Finite Group Databasebeta

← #11775405

Subgroups — #11775405

Order 1152.

612 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594892C211yesmaximal, characteristic
2C3×#4726C211yesmaximal, characteristic, complemented
3#10591295C211yesmaximal, characteristic, complemented
4#10589333C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#69979—31nomaximal
9#68305—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×#3795C411yescharacteristic, complemented
12#64133C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C2×C3×ΓL(1,𝔽25)—21no—
15#63976—21no—
16Dic3×#67—21no—
17C2×Dic3⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19#63908C411yescharacteristic, complemented
20#63905—21no—
21#63879—21no—
22#63857C411yescharacteristic, complemented
23#63841C411yescharacteristic, complemented
24C32×C22⋊C8C2211yescharacteristic
25#63658C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28C3×(C2×D3)⋊C8—21no—
29#5791—31no—
30#5606—31no—
31C3×#407—31no—
32#5212—31no—
33#4726D311yescharacteristic, complemented
34#4667—31no—
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4470D311yescharacteristic, complemented
39#4467—31no—
40#4467—31no—
41#4467—31no—
42#4467—61no—
43#4452—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×#634C2×C411yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—42no—
53C2×C3×C4×D3C2×C411yescharacteristic
54C2×C3×C4×D3C2×C411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×#625—21no—
58C2×#625—21no—
59C2×D3×Dic3—21no—
60#3795—42no—
61C2×C32×C8—21no—
62#3757—21no—
63C4⋊(C3⋊Dic3)C2×C411yescharacteristic
64#3750—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3C2×C411yescharacteristic
67C2×C3×C3⋊C8—21no—
68C3×ΓL(1,𝔽25)—42no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—42no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74(C2×D3)⋊Dic3—42no—
75Dic32—21no—
76#1513—91noSylow
77C23×C3×C4—31no—
78C2×#237—31no—
79C2×#235—31no—
80C22×C4×D3C2×D311yescharacteristic
81C2×C3×M16—61no—
82C3×#121—31no—
83#953—61no—
84C2×#217—61no—
85#938—31no—
86#937—61no—
87D4×Dic3—61no—
88#930—31no—
89#930C2×D311yescharacteristic
90#929—61no—
91C4×#67—61no—
92C4×#67—61no—
93C2×(C2×D3)⋊C4—61no—
94#926—31no—
95C2×C4⋊Dic3—61no—
96#924—31no—
97#924—31no—
98#924—31no—
99#924—61no—
100C2×Dic3⋊C4—61no—
101C2×ΓL(1,𝔽25)—21no—
102#897—31no—
103#892—31no—
104#883—61no—
105#67⋊C4—61no—
106C3×C22⋊C8—21no—
107C3×C22⋊C8—31no—
108C3×C22⋊C8—61no—
109C3×C22⋊C8C2×D311yescharacteristic
110C3×C22⋊C8C2×D311yescharacteristic
111C3×#95—31no—
112C3⋊#95—31no—
113C3⋊#95—31no—
114C3⋊#95—61no—
115C3⋊#95C2×D311yescharacteristic
116#830C2×D311yescharacteristic
117(C2×D3)⋊C8—21no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3C22⋊C411yescharacteristic
125C22×C3×D3C22⋊C411yescharacteristic
126C2×C32×C4—41no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134#634—41no—
135C3×#67—41no—
136C3×#67—41no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3C22⋊C411yescharacteristic
143C2×C3×Dic3C22⋊C411yescharacteristic
144C3×D12—41no—
145C3×C4×D3—22no—
146C3×C4×D3—22no—
147C3×C4×D3—41no—
148C3×C4×D3—41no—
149#625—42no—
150#625—42no—
151D3×Dic3—42no—
152C32×C8—41no—
153C3×C3⋊C8—41no—
154#525—91no—
155#407—31no—
156#380—91no—
157#328—91no—
158#328—91no—
159#327—31no—
160#327—91no—
161C24×C3—31no—
162C23×D3D1211yescharacteristic
163C2×C3×D4—31no—
164C2×C3×D4—61no—
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—61no—
172C22×C3×C4—122no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—21no—
