Finite Group Databasebeta

← #11897574

Subgroups — #11897574

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2Dic6×D12C211yesmaximal, characteristic, complemented
3#10592779C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590558C212yesmaximal, complemented
6#10590469C212yesmaximal, complemented
7#10590455C212yesmaximal
8#10590419C212yesmaximal, complemented
9C4×#3713C211yesmaximal, characteristic
10#10590272C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83630—31nomaximal
13#81089—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#946—22no—
18C3×#897—21no—
19C3×#893C2212yes—
20C3×D3×C4⋊C4—21no—
21C3×#890C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918C2212yes—
26#63893—22no—
27Dic3×D12C2212yes—
28#63857—21no—
29C2×#3713C2211yescharacteristic
30#63635C2212yes—
31#63635C2212yes—
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33C3×#809C2212yes—
34C3×#808C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63576C2211yescharacteristic
37#63575C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42#63554C2212yes—
43C3×#554—31no—
44#5730D311yescharacteristic, complemented
45Q8×D12—31no—
46D4×Dic6—31no—
47C3×#476—31no—
48#5084D311yescharacteristic, complemented
49#5080—31no—
50#5080—31no—
51#5080—61no—
52#5066—32no—
53#5064—32no—
54#5024—31no—
55#5014—32no—
56C4×#213—31no—
57C4×#213—31no—
58#5008—32no—
59#5007—31no—
60#4870—32no—
61#4856—32no—
62#4846—31no—
63#4831—31no—
64#4785—32no—
65#4766—32no—
66C2×C32×Q8—21no—
67C2×#634—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×#627—22no—
75C2×D3×Dic3—22no—
76D3×Dic6—44no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3713Q814yescomplemented
98#3384—91noSylow
99C2×D3×Q8—61no—
100C22×Dic6—61no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×#125—32no—
105C3×C22⋊Q8—61no—
106C3×C22⋊Q8—62no—
107C3×C4×Q8—31no—
108C3×C4×D4—32no—
109C3×C4×D4—31no—
110C3×C4×D4—31no—
111C2×C3×C4⋊C4—61no—
112#946—22no—
113D4×Dic3—32no—
114C2×#213—31no—
115C2×#213—31no—
116#924—61no—
117#897—21no—
118#897—62no—
119#897—61no—
120#893C2×D312yes—
121D3×C4⋊C4—21no—
122#890C2×D312yes—
123#888—32no—
124#878—62no—
125C4×D12—32no—
126C4×D12C2×D311yescharacteristic
127C4×D12C2×D311yescharacteristic
128#869—31no—
129#869—31no—
130#869—32no—
131#869—61no—
132C4×Dic6C2×D311yescharacteristic
133C3×#106—32no—
134C3×C4⋊C8—31no—
135C3×#102—32no—
136#832—31no—
137#832—31no—
138#832—32no—
139#821—32no—
140#818—32no—
141#815—32no—
142Dic3⋊C8—32no—
143#809—31no—
144#809—31no—
145#809C2×D312yes—
146#808—32no—
147#808—32no—
148#808—32no—
149#808—32no—
150#808—62no—
151#808—62no—
152#808C2×D312yes—
153#807—31no—
154#807—31no—
155#807—32no—
156C4⋊(C3⋊C8)—32no—
157C4⋊(C3⋊C8)C2×D311yescharacteristic
158#803—32no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—61no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C32×Q8—81no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170#634—42no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D412yes—
175C3×D12—21no—
176C3×D12—21no—
177C3×D12C2×Q812yes—
178C3×D12C2×Q812yescomplemented
179C3×C4×D3—42no—
180C3×C4×D3—42no—
181C3×C4×D3—82no—
182C3×Dic6—22no—
183#627—44no—
