Finite Group Databasebeta

← #11906258

Subgroups — #11906258

Order 1152.

2892 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2#10596200C213yesmaximal
3#10596193C213yesmaximal, complemented
4#10596160C213yesmaximal
5#10596159C213yesmaximal
6#10596156C213yesmaximal, complemented
7#10596156C213yesmaximal, complemented
8#10596049C213yesmaximal
9#10596043C211yesmaximal, characteristic
10#10596043C211yesmaximal, characteristic
11C4×Q8×C3⋊D3C211yesmaximal, characteristic
12#10596040C211yesmaximal, characteristic, complemented
13#10596040C211yesmaximal, characteristic, complemented
14#10596038C213yesmaximal, complemented
15Q8×#634C211yesmaximal, characteristic, complemented
16#87032—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C32×C4⋊Q8C2213yes—
19C32×#125C2213yes—
20C32×#125C2213yes—
21C32×C4×Q8C2211yescharacteristic
22C32×C4×Q8C2213yes—
23C32×C4×Q8C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic
25#64155C2213yes—
26Q8×C3⋊Dic3C2211yescharacteristic
27Q8×C3⋊Dic3C2211yescharacteristic
28Q8×C3⋊Dic3C2211yescharacteristic
29#64153C2213yes—
30#64153C2216yes—
31#64106C2213yes—
32#64105C2213yes—
33#64105C2216yes—
34#64105C2211yescharacteristic
35#64101C2213yes—
36#64101C2213yes—
37C4⋊C4×C3⋊D3C2213yes—
38#64099C2213yes—
39#64099C2213yes—
40#64098C2216yes—
41#64098C2213yes—
42#64098C2216yes—
43#64098C2213yes—
44#64097C2213yes—
45#64097C2213yes—
46#64097C2216yes—
47#64097C2213yes—
48#64097C2213yes—
49#64097C2213yes—
50#64096C2213yes—
51#64096C2216yes—
52#64096C2216yes—
53#64096C2213yes—
54#64096C2213yes—
55#64081C2213yes—
56#64081C2213yes—
57C42×C3⋊D3C2213yes—
58#64079C2213yes—
59#64079C2213yes—
60#64078C2213yes—
61C4×#634C2213yes—
62C4×#634C2213yes—
63C4×#634C2213yes—
64C4×#634C2213yes—
65C4×#634C2213yes—
66C4×#634C2213yes—
67C3×#557D314yescomplemented
68#5729—312no—
69#5722—312no—
70#5689—312no—
71#5688—312no—
72#5685—312no—
73#5685—312no—
74#5578—312no—
75#5572—34no—
76#5572—34no—
77C4×D3×Q8—34no—
78#5569—34no—
79#5569—34no—
80#5567—312no—
81Q8×Dic6—34no—
82C2×C32×Q8C2313yes—
83C2×C32×Q8C2311yescharacteristic
84Q8×C3⋊D3Q818yescomplemented
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×C4×C3⋊D3C2313yes—
87C2×C4×C3⋊D3C2313yes—
88C2×#634C2311yescharacteristic
89C2×#634C2313yes—
90C2×#634C2313yes—
91C2×#634C2316yes—
92C2×#634C2313yes—
93C32×C4⋊C4C2313yes—
94C32×C4⋊C4C2313yes—
95C32×C4⋊C4C2316yes—
96C32×C4⋊C4C2313yes—
97C32×C4⋊C4C2313yes—
98C32×C4⋊C4C2313yes—
99C32×C4⋊C4C2311yescharacteristic
100C32×C42C2313yes—
101C32×C42C2313yes—
102C32×C42C2313yes—
103#3752C2311yescharacteristic
104#3752C2311yescharacteristic
105#3752C2313yes—
106#3752C2313yes—
