Finite Group Databasebeta

← #11887587

Subgroups — #11887587

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#638C211yesmaximal, characteristic
2#10596106C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic, complemented
4C2×#63662C211yesmaximal, characteristic, complemented
5#10592887C211yesmaximal, characteristic, complemented
6#10592885C211yesmaximal, characteristic, complemented
7#10592881C211yesmaximal, characteristic, complemented
8Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
9#10592750C211yesmaximal, characteristic, complemented
10#10592510C211yesmaximal, characteristic, complemented
11C3⋊D3×#103C211yesmaximal, characteristic, complemented
12#10592492C211yesmaximal, characteristic, complemented
13#10592491C211yesmaximal, characteristic, complemented
14#10592424C211yesmaximal, characteristic
15#10592421C211yesmaximal, characteristic, complemented
16#80193—34nomaximal
17C22×C32×Q8C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22#64155—21no—
23#64155C2211yescharacteristic
24#64155C2211yescharacteristic
25Q8×C3⋊Dic3C2211yescharacteristic
26Q8×C3⋊Dic3C2211yescharacteristic
27#64153—21no—
28#64153C2211yescharacteristic
29C2×#3756C2211yescharacteristic
30C4×#638—21no—
31C4×#638C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33#64133—21no—
34#64133C2211yescharacteristic
35C22×C3⋊(C3⋊C8)C2211yescharacteristic
36C2×C8×C3⋊D3C2211yescharacteristic
37#64106—21no—
38C4⋊C4×C3⋊D3C2211yescharacteristic
39#64098—21no—
40#64097C2211yescharacteristic
41#64090—21no—
42#64087—21no—
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63662C2211yescharacteristic
50#63662C2211yescharacteristic
51#63647C2211yescharacteristic
52#63645C2211yescharacteristic
53#63645C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63641C2211yescharacteristic
57C8×C3⋊Dic3C2211yescharacteristic
58#63637C2211yescharacteristic
59#63634C2211yescharacteristic
60Q8×#67—34no—
61#5635—34no—
62C3×#451D314yescomplemented
63C2×#835—34no—
64#5188—34no—
65#5186—34no—
66#5182—34no—
67Dic3×Q16—34no—
68#5051—34no—
69#4811—34no—
70D3×#103—34no—
71#4793—34no—
72#4792—34no—
73#67⋊C8—34no—
74#4722—34no—
75C2×C32×Q8—21no—
76C2×C32×Q8—22no—
77C2×C32×Q8—41no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×Q8C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638D411yescharacteristic
84C22×C3⋊Dic3—21no—
85Q8×C3⋊D3—22no—
86Q8×C3⋊D3—41no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634—21no—
91C2×#634—21no—
92C2×#634C2311yescharacteristic
93C32×Q16—22no—
94C32×Q16—41no—
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4—21no—
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100#3757—21no—
101#3757D411yescharacteristic
102#3756—41no—
103#3752—21no—
104#3752—21no—
105#3752D411yescharacteristic
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3299—91noSylow
128C22×C3×Q8C2×D314yes—
129C2×D3×Q8—34no—
130C2×C3×Q16C2×D314yes—
131C2×C3×Q16C2×D314yes—
132C3×C22⋊Q8C2×D314yes—
133#946—34no—
134#946—34no—
135#946—64no—
136Q8×Dic3—34no—
137Q8×Dic3—34no—
138#944—34no—
139#944—64no—
140C2×#216—34no—
141C4×#67—34no—
142C4×#67—64no—
143C2×C4⋊Dic3—34no—
144#924—34no—
145#924—64no—
146C22×C3⋊C8—34no—
147C2×D3×C8—34no—
148#897—64no—
149D3×C4⋊C4—34no—
150#889—64no—
151#888—34no—
152#67⋊C4—64no—
153#878—64no—
154C3×#103C2×D314yes—
155C3×#103C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157#835—34no—
158#835—34no—
159#835—34no—