184D3×Dic3—44no—
185C3⋊(C3⋊C8)—21no—
186C3⋊(C3⋊C8)C2×Q812yescomplemented
187C3×C3⋊C8—22no—
188#554—31no—
189D4×Q8—91no—
190#501—92no—
191#498—91no—
192#478—92no—
193#476—31no—
194#476—92no—
195#474—91no—
196#446—91no—
197#442—92no—
198C4×D8—91no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—31no—
202C2×C3×Q8—41no—
203C2×C3×D4—31no—
204C2×C3×D4—31no—
205C22×C3×C4—62no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×Dic3—62no—
209D3×Q8—124no—
210C2×D12C22×D311yescharacteristic
211C2×D12C22×D311yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—22no—
215C2×C4×D3—62no—
216C2×Dic6—62no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6—62no—
220C2×Dic6—121no—
221C2×Dic6—124no—
222C2×Dic6#6711yescharacteristic
223C2×C3×C8—32no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4C22×D312yes—
235C3×C4⋊C4C22×D312yes—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—61no—
238C3×C22⋊C4—61no—
239C3×C42—21no—
240C3×C42—32no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#217—62no—
244#213—34no—
245#213—34no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—22no—
249(C2×D3)⋊C4—62no—
250C4⋊Dic3—22no—
251C4⋊Dic3—32no—
252C4⋊Dic3—32no—
253C4⋊Dic3—62no—
254C4⋊Dic3—62no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—121no—
258C4⋊Dic3#6711yescharacteristic
259C4⋊Dic3C22×D311yescharacteristic
260C4⋊Dic3C22×D311yescharacteristic
261Dic3⋊C4—22no—
262Dic3⋊C4—62no—
263Dic3⋊C4#6712yes—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8C22×D312yes—
272C22×C32C22×D411yescharacteristic
273C2×C3×D3—22no—
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4—42no—
281C32×C4AGL(1,ℤ/8)12yes—
282C32×C4C22×Q811yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—41no—
289C22×Q8—181no—
290C2×D8—91no—
291C4⋊Q8—92no—
292C4⋊Q8—91no—
293C4⋊Q8D3211yescharacteristic
294#125—32no—
295C22⋊Q8—61no—
296C22⋊Q8—62no—
297C22⋊Q8—182no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×D4—32no—
301C4×D4—31no—
302C4×D4—31no—
303C4×D4—92no—
304C2×C4⋊C4—61no—
305#107—91no—
306#107—92no—
307#106—32no—
308#106—92no—
309#106—92no—
310C4⋊C8—31no—
311C4⋊C8—92no—
312#102—32no—
313#102—91no—
314#102—91no—
315#102—92no—
316#97—92no—
317C4×C8—91no—
318C23×C3—61no—
319C23×C3—61no—
320C22×D3—21no—
321C22×D3—21no—
322C3×Q8—62no—
323C3×Q8—81no—
324C3×Q8—81no—
325C3×Q8—82no—
326C3×D4—32no—
327C3×D4—32no—
328C3×D4—61no—
329C3×D4—61no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—42no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—122no—
341C2×C3×C4—122no—
342C2×C3×C4—242no—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—122no—
354C2×Dic3—124no—
355C2×Dic3C2×#6712yes—
356C2×Dic3C2×#6712yes—
357D12—21no—
358D12—21no—
359D12D3×Q812yes—
360D12D3×Q812yescomplemented
361C4×D3—42no—
362C4×D3—42no—
363C4×D3—82no—
364C4×D3—124no—
365Dic6—22no—
366Dic6—124no—
367Dic6—124no—
368Dic6—122no—
369Dic6—122no—
370Dic6—242no—
371C3×C8—62no—
372C3⋊C8—22no—
373C3⋊C8—32no—
374C3⋊C8—32no—
375C3⋊C8—62no—
376C3⋊C8—62no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C2×C32D4×Q811yescharacteristic
380C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
381C2×C32#57711yescharacteristic
382C3×D3—42no—
