Finite Group Databasebeta

← #11878504

Subgroups — #11878504

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C212yesmaximal, complemented
2#10592933C211yesmaximal, characteristic, complemented
3#10591188C211yesmaximal, characteristic, complemented
4#10591180C212yesmaximal, complemented
5#10591170C212yesmaximal, complemented
6#10591166C211yesmaximal, characteristic, complemented
7#10591161C212yesmaximal, complemented
8#10591132C212yesmaximal, complemented
9#10591089C212yesmaximal, complemented
10#83426—32nomaximal
11C2×C32×#41C2211yescharacteristic
12C2×C3×#235C2212yes—
13C2×#3748C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#946—22no—
16C3×#939—22no—
17C3×#939—22no—
18C3×#938—22no—
19C3×#930C2212yes—
20C3×#930C2212yes—
21C2×C3×C4⋊Dic3C2212yes—
22C3×#924C2212yes—
23C3×#924C2212yes—
24C2×#3718C2211yescharacteristic
25C2×#3715C2212yes—
26C2×#3713C2211yescharacteristic
27#63657C2212yes—
28#63657C2212yes—
29#63576C2211yescharacteristic
30#63576C2212yes—
31#63576C2211yescharacteristic
32#63565C2212yes—
33#63565C2212yes—
34#63562C2212yes—
35#63562C2212yes—
36C3×#537—32no—
37#5833D312yescomplemented
38#5239—32no—
39#5238—32no—
40#5234—32no—
41#5234—61no—
42#5051—32no—
43#5049—32no—
44#5047—32no—
45#5044—32no—
46#5042—32no—
47#5038—32no—
48#5037—32no—
49#5033—32no—
50#4970—32no—
51#4967—32no—
52C32×#41—41no—
53C32×#41—41no—
54C2×C32×Q8D411yescharacteristic
55C2×C32×D4D412yes—
56C2×C32×D4D411yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2312yes—
59C2×C3×#67—22no—
60C2×C3×#67—22no—
61C2×C3×#67—22no—
62C22×C3×Dic3—22no—
63C3×#235—42no—
64C3×#235—42no—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—22no—
67C2×C3×Dic6C2312yes—
68#3748—41no—
69C2×C3⋊(C3⋊C8)—41no—
70C2×C3⋊(C3⋊C8)C2311yescharacteristic
71C2×C3⋊(C3⋊C8)C2312yes—
72C2×C3⋊(C3⋊C8)C2311yescharacteristic
73C3×#217—22no—
74C3×#217—22no—
75C3×(C2×D3)⋊C4—22no—
76C3×(C2×D3)⋊C4—22no—
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2312yes—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82#3718—41no—
83#3715—42no—
84#3713—41no—
85#3203—91noSylow
86C2×C3×#41—21no—
87C2×C3×#41—32no—
88C2×C3×#41C2×D312yes—
89C2×#235C2×D312yes—
90C3×C22⋊Q8—32no—
91C3×C22⋊Q8—32no—
92C3×C22⋊Q8—62no—
93C3×#121—32no—
94C3×#121—32no—
95C3×#121—62no—
96C3×#121—62no—
97C3×#121—62no—
98C2×C3×C4⋊C4—32no—
99#946—22no—
100C2×#216—32no—
101C2×#215—32no—
102#939—22no—
103#939—22no—
104#938—22no—
105C2×#214—32no—
106C2×#213—32no—
107#930C2×D312yes—
108#930C2×D312yes—
109C2×C4⋊Dic3C2×D312yes—
110#924C2×D312yes—
111#924C2×D312yes—
112C2×#208—32no—
113C2×#208—61no—
114C22×C3⋊C8—32no—
115C22×C3⋊C8—61no—
116#835—32no—
117#835—32no—
118#832—32no—
119#832—32no—
120#830—32no—
121#830—32no—
122#830—32no—
123#830—32no—
124#830—62no—
125#830—62no—
126#810—32no—
127#810—32no—
128#809—32no—
129#809—32no—
130#807—32no—
131#807—32no—
132#807—32no—
133#807—32no—
134C23×C32C2×D411yescharacteristic
135C23×C32C2×D412yes—
136C22×C3×D3—22no—
137C32×Q8—41no—
138C32×D4—41no—