107C4⋊(C3⋊Dic3)C2313yes—
108C4⋊(C3⋊Dic3)C2313yes—
109C4⋊(C3⋊Dic3)C2313yes—
110C4⋊(C3⋊Dic3)C2313yes—
111C4⋊(C3⋊Dic3)C2313yes—
112C4⋊(C3⋊Dic3)C2313yes—
113#3750C2311yescharacteristic
114#3750C2311yescharacteristic
115#3750C2313yes—
116#3750C2313yes—
117#3750C2313yes—
118#3750C2313yes—
119#3750C2313yes—
120#3750C2316yes—
121#3750C2313yes—
122#3750C2316yes—
123#3750C2316yes—
124#3750C2313yes—
125#3750C2313yes—
126C4×C3⋊Dic3C2313yes—
127C4×C3⋊Dic3C2313yes—
128C4×C3⋊Dic3C2313yes—
129C4×C3⋊Dic3C2313yes—
130C4×C3⋊Dic3C2316yes—
131C4×C3⋊Dic3C2316yes—
132C4×C3⋊Dic3C2313yes—
133#3502—91noSylow
134C2×D3×Q8—34no—
135C3×C4⋊Q8C2×D3112yes—
136C3×#125C2×D3112yes—
137C3×#125C2×D3112yes—
138C3×C4×Q8C2×D314yes—
139C3×C4×Q8C2×D3112yes—
140C3×C4×Q8C2×D314yes—
141C3×C4×Q8C2×D314yes—
142#946—312no—
143Q8×Dic3—34no—
144Q8×Dic3—34no—
145Q8×Dic3—34no—
146#944—312no—
147#944—324no—
148#897—312no—
149#896—312no—
150#896—324no—
151#896—34no—
152#892—312no—
153#892—312no—
154D3×C4⋊C4—312no—
155#890—312no—
156#890—312no—
157#889—324no—
158#889—312no—
159#889—324no—
160#889—312no—
161#888—312no—
162#888—312no—
163#888—324no—
164#888—312no—
165#888—312no—
166#888—312no—
167#887—312no—
168#887—324no—
169#887—324no—
170#887—312no—
171#887—312no—
172#872—312no—
173#872—312no—
174C42×D3—312no—
175#870—312no—
176#870—312no—
177#869—312no—
178C4×Dic6—312no—
179C4×Dic6—312no—
180C4×Dic6—312no—
181C4×Dic6—312no—
182C4×Dic6—312no—
183C4×Dic6—312no—
184C22×C3⋊D3C2411yescharacteristic
185C32×Q8—43no—
186C32×Q8C2×Q814yes—
187C2×C32×C4C2411yescharacteristic
188C2×C32×C4C2413yes—
189C2×C32×C4C2413yes—
190C2×C32×C4C2413yes—
191C2×C32×C4C2411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C2×C32×C4C2413yes—
194C2×C3⋊Dic3C2411yescharacteristic
195C2×C3⋊Dic3C2413yes—
196C2×C3⋊Dic3C2411yescharacteristic
197C2×C3⋊Dic3C2413yes—
198C2×C3⋊Dic3C2413yes—
199C2×C3⋊Dic3C2413yes—
200C2×C3⋊Dic3C2411yescharacteristic
201C4×C3⋊D3—22no—
202C4×C3⋊D3—43no—
203C4×C3⋊D3C2×Q8112yes—
204#634—22no—
205#634—26no—
206#634—43no—
207#634—46no—
208#634C2×Q8112yes—
209Q82—93no—
210Q82—91no—
211#557—93no—
212#557—93no—
213#557—93no—
214#557—91no—
215#557—91no—
216#557C3⋊D311yescharacteristic, complemented
217#544—93no—
218#544—93no—
219#533—93no—
220#533—93no—
221#519—91no—
222#519—91no—
223C2×C4×Q8—91no—
224C2×C3×Q8C22×D3112yes—
225C2×C3×Q8C22×D314yes—
226D3×Q8—332no—
227C2×C4×D3—312no—
228C2×C4×D3—34no—
229C2×C4×D3—312no—
230C2×Dic6—312no—
231C2×Dic6—34no—
232C2×Dic6—312no—
233C2×Dic6—312no—
234C2×Dic6—324no—
235C3×C4⋊C4C22×D3112yes—
236C3×C4⋊C4C22×D3112yes—
237C3×C4⋊C4C22×D3124yes—
238C3×C4⋊C4C22×D3112yes—
239C3×C4⋊C4C22×D3112yes—
