Finite Group Databasebeta

← #11897664

Subgroups — #11897664

Order 1152.

727 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3#10592723C211yesmaximal, characteristic, complemented
4#10590358C212yesmaximal
5C4×#3715C211yesmaximal, characteristic
6#10590315C212yesmaximal, complemented
7#10590312C211yesmaximal, characteristic, complemented
8#10590310C211yesmaximal, characteristic, complemented
9#10590286C212yesmaximal, complemented
10#10590269C212yesmaximal
11#10590266C211yesmaximal, characteristic
12#83706—31nomaximal
13#83631—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C3×#946—21no—
16C3×Q8×Dic3—21no—
17C3×#896—22no—
18C3×D3×C4⋊C4—21no—
19C3×#888—21no—
20C3×#888—22no—
21C3×C4×D12C2211yescharacteristic
22C3×C4×D12C2212yes—
23C3×#870C2212yes—
24C3×#869C2211yescharacteristic
25C3×#869C2212yes—
26C3×#869C2211yescharacteristic
27C3×C4×Dic6C2212yes—
28C3×C4×Dic6C2211yescharacteristic
29C2×#3715C2211yescharacteristic
30C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
31C4⋊(C3⋊(C3⋊C8))C2212yes—
32#63630C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34#63576C2212yes—
35#63576C2212yes—
36#63576C2212yes—
37#63574C2212yes—
38#63574C2211yescharacteristic
39#63565C2211yescharacteristic
40#63565C2212yes—
41#63562C2212yes—
42#63562C2211yescharacteristic
43C3×Q82—31no—
44C3×#554—31no—
45#5579D311yescharacteristic
46Q8×Dic6D311yescharacteristic, complemented
47#5091—31no—
48#5087—32no—
49#5084—31no—
50#5081—32no—
51#5078—31no—
52#5078—31no—
53#5064—32no—
54#5063—32no—
55#5026—32no—
56C4×#215—31no—
57#5024—31no—
58#5024—31no—
59#5024—61no—
60#5022—32no—
61#5021—31no—
62#5018—32no—
63C4×#214—31no—
64#5008—31no—
65#5007—32no—
66C2×C32×Q8D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2311yescharacteristic
74C32×C4⋊C4D411yescharacteristic
75C32×C4⋊C4D412yes—
76C32×C42C2311yescharacteristic
77C32×C42C2312yes—
78C2×C3⋊(C3⋊C8)C2312yes—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3—21no—
96#3715Q814yescomplemented
97#3385—91noSylow
98C3×C4⋊Q8—31no—
99C3×C4⋊Q8—32no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—61no—
102C3×C4⋊Q8—62no—
103C3×#125—32no—
104C3×C22⋊Q8—61no—
105C3×C22⋊Q8—62no—
106C3×C4×Q8—21no—
107C3×C4×Q8—31no—
108C3×C4×Q8—32no—
109C3×C4×Q8—61no—
110C3×C4×Q8C2×D311yescharacteristic
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×D4—32no—
113C3×C4×D4—31no—
114C2×C3×C4⋊C4—61no—
115#946—21no—
116Q8×Dic3—21no—
117C2×#215—31no—
118C2×#214—31no—
119#896—22no—
120D3×C4⋊C4—21no—
121#888—21no—
122#888—22no—
123C4×D12C2×D311yescharacteristic
124C4×D12C2×D312yes—
125#870C2×D312yes—
126#869C2×D312yes—
127#869C2×D311yescharacteristic
128#869C2×D311yescharacteristic
129C4×Dic6C2×D311yescharacteristic
130C4×Dic6C2×D312yes—
131#835—32no—
132#835—31no—
133#832—31no—
134#832—32no—
135#810—31no—
136#810—32no—
137#809—31no—
138#809—32no—
139#808—32no—
140#808—31no—
141#808—32no—
142#808—31no—
143#807—32no—
144#807—32no—
145#807—32no—
146#807—32no—
147#807—32no—
148#807—32no—
149C4⋊(C3⋊C8)—32no—
150C4⋊(C3⋊C8)—31no—
151C4⋊(C3⋊C8)—31no—
152C4⋊(C3⋊C8)—32no—
153C4⋊(C3⋊C8)—62no—
154C4⋊(C3⋊C8)—61no—
155#803—32no—
156#803—32no—
157#803—62no—
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—61no—
161C22×C3×D3—21no—