160#835—34no—
161#835—34no—
162(C2×D3)⋊C8—34no—
163#818—34no—
164#818—34no—
165#816—34no—
166#816—34no—
167Dic3⋊C8—34no—
168C8×Dic3—34no—
169#810—34no—
170#807—34no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3C2×D411yescharacteristic
173C32×Q8—21no—
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8—21no—
178C32×Q8—42no—
179C32×Q8#4112yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—42no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638Q1614yescomplemented
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—81no—
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C4×C3⋊D3—21no—
199C4×C3⋊D3—21no—
200C4×C3⋊D3—42no—
201C4×C3⋊D3—81no—
202#634—21no—
203#634—21no—
204#634—42no—
205#634—81no—
206C32×C8—21no—
207C32×C8—21no—
208C3⋊(C3⋊C8)—21no—
209C3⋊(C3⋊C8)—21no—
210#554—91no—
211D4×Q8—91no—
212#487—91no—
213#484—91no—
214#484—91no—
215#477—91no—
216#467—91no—
217#467—91no—
218#462—91no—
219#451—91no—
220#451C3⋊D311yescharacteristic, complemented
221C4×Q16—91no—
222C8×D4—91no—
223C2×#103—91no—
224C2×#103—91no—
225C2×C3×Q8—24no—
226C2×C3×Q8—28no—
227C2×C3×Q8—44no—
228C2×C3×Q8C22×D314yes—
229C2×C3×Q8C22×D314yes—
230C2×C3×Q8C22×D314yes—
231C22×C3×C4—24no—
232C22×C3×C4C22×D314yes—
233C2×#67—34no—
234C22×Dic3—64no—
235D3×Q8—68no—
236D3×Q8—124no—
237C2×C4×D3—34no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×Dic6—34no—
241C2×Dic6—64no—
242C2×Dic6—64no—
243C3×Q16—28no—
244C3×Q16—44no—
245C2×C3×C8C22×D314yes—
246C2×C3×C8C22×D314yes—
247C3×C4⋊C4—24no—
248C3×C4⋊C4C22×D314yes—
249C3×C22⋊C4—24no—
250#217—34no—
251#217—64no—
252#216—124no—
253(C2×D3)⋊C4—34no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256C4⋊Dic3—34no—
257C4⋊Dic3—34no—
258C4⋊Dic3—34no—
259C4⋊Dic3—64no—
260C4⋊Dic3—64no—
261C4⋊Dic3—64no—
262Dic3⋊C4—34no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270C4×Dic3—34no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275C2×C3⋊C8—124no—
276D3×C8—124no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32C2×Q1612yes—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3C2×Q1612yes—
284C32×C4—22no—
285C32×C4—21no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4C2×#4111yescharacteristic
290C32×C4H(5,𝔽2)11yescharacteristic
291C3⋊Dic3—21no—
292C3⋊Dic3—21no—
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3C2×Q1612yes—
298C22×Q8—91no—
299C22×Q8C2×C3⋊D311yescharacteristic
300C2×Q16—91no—
301C2×Q16C2×C3⋊D311yescharacteristic
302C2×Q16C2×C3⋊D311yescharacteristic
303C22×C8—91no—
304C22×C8—91no—
305C4⋊Q8—91no—
306C4⋊Q8—91no—
307C4⋊Q8—181no—
308#125—181no—
309C22⋊Q8—91no—
310C22⋊Q8—91no—
311C22⋊Q8—91no—
312C22⋊Q8—181no—
313C22⋊Q8—181no—
314C22⋊Q8—181no—
315C22⋊Q8—181no—
316C22⋊Q8C2×C3⋊D311yescharacteristic
317C4×Q8—91no—
318C4×Q8—91no—
319C4×D4—91no—
320C4×D4—181no—
321C4×D4—181no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—91no—
324#107—91no—
325#107—91no—
326#107—91no—
327C4⋊C8—91no—
328#103—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#103C2×C3⋊D311yescharacteristic
337#103C2×C3⋊D311yescharacteristic
338C22⋊C8—91no—
339C22⋊C8C2×C3⋊D311yescharacteristic
340C4×C8—91no—
341C23×C3D3×D414yes—
342C22×D3—34no—
343C3×Q8—24no—
344C3×Q8—24no—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8—24no—
348C3×Q8—48no—
349C3×Q8#23718yes—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—48no—
357C2×C3×C4D3×D414yes—
358C2×C3×C4C23×D314yes—