240C3×C4⋊C4C22×D3112yes—
241C3×C4⋊C4C22×D314yes—
242C3×C42C22×D3112yes—
243C3×C42C22×D3112yes—
244C3×C42C22×D3112yes—
245(C2×D3)⋊C4—34no—
246(C2×D3)⋊C4—34no—
247(C2×D3)⋊C4—312no—
248(C2×D3)⋊C4—312no—
249C4⋊Dic3—312no—
250C4⋊Dic3—312no—
251C4⋊Dic3—312no—
252C4⋊Dic3—312no—
253C4⋊Dic3—312no—
254C4⋊Dic3—312no—
255Dic3⋊C4—34no—
256Dic3⋊C4—34no—
257Dic3⋊C4—312no—
258Dic3⋊C4—312no—
259Dic3⋊C4—312no—
260Dic3⋊C4—312no—
261Dic3⋊C4—312no—
262Dic3⋊C4—324no—
263Dic3⋊C4—312no—
264Dic3⋊C4—324no—
265Dic3⋊C4—324no—
266Dic3⋊C4—312no—
267Dic3⋊C4—312no—
268C4×Dic3—312no—
269C4×Dic3—312no—
270C4×Dic3—312no—
271C4×Dic3—312no—
272C4×Dic3—324no—
273C4×Dic3—324no—
274C4×Dic3—312no—
275C22×C32C2511yescharacteristic
276C2×C3⋊D3—21no—
277C2×C3⋊D3—21no—
278C2×C3⋊D3C22×Q812yes—
279C32×C4—23no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—23no—
283C32×C4—23no—
284C32×C4—21no—
285C32×C4C22×Q816yes—
286C3⋊Dic3—21no—
287C3⋊Dic3—23no—
288C3⋊Dic3—21no—
289C3⋊Dic3—23no—
290C3⋊Dic3—23no—
291C3⋊Dic3C22×Q816yes—
292C3⋊Dic32−1+412yes—
293C22×Q8—91no—
294C4⋊Q8—93no—
295C4⋊Q8—96no—
296C4⋊Q8—93no—
297C4⋊Q8—93no—
298C4⋊Q8—93no—
299C4⋊Q8—96no—
300C4⋊Q8—93no—
301C4⋊Q8—93no—
302C4⋊Q8—93no—
303C4⋊Q8C2×C3⋊D313yes—
304#125—93no—
305#125—93no—
306#125—96no—
307#125—96no—
308#125—93no—
309#125—93no—
310#125—93no—
311#125—93no—
312#125C2×C3⋊D313yes—
313#125C2×C3⋊D313yes—
314C22⋊Q8—93no—
315C22⋊Q8—93no—
316C22⋊Q8—91no—
317C22⋊Q8—96no—
318C22⋊Q8—93no—
319C4×Q8—91no—
320C4×Q8—91no—
321C4×Q8—91no—
322C4×Q8—93no—
323C4×Q8—93no—
324C4×Q8—93no—
325C4×Q8—96no—
326C4×Q8—96no—
327C4×Q8—93no—
328C4×Q8—93no—
329C4×Q8—93no—
330C4×Q8—93no—
331C4×Q8—93no—
332C4×Q8—93no—
333C4×Q8C2×C3⋊D311yescharacteristic
334C4×Q8C2×C3⋊D311yescharacteristic
335C4×Q8C2×C3⋊D311yescharacteristic
336C4×Q8C2×C3⋊D313yes—
337#117—93no—
338#117—93no—
339#117—93no—
340#117—93no—
341C2×C4⋊C4—93no—
342C2×C42—93no—
343C22×D3—34no—
344C3×Q8—412no—
345C3×Q8D3×Q8116yes—
346C2×C3×C4C23×D314yes—
347C2×C3×C4C23×D3112yes—
348C2×C3×C4C23×D3112yes—
349C2×C3×C4C23×D3112yes—
350C2×C3×C4C23×D314yes—
351C2×C3×C4C23×D314yes—
352C2×C3×C4C23×D3112yes—
353C2×Dic3—312no—
354C2×Dic3—34no—
355C2×Dic3—34no—
356C2×Dic3—312no—
357C2×Dic3—34no—
358C2×Dic3—312no—
359C2×Dic3—312no—
360C4×D3—348no—
361C4×D3—68no—
362C4×D3—1212no—
363Dic6—348no—
364Dic6—68no—
365Dic6—624no—
366Dic6—1212no—
367Dic6—1224no—
368C2×C32C23×Q811yescharacteristic
369C2×C32C2×2−1+411yescharacteristic
370C2×C32#58511yescharacteristic
371C3⋊D3—22no—
372C2×Q8—98no—
373C2×Q8—93no—
374C2×Q8—93no—
375C2×Q8—91no—
376C2×Q8—93no—
377C2×Q8—96no—
378C2×Q8C22×C3⋊D313yes—
379C2×Q8C22×C3⋊D311yescharacteristic
380C22×C4—93no—
