Finite Group Databasebeta

← #11784133

Subgroups — #11784133

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic
2C2×#63570C211yesmaximal, characteristic
3#10591105C211yesmaximal, characteristic
4C2×#63554C211yesmaximal, characteristic, complemented
5#10591057C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7C3×#4555C211yesmaximal, characteristic, complemented
8#68927—31nomaximal
9#68740—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13#64116—22no—
14#64116C414yescomplemented
15C2×#3743—21no—
16C2×C8×C3⋊D3—21no—
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63570C414yescomplemented
22#63567C412yescomplemented
23#63564C412yescomplemented
24#63554—21no—
25#63554—22no—
26Dic3×C3⋊C8—21no—
27C2×#907—31no—
28C2×#907—31no—
29C2×#907—61no—
30C2×#825—31no—
31#5122—31no—
32#5113—31no—
33C2×#815—31no—
34#5002—31no—
35#4997—31no—
36C2×#805—31no—
37C2×#803—31no—
38C3×#341—31no—
39C3×#339—31no—
40#4558D311yescharacteristic, complemented
41#4555D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C2×#638—21no—
44#3828—21no—
45#3828—21no—
46#3828C2×C412yes—
47#3828C2×C412yes—
48C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×#634C2×C411yescharacteristic
51C22×C3×Dic3—21no—
52C32×M16—21no—
53C32×M16C2×C412yes—
54C2×C32×C8—21no—
55C2×C3⋊(C3⋊C8)C2×C412yes—
56C2×C3⋊(C3⋊C8)D411yescharacteristic
57C2×C3⋊(C3⋊C8)D411yescharacteristic
58C2×C3⋊(C3⋊C8)D412yes—
59#3743—24no—
60C8×C3⋊D3—24no—
61C3×#217—21no—
62C3×C4⋊Dic3C2×C412yes—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3C2×C412yes—
66C3×#208—21no—
67C3×#208C2×C412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yes—
72#1765—91noSylow
73C2×#235—31no—
74C2×#235—31no—
75C2×#235—61no—
76C2×C3×M16—21no—
77C2×C3×M16—31no—
78C2×C3×M16C2×D311yescharacteristic
79C2×C3×M16C2×D311yescharacteristic
80C22×C3×C8—31no—
81C3×#117—31no—
82C2×C3×C42—31no—
83#926C2×D311yescharacteristic
84C2×C4×Dic3C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8—31no—
87C22×C3⋊C8—31no—
88C22×C3⋊C8—61no—
89C22×C3⋊C8C2×D311yescharacteristic
90#907—34no—
91#907—34no—
92#907—64no—
93#907—62no—
94#907—62no—
95#907—64no—
96C2×ΓL(1,𝔽25)—61no—
97C2×ΓL(1,𝔽25)—61no—
98C2×ΓL(1,𝔽25)—62no—
99C2×D3×C8—61no—
100C2×D3×C8—61no—
101C2×D3×C8—62no—
102#825—34no—
103#821—32no—
104#816—32no—
105#815—61no—
106#815—62no—
107C8×Dic3—61no—
108#810—32no—
109#809—32no—
110#805—34no—
111#803—62no—
112#803—61no—
113C4×C3⋊C8—61no—
114C23×C32#4111yescharacteristic
115C22×C3⋊D3—21no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4#4111yescharacteristic
122#638—22no—
123#638—22no—
124C2×C3⋊Dic3—21no—
125C4⋊(C3⋊D3)—21no—
126C4⋊(C3⋊D3)C4212yes—
127C4×C3⋊D3—22no—
128C4×C3⋊D3—22no—
129#634—21no—
130#634C4212yes—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—42no—
134C32×C8—22no—
135C3⋊(C3⋊C8)C22⋊C412yes—
136C3⋊(C3⋊C8)C22⋊C412yes—
137C3×C3⋊C8—22no—
138C3×C3⋊C8—22no—
139C2×#131—91no—
140C2×#104—91no—
141#416—91no—
142#405—91no—
143C2×#97—91no—
144#341—31no—
145#339—31no—
146C22×C3×C4—21no—
147C22×C3×C4—61no—
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C2×#67—62no—