359#67—316no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—34no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C2×Dic3—244no—
368C4×D3—64no—
369C4×D3—64no—
370C4×D3—128no—
371C4×D3—244no—
372Dic6—64no—
373Dic6—64no—
374Dic6—128no—
375Dic6—244no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—22no—
381C2×C32#54611yescharacteristic
382C2×C32C22×Q1611yescharacteristic
383C2×C32#57711yescharacteristic
384C3⋊D3—22no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—41no—
388C2×Q8—91no—
389C2×Q8—181no—
390C2×Q8—181no—
391C2×Q8—182no—
392C2×Q8—361no—
393C2×Q8C22×C3⋊D311yescharacteristic
394C2×Q8C22×C3⋊D311yescharacteristic
395C2×Q8C22×C3⋊D311yescharacteristic
396C2×D4—91no—
397C22×C4—21no—
398C22×C4—91no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—22no—
404Q16—41no—
405Q16—361no—
406C2×C8—91no—
407C2×C8—91no—
408C2×C8—361no—
409C2×C8—361no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C4⋊C4—181no—
427C4⋊C4C22×C3⋊D311yescharacteristic
428C22⋊C4—21no—
429C22⋊C4—91no—
430C22⋊C4—91no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—91no—
435C42—181no—
436C42—181no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3D3×Q1618yes—
440C22×C3C2×D3×D414yes—
441C2×D3—38no—
442C2×D3—64no—
443C2×D3—64no—
444C3×C4—28no—
445C3×C4—24no—
446C3×C4—44no—
447C3×C4—44no—
448C3×C4—44no—
449C3×C4C2×#23714yes—
450C3×C4#100414yes—
451Dic3—38no—
452Dic3—64no—
453Dic3—64no—
454Dic3—124no—
455Dic3—124no—
456Dic3—124no—
457Dic3—124no—
458C32#329911yescharacteristic, complemented, Sylow
459C23—91no—
460C23D4×C3⋊D311yescharacteristic
461Q8—21no—
462Q8—21no—
463Q8—21no—
464Q8—21no—
465Q8—21no—
466Q8—42no—
467Q8—181no—
468Q8—181no—
469Q8—362no—
470Q8—721no—
471Q8#383012yes—
472D4—94no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—42no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—91no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—362no—
490C2×C4—721no—
491C2×C4—721no—
492C2×C4D4×C3⋊D311yescharacteristic
493C2×C4C23×C3⋊D311yescharacteristic
494C8—21no—
495C8—21no—
496C8—181no—
497C8—181no—
498C2×C3—28no—
499C2×C3#559114yes—
500C2×C3C2×D3×Q1614yes—
501C2×C3#577814yes—
502D3—68no—
503C22—21no—
504C22—21no—
505C22—92no—
506C22—181no—
507C22—181no—
508C22Q16×C3⋊D312yes—
509C22C2×D4×C3⋊D311yescharacteristic
510C4—21no—
511C4—22no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—92no—
516C4—181no—
517C4—181no—
518C4—361no—
519C4—361no—
520C4—361no—
521C4—361no—
522C4C2×#383011yescharacteristic
523C4#6436111yescharacteristic
524C3#8019314yescomplemented
525C2—22no—
526C2—182no—
527C2#1059606211yescharacteristic
528C2C2×Q16×C3⋊D311yescharacteristic
529C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC2×#638D4
hypercenter#451C3⋊D3
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. C32×#451C2semidirect
4. C2×#63662C2semidirect
5. #10592887C2semidirect
6. #10592885C2semidirect
7. #10592881C2semidirect
8. Q16×C3⋊Dic3C2semidirect
9. #10592750C2semidirect
10. #10592510C2semidirect
11. C3⋊D3×#103C2semidirect
12. #10592492C2semidirect
13. #10592491C2semidirect
15. #10592421C2semidirect
62. C3×#451D3semidirect
189. #638Q16semidirect
220. #451C3⋊D3semidirect
458. C32#3299semidirect
524. C3#80193semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
#105961062
C32×#4512
C2×#636622
#105928872
#105928852
#105928812
Q16×C3⋊Dic32
#105927502
#105925102
C3⋊D3×#1032
#105924922
#105924912
#105924242
#105924212
#801933