162C32×Q8—22no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3×Dic3—21no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C3×D12—21no—
174C3×D12C2×Q812yes—
175C3×C4×D3—42no—
176C3×C4×D3—82no—
177C3×Dic6—21no—
178C3×Dic6—81no—
179C3×Dic6—82no—
180C3×Dic6—81no—
181C3×Dic6C2×Q812yes—
182C3⋊(C3⋊C8)—22no—
183C3⋊(C3⋊C8)—21no—
184C3⋊(C3⋊C8)C2×Q812yes—
185Q82—31no—
186#554—31no—
187#501—92no—
188#500—91no—
189#479—92no—
190#477—91no—
191#476—91no—
192#474—92no—
193#446—91no—
194#440—92no—
195C4×SD16—91no—
196C2×C3×Q8—21no—
197C2×C3×Q8—31no—
198C2×C3×Q8—61no—
199C2×C3×Q8—62no—
200C2×C3×Q8—61no—
201C2×C3×Q8#6711yescharacteristic
202C2×C3×Q8#6711yescharacteristic
203C2×C3×D4—31no—
204C22×C3×C4—61no—
205C22×C3×C4—62no—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×C4×D3—22no—
209C2×Dic6—21no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6C22×D311yescharacteristic
213C3×C4⋊C4—21no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—31no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—62no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4#6711yescharacteristic
227C3×C4⋊C4#6712yes—
228C3×C4⋊C4#6711yescharacteristic
229C3×C4⋊C4#6712yes—
230C3×C22⋊C4—61no—
231C3×C22⋊C4—62no—
232C3×C42—21no—
233C3×C42—22no—
234C3×C42—62no—
235C3×C42—61no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D312yes—
239C3×C42C22×D312yes—
240#215—34no—
241#214—34no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—22no—
244C4⋊Dic3—22no—
245C4⋊Dic3—21no—
246C4⋊Dic3—21no—
247C4⋊Dic3C22×D312yes—
248C4⋊Dic3C22×D312yes—
249C4⋊Dic3C22×D311yescharacteristic
250C4⋊Dic3C22×D311yescharacteristic
251Dic3⋊C4—21no—
252Dic3⋊C4—22no—
253Dic3⋊C4—22no—
254Dic3⋊C4—22no—
255C4×Dic3—22no—
256C4×Dic3—21no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—32no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—62no—
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—41no—
269C2×C3×D3—41no—
270C32×C4—22no—
271C32×C4—21no—
272C32×C4—22no—
273C32×C4#13712yes—
274C32×C4C22×Q811yescharacteristic
275C32×C42−1+411yescharacteristic
276C3×Dic3—22no—
277C3×Dic3—41no—
278C3×Dic3—42no—
279C3×Dic3—41no—
280C3×Dic3—42no—
281C2×SD16—91no—
282C4⋊Q8—31no—
283C4⋊Q8—32no—
284C4⋊Q8—31no—
285C4⋊Q8—61no—
286C4⋊Q8—62no—
287#125—32no—
288C22⋊Q8—61no—
289C22⋊Q8—62no—
290C4×Q8—31no—
291C4×Q8—32no—
292C4×Q8—61no—
293C4×Q8D3211yescharacteristic
294C4×D4—31no—
295C4×D4—32no—
296C2×C4⋊C4—61no—
297#107—92no—
298#107—92no—
299#107—92no—
300#106—91no—
301#106—92no—
302C4⋊C8—92no—
303C4⋊C8—91no—
304#103—91no—
305#103—92no—
306#102—91no—
307#102—92no—
308#97—92no—
309C4×C8—91no—
310C23×C3—61no—
311C22×D3—21no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—32no—
315C3×Q8—42no—
316C3×Q8—61no—
317C3×Q8—241no—
318C3×Q8—241no—
319C3×Q8—242no—
320C3×D4—32no—
321C3×D4—61no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—61no—
328C2×C3×C4—62no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—62no—
332C2×C3×C4—122no—
333C2×C3×C4—242no—
334C2×C3×C4C2×#6712yes—
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6712yes—
338C2×C3×C4C2×#6712yes—
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—22no—
349D12—21no—
350D12D3×Q812yes—
351C4×D3—42no—
352C4×D3—82no—
353Dic6—21no—
354Dic6—82no—
