Finite Group Databasebeta

← #11804928

Subgroups — #11804928

Order 1152.

2189 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×#63844C212yesmaximal, complemented
3C3×#5212C211yesmaximal, characteristic, complemented
4C3×C4×#217C211yesmaximal, characteristic, complemented
5#10591704C214yesmaximal, complemented
6#10591355C212yesmaximal, complemented
7#10591320C212yesmaximal, complemented
8#10591260C212yesmaximal, complemented
9#73877—31nomaximal
10#73454—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638C2212yes—
13C2×#3828—28no—
14C2×#3828C418yescomplemented
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2212yes—
17C22×#634C2211yescharacteristic
18C2×C3×#217C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×#3724C2214yes—
23C2×#3722C2214yes—
24C2×#3722C2214yes—
25C2×Dic32C2214yes—
26#63844—28no—
27C3×C3⋊#95C2211yescharacteristic
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2211yescharacteristic
30C22×#235—31no—
31C22×#235—31no—
32C22×#235—61no—
33C2×#887—32no—
34C2×C4×Dic6—32no—
35C3×#380—31no—
36C3×C4×C22⋊C4—31no—
37#5212D311yescharacteristic, complemented
38C4×#217D311yescharacteristic, complemented
39#4988—32no—
40#4957—34no—
41#4957—34no—
42#4939—32no—
43#4667—32no—
44#4667—32no—
45#4666—32no—
46#4666—32no—
47C24×C32C2311yescharacteristic
48C23×C3⋊D3C2312yes—
49C22×C32×C4—24no—
50C22×C32×C4C2×C414yes—
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C2×#638—28no—
54C2×#638C2×C418yes—
55C22×C3⋊Dic3C2312yes—
56#3828—232no—
57C2×C4⋊(C3⋊D3)—24no—
58C2×C4⋊(C3⋊D3)C2×C414yes—
59C2×C4×C3⋊D3—28no—
60C2×C4×C3⋊D3C2×C418yes—
61C2×#634C2×C414yes—
62C2×#634D418yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2314yes—
65C22×C3×Dic3C2312yes—
66C3×#217—24no—
67C3×#217—42no—
68C3×C4⋊Dic3—24no—
69C3×C4×Dic3—24no—
70#3724—28no—
71#3722—28no—
72#3722—44no—
73Dic32—28no—
74#2341—91noSylow
75C23×C3×C4—21no—
76C23×C3×C4C2×D311yescharacteristic
77C23×C3×C4C2×D311yescharacteristic
78C22×#67—32no—
79C22×#67—32no—
80C22×#67—62no—
81C2×#235—38no—
82C2×#235—38no—
83C2×#235—68no—
84C2×#235—68no—
85C2×#235—68no—
86C2×#235—616no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×C4×D3—32no—
91C22×C4×D3—32no—
92C22×C4×D3—62no—
93C22×Dic6—31no—
94C22×Dic6—31no—
95C22×Dic6—61no—
96C2×C3×C4⋊C4—32no—
97C2×C3×C22⋊C4—32no—
98C2×C3×C22⋊C4—32no—
99C2×C3×C42—32no—
100C2×#217C2×D312yes—
101C2×#217C2×D312yes—
102C2×(C2×D3)⋊C4—34no—
103C2×(C2×D3)⋊C4—34no—
104C2×(C2×D3)⋊C4—34no—
105C2×(C2×D3)⋊C4—34no—
106C2×C4⋊Dic3C2×D312yes—
107C2×Dic3⋊C4—34no—
108C2×Dic3⋊C4—34no—
109C2×C4×Dic3—34no—
110C2×C4×Dic3—34no—
111C2×C4×Dic3C2×D312yes—
112#887—68no—
113C4×Dic6—68no—
114C3×#95—31no—
115C3×#95—32no—
116C3×#95—31no—
117C3⋊#95C2×D311yescharacteristic
118C3⋊#95C2×D312yes—
119C3⋊#95C2×D311yescharacteristic
120C23×C32—22no—
121C23×C32—22no—
122C23×C32—21no—
123C23×C32—21no—
124C23×C32C22×C412yes—
125C23×C32C2411yescharacteristic
126C22×C3⋊D3—24no—
127C22×C3⋊D3—24no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3C22×C414yes—
131C2×C32×C4—22no—
132C2×C32×C4—28no—
133C2×C32×C4C22×C412yes—
134C2×C32×C4C22×C412yes—
135C2×C32×C4C2×D414yes—
136#638—216no—
137C2×C3⋊Dic3C22×C414yes—
138C2×C3⋊Dic3C2×D418yes—
139C4⋊(C3⋊D3)—28no—
140C4×C3⋊D3—216no—
141#634C22⋊C4116yescomplemented
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3#4114yescomplemented
151C22×#41—91no—
152C2×C4×Q8—92no—
153#390—92no—
154#390—94no—
155#380—31no—
156#380—92no—
157C4×C22⋊C4—31no—
158C4×C22⋊C4—92no—
159C24×C3—21no—
160C24×C3C22×D311yescharacteristic
161C24×C3C22×D311yescharacteristic
162C23×D3—32no—
163C23×D3—32no—
164C23×D3—62no—
165C22×C3×C4—28no—
166C22×C3×C4—24no—
167C22×C3×C4—24no—
