Finite Group Databasebeta

← #11773998

Subgroups — #11773998

Order 1152.

661 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 661 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63853C211yesmaximal, characteristic
2C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
3#10591159C211yesmaximal, characteristic, complemented
4C3×#4469C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic, complemented
6#10589147C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#68146—31nomaximal
9#68122—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×#626C411yescharacteristic
12C2×C8×C3⋊D3—21no—
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C2×Dic3⋊Dic3C411yescharacteristic
16C2×#3722C411yescharacteristic
17C2×(C2×D3)⋊Dic3C411yescharacteristic
18#63853—21no—
19#63853—21no—
20#63853—21no—
21#63853—21no—
22C2×#3712—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25#63647—21no—
26C3×#830C2211yescharacteristic
27C3×#830C2211yescharacteristic
28#63557—21no—
29C2×#894—31no—
30C2×#883—31no—
31#4726—31no—
32#4726—31no—
33D3×C22⋊C8—31no—
34D3×C22⋊C8—31no—
35D3×C22⋊C8—61no—
36C3×#324—31no—
37C3×#323—31no—
38#4528—31no—
39#4525—31no—
40#4469—31no—
41#4469D311yescharacteristic, complemented
42#4468—31no—
43#4468D311yescharacteristic, complemented
44C23×C3⋊D3C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C2×C4×C3⋊D3—42no—
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C22×C3×Dic3C2×C411yescharacteristic
54C22×C3×Dic3C2×C411yescharacteristic
55C22×C3×Dic3C2×C411yescharacteristic
56C2×#626—21no—
57C2×#626—21no—
58C2×#626—42no—
59C2×C32×C8—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C8×C3⋊D3—42no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70#3722—21no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74#3712—42no—
75#1468—91noSylow
76C22×#67—31no—
77C22×D12—31no—
78C22×C4×D3—31no—
79C22×C4×D3—31no—
80C22×C4×D3—61no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C22⋊C4—31no—
83C2×#217—31no—
84C2×(C2×D3)⋊C4—31no—
85C2×(C2×D3)⋊C4—31no—
86C2×(C2×D3)⋊C4—31no—
87C2×(C2×D3)⋊C4C2×D311yescharacteristic
88C2×C4⋊Dic3—31no—
89C2×Dic3⋊C4—31no—
90C2×Dic3⋊C4C2×D311yescharacteristic
91C2×ΓL(1,𝔽25)—61no—
92C2×ΓL(1,𝔽25)—61no—
93C2×D3×C8—61no—
94C2×D3×C8—61no—
95C2×D3×C8—62no—
96#894—61no—
97#894—61no—
98#894—61no—
99#894—61no—
100#883—61no—
101#883—61no—
102#883—61no—
103#883—61no—
104C3×C22⋊C8—21no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C22⋊C8C2×D311yescharacteristic
109#830—31no—
110#830—31no—
111#830—61no—
112#830C2×D311yescharacteristic
113#830C2×D311yescharacteristic
114(C2×D3)⋊C8—61no—
115(C2×D3)⋊C8—61no—
116(C2×D3)⋊C8—61no—
117(C2×D3)⋊C8—61no—
118(C2×D3)⋊C8—62no—
119C23×C32C22×C411yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3⋊D3—21no—
122C22×C3⋊D3—22no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3C22⋊C411yescharacteristic
125C22×C3⋊D3C22⋊C411yescharacteristic
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C2×C32×C4—41no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3C22⋊C411yescharacteristic
136C2×C3⋊Dic3C22⋊C411yescharacteristic
137C4×C3⋊D3—22no—
138C4×C3⋊D3—22no—
139C4×C3⋊D3—41no—
140C4×C3⋊D3—41no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148#626—42no—
149#626—42no—
150C32×C8—41no—
151C3⋊(C3⋊C8)—41no—
152C3×C3⋊C8—41no—
153C3×C3⋊C8—41no—
154C2×#123—91no—
155#407—91no—
156C2×C22⋊C8—91no—
157#324—31no—
158#324—91no—
159#323—31no—
160#323—91no—
161C24×C3—31no—
162C23×D3—31no—
163C23×D3—31no—
164C23×D3—61no—