176C2×#67—61no—
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—61no—
180C22×Dic3—21no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—121no—
185C22×Dic3D1211yescharacteristic
186#237—122no—
187#235—122no—
188C2×D12C4×D311yescharacteristic
189C2×C4×D3—42no—
190C2×C4×D3—61no—
191C2×C4×D3C4×D311yescharacteristic
192C2×C4×D3C4×D311yescharacteristic
193C2×C4×D3#6711yescharacteristic
194C2×C4×D3#6711yescharacteristic
195C2×Dic6—31no—
196C2×Dic6—31no—
197C2×Dic6—61no—
198C3×M16—122no—
199C2×C3×C8—21no—
200C2×C3×C8—21no—
201C2×C3×C8—41no—
202C2×C3×C8—61no—
203C3×C4⋊C4—31no—
204C3×C22⋊C4—61no—
205#217—61no—
206#217—61no—
207#217—61no—
208#217—61no—
209#217—61no—
210#217—121no—
211#217—122no—
212(C2×D3)⋊C4—21no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—122no—
217C4⋊Dic3—31no—
218C4⋊Dic3—31no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—122no—
222C4⋊Dic3C4×D311yescharacteristic
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—121no—
227Dic3⋊C4—122no—
228C4×Dic3—61no—
229C4×Dic3—61no—
230C2×C3⋊C8—21no—
231ΓL(1,𝔽25)—42no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32C2×C22⋊C411yescharacteristic
235C22×C32AGL(1,ℤ/8)11yescharacteristic
236C22×C32#13711yescharacteristic
237C2×C3×D3—21no—
238C2×C3×D3—21no—
239C2×C3×D3—21no—
240C2×C3×D3—21no—
241C2×C3×D3—21no—
242C2×C3×D3—21no—
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C2×C3×D3—41no—
246C2×C3×D3—41no—
247C2×C3×D3—41no—
248C32×C4—21no—
249C32×C4—21no—
250C3⋊Dic3—41no—
251C3⋊Dic3—41no—
252C3⋊Dic3—81no—
253C3×Dic3—21no—
254C3×Dic3—41no—
255C3×Dic3—81no—
256C3×Dic3#9912yes—
257C2×#41—91no—
258C23×C4—31no—
259C2×M16—61no—
260#123—181no—
261C22⋊Q8—91no—
262C22⋊Q8—91no—
263#121—31no—
264#121—91no—
265#120—181no—
266C4×D4—181no—
267C4×D4—181no—
268#117—91no—
269C2×C4⋊C4—181no—
270C2×C22⋊C4—181no—
271C22⋊C8—31no—
272C22⋊C8—61no—
273C22⋊C8D3211yescharacteristic
274#95—31no—
275#95—91no—
276C23×C3—21no—
277C23×C3—31no—
278C23×C3—31no—
279C23×C3—61no—
280C23×C3—61no—
281C23×C3—61no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3C2×D1211yescharacteristic
285C23×C3D3×D411yescharacteristic
286C22×D3—21no—
287C22×D3—21no—
288C22×D3—21no—
289C22×D3—41no—
290C22×D3—41no—
291C22×D3(C2×D3)⋊C411yescharacteristic
292C22×D3(C2×D3)⋊C411yescharacteristic
293C3×D4—121no—
294C3×D4—121no—
295C3×D4—121no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—61no—
306C2×C3×C4—81no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316#67—41no—
317#67—41no—
318#67—122no—
319#67—122no—
320#67—122no—
321#67—122no—
322C2×Dic3—22no—
323C2×Dic3—21no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—122no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—122no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—241no—
342C2×Dic3—241no—
343C2×Dic3(C2×D3)⋊C411yescharacteristic
344C2×Dic3(C2×D3)⋊C411yescharacteristic
345D12—41no—
346C4×D3—22no—
347C4×D3—22no—
348C4×D3—41no—
349C4×D3—41no—
350C4×D3—122no—
351Dic6—121no—
352Dic6—121no—
353Dic6—241no—
354C3×C8—41no—
355C3×C8—41no—
356C3×C8—81no—
357C3×C8—121no—
358C3⋊C8—41no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32C2×#9911yescharacteristic
362C2×C32#41711yescharacteristic
363C2×C32#42111yescharacteristic
364C3×D3—41no—
365C3×D3—41no—
366C3×D3—81no—
367C24—31no—
368#41—362no—
369C2×Q8—91no—
370C2×D4—31no—
371C2×D4—61no—
372C2×D4—181no—
373C2×D4—181no—
374C22×C4—31no—
375C22×C4—31no—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—31no—
379C22×C4—61no—