168C22×C3×C4—24no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—32no—
172C22×C3×C4—34no—
173C22×C3×C4—32no—
174C22×C3×C4C4×D314yes—
175C22×C3×C4C4×D314yes—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—38no—
181C2×#67—38no—
182C2×#67—68no—
183C2×#67—68no—
184C2×#67—68no—
185C2×#67—616no—
186C22×Dic3—32no—
187C22×Dic3—32no—
188C22×Dic3—62no—
189C22×Dic3C22×D314yes—
190C22×Dic3C22×D312yes—
191C22×Dic3C22×D312yes—
192#235—632no—
193#235—632no—
194#235—664no—
195C2×D12—34no—
196C2×D12—34no—
197C2×D12—64no—
198C2×D12—68no—
199C2×D12—64no—
200C2×D12—64no—
201C2×C4×D3—38no—
202C2×C4×D3—38no—
203C2×C4×D3—68no—
204C2×C4×D3—68no—
205C2×C4×D3—68no—
206C2×C4×D3—616no—
207C2×Dic6—34no—
208C2×Dic6—34no—
209C2×Dic6—38no—
210C2×Dic6—38no—
211C2×Dic6—64no—
212C2×Dic6—68no—
213C3×C4⋊C4—64no—
214C3×C22⋊C4—64no—
215C3×C22⋊C4—122no—
216C3×C42—64no—
217#217—24no—
218#217—42no—
219(C2×D3)⋊C4—68no—
220(C2×D3)⋊C4—68no—
221(C2×D3)⋊C4—124no—
222(C2×D3)⋊C4—124no—
223C4⋊Dic3—24no—
224Dic3⋊C4—68no—
225Dic3⋊C4—68no—
226C4×Dic3—24no—
227C4×Dic3—68no—
228C4×Dic3—68no—
229C22×C32—22no—
230C22×C32—22no—
231C22×C32—22no—
232C22×C32—42no—
233C22×C32—42no—
234C22×C32C23×C411yescharacteristic
235C22×C32C22×D412yes—
236C22×C32C2×#4112yes—
237C22×C32H(5,𝔽2)11yescharacteristic
238C22×C322−1+411yescharacteristic
239C2×C3⋊D3—24no—
240C2×C3⋊D3—24no—
241C2×C3⋊D3—24no—
242C2×C3⋊D3—44no—
243C2×C3⋊D3—44no—
244C32×C4—22no—
245C32×C4C2×C22⋊C414yes—
246C3⋊Dic3C2×C22⋊C418yes—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3—44no—
250C2×#41—98no—
251C2×#41—188no—
252C22×Q8—91no—
253C22×D4—92no—
254C22×D4—91no—
255C23×C4—92no—
256C23×C4D3211yescharacteristic
257C4×Q8—188no—
258C2×C4⋊C4—32no—
259C2×C4⋊C4—94no—
260C2×C22⋊C4—32no—
261C2×C22⋊C4—32no—
262C2×C22⋊C4—94no—
263C2×C22⋊C4—94no—
264C2×C42—32no—
265C2×C42—94no—
266#95—31no—
267#95—31no—
268#95—32no—
269C23×C3—24no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—22no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—22no—
280C23×C3—41no—
281C23×C3—42no—
282C23×C3—41no—
283C23×C3C2×C4×D312yes—
284C23×C3C2×C4×D312yes—
285C23×C3C23×D311yescharacteristic
286C23×C3C23×D311yescharacteristic
287C22×D3—34no—
288C22×D3—34no—
289C22×D3—64no—
290C22×D3—68no—
291C22×D3—64no—
292C22×D3—64no—
293C22×D3—64no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—64no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—122no—
300C22×D3—124no—
301C22×D3—122no—
302C2×C3×C4—24no—
303C2×C3×C4—216no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—28no—
307C2×C3×C4—28no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—24no—
311C2×C3×C4—34no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—64no—
315C2×C3×C4—64no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—64no—
320C2×C3×C4C2×C4×D312yes—
321C2×C3×C4C2×C4×D312yes—
322C2×C3×C4C2×C4×D312yes—
323C2×C3×C4C2×C4×D312yes—
324C2×C3×C4D3×D414yes—
325C2×C3×C4D3×D414yes—
326#67—616no—
327#67—616no—
328#67—632no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—24no—
334C2×Dic3—24no—
335C2×Dic3—24no—
336C2×Dic3—22no—
337C2×Dic3—34no—
338C2×Dic3—34no—
339C2×Dic3—38no—
340C2×Dic3—38no—
341C2×Dic3—64no—
342C2×Dic3—68no—
343C2×Dic3#23514yescomplemented
344D12—616no—
345D12—68no—
346D12—68no—
347C4×D3—616no—
348C4×D3—616no—
349C4×D3—632no—
350Dic6—316no—
351Dic6—316no—
352Dic6—616no—
353C2×C32—42no—
354C2×C32C22×C22⋊C411yescharacteristic
355C2×C32C4×#4111yescharacteristic
356C2×C32#52011yescharacteristic
357C2×C32#54812yes—
358C2×C32#55012yes—
359C3⋊D3—44no—
360C24—92no—
361C24C2×D3211yescharacteristic
362#41—1832no—
363C2×Q8—94no—
364C2×Q8—98no—
365C2×D4—98no—
366C2×D4—94no—
367C2×D4—188no—
368C2×D4—184no—
