Finite Group Databasebeta

← #11787043

Subgroups — #11787043

Order 1152.

625 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63817C211yesmaximal, characteristic
2C2×#63632C211yesmaximal, characteristic
3C2×#63577C211yesmaximal, characteristic, complemented
4#10591116C211yesmaximal, characteristic, complemented
5#10591105C211yesmaximal, characteristic
6C3×#4524C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8#68774—31nomaximal
9#68694—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3712—21no—
18#63817—22no—
19#63817—22no—
20C2×#3710—21no—
21#63632—22no—
22#63577—22no—
23Dic3⋊(C3⋊C8)—21no—
24Dic3⋊(C3⋊C8)—21no—
25#63567C411yescharacteristic, complemented
26#63567C411yescharacteristic, complemented
27#63564C411yescharacteristic, complemented
28#63564C411yescharacteristic, complemented
29C2×#907—31no—
30C2×#901—31no—
31C2×#822—31no—
32#5113—31no—
33C2×#819—31no—
34#5102—31no—
35#5002—31no—
36#4999—31no—
37C2×#805—31no—
38C2×#805—31no—
39C2×#805—61no—
40C3×#339—31no—
41C3×#336—31no—
42#4524D311yescharacteristic, complemented
43#4523D311yescharacteristic, complemented
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47#3828—21no—
48#3828—21no—
49#3828D412yes—
50#3828Q812yes—
51C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
52C2×C4×C3⋊D3—21no—
53C2×#634C2×C411yescharacteristic
54C32×C42—21no—
55C32×C42—21no—
56#3748—21no—
57#3748—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×C4×Dic3—21no—
63C3×#208—21no—
64C3×#208D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8C2×C411yescharacteristic
71C2×C3×C3⋊C8C2×C411yescharacteristic
72C2×C3×C3⋊C8D411yescharacteristic
73C2×C3×C3⋊C8D411yescharacteristic
74#3712—24no—
75#3710—24no—
76#1866—91noSylow
77C2×#235—31no—
78C2×#235—31no—
79C2×#235—61no—
80C2×C3×M16—31no—
81C22×C3×C8—31no—
82C22×C3×C8—31no—
83C3×#117—31no—
84C2×C3×C42—21no—
85C2×C3×C42C2×D311yescharacteristic
86C2×C3×C42C2×D311yescharacteristic
87#926C2×D311yescharacteristic
88C2×#208—31no—
89C2×#208—31no—
90C2×#208—61no—
91C2×#208C2×D311yescharacteristic
92C22×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊C8C2×D311yescharacteristic
94#907—62no—
95#907—62no—
96#901—62no—
97#901—62no—
98C2×ΓL(1,𝔽25)—61no—
99C2×ΓL(1,𝔽25)—61no—
100C2×D3×C8—61no—
101C2×D3×C8—61no—
102#822—62no—
103#821—31no—
104#821—31no—
105#819—62no—
106#816—31no—
107#816—31no—
108Dic3⋊C8—61no—
109Dic3⋊C8—61no—
110#810—31no—
111#810—31no—
112#809—31no—
113#809—31no—
114#805—62no—
115#805—62no—
116#805—64no—
117C4⋊(C3⋊C8)—61no—
118C4⋊(C3⋊C8)—61no—
119C23×C32#4111yescharacteristic
120C22×C3⋊D3—21no—
121C2×C32×C4—22no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
130#638—22no—
131#638—22no—
132C2×C3⋊Dic3—21no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)C4⋊C412yes—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137#634—21no—
138#634C4⋊C412yes—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—21no—
143C3×C3⋊C8—21no—
144C3×C3⋊C8—21no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—21no—
147C2×#131—91no—
148C2×#108—91no—
149#424—91no—
150C2×#104—91no—
151#416—91no—
152#339—31no—
153#336—31no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—41no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—61no—