139C32×D4—42no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2411yescharacteristic
147C3×#67—44no—
148C3×#67—82no—
149C3×#67—82no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—82no—
154C3×D12—22no—
155C3×D12—22no—
156C3×C4×D3—44no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3⋊(C3⋊C8)—21no—
160C3⋊(C3⋊C8)—22no—
161C3⋊(C3⋊C8)—21no—
162#537—32no—
163#484—92no—
164#480—92no—
165#468—92no—
166#467—91no—
167#466—91no—
168#452—92no—
169#449—92no—
170#408—91no—
171C3×#41—42no—
172C3×#41—42no—
173C3×#41—42no—
174C3×#41—42no—
175C3×#41—122no—
176C3×#41—122no—
177C2×C3×Q8—21no—
178C2×C3×Q8—32no—
179C2×C3×Q8#6712yes—
180C2×C3×D4—21no—
181C2×C3×D4—22no—
182C2×C3×D4—32no—
183C2×C3×D4—62no—
184C2×C3×D4—62no—
185C2×C3×D4—62no—
186C2×C3×D4#6712yes—
187C2×C3×D4#6712yes—
188C2×C3×D4#6712yes—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—62no—
192C22×C3×C4—62no—
193C22×C3×C4C22×D312yes—
194C22×C3×C4C22×D312yes—
195C22×C3×C4C22×D312yes—
196C2×#67—22no—
197C2×#67—22no—
198C2×#67—22no—
199C22×Dic3—22no—
200#235—42no—
201#235—42no—
202C2×D12C22×D312yes—
203C2×C4×D3—22no—
204C2×Dic6C22×D312yes—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—62no—
208C3×C4⋊C4—62no—
209C3×C4⋊C4—62no—
210C3×C22⋊C4—62no—
211C3×C22⋊C4—62no—
212C3×C22⋊C4—62no—
213C3×C22⋊C4—62no—
214#217—22no—
215#217—22no—
216#216—122no—
217#215—122no—
218#214—122no—
219#213—122no—
220(C2×D3)⋊C4—22no—
221(C2×D3)⋊C4—22no—
222C4⋊Dic3—22no—
223C4⋊Dic3C22×D312yes—
224C4⋊Dic3C22×D312yes—
225Dic3⋊C4—22no—
226Dic3⋊C4—22no—
227#208—122no—
228#208—122no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—122no—
237C2×C3⋊C8—122no—
238C22×C32—21no—
239C22×C32—22no—
240C22×C32—22no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—22no—
244C22×C32C22×D411yescharacteristic
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C32×C4—21no—
249C32×C4—22no—
250C32×C4H(5,𝔽2)11yescharacteristic
251C32×C4H(5,𝔽2)11yescharacteristic
252C3×Dic3—42no—
253C3×Dic3—42no—
254C3×Dic3—42no—
255C2×#41—32no—
256C2×#41D3211yescharacteristic
257C2×Q16—91no—
258C2×SD16—92no—
259C2×D8—91no—
260C2×M16—91no—
261C22×C8—91no—
262C22⋊Q8—32no—
263C22⋊Q8—32no—
264C22⋊Q8—62no—
265#121—32no—
266#121—32no—
267#121—62no—
268#121—62no—
269#121—62no—
270C2×C4⋊C4—32no—
271#107—91no—
272#107—91no—
273#107—92no—
274#103—92no—
275#103—92no—
276#102—92no—
277#102—92no—
278C22⋊C8—92no—
279C22⋊C8—92no—
280C23×C3—21no—
281C23×C3—22no—
282C23×C3—62no—
283C23×C3C2×#6712yes—
284C23×C3C2×#6712yes—
285C23×C3C2×#6712yes—
286C22×D3—22no—
287C3×Q8—42no—
288C3×Q8—42no—
289C3×Q8—62no—
290C3×Q8—62no—
291C3×D4—42no—
292C3×D4—42no—
293C3×D4—42no—
294C3×D4—42no—
295C3×D4—44no—
296C3×D4—62no—
297C3×D4—62no—
298C3×D4—124no—
299C3×D4—242no—
300C3×D4—242no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—124no—
318C2×C3×C4—242no—
319C2×C3×C4C2×#6712yes—
320C2×C3×C4C2×#6712yes—
321C2×C3×C4C2×#6712yes—
322C2×C3×C4C23×D312yes—
323#67—44no—
324#67—82no—
325#67—82no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—82no—
330D12—22no—
331D12—22no—