380C22×C4—122no—
381C22×C4—181no—
382C22×C4—181no—
383C22×C4C2×D3211yescharacteristic
384M16—122no—
385C2×C8—21no—
386C2×C8—61no—
387C4⋊C4—31no—
388C4⋊C4—91no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—362no—
392C22⋊C4—61no—
393C22⋊C4—181no—
394C22⋊C4—181no—
395C22⋊C4—181no—
396C22⋊C4—181no—
397C22⋊C4—362no—
398C42—181no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—61no—
409C22×C3—61no—
410C22×C3—61no—
411C22×C3—61no—
412C22×C3—61no—
413C22×C3—61no—
414C22×C3—122no—
415C22×C3—122no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3D3×C22⋊C411yescharacteristic
420C22×C3#90811yescharacteristic
421C22×C3#90911yescharacteristic
422C22×C3#91111yescharacteristic
423C22×C3#91511yescharacteristic
424C22×C3C2×(C2×D3)⋊C411yescharacteristic
425C2×D3—21no—
426C2×D3—21no—
427C2×D3—21no—
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—21no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—32no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—61no—
444C3×C4—121no—
445C3×C4—241no—
446Dic3—21no—
447Dic3—41no—
448Dic3—81no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452Dic3—121no—
453Dic3—241no—
454Dic3—241no—
455Dic3—241no—
456Dic3—241no—
457Dic3—242no—
458Dic3#80612yes—
459C32#151311yescharacteristic, complemented, Sylow
460C23—31no—
461C23—31no—
462C23—61no—
463C23—61no—
464C23—61no—
465C23—121no—
466C23—121no—
467C23D3×D1211yescharacteristic
468Q8—361no—
469D4—121no—
470D4—121no—
471D4—121no—
472D4—362no—
473D4—362no—
474C2×C4—31no—
475C2×C4—31no—
476C2×C4—41no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—61no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4—361no—
490C2×C4—361no—
491C2×C4—361no—
492C2×C4C4×D3211yescharacteristic
493C2×C4D3×#6711yescharacteristic
494C8—41no—
495C8—121no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—41no—
504C2×C3—41no—
505C2×C3—121no—
506C2×C3—121no—
507C2×C3—241no—
508C2×C3D3×#9911yescharacteristic
509C2×C3#477111yescharacteristic
510C2×C3#482111yescharacteristic
511C2×C3C2×#80611yescharacteristic
512C2×C3#513311yescharacteristic
513C2×C3#513911yescharacteristic
514D3—41no—
515D3—41no—
516D3—81no—
517C22—21no—
518C22—21no—
519C22—61no—
520C22—61no—
521C22—61no—
522C22—61no—
523C22—61no—
524C22—61no—
525C22—122no—
526C22—122no—
527C22—121no—
528C22—121no—
529C22—121no—
530C22#6379511yescharacteristic
531C22#6380011yescharacteristic
532C22D3×(C2×D3)⋊C411yescharacteristic
533C4—21no—
534C4—21no—
535C4—32no—
536C4—61no—
537C4—121no—
538C4—241no—
539C4—361no—
540C4—361no—
541C4—721no—
542C3—21no—
543C3#6830511yescharacteristic, complemented
544C3#6997911yescharacteristic, complemented
545C2—21no—
546C2—21no—
547C2—121no—
548C2—121no—
549C2—241no—
550C2D3×#80611yescharacteristic
551C2#1059067011yescharacteristic
552C2#1059100511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10594892C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1513
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4726C2semidirect
3. #10591295C2semidirect
4. #10589333C2semidirect
5. C3×#4470C2semidirect
6. #10589154C2semidirect
7. #10589150C2semidirect
11. C2×#3795C4semidirect
19. #63908C4semidirect
22. #63857C4semidirect
23. #63841C4semidirect
33. #4726D3semidirect
38. #4470D3semidirect
459. C32#1513semidirect
543. C3#68305semidirect
544. C3#69979semidirect

Maximal subgroups

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

subgroupindex
#105948922
C3×#47262
#105912952
#105893332
C3×#44702
#105891542
#105891502
#699793
#683053