Finite Group Databasebeta

← #11898381

Subgroups — #11898381

Order 1152.

780 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3#10592782C211yesmaximal, characteristic, complemented
4C3×#5092C211yesmaximal, characteristic, complemented
5#10591609C212yesmaximal
6#10591607C212yesmaximal, complemented
7#10591578C212yesmaximal, complemented
8Dic3×#216C212yesmaximal, complemented
9#10590363C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83670—31nomaximal
13#81795—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15C2×#3755C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#947C2212yes—
18C3×Q8×Dic3C2212yes—
19C2×C3×#216C2212yes—
20C2×C3×#216C2212yes—
21C3×#898—22no—
22C3×#897—21no—
23C3×#892—21no—
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63871—21no—
28#63864C2212yes—
29#63849—21no—
30#63848—22no—
31Dic3×Dic6C2212yes—
32C2×#3715C2212yes—
33C2×#3714C2211yescharacteristic
34#63662C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2212yes—
40#63564C2211yescharacteristic
41#63563C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#556—31no—
44#5732—31no—
45#5732D311yescharacteristic, complemented
46#5584—31no—
47C3×#494—31no—
48#5191—32no—
49#5185—32no—
50#5185—32no—
51Dic3×Q16—32no—
52#5092D311yescharacteristic, complemented
53#5083—31no—
54#5083—31no—
55#5083—31no—
56#5083—61no—
57#5059—32no—
58#5054—32no—
59C4×#216—32no—
60#5028—32no—
61Q8×C3⋊C8—31no—
62#5019—31no—
63C4×#213—31no—
64C4×D24—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2312yes—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C32×C4⋊C4—21no—
74C32×C4⋊C4—21no—
75C32×C42C2311yescharacteristic
76#3755—42no—
77#3752—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×#216—24no—
81C3×#216—42no—
82C3×(C2×D3)⋊C4—21no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95Dic3⋊Dic3—22no—
96#3722—22no—
97#3722—22no—
98Dic32—22no—
99#3715—42no—
100#3714—22no—
101#3393—91noSylow
102C2×C3×Q16—32no—
103C2×C3×Q16—32no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C2×D311yescharacteristic
108C3×#126—62no—
109C3×#124—32no—
110C3×C22⋊Q8—61no—
111C3×C4×Q8—31no—
112C3×C4×Q8—32no—
113C3×C4×D4—31no—
114C3×#117—61no—
115#947—32no—
116#947C2×D312yes—
117#946—61no—
118Q8×Dic3—32no—
119Q8×Dic3C2×D312yes—
120C2×#216C2×D312yes—
121C2×#216C2×D312yes—
122C2×#215—32no—
123C2×#215—32no—
124C2×#215—32no—
125C2×#215—62no—
126C2×#214—32no—
127C2×#213—31no—
128C2×D24—31no—
129#898—22no—
130#898—62no—
131#898—62no—
132#897—21no—
133#897—61no—
134#892—21no—
135#892—61no—
136#892—61no—
137#875—32no—
138C4×D12—31no—
139C4×D12—31no—
140C4×D12—61no—
141C4×D12C2×D311yescharacteristic
142#869C2×D311yescharacteristic
143C4×Dic6—32no—
144C4×Dic6C2×D311yescharacteristic
145C3×C4×C8—31no—
146#835—32no—
147#835—32no—
148#835—32no—
149#835—62no—
150#832—31no—
151#821—31no—
152#821—31no—
153#818—31no—
154Dic3⋊C8—32no—
155C8×Dic3—32no—
156#810—32no—
157#809—31no—
158#807—31no—
159C4⋊(C3⋊C8)—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—32no—
162C4⋊(C3⋊C8)—61no—
163C4×C3⋊C8—32no—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C32×Q8—22no—
168C32×Q8—22no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C4⋊(C3⋊D3)—21no—
175C4⋊(C3⋊D3)—21no—
176C4×C3⋊D3—42no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—21no—
182C3×D12—21no—
183C3×C4×D3—42no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C3⋊(C3⋊C8)—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8#4112yes—
190#556—31no—
191#556—91no—
192#495—92no—
193#494—31no—
194#464—92no—
195#464—92no—
196#461—91no—
197#461—91no—
198C8×Q8—91no—
199C4×Q16—92no—
200C4×D8—91no—
201C2×C3×Q8—22no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8C22×D312yes—
205C2×C3×Q8C22×D312yes—
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C2×D12—31no—
209C2×D12—31no—
210C2×D12—61no—
211C2×D12C22×D311yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—121no—
216C2×Dic6#6711yescharacteristic
217C2×Dic6C22×D312yes—
218C3×Q16—64no—
219C3×Q16—122no—
220C2×C3×C8—31no—
221C2×C3×C8—31no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—41no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C22⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42—32no—
239C3×C42—62no—
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D311yescharacteristic
242#216—24no—
243#216—42no—
244#215—122no—
245#215—122no—
246#215—122no—
247#215—124no—
248#214—122no—
249#213—62no—
250(C2×D3)⋊C4—21no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—121no—
260C4⋊Dic3—21no—
261C4⋊Dic3—21no—
262C4⋊Dic3—22no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266C4⋊Dic3—62no—
267C4⋊Dic3#6711yescharacteristic
268C4⋊Dic3C22×D311yescharacteristic
269Dic3⋊C4—62no—
270Dic3⋊C4#6712yes—
271C4×Dic3—22no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C4×Dic3C22×D312yes—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D311yescharacteristic
