Finite Group Databasebeta

← #11859128

Subgroups — #11859128

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C3×#4924C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10591073C212yesmaximal
5#10591059C212yesmaximal, complemented
6#10590260C212yesmaximal, complemented
7#10590257C214yesmaximal, complemented
8#10590256C212yesmaximal, complemented
9#79040—31nomaximal
10#79000—31nomaximal
11C2×#3828C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C4×#638C412yes—
14C4×#638C412yes—
15#64135C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C411yescharacteristic
17C4×C4⋊(C3⋊D3)C411yescharacteristic
18#64081C2212yes—
19C42×C3⋊D3C2212yes—
20C4×#634C411yescharacteristic
21C4×#634C411yescharacteristic
22C2×C3×#208C2212yes—
23C22×C3×C3⋊C8C2212yes—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2212yes—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×C4⋊(C3⋊C8)C2212yes—
28C3×C4⋊(C3⋊C8)C2212yes—
29#63557C2214yes—
30#63557C2214yes—
31#63555C2214yes—
32#63553C2214yes—
33C4×#235—31no—
34C4×#235—31no—
35C4×#235—61no—
36C3×#423—31no—
37C2×C3×C4⋊C8—31no—
38#5129—32no—
39#5122—32no—
40#5110—32no—
41#5101—32no—
42#4924D311yescharacteristic, complemented
43C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
44#4840—34no—
45#4840—34no—
46#4835—32no—
47#4835—32no—
48#4833—32no—
49#4833—32no—
50C22×C32×C4C2×C411yescharacteristic
51C22×C32×C4C2×C411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C2×#638C2×C412yes—
54#3828—22no—
55#3828—22no—
56C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
57C2×C4×C3⋊D3C2×C412yes—
58C2×C4×C3⋊D3C2×C412yes—
59C2×C4×C3⋊D3C2312yes—
60C2×#634C2×C411yescharacteristic
61C32×C42C2×C411yescharacteristic
62C32×C42C2×C411yescharacteristic
63C32×C42C2311yescharacteristic
64C32×C42C2311yescharacteristic
65#3757C2×C412yes—
66#3752C2×C412yes—
67#3752C2×C412yes—
68C4⋊(C3⋊Dic3)C2×C411yescharacteristic
69C4⋊(C3⋊Dic3)C2×C411yescharacteristic
70#3750C2×C412yes—
71#3750C2×C412yes—
72C4×C3⋊Dic3C2×C412yes—
73C4×C3⋊Dic3C2×C412yes—
74C4×C3⋊Dic3C2312yes—
75C3×#208—24no—
76C2×C3×C3⋊C8—24no—
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2314yes—
80#2925—91noSylow
81C2×#235—31no—
82C2×#235—31no—
83C2×#235—61no—
84C2×C3×M16—32no—
85C22×C3×C8—32no—
86C2×C3×C42—21no—
87C2×C3×C42C2×D311yescharacteristic
88C2×C3×C42C2×D311yescharacteristic
89C4×#67—32no—
90C4×#67—32no—
91C4×#67—32no—
92C4×#67—32no—
93C4×#67—62no—
94C4×#67—62no—
95#926—31no—
96#926—31no—
97#926—61no—
98C2×#208C2×D312yes—
99C22×C3⋊C8C2×D312yes—
100C4×D12—31no—
101C4×D12—31no—
102C4×D12—31no—
103C4×D12—31no—
104C4×D12—61no—
105C4×D12—61no—
106#872—32no—
107#872—32no—
108#872—62no—
109C42×D3—32no—
110C42×D3—32no—
111C42×D3—62no—
112C4×Dic6—31no—
113C4×Dic6—31no—
114C4×Dic6—31no—
115C4×Dic6—31no—
116C4×Dic6—61no—
117C4×Dic6—61no—
118C3×C4⋊C8—31no—
119C3×C4⋊C8—31no—
120C3×C4⋊C8—32no—
121C3×C4⋊C8—32no—
122C3×C4⋊C8—32no—
123(C2×D3)⋊C8—34no—
124(C2×D3)⋊C8—34no—
125(C2×D3)⋊C8—34no—
126(C2×D3)⋊C8—34no—
127#815—34no—
128#815—34no—
129C8×Dic3—34no—
130C8×Dic3—34no—
131C4⋊(C3⋊C8)C2×D311yescharacteristic
132C4⋊(C3⋊C8)C2×D311yescharacteristic
133C4⋊(C3⋊C8)C2×D312yes—
134C4⋊(C3⋊C8)C2×D312yes—
135C4⋊(C3⋊C8)C2×D312yes—
136C23×C32C22×C411yescharacteristic
137C22×C3⋊D3C22×C412yes—
138C2×C32×C4—22no—
139C2×C32×C4—41no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4#4112yes—
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148#638—24no—
149C2×C3⋊Dic3C22×C412yes—
150C2×C3⋊Dic3C22×C412yes—
151C2×C3⋊Dic3C22×C412yes—
152C4⋊(C3⋊D3)—22no—
153C4×C3⋊D3—22no—
154C4×C3⋊D3—22no—
155C4×C3⋊D3—24no—
156C4×C3⋊D3—42no—