355Dic6—81no—
356Dic6—81no—
357Dic6D3×Q812yes—
358C3⋊C8—32no—
359C3⋊C8—32no—
360C3⋊C8—62no—
361C3⋊C8—61no—
362C3⋊C8—62no—
363C3⋊C8—61no—
364C3⋊C8—62no—
365C3⋊C8—121no—
366C3⋊C8—122no—
367C2×C32D4×Q811yescharacteristic
368C2×C32C2×#13711yescharacteristic
369C2×C32#57611yescharacteristic
370C3×D3—42no—
371C2×Q8—31no—
372C2×Q8—61no—
373C2×Q8—61no—
374C2×Q8—62no—
375C2×Q8#62511yescharacteristic
376C2×D4—31no—
377C22×C4—61no—
378C22×C4—62no—
379SD16—94no—
380C2×C8—91no—
381C2×C8—91no—
382C2×C8—92no—
383C4⋊C4—31no—
384C4⋊C4—32no—
385C4⋊C4—31no—
386C4⋊C4—32no—
387C4⋊C4—62no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—61no—
393C4⋊C4—62no—
394C4⋊C4#62511yescharacteristic
395C4⋊C4#62512yes—
396C22⋊C4—61no—
397C22⋊C4—62no—
398C42—62no—
399C42—61no—
400C42C2×D3211yescharacteristic
401C42C2×D3212yes—
402C22×C3—21no—
403C22×C3—62no—
404C22×C3—121no—
405C22×C3—121no—
406C22×C3C22×#6711yescharacteristic
407C22×C3C22×#6711yescharacteristic
408C2×D3—22no—
409C2×D3—41no—
410C2×D3—41no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—22no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—22no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—62no—
424C3×C4—121no—
425C3×C4—122no—
426C3×C4—122no—
427C3×C4—121no—
428C3×C4#94212yes—
429C3×C4#95112yes—
430C3×C4C2×D3×Q811yescharacteristic
431C3×C4C2×D3×Q811yescharacteristic
432C3×C4#100711yescharacteristic
433C3×C4#100711yescharacteristic
434Dic3—22no—
435Dic3—41no—
436Dic3—41no—
437Dic3—42no—
438Dic3—42no—
439C32#338511yescharacteristic, complemented, Sylow
440C23—61no—
441Q8—22no—
442Q8—32no—
443Q8—61no—
444Q8—242no—
445Q8—241no—
446Q8—241no—
447D4—32no—
448D4—61no—
449C2×C4—61no—
450C2×C4—62no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—62no—
454C2×C4—122no—
455C2×C4—242no—
456C2×C4C2×#62512yes—
457C2×C4C2×#62511yescharacteristic
458C2×C4C2×#62512yes—
459C2×C4C2×#62511yescharacteristic
460C2×C4C22×D3211yescharacteristic
461C8—92no—
462C8—181no—
463C8—182no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—122no—
468C2×C3C2×#94211yescharacteristic
469C2×C3Q8×#6711yescharacteristic
470C2×C3Q8×#6711yescharacteristic
471C2×C3C2×#95111yescharacteristic
472C2×C3#583511yescharacteristic
473C2×C3#583511yescharacteristic
474D3—42no—
475C22—62no—
476C22—121no—
477C22—121no—
478C22C22×#62511yescharacteristic
479C4—22no—
480C4—21no—
481C4—22no—
482C4—62no—
483C4—122no—
484C4—121no—
485C4—122no—
486C4—121no—
487C4#6382712yes—
488C4#6431611yescharacteristic
489C4D32×Q811yescharacteristic
490C3—21no—
491C3#8363111yescharacteristic, complemented
492C3#8370611yescharacteristic, complemented
493C2—122no—
494C2C2×#6382711yescharacteristic
495C2Q8×#62511yescharacteristic
496C2#1059544411yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4×Q8D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. #10592723C2semidirect
6. #10590315C2semidirect
7. #10590312C2semidirect
8. #10590310C2semidirect
9. #10590286C2semidirect
46. Q8×Dic6D3semidirect
96. #3715Q8semidirect
439. C32#3385semidirect
491. C3#83631semidirect
492. C3#83706semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×Q8×Dic62
#105927232
#105903582
C4×#37152
#105903152
#105903122
#105903102
#105902862
#105902692
#105902662
#837063
#836313