332C4×D3—44no—
333Dic6—22no—
334Dic6—22no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C3⋊C8—62no—
338C3⋊C8—62no—
339C3⋊C8—121no—
340C3⋊C8—121no—
341C3⋊C8—122no—
342C2×C32—41no—
343C2×C32—42no—
344C2×C32#53411yescharacteristic
345C2×C32#57611yescharacteristic
346C2×C32#57811yescharacteristic
347C3×D3—82no—
348#41—41no—
349#41—41no—
350#41—122no—
351#41—122no—
352C2×Q8—32no—
353C2×Q8#62511yescharacteristic
354C2×D4—32no—
355C2×D4—62no—
356C2×D4—62no—
357C2×D4—62no—
358C2×D4#62511yescharacteristic
359C2×D4#62512yes—
360C22×C4—62no—
361C22×C4—62no—
362C22×C4C2×D3212yes—
363C22×C4C2×D3211yescharacteristic
364Q16—361no—
365SD16—362no—
366D8—361no—
367M16—361no—
368C2×C8—91no—
369C2×C8—92no—
370C2×C8—91no—
371C2×C8—361no—
372C4⋊C4—32no—
373C4⋊C4—32no—
374C4⋊C4—62no—
375C4⋊C4—62no—
376C4⋊C4—62no—
377C22⋊C4—62no—
378C22⋊C4—62no—
379C22⋊C4—62no—
380C22⋊C4—62no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—21no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—122no—
398C22×C3—122no—
399C22×C3—122no—
400C22×C3C22×#6712yes—
401C2×D3—42no—
402C2×D3—42no—
403C2×D3—42no—
404C3×C4—22no—
405C3×C4—22no—
406C3×C4—22no—
407C3×C4—22no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—42no—
411C3×C4—122no—
412C3×C4—122no—
413C3×C4—122no—
414C3×C4#100412yes—
415C3×C4#100412yes—
416Dic3—42no—
417Dic3—42no—
418Dic3—42no—
419C32#320311yescharacteristic, complemented, Sylow
420C23—62no—
421C23C2×#62511yescharacteristic
422C23C2×#62512yes—
423Q8—41no—
424Q8—62no—
425Q8—62no—
426D4—42no—
427D4—41no—
428D4—62no—
429D4—62no—
430D4—124no—
431D4—242no—
432D4—242no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—124no—
441C2×C4—242no—
442C2×C4C2×#62511yescharacteristic
443C2×C4C2×#62512yes—
444C2×C4C22×D3211yescharacteristic
445C8—181no—
446C8—181no—
447C8—182no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—42no—
452C2×C3—42no—
453C2×C3—42no—
454C2×C3—42no—
455C2×C3—82no—
456C2×C3—242no—
457C2×C3#580412yes—
458C2×C3#583512yes—
459C2×C3#583812yes—
460D3—82no—
461C22—22no—
462C22—21no—
463C22—21no—
464C22—22no—
465C22—22no—
466C22—21no—
467C22—122no—
468C22—122no—
469C22—122no—
470C22C22×#62511yescharacteristic
471C4—22no—
472C4—21no—
473C4—122no—
474C4—122no—
475C4—122no—
476C4#6433011yescharacteristic
477C4#6433011yescharacteristic
478C3—21no—
479C3#8342612yescomplemented
480C2—41no—
481C2—42no—
482C2—242no—
483C2#1059544411yescharacteristic
484C2#1059544511yescharacteristic
485C2#1059551811yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3203
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5833C2semidirect
2. #10592933C2semidirect
3. #10591188C2semidirect
4. #10591180C2semidirect
5. #10591170C2semidirect
6. #10591166C2semidirect
7. #10591161C2semidirect
8. #10591132C2semidirect
9. #10591089C2semidirect
37. #5833D3semidirect
419. C32#3203semidirect
479. C3#83426semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
#105929332
#105911882
#105911802
#105911702
#105911662
#105911612
#105911322
#105910892
#834263