151C2×#67—61no—
152C2×#67—61no—
153C22×Dic3—21no—
154#235—32no—
155#235—32no—
156#235—32no—
157#235—32no—
158#235—62no—
159#235—62no—
160#235—62no—
161#235—62no—
162#235—61no—
163#235—61no—
164#235—61no—
165#235—61no—
166C2×D12—31no—
167C2×D12—31no—
168C2×D12—61no—
169C2×C4×D3—62no—
170C2×C4×D3—61no—
171C2×C4×D3—61no—
172C2×Dic6—31no—
173C2×Dic6—31no—
174C2×Dic6—61no—
175C3×M16—22no—
176C3×M16—21no—
177C3×M16—21no—
178C3×M16—22no—
179C3×M16—32no—
180C3×M16—61no—
181C3×M16C4×D312yes—
182C3×M16C4×D312yes—
183C2×C3×C8—22no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—32no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C3×C4⋊C4—32no—
191C3×C22⋊C4—61no—
192C3×C42—32no—
193C3×C42—61no—
194C3×C42—61no—
195#217—21no—
196C4⋊Dic3C4×D312yes—
197C4×Dic3—21no—
198C4×Dic3—21no—
199C4×Dic3C4×D312yes—
200#208—21no—
201#208C4×D312yes—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—32no—
206C2×C3⋊C8—32no—
207C2×C3⋊C8—31no—
208C2×C3⋊C8—31no—
209C2×C3⋊C8—32no—
210C2×C3⋊C8—31no—
211C2×C3⋊C8—31no—
212C2×C3⋊C8—32no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—62no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8C4×D312yes—
218ΓL(1,𝔽25)—64no—
219ΓL(1,𝔽25)—64no—
220ΓL(1,𝔽25)—68no—
221D3×C8—64no—
222D3×C8—64no—
223D3×C8—68no—
224C22×C32—22no—
225C22×C32#11711yescharacteristic
226C22×C32C4×D411yescharacteristic
227C22×C32C4×D411yescharacteristic
228C2×C3⋊D3—22no—
229C2×C3⋊D3—42no—
230C32×C4C2×C4211yescharacteristic
231C32×C4C2×C22⋊C411yescharacteristic
232C32×C4C4×D411yescharacteristic
233C32×C4C4×D411yescharacteristic
234C3⋊Dic3—22no—
235C3×Dic3—42no—
236C3×Dic3—42no—
237C2×#41—91no—
238#131—94no—
239#131—182no—
240C2×M16—31no—
241C2×M16—181no—
242C2×M16D3211yescharacteristic
243C22×C8—31no—
244C22×C8—91no—
245C22×C8—181no—
246#117—31no—
247C2×C42—31no—
248#104—94no—
249#103—92no—
250#102—92no—
251#97—182no—
252#97—181no—
253C4×C8—181no—
254C23×C3—21no—
255C23×C3#23711yescharacteristic
256C23×C3#23911yescharacteristic
257C22×D3—62no—
258C22×D3—61no—
259C22×D3—61no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—122no—
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4C2×C4×D311yescharacteristic
273C2×C3×C4C2×C4×D311yescharacteristic
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4#23711yescharacteristic
280C2×C3×C4#23911yescharacteristic
281#67—64no—
282#67—64no—
283#67—62no—
284#67—62no—
285#67—62no—
286#67—62no—
287C2×Dic3—22no—
288C2×Dic3—22no—
289C2×Dic3—42no—
290C2×Dic3—62no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293D12—32no—
294D12—32no—
295D12—62no—
296D12—62no—
297D12—61no—
298D12—61no—
299C4×D3—64no—
300C4×D3—64no—
301C4×D3—62no—
302C4×D3—62no—
303C4×D3—62no—
304C4×D3—62no—
305Dic6—32no—
306Dic6—32no—
307Dic6—62no—
308Dic6—62no—
309Dic6—61no—
310Dic6—61no—
311C3×C8—24no—
312C3×C8—22no—
313C3×C8—22no—
314C3×C8—62no—
315C3×C8—62no—
316C3⋊C8—22no—
317C3⋊C8—22no—
318C3⋊C8—32no—
319C3⋊C8—32no—
320C3⋊C8—32no—
321C3⋊C8—32no—
322C3⋊C8—62no—
323C3⋊C8—62no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32C4×C22⋊C411yescharacteristic