161C2×#67—61no—
162C2×#67—121no—
163#235—32no—
164#235—32no—
165#235—32no—
166#235—32no—
167#235—62no—
168#235—62no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—61no—
173#235—121no—
174#235—121no—
175C2×D12—31no—
176C2×D12—31no—
177C2×D12—61no—
178C2×C4×D3—61no—
179C2×C4×D3—61no—
180C2×C4×D3—121no—
181C2×Dic6—31no—
182C2×Dic6—31no—
183C2×Dic6—61no—
184C3×M16—32no—
185C3×M16—61no—
186C2×C3×C8—31no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C3×C4⋊C4—31no—
196C3×C4⋊C4—31no—
197C3×C22⋊C4—61no—
198C3×C42—22no—
199C3×C42—21no—
200C3×C42—21no—
201C3×C42—21no—
202C3×C42—21no—
203C3×C42—41no—
204C3×C42—61no—
205#217—21no—
206C4⋊Dic3C4×D311yescharacteristic
207C4⋊Dic3C4×D311yescharacteristic
208C4×Dic3—21no—
209#208—21no—
210#208—62no—
211#208—61no—
212#208—61no—
213#208—61no—
214#208—61no—
215#208—121no—
216#208D1212yes—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—121no—
225C2×C3⋊C8C4×D311yescharacteristic
226C2×C3⋊C8C4×D311yescharacteristic
227C2×C3⋊C8D1211yescharacteristic
228C2×C3⋊C8D1211yescharacteristic
229ΓL(1,𝔽25)—64no—
230ΓL(1,𝔽25)—64no—
231D3×C8—64no—
232D3×C8—64no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32C4×D411yescharacteristic
236C22×C32C22⋊Q811yescharacteristic
237C22×C32#12311yescharacteristic
238C2×C3⋊D3—22no—
239C2×C3⋊D3—41no—
240C2×C3⋊D3—41no—
241C32×C4—42no—
242C32×C4C2×C4⋊C411yescharacteristic
243C32×C4C4×D411yescharacteristic
244C32×C4#12011yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C3⋊Dic3—22no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C2×#41—91no—
250#131—182no—
251#131—182no—
252C2×M16—31no—
253C2×M16—91no—
254C2×M16—181no—
255C22×C8—31no—
256C22×C8—31no—
257C22×C8—181no—
258#117—31no—
259C2×C42D3211yescharacteristic
260#108—182no—
261C4⋊C8—181no—
262C4⋊C8—181no—
263#104—182no—
264#103—91no—
265#103—91no—
266#102—91no—
267#102—91no—
268C23×C3—21no—
269C23×C3#23511yescharacteristic
270C23×C3#23711yescharacteristic
271C22×D3—61no—
272C22×D3—61no—
273C22×D3—121no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—42no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4C2×D1211yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4D3×Q811yescharacteristic
302C2×C3×C4D3×Q811yescharacteristic
303#67—62no—
304#67—62no—
305#67—62no—
306#67—62no—
307#67—122no—
308#67—122no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—121no—
314D12—32no—
315D12—32no—
316D12—62no—
317D12—61no—
318D12—61no—
319D12—121no—
320C4×D3—62no—
321C4×D3—62no—
322C4×D3—62no—
323C4×D3—62no—
324C4×D3—122no—
325C4×D3—122no—
326Dic6—32no—
327Dic6—32no—
328Dic6—62no—
329Dic6—61no—
330Dic6—61no—
331Dic6—121no—
332C3×C8—61no—
333C3×C8—61no—
334C3×C8—61no—
335C3×C8—62no—
336C3×C8—61no—
337C3⋊C8—21no—
338C3⋊C8—21no—
339C3⋊C8—21no—
340C3⋊C8—22no—
341C3⋊C8—21no—
342C3⋊C8—122no—
343C3⋊C8—121no—
344C3⋊C8—121no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32#38511yescharacteristic
348C2×C32#44311yescharacteristic
349C2×C32#44411yescharacteristic
350C3⋊D3—42no—
351#41—92no—
352#41—92no—
353#41—181no—
354#41—181no—
355C2×Q8—91no—
356C2×D4—91no—
357C2×D4—181no—
358C22×C4—21no—
359C22×C4—181no—