157#634—22no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—24no—
161C4×#41—91no—
162#433—94no—
163#432—92no—
164#431—92no—
165#423—31no—
166C2×C4⋊C8—31no—
167#408—92no—
168#405—92no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4C4×D311yescharacteristic
173C22×C3×C4C4×D311yescharacteristic
174C22×C3×C4C4×D311yescharacteristic
175C22×C3×C4C4×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C2×#67—32no—
179C2×#67—32no—
180C2×#67—62no—
181#235—64no—
182#235—64no—
183#235—62no—
184#235—62no—
185#235—62no—
186#235—62no—
187C2×D12—31no—
188C2×D12—31no—
189C2×D12—61no—
190C2×C4×D3—32no—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—32no—
195C2×C4×D3—32no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×Dic6—31no—
200C2×Dic6—31no—
201C2×Dic6—61no—
202C3×M16—64no—
203C2×C3×C8—32no—
204C2×C3×C8—34no—
205C2×C3×C8—32no—
206C2×C3×C8—64no—
207C3×C42—21no—
208C3×C42—21no—
209C3×C42—21no—
210C3×C42—21no—
211C3×C42C4×D311yescharacteristic
212C3×C42C4×D311yescharacteristic
213C3×C42C4×D311yescharacteristic
214C3×C42C4×D311yescharacteristic
215C3×C42C22×D311yescharacteristic
216C3×C42C22×D311yescharacteristic
217C3×C42C22×D311yescharacteristic
218C3×C42C22×D311yescharacteristic
219#217—32no—
220#217—32no—
221#217—62no—
222(C2×D3)⋊C4—32no—
223(C2×D3)⋊C4—32no—
224(C2×D3)⋊C4—32no—
225(C2×D3)⋊C4—32no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228C4⋊Dic3—31no—
229C4⋊Dic3—31no—
230C4⋊Dic3—31no—
231C4⋊Dic3—31no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234Dic3⋊C4—32no—
235Dic3⋊C4—32no—
236Dic3⋊C4—32no—
237Dic3⋊C4—32no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240C4×Dic3—32no—
241C4×Dic3—32no—
242C4×Dic3—32no—
243C4×Dic3—32no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—62no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249#208—24no—
250C2×C3⋊C8—24no—
251C2×C3⋊C8C22×D312yes—
252C2×C3⋊C8C22×D314yes—
253C2×C3⋊C8C22×D312yes—
254C22×C32—21no—
255C22×C32—21no—
256C22×C32#11712yes—
257C22×C32C23×C411yescharacteristic
258C2×C3⋊D3—22no—
259C2×C3⋊D3—22no—
260C2×C3⋊D3—22no—
261C32×C4—21no—
262C32×C4—21no—
263C32×C4—21no—
264C32×C4#11712yes—
265C32×C4#13112yes—
266C32×C4C2×#4111yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—22no—
269C3⋊Dic3—22no—
270C3⋊Dic3—22no—
271C2×#41—91no—
272C2×M16—32no—
273C22×C8—32no—
274C4×Q8—91no—
275C4×Q8—91no—
276C4×D4—92no—
277C4×D4—92no—
278C4×D4—91no—
279C4×D4—91no—
280#117—91no—
281#117—92no—
282C2×C42—92no—
283C2×C42D3211yescharacteristic
284C4⋊C8—31no—
285C4⋊C8—31no—
286C4⋊C8—32no—
287C4⋊C8—32no—
288C4⋊C8—32no—
289C22⋊C8—94no—
290C22⋊C8—94no—
291#97—94no—
292C4×C8—94no—
293C23×C3—21no—
294C23×C3C2×C4×D311yescharacteristic
295C23×C3C2×C4×D311yescharacteristic
296C22×D3—32no—
297C22×D3—32no—
298C22×D3—62no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—42no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—42no—
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×C4×D311yescharacteristic
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4C2×C4×D311yescharacteristic
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4#23712yes—
324C2×C3×C4#23712yes—
325C2×C3×C4#23912yes—
326C2×C3×C4#23912yes—
327C2×C3×C4C23×D311yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329#67—68no—
330#67—64no—
331#67—64no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—32no—
335C2×Dic3—32no—
336C2×Dic3—32no—
337C2×Dic3—32no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341D12—64no—
342D12—62no—
343D12—62no—
344C4×D3—64no—
345C4×D3—64no—
346C4×D3—64no—
347C4×D3—64no—
348C4×D3—62no—
349C4×D3—62no—
350C4×D3—62no—
351C4×D3—62no—
352C4×D3—124no—
353C4×D3—122no—