165C23×D3C4×D311yescharacteristic
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—61no—
173C2×#67—61no—
174C2×#67—122no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—61no—
178C22×Dic3C4×D311yescharacteristic
179C22×Dic3C4×D311yescharacteristic
180C22×Dic3C4×D311yescharacteristic
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—122no—
184C2×C4×D3—31no—
185C2×C4×D3—31no—
186C2×C4×D3—31no—
187C2×C4×D3—31no—
188C2×C4×D3—31no—
189C2×C4×D3—31no—
190C2×C4×D3—31no—
191C2×C4×D3—31no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C4×D3—61no—
195C2×C4×D3—61no—
196C2×C4×D3—122no—
197C2×C4×D3—122no—
198C2×C4×D3—124no—
199C2×C3×C8—22no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C22⋊C4—61no—
208#217—61no—
209#217—61no—
210(C2×D3)⋊C4—21no—
211(C2×D3)⋊C4—21no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220Dic3⋊C4—21no—
221Dic3⋊C4—21no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229ΓL(1,𝔽25)—122no—
230ΓL(1,𝔽25)—122no—
231D3×C8—122no—
232D3×C8—122no—
233D3×C8—124no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32C2×C22⋊C411yescharacteristic
237C22×C32#13111yescharacteristic
238C22×C32#13111yescharacteristic
239C2×C3⋊D3—21no—
240C2×C3⋊D3—21no—
241C2×C3⋊D3—21no—
242C2×C3⋊D3—21no—
243C2×C3⋊D3—21no—
244C2×C3⋊D3—42no—
245C2×C3⋊D3—42no—
246C2×C3⋊D3#9912yes—
247C2×C3×D3—41no—
248C2×C3×D3—41no—
249C2×C3×D3—41no—
250C2×C3×D3—81no—
251C2×C3×D3—81no—
252C32×C4—21no—
253C32×C4—21no—
254C3⋊Dic3—21no—
255C3⋊Dic3—21no—
256C3×Dic3—41no—
257C3×Dic3—41no—
258C3×Dic3—41no—
259C22×D4—91no—
260C23×C4—91no—
261C2×M16—181no—
262C22×C8—181no—
263#123—181no—
264#123—181no—
265#123—181no—
266#123—181no—
267C2×C4⋊C4—31no—
268C2×C4⋊C4—91no—
269C2×C22⋊C4—31no—
270C2×C22⋊C4—91no—
271C2×C22⋊C4—91no—
272C22⋊C8—31no—
273C22⋊C8—31no—
274C22⋊C8—91no—
275C22⋊C8—181no—
276C22⋊C8—181no—
277C22⋊C8D3211yescharacteristic
278C23×C3—21no—
279C23×C3—61no—
280C23×C3—61no—
281C23×C3—61no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3C2×C4×D311yescharacteristic
285C23×C3C2×C4×D311yescharacteristic
286C22×D3—21no—
287C22×D3—21no—
288C22×D3—21no—
289C22×D3—31no—
290C22×D3—31no—
291C22×D3—31no—
292C22×D3—31no—
293C22×D3—41no—
294C22×D3—41no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—61no—
302C22×D3—61no—
303C22×D3—61no—
304C22×D3—61no—
305C22×D3—122no—
306C22×D3—121no—
307C22×D3—121no—
308C22×D3—122no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—42no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325#67—122no—
326#67—122no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—31no—
335C2×Dic3—31no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—122no—
343D12—122no—
344D12—122no—
345C4×D3—62no—
346C4×D3—62no—
347C4×D3—62no—
348C4×D3—62no—
349C4×D3—64no—
350C4×D3—122no—
351C4×D3—121no—
352C4×D3—121no—
353C4×D3—121no—
354C4×D3—121no—
355C4×D3—122no—
356C4×D3—122no—
357C3×C8—42no—
358C3×C8—41no—
359C3×C8—41no—
360C3×C8—121no—
361C3×C8—121no—
362C3⋊C8—41no—
363C3⋊C8—41no—
364C3⋊C8—122no—
365C3⋊C8—121no—
366C3⋊C8—121no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32#40811yescharacteristic
370C2×C32C2×#9911yescharacteristic
371C2×C32#41311yescharacteristic
372C3⋊D3—22no—
373C3⋊D3—41no—
374C3×D3—81no—
375C24—31no—
376C24—91no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4—362no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—362no—
389C22×C4C2×D3211yescharacteristic
390M16—362no—
391C2×C8—21no—
392C2×C8—61no—
393C2×C8—61no—
394C2×C8—181no—
395C2×C8—362no—
396C4⋊C4—61no—