381C22×C4—91no—
382C22×C4—93no—
383C4⋊C4—96no—
384C4⋊C4—93no—
385C4⋊C4—93no—
386C4⋊C4—93no—
387C4⋊C4—93no—
388C4⋊C4—93no—
389C4⋊C4—93no—
390C4⋊C4—93no—
391C4⋊C4—93no—
392C4⋊C4—91no—
393C4⋊C4—93no—
394C4⋊C4—91no—
395C4⋊C4—96no—
396C4⋊C4—93no—
397C4⋊C4—96no—
398C4⋊C4—93no—
399C4⋊C4—93no—
400C4⋊C4—93no—
401C4⋊C4—93no—
402C4⋊C4C22×C3⋊D313yes—
403C4⋊C4C22×C3⋊D313yes—
404C4⋊C4C22×C3⋊D313yes—
405C4⋊C4C22×C3⋊D313yes—
406C4⋊C4C22×C3⋊D316yes—
407C4⋊C4C22×C3⋊D311yescharacteristic
408C4⋊C4C22×C3⋊D313yes—
409C22⋊C4—93no—
410C22⋊C4—91no—
411C22⋊C4—93no—
412C22⋊C4—91no—
413C42—93no—
414C42—93no—
415C42—93no—
416C42—96no—
417C42—96no—
418C42—93no—
419C42—93no—
420C42C22×C3⋊D313yes—
421C42C22×C3⋊D313yes—
422C42C22×C3⋊D313yes—
423C22×C3C24×D314yes—
424C2×D3—38no—
425C2×D3—64no—
426C2×D3—64no—
427C3×C4—212no—
428C3×C4—212no—
429C3×C4—24no—
430C3×C4—212no—
431C3×C4—24no—
432C3×C4—24no—
433C3×C4C2×D3×Q8124yes—
434Dic3—324no—
435Dic3—38no—
436Dic3—64no—
437Dic3—612no—
438Dic3—612no—
439Dic3—64no—
440Dic3—612no—
441C32#350211yescharacteristic, complemented, Sylow
442C23—91no—
443Q8—43no—
444Q8—912no—
445Q8—186no—
446Q8—182no—
447Q8—363no—
448Q8—366no—
449Q8Q8×C3⋊D314yes—
450C2×C4—93no—
451C2×C4—91no—
452C2×C4—912no—
453C2×C4—91no—
454C2×C4—93no—
455C2×C4—91no—
456C2×C4—93no—
457C2×C4—93no—
458C2×C4—182no—
459C2×C4—363no—
460C2×C4C23×C3⋊D311yescharacteristic
461C2×C4C23×C3⋊D313yes—
462C2×C4C23×C3⋊D313yes—
463C2×C4C23×C3⋊D313yes—
464C2×C4C23×C3⋊D311yescharacteristic
465C2×C4C23×C3⋊D311yescharacteristic
466C2×C4C23×C3⋊D313yes—
467C2×C3C22×D3×Q814yes—
468C2×C3#596414yes—
469C2×C3D3×2−1+414yes—
470D3—68no—
471C22—92no—
472C22—181no—
473C22—181no—
474C22C24×C3⋊D311yescharacteristic
475C4—23no—
476C4—21no—
477C4—23no—
478C4—21no—
479C4—23no—
480C4—21no—
481C4—96no—
482C4—92no—
483C4—183no—
484C4—181no—
485C4—183no—
486C4—181no—
487C4—183no—
488C4C2×Q8×C3⋊D316yes—
489C3#8703214yescomplemented
490C2—182no—
491C2C22×Q8×C3⋊D311yescharacteristic
492C2#1059675611yescharacteristic
493C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#557C2
prime radicalC22×C3⋊D3C24
hypercenter#557C3⋊D3
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
3. #10596193C2semidirect
6. #10596156C2semidirect
7. #10596156C2semidirect
12. #10596040C2semidirect
13. #10596040C2semidirect
14. #10596038C2semidirect
15. Q8×#634C2semidirect
67. C3×#557D3semidirect
84. Q8×C3⋊D3Q8semidirect
216. #557C3⋊D3semidirect
441. C32#3502semidirect
489. C3#87032semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
#105962002
#105961932
#105961602
#105961592
#105961562
#105960492
#105960432
C4×Q8×C3⋊D32
#105960402
#105960382
Q8×#6342
#870323