280D24—62no—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—21no—
289C32×C4—42no—
290C32×C4#13512yes—
291C32×C4C2×#4111yescharacteristic
292C32×C4H(5,𝔽2)11yescharacteristic
293C3⋊Dic3—41no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C2×Q16—32no—
299C2×Q16—32no—
300C2×SD16—92no—
301C2×SD16—92no—
302C2×D8—91no—
303C4⋊Q8—31no—
304C4⋊Q8D3211yescharacteristic
305#126—62no—
306#126—182no—
307#124—32no—
308#124—92no—
309C22⋊Q8—61no—
310C22⋊Q8—181no—
311C4×Q8—31no—
312C4×Q8—32no—
313C4×Q8—92no—
314C4×D4—31no—
315C4×D4—91no—
316#117—61no—
317#117—181no—
318#107—91no—
319C4⋊C8—92no—
320C4⋊C8—91no—
321#103—92no—
322#103—92no—
323#102—91no—
324#102—91no—
325C4×C8—31no—
326C4×C8—92no—
327C23×C3—61no—
328C22×D3—21no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—121no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×Q8—42no—
337C3×Q8—42no—
338C3×Q8—62no—
339C3×Q8—62no—
340C3×Q8—62no—
341C3×D4—61no—
342C3×D4—61no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—42no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4—122no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—121no—
365C2×Dic3C2×#6712yes—
366C2×Dic3C2×#6712yes—
367D12—21no—
368D12—21no—
369D12—62no—
370D12—61no—
371D12—61no—
372D12—61no—
373D12—61no—
374D12—121no—
375C4×D3—42no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—242no—
379Dic6—22no—
380Dic6—22no—
381Dic6—22no—
382C3×C8—32no—
383C3×C8—61no—
384C3⋊C8—21no—
385C3⋊C8—62no—
386C3⋊C8—62no—
387C3⋊C8—122no—
388C3⋊C8#23712yes—
389C2×C32#55011yescharacteristic
390C2×C32C2×#13511yescharacteristic
391C2×C32#57811yescharacteristic
392C3⋊D3—81no—
393C3×D3—81no—
394C2×Q8—31no—
395C2×Q8—32no—
396C2×Q8C2×D3212yes—
397C2×D4—31no—
398C2×D4—91no—
399C22×C4—61no—
400C22×C4—181no—
401Q16—64no—
402Q16—122no—
403SD16—362no—
404SD16—362no—
405D8—182no—
406C2×C8—31no—
407C2×C8—31no—
408C2×C8—92no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—31no—
412C4⋊C4—32no—
413C4⋊C4—31no—
414C4⋊C4—62no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C4⋊C4—91no—
418C4⋊C4—182no—
419C22⋊C4—62no—
420C22⋊C4—62no—
421C22⋊C4—61no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—181no—
425C42—32no—
426C42—62no—
427C42—182no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3—121no—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×#6711yescharacteristic
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—41no—
438C2×D3—122no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—241no—
446C2×D3—241no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—41no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—82no—
458C3×C4—121no—
459C3×C4—122no—
460C3×C4#91912yes—
461C3×C4#95012yes—
462C3×C4C2×#23711yescharacteristic
463C3×C4#100411yescharacteristic
464C3×C4D3×#4111yescharacteristic
465C3×C4#100911yescharacteristic
466Dic3—22no—
467Dic3—22no—
468Dic3—42no—
469Dic3—41no—
470Dic3—121no—
471Dic3—121no—
472Dic3—241no—
473C32#339311yescharacteristic, complemented, Sylow
474C23—61no—
475C23—181no—
476Q8—22no—
477Q8—22no—
478Q8—62no—
479Q8—62no—
480Q8—62no—
481D4—61no—
482D4—61no—
483D4—181no—
484D4—181no—
485C2×C4—22no—
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—61no—
489C2×C4—62no—
490C2×C4—122no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4D3×#6711yescharacteristic
494C2×C4D3×#6711yescharacteristic
495C2×C4C22×D3211yescharacteristic
496C8—32no—
497C8—61no—
498C8—182no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—241no—
503C2×C3#571811yescharacteristic
504C2×C3C2×#91911yescharacteristic
505C2×C3#576611yescharacteristic
506C2×C3C2×#95011yescharacteristic
507C2×C3#583411yescharacteristic
508C2×C3#583811yescharacteristic
509D3—81no—
510D3—242no—
511D3—241no—
512D3—241no—
513C22—121no—
514C22—121no—
515C22—121no—
516C22—361no—
517C22—361no—
518C22—361no—
519C22C2×D3×#6711yescharacteristic
520C4—21no—
521C4—42no—
522C4—62no—
523C4—62no—
524C4—121no—
525C4—122no—
526C4—361no—
527C4#6394912yes—
528C4D3×#23711yescharacteristic
529C4#6431411yescharacteristic
530C3—21no—
531C3#8179511yescharacteristic, complemented
532C3#8367011yescharacteristic, complemented
533C2—241no—
534C2—721no—
535C2#1059515811yescharacteristic
536C2#1059532711yescharacteristic
537C2C2×#6394911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊Q8D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5732C2semidirect
2. #10593865C2semidirect
3. #10592782C2semidirect
4. C3×#5092C2semidirect
6. #10591607C2semidirect
7. #10591578C2semidirect
8. Dic3×#216C2semidirect
9. #10590363C2semidirect
11. C3⋊C8×Dic6C2semidirect
45. #5732D3semidirect
52. #5092D3semidirect
473. C32#3393semidirect
531. C3#81795semidirect
532. C3#83670semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
#105938652
#105927822
C3×#50922
#105916092
#105916072
#105915782
Dic3×#2162
#105903632
C4×#37142
C3⋊C8×Dic62
#836703
#817953