327C2×C32#44412yes—
328C3⋊D3—42no—
329#41—92no—
330#41—92no—
331#41—181no—
332#41—181no—
333C2×Q8—91no—
334C2×D4—91no—
335C2×D4—181no—
336C22×C4—61no—
337C22×C4—181no—
338C22×C4C2×D3211yescharacteristic
339M16—21no—
340M16—32no—
341M16—61no—
342M16—184no—
343M16#62412yes—
344C2×C8—21no—
345C2×C8—32no—
346C2×C8—61no—
347C2×C8—61no—
348C2×C8—61no—
349C2×C8—92no—
350C2×C8—92no—
351C2×C8—91no—
352C2×C8—91no—
353C2×C8—184no—
354C4⋊C4—32no—
355C22⋊C4—61no—
356C42—32no—
357C42—61no—
358C42—61no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—42no—
365C22×C3#67⋊C411yescharacteristic
366C22×C3#67⋊C411yescharacteristic
367C22×C3#89211yescharacteristic
368C22×C3#89211yescharacteristic
369C22×C3#89311yescharacteristic
370C22×C3#89311yescharacteristic
371C2×D3—64no—
372C2×D3—62no—
373C2×D3—62no—
374C2×D3—124no—
375C2×D3—122no—
376C2×D3—122no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—122no—
382C3×C4—122no—
383C3×C4C42×D311yescharacteristic
384C3×C4C42×D311yescharacteristic
385C3×C4D3×C22⋊C411yescharacteristic
386C3×C4D3×C22⋊C411yescharacteristic
387C3×C4#67⋊C411yescharacteristic
388C3×C4#67⋊C411yescharacteristic
389C3×C4#89311yescharacteristic
390C3×C4#89311yescharacteristic
391Dic3—42no—
392Dic3—42no—
393Dic3—64no—
394Dic3—62no—
395Dic3—62no—
396C32#176511yescharacteristic, complemented, Sylow
397C23—181no—
398C23#379611yescharacteristic
399Q8—92no—
400Q8—181no—
401D4—92no—
402D4—182no—
403D4—182no—
404D4—181no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—122no—
408C2×C4—181no—
409C2×C4—182no—
410C2×C4—182no—
411C2×C4#379611yescharacteristic
412C2×C4C4×D3211yescharacteristic
413C2×C4C4×D3211yescharacteristic
414C2×C4C2×#62411yescharacteristic
415C2×C4#381111yescharacteristic
416C2×C4#381111yescharacteristic
417C8—22no—
418C8—62no—
419C8—62no—
420C8—92no—
421C8—92no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—41no—
429C2×C3—41no—
430C2×C3#466611yescharacteristic
431C2×C3#466611yescharacteristic
432C2×C3#482312yes—
433C2×C3#489412yes—
434D3—124no—
435D3—122no—
436D3—122no—
437C22—22no—
438C22—182no—
439C22—362no—
440C22#6384911yescharacteristic
441C22#6388111yescharacteristic
442C22#6388111yescharacteristic
443C4—122no—
444C4—122no—
445C4—182no—
446C4#6388111yescharacteristic
447C4#6388111yescharacteristic
448C4C4×#62411yescharacteristic
449C4#6397411yescharacteristic
450C3—21no—
451C3#6874011yescharacteristic, complemented
452C3#6892711yescharacteristic, complemented
453C2—21no—
454C2—21no—
455C2—362no—
456C2#1059097812yes—
457C2#1059126011yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1765
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. C2×#63554C2semidirect
5. #10591057C2semidirect
6. C3×#4558C2semidirect
7. C3×#4555C2semidirect
14. #64116C4semidirect
21. #63570C4semidirect
22. #63567C4semidirect
23. #63564C4semidirect
40. #4558D3semidirect
41. #4555D3semidirect
396. C32#1765semidirect
451. C3#68740semidirect
452. C3#68927semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
C2×#635702
#105911052
C2×#635542
#105910572
C3×#45582
C3×#45552
#689273
#687403