354C4×D3—122no—
355C4×D3—124no—
356Dic6—64no—
357Dic6—62no—
358Dic6—62no—
359C3×C8—62no—
360C3×C8—62no—
361C3×C8—64no—
362C3⋊C8—22no—
363C3⋊C8—22no—
364C3⋊C8—24no—
365C2×C32—22no—
366C2×C32C2×#11711yescharacteristic
367C2×C32C2×#13111yescharacteristic
368C2×C32#56811yescharacteristic
369C3⋊D3—42no—
370#41—182no—
371#41—182no—
372C2×Q8—91no—
373C2×D4—92no—
374C2×D4—91no—
375C22×C4—92no—
376C22×C4—92no—
377C22×C4—92no—
378C22×C4#62411yescharacteristic
379C22×C4#62411yescharacteristic
380C22×C4C2×D3211yescharacteristic
381M16—64no—
382C2×C8—32no—
383C2×C8—34no—
384C2×C8—32no—
385C2×C8—64no—
386C4⋊C4—92no—
387C4⋊C4—92no—
388C4⋊C4—91no—
389C4⋊C4—91no—
390C22⋊C4—92no—
391C22⋊C4—92no—
392C22⋊C4—92no—
393C42—92no—
394C42—92no—
395C42—92no—
396C42#62411yescharacteristic
397C42#62411yescharacteristic
398C42C2×D3211yescharacteristic
399C42C2×D3211yescharacteristic
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—22no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3#89212yes—
409C22×C3#89212yes—
410C22×C3C22×C4×D311yescharacteristic
411C22×C3C22×C4×D311yescharacteristic
412C2×D3—64no—
413C2×D3—62no—
414C2×D3—62no—
415C2×D3—62no—
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—62no—
419C2×D3—122no—
420C2×D3—122no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4#89212yes—
435C3×C4#89212yes—
436C3×C4#90112yes—
437C3×C4#90712yes—
438C3×C4C2×#23711yescharacteristic
439C3×C4C2×#23711yescharacteristic
440C3×C4C2×#23911yescharacteristic
441C3×C4C2×#23911yescharacteristic
442Dic3—64no—
443Dic3—62no—
444Dic3—62no—
445Dic3—62no—
446Dic3—62no—
447Dic3—62no—
448Dic3—62no—
449Dic3—122no—
450Dic3—122no—
451C32#292511yescharacteristic, complemented, Sylow
452C23—92no—
453C23C2×#62411yescharacteristic
454Q8—182no—
455D4—184no—
456D4—182no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—92no—
460C2×C4—92no—
461C2×C4—92no—
462C2×C4—182no—
463C2×C4—182no—
464C2×C4—184no—
465C2×C4—362no—
466C2×C4#379612yes—
467C2×C4#379612yes—
468C2×C4C2×#62411yescharacteristic
469C2×C4C2×#62411yescharacteristic
470C2×C4C2×#62411yescharacteristic
471C2×C4C2×#62411yescharacteristic
472C2×C4C2×#62411yescharacteristic
473C2×C4C22×D3211yescharacteristic
474C8—62no—
475C8—62no—
476C8—64no—
477C2×C3—22no—
478C2×C3—22no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—42no—
483C2×C3C2×#89211yescharacteristic
484C2×C3C2×#89211yescharacteristic
485C2×C3C2×#90111yescharacteristic
486C2×C3C2×#90711yescharacteristic
487C2×C3#574511yescharacteristic
488C2×C3#574511yescharacteristic
489D3—124no—
490D3—122no—
491D3—122no—
492C22—21no—
493C22—21no—
494C22—182no—
495C22—182no—
496C22—182no—
497C22#6384912yes—
498C22C22×#62411yescharacteristic
499C4—21no—
500C4—21no—
501C4—21no—
502C4—182no—
503C4—182no—
504C4—182no—
505C4#6381712yes—
506C4#6384912yes—
507C4C2×#379611yescharacteristic
508C4C2×#379611yescharacteristic
509C3—21no—
510C3#7900011yescharacteristic, complemented
511C3#7904011yescharacteristic, complemented
512C2—22no—
513C2—362no—
514C2C2×#6381711yescharacteristic
515C2#1059478011yescharacteristic
516C2C2×#6384911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×C42C22
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4924C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
5. #10591059C2semidirect
6. #10590260C2semidirect
7. #10590257C2semidirect
8. #10590256C2semidirect
42. #4924D3semidirect
43. C2×C4⋊(C3⋊C8)D3semidirect
451. C32#2925semidirect
510. C3#79000semidirect
511. C3#79040semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×#49242
C2×C3×C4⋊(C3⋊C8)2
#105910732
#105910592
#105902602
#105902572
#105902562
#790403
#790003