369C22×C4—24no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—34no—
373C22×C4—92no—
374C22×C4—98no—
375C22×C4—188no—
376C22×C4#62414yes—
377C22×C4C2×D3211yescharacteristic
378C22×C4C2×D3211yescharacteristic
379C4⋊C4—64no—
380C4⋊C4—188no—
381C22⋊C4—64no—
382C22⋊C4—122no—
383C22⋊C4—188no—
384C22⋊C4—364no—
385C42—64no—
386C42—188no—
387C22×C3—24no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—22no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—22no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—44no—
402C22×C3—44no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3C22×C4×D311yescharacteristic
408C22×C3C22×C4×D311yescharacteristic
409C22×C3C2×#23512yes—
410C22×C3C2×D3×D412yes—
411C22×C3C2×D3×D412yes—
412C22×C3#100411yescharacteristic
413C22×C3#100711yescharacteristic
414C22×C3D3×#4112yes—
415C22×C3#100911yescharacteristic
416C22×C3#101011yescharacteristic
417C2×D3—68no—
418C2×D3—64no—
419C2×D3—64no—
420C2×D3—64no—
421C2×D3—64no—
422C2×D3—64no—
423C2×D3—64no—
424C2×D3—124no—
425C2×D3—124no—
426C2×D3—128no—
427C2×D3—128no—
428C2×D3—124no—
429C2×D3—124no—
430C2×D3—124no—
431C2×D3—124no—
432C3×C4—24no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—24no—
436C3×C4—64no—
437C3×C4—124no—
438C3×C4—122no—
439C3×C4D3×C22⋊C414yes—
440C3×C4D3×C22⋊C414yes—
441Dic3—24no—
442Dic3—38no—
443Dic3—38no—
444Dic3—42no—
445Dic3—44no—
446Dic3—68no—
447C32#234111yescharacteristic, complemented, Sylow
448C23—21no—
449C23—22no—
450C23—21no—
451C23—22no—
452C23—94no—
453C23—182no—
454C23—184no—
455C23—182no—
456C23—184no—
457C23C2×#62412yes—
458C23C22×D3211yescharacteristic
459Q8—916no—
460D4—1816no—
461D4—188no—
462C2×C4—22no—
463C2×C4—28no—
464C2×C4—34no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—64no—
469C2×C4—64no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—64no—
473C2×C4—94no—
474C2×C4—98no—
475C2×C4—1816no—
476C2×C4C2×#62412yes—
477C2×C4C2×#62412yes—
478C2×C4#381114yes—
479C2×C3—22no—
480C2×C3—22no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—44no—
485C2×C3—42no—
486C2×C3—42no—
487C2×C3C4×#23511yescharacteristic
488C2×C3C2×D3×C22⋊C411yescharacteristic
489C2×C3C2×D3×C22⋊C411yescharacteristic
490C2×C3#550411yescharacteristic
491C2×C3#552211yescharacteristic
492C2×C3#552311yescharacteristic
493C2×C3#555212yes—
494C2×C3#555312yes—
495C2×C3#559912yes—
496C2×C3#563312yes—
497D3—128no—
498D3—124no—
499D3—124no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—184no—
506C22—184no—
507C22—184no—
508C22—364no—
509C22—364no—
510C22#6429711yescharacteristic
511C22D3×#23512yes—
512C22#6430711yescharacteristic
513C22C22×#62411yescharacteristic
514C22C2×#381112yes—
515C4—22no—
516C4—64no—
517C4—98no—
518C4—122no—
519C4—124no—
520C4#6397414yes—
521C3—21no—
522C3#7345411yescharacteristic, complemented
523C3#7387711yescharacteristic, complemented
524C2—42no—
525C2—364no—
526C2#1059491612yes—
527C2#1059491912yes—
528C2#1059495411yescharacteristic
529C2#1059499011yescharacteristic
530C2C2×#6397411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#3828C2
hypercenterC23×C4D32
hypocenterC32#2341
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
3. C3×#5212C2semidirect
4. C3×C4×#217C2semidirect
5. #10591704C2semidirect
6. #10591355C2semidirect
7. #10591320C2semidirect
8. #10591260C2semidirect
14. C2×#3828C4semidirect
37. #5212D3semidirect
38. C4×#217D3semidirect
141. #634C22⋊C4semidirect
150. C2×C3×Dic3#41semidirect
343. C2×Dic3#235semidirect
447. C32#2341semidirect
522. C3#73454semidirect
523. C3#73877semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×#638442
C3×#52122
C3×C4×#2172
#105917042
#105913552
#105913202
#105912602
#738773
#734543