397C4⋊C4—61no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C22⋊C4—61no—
401C22⋊C4—61no—
402C22⋊C4—181no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C22⋊C4—181no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—121no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—241no—
419C22×C3—241no—
420C22×C3D3×C22⋊C411yescharacteristic
421C22×C3D3×C22⋊C411yescharacteristic
422C22×C3#90111yescharacteristic
423C22×C3#90111yescharacteristic
424C22×C3#90711yescharacteristic
425C22×C3#90711yescharacteristic
426C2×D3—32no—
427C2×D3—32no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—41no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—61no—
435C2×D3—61no—
436C2×D3—61no—
437C2×D3—61no—
438C2×D3—62no—
439C2×D3—61no—
440C2×D3—61no—
441C2×D3—61no—
442C2×D3—61no—
443C2×D3—61no—
444C2×D3—61no—
445C2×D3—81no—
446C2×D3—81no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—124no—
454C2×D3—124no—
455C3×C4—22no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—41no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4—121no—
464Dic3—41no—
465Dic3—41no—
466Dic3—41no—
467Dic3—62no—
468Dic3—61no—
469Dic3—61no—
470Dic3—61no—
471Dic3—61no—
472Dic3—121no—
473C32#146811yescharacteristic, complemented, Sylow
474C23—61no—
475C23—61no—
476C23—61no—
477C23—91no—
478C23—91no—
479C23—121no—
480C23—121no—
481C23—182no—
482C23—181no—
483C23—181no—
484C23—361no—
485C23C4×D3211yescharacteristic
486D4—362no—
487D4—362no—
488C2×C4—41no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—91no—
495C2×C4—91no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—182no—
499C2×C4—182no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4—361no—
503C2×C4#380211yescharacteristic
504C2×C4#381111yescharacteristic
505C8—41no—
506C8—121no—
507C8—121no—
508C8—361no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—41no—
517C2×C3—41no—
518C2×C3—241no—
519C2×C3#472711yescharacteristic
520C2×C3#472711yescharacteristic
521C2×C3D3×#9911yescharacteristic
522C2×C3D3×#9911yescharacteristic
523C2×C3#474511yescharacteristic
524C2×C3#475111yescharacteristic
525D3—64no—
526D3—62no—
527D3—62no—
528D3—81no—
529D3—122no—
530D3—121no—
531D3—121no—
532C22—21no—
533C22—21no—
534C22—92no—
535C22—121no—
536C22—121no—
537C22—121no—
538C22—181no—
539C22—181no—
540C22—181no—
541C22—181no—
542C22—181no—
543C22—241no—
544C22—241no—
545C22—362no—
546C22—362no—
547C22#6380311yescharacteristic
548C22#6380511yescharacteristic
549C22#6392111yescharacteristic
550C4—21no—
551C4—21no—
552C4—121no—
553C4—121no—
554C4—121no—
555C4—181no—
556C4—181no—
557C3—21no—
558C3#6812211yescharacteristic, complemented
559C3#6814611yescharacteristic, complemented
560C2—21no—
561C2—21no—
562C2—182no—
563C2—241no—
564C2—361no—
565C2#1059040411yescharacteristic
566C2#1059095811yescharacteristic
567C2#1059101011yescharacteristic
subgroupG/H
centerC22#63921
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#626C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1468
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C22⋊C8C2semidirect
3. #10591159C2semidirect
4. C3×#4469C2semidirect
5. C3×#4468C2semidirect
6. #10589147C2semidirect
7. #10589145C2semidirect
41. #4469D3semidirect
43. #4468D3semidirect
473. C32#1468semidirect
558. C3#68122semidirect
559. C3#68146semidirect

Maximal subgroups

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

subgroupindex
C2×#638532
C3⋊D3×C22⋊C82
#105911592
C3×#44692
C3×#44682
#105891472
#105891452
#681463
#681223