360C22×C4C2×D3211yescharacteristic
361M16—32no—
362M16—61no—
363M16—184no—
364M16—181no—
365M16—181no—
366C2×C8—31no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—31no—
370C2×C8—61no—
371C2×C8—61no—
372C2×C8—61no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—184no—
376C2×C8—181no—
377C4⋊C4—31no—
378C4⋊C4—31no—
379C22⋊C4—61no—
380C42—21no—
381C42—21no—
382C42—61no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3C4×D1211yescharacteristic
393C22×C3#67⋊C411yescharacteristic
394C22×C3#88311yescharacteristic
395C22×C3#88311yescharacteristic
396C22×C3#89611yescharacteristic
397C22×C3#89711yescharacteristic
398C2×D3—62no—
399C2×D3—62no—
400C2×D3—122no—
401C2×D3—121no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—241no—
406C2×D3—241no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—42no—
413C3×C4—44no—
414C3×C4—121no—
415C3×C4—121no—
416C3×C4C4×D1211yescharacteristic
417C3×C4#67⋊C411yescharacteristic
418C3×C4#88211yescharacteristic
419C3×C4#88211yescharacteristic
420C3×C4D3×C4⋊C411yescharacteristic
421C3×C4D3×C4⋊C411yescharacteristic
422C3×C4#89611yescharacteristic
423C3×C4#89711yescharacteristic
424Dic3—41no—
425Dic3—41no—
426Dic3—62no—
427Dic3—62no—
428Dic3—122no—
429C32#186611yescharacteristic, complemented, Sylow
430C23—181no—
431C23#380411yescharacteristic
432Q8—92no—
433Q8—181no—
434D4—92no—
435D4—182no—
436D4—182no—
437D4—181no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—181no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4#379711yescharacteristic
447C2×C4C4×D3211yescharacteristic
448C2×C4D3×D1211yescharacteristic
449C2×C4D3×D1211yescharacteristic
450C2×C4#380411yescharacteristic
451C2×C4#381111yescharacteristic
452C8—61no—
453C8—61no—
454C8—61no—
455C8—61no—
456C8—62no—
457C8—361no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3#466811yescharacteristic
468C2×C3#466811yescharacteristic
469C2×C3#470011yescharacteristic
470C2×C3#471711yescharacteristic
471C2×C3#482311yescharacteristic
472C2×C3#482411yescharacteristic
473D3—122no—
474D3—122no—
475D3—242no—
476C22—21no—
477C22—21no—
478C22—182no—
479C22—361no—
480C22—361no—
481C22#6388011yescharacteristic
482C22#6389511yescharacteristic
483C22#6397511yescharacteristic
484C4—42no—
485C4—121no—
486C4—121no—
487C4—182no—
488C4#6388011yescharacteristic
489C4#6388311yescharacteristic
490C4#6389511yescharacteristic
491C4#6392311yescharacteristic
492C3—21no—
493C3#6869411yescharacteristic, complemented
494C3#6877411yescharacteristic, complemented
495C2—21no—
496C2—21no—
497C2—362no—
498C2#1059034111yescharacteristic
499C2#1059034211yescharacteristic
500C2#1059137511yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#63577C2semidirect
4. #10591116C2semidirect
6. C3×#4524C2semidirect
7. C3×#4523C2semidirect
25. #63567C4semidirect
26. #63567C4semidirect
27. #63564C4semidirect
28. #63564C4semidirect
42. #4524D3semidirect
43. #4523D3semidirect
429. C32#1866semidirect
493. C3#68694semidirect
494. C3#68774semidirect

Maximal subgroups

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

subgroupindex
C2×#638172
C2×#636322
C2×#635772
#105911162
#105911052
C3×#45242
C3×#45232
#687743
#686943