574C2semidirect
9. #10592553C2semidirect
11. #10592528C2semidirect
14. #10592492C2semidirect
15. #10592490C2semidirect
62. C3×#479D3semidirect
77. Q8×C3⋊D3Q8semidirect
203. #479C3⋊D3semidirect
424. C32#3078semidirect
480. C3#81230semidirect

Maximal subgroups

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

subgroupindex
#105961592
C4×Q8×C3⋊D32
C32×#4792
#105927622
#105927212
#105925802
#105925742
#105925602
#105925532
#105925362
#105925282
#105925012
#105924922
#105924902
#812303