383C3×D3—42no—
384C2×Q8—21no—
385C2×Q8—31no—
386C2×Q8—182no—
387C2×Q8—181no—
388C2×Q8—364no—
389C2×D4—31no—
390C2×D4—31no—
391C22×C4—62no—
392C22×C4—61no—
393C22×C4—61no—
394C22×C4—182no—
395D8—94no—
396C2×C8—32no—
397C2×C8—91no—
398C2×C8—91no—
399C4⋊C4—21no—
400C4⋊C4—31no—
401C4⋊C4—32no—
402C4⋊C4—31no—
403C4⋊C4—31no—
404C4⋊C4—62no—
405C4⋊C4—62no—
406C4⋊C4—92no—
407C4⋊C4—182no—
408C4⋊C4—181no—
409C4⋊C4C2×D3212yes—
410C22⋊C4—62no—
411C22⋊C4—61no—
412C22⋊C4—61no—
413C22⋊C4—182no—
414C42—32no—
415C42C2×D3211yescharacteristic
416C22×C3—21no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C22×#6711yescharacteristic
425C2×D3—22no—
426C2×D3—22no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—41no—
431C3×C4—22no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—62no—
440C3×C4—62no—
441C3×C4—82no—
442C3×C4—121no—
443C3×C4—121no—
444C3×C4#91412yes—
445C3×C4#94912yes—
446C3×C4C2×D3×Q811yescharacteristic
447C3×C4C2×D3×Q811yescharacteristic
448C3×C4#100711yescharacteristic
449C3×C4#101011yescharacteristic
450Dic3—22no—
451Dic3—22no—
452Dic3—41no—
453Dic3—41no—
454Dic3—122no—
455Dic3—122no—
456Dic3—242no—
457C32#338411yescharacteristic, complemented, Sylow
458C23—61no—
459C23—61no—
460Q8—62no—
461Q8—81no—
462Q8—364no—
463Q8—362no—
464D4—32no—
465D4—32no—
466D4—61no—
467D4—61no—
468C2×C4—22no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—122no—
474C2×C4—122no—
475C2×C4—182no—
476C2×C4—242no—
477C2×C4—364no—
478C2×C4D3×#6711yescharacteristic
479C2×C4D3×#6711yescharacteristic
480C2×C4C22×D3211yescharacteristic
481C8—62no—
482C8—92no—
483C8—181no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—122no—
488C2×C3—122no—
489C2×C3#563211yescharacteristic
490C2×C3C2×#91411yescharacteristic
491C2×C3#577511yescharacteristic
492C2×C3Q8×#6711yescharacteristic
493C2×C3C2×#94911yescharacteristic
494C2×C3#583611yescharacteristic
495D3—42no—
496D3—42no—
497C22—62no—
498C22—62no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22—121no—
503C22C2×D3×#6711yescharacteristic
504C4—21no—
505C4—42no—
506C4—62no—
507C4—62no—
508C4—121no—
509C4—121no—
510C4—362no—
511C4#6393912yes—
512C4#6431511yescharacteristic
513C4D32×Q811yescharacteristic
514C3—21no—
515C3#8108911yescharacteristic, complemented
516C3#8363011yescharacteristic, complemented
517C2—122no—
518C2—122no—
519C2#1059510611yescharacteristic
520C2C2×#6393911yescharacteristic
521C2#1059540011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4⋊Q8D32
hypocenterC32#3384
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×#5730C2semidirect
2. Dic6×D12C2semidirect
3. #10592779C2semidirect
4. C3×#5084C2semidirect
5. #10590558C2semidirect
6. #10590469C2semidirect
8. #10590419C2semidirect
10. #10590272C2semidirect
11. #10590259C2semidirect
44. #5730D3semidirect
48. #5084D3semidirect
97. #3713Q8semidirect
178. C3×D12C2×Q8semidirect
186. C3⋊(C3⋊C8)C2×Q8semidirect
360. D12D3×Q8semidirect
457. C32#3384semidirect
515. C3#81089semidirect
516. C3#83630semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
Dic6×D122
#105927792
C3×#50842
#105905582
#105904692
#105904552
#105904192
C4×#37132
#105902722
#105902592
#836303
#810893