Finite Group Databasebeta

← #11778189

Subgroups — #11778189

Order 1152.

680 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 78 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
1#10594977C211yesmaximal, characteristic, complemented
2C3×#4671C211yesmaximal, characteristic, complemented
3#10591172C211yesmaximal, characteristic, complemented
4#10591160C211yesmaximal, characteristic, complemented
5#10589318C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#69697—31nomaximal
9#68285—31nomaximal
10C22×C3×D12—21no—
11C22×C3×D12C2211yescharacteristic
12#64133C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4C2211yescharacteristic
16#63976—21no—
17Dic3×#67—21no—
18#63913—21no—
19#63891—21no—
20#63885—21no—
21#63858—21no—
22C2×#3716—21no—
23C2×#3713—21no—
24C32×#95C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63563—21no—
28#63562—21no—
29#5617—31no—
30#5494—31no—
31C3×#392—31no—
32#5218—31no—
33#5217—31no—
34#5036—31no—
35#4731—31no—
36#4671D311yescharacteristic, complemented
37C3×#327—31no—
38#4525—31no—
39#4468—31no—
40#4452—31no—
41#4452—31no—
42#4452—61no—
43#4451D311yescharacteristic, complemented
44C23×C3×D3—21no—
45C23×C3×D3D411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×#634D411yescharacteristic, complemented
49C2×C3×#67—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—42no—
54C2×C3×D12—42no—
55C2×C3×D12—42no—
56C2×C3×D12—42no—
57C2×C3×D12D411yescharacteristic, complemented
58C2×#625—21no—
59C2×#625—21no—
60C2×D3×Dic3—21no—
61#3757—21no—
62C4⋊(C3⋊Dic3)D411yescharacteristic, complemented
63#3750—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—42no—
69C3×C4⋊Dic3D411yescharacteristic, complemented
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74(C2×D3)⋊Dic3—21no—
75Dic32—21no—
76#3716—42no—
77#3713—42no—
78#1600—91noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C22×D12—21no—
82C22×D12C2×D311yescharacteristic
83C3×#121—31no—
84C2×C3×C22⋊C4—31no—
85C2×C3×C22⋊C4—61no—
86#953—61no—
87#939—61no—
88#937—61no—
89D4×Dic3—61no—
90C2×#214—61no—
91C2×#213—61no—
92C2×#213—61no—
93#930C2×D311yescharacteristic
94C4×#67—61no—
95C2×(C2×D3)⋊C4—21no—
96C2×(C2×D3)⋊C4C2×D311yescharacteristic
97#924—31no—
98#924—31no—
99#924—61no—
100C2×#204—61no—
101#898—61no—
102#886—61no—
103#885—61no—
104#885—61no—
105#884—61no—
106#883—61no—
107#879—61no—
108C3×C22⋊C8—31no—
109C3×#95—21no—
110C3×#95C2×D311yescharacteristic
111C3×#95C2×D311yescharacteristic
112#832—61no—
113#832—61no—
114#830—31no—
115#830—31no—
116#830—61no—
117#830C2×D311yescharacteristic
118#821—61no—
119#809—61no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—22no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—21no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C2×C32×C4—22no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142#634—41no—
143C3×#67—41no—
144C3×#67—41no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—41no—
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C3×D12—41no—
153C3×D12—48no—
154#625—81no—
155#625—81no—
156D3×Dic3—81no—
157C3⋊(C3⋊C8)—41no—
158C3×C3⋊C8—41no—
159#538—91no—
160#450—91no—
161#447—91no—
162#392—31no—
163#328—91no—
164#327—31no—
165#323—91no—
166C24×C3—31no—
167C24×C3—61no—
168C23×D3—21no—
169C23×D3#6711yescharacteristic
170C2×C3×D4—31no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—122no—
175C2×C3×D4—122no—
176C2×C3×D4—122no—
177C2×C3×D4—122no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—31no—
182C22×C3×C4—41no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—21no—
186C2×#67—61no—
187C2×#67—61no—
188C2×#67—61no—
189C2×#67—61no—
190C22×Dic3—61no—
191C22×Dic3#6711yescharacteristic
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—42no—
195C2×D12—42no—
196C2×D12—42no—
197C2×D12—42no—
198C2×D12D1211yescharacteristic, complemented
199C2×C4×D3—61no—
200C2×Dic6—31no—
201C2×Dic6—31no—
202C2×Dic6—61no—
203C2×C3×C8—61no—
204C3×C4⋊C4—31no—
205C3×C22⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—122no—
209#217—61no—
210#217—61no—
211#217—61no—
212#217—61no—
213#217—61no—
214#217—121no—
215#214—122no—
216#213—122no—
217#213—122no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—21no—
220(C2×D3)⋊C4—21no—
221(C2×D3)⋊C4—42no—
222(C2×D3)⋊C4—61no—
223(C2×D3)⋊C4—61no—
224(C2×D3)⋊C4—61no—
225C4⋊Dic3—31no—
226C4⋊Dic3—31no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3D1211yescharacteristic, complemented
230Dic3⋊C4—61no—
231Dic3⋊C4—61no—
232Dic3⋊C4—61no—
233Dic3⋊C4—121no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—121no—
240#204—122no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32#12011yescharacteristic
244C22×C32#13511yescharacteristic
245C22×C32AGL(1,ℤ/8)11yescharacteristic
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C2×C3×D3—41no—
255C2×C3×D3—42no—
256C2×C3×D3—81no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C2×C3×D3—81no—
260C2×C3×D3—81no—
261C32×C4—21no—
262C32×C4—21no—
263C32×C4—42no—
264C3⋊Dic3—41no—
265C3⋊Dic3—41no—
266C3×Dic3—41no—
267C3×Dic3—41no—
268C22×D4—31no—
269C22×D4—61no—
270C2×SD16—181no—
271C2×D8—181no—
272#126—181no—
273#124—181no—
274#123—181no—
275C22⋊Q8—91no—
276#121—31no—
277#121—181no—
278#120—181no—
279C4×D4—181no—
280C2×C22⋊C4—31no—
281C2×C22⋊C4—61no—
282#102—181no—
283#102—181no—
284C22⋊C8—31no—
285C22⋊C8—91no—
286#95D3211yescharacteristic
287C23×C3—21no—
288C23×C3—62no—
289C23×C3—61no—
290C23×C3—61no—
291C23×C3—61no—
292C23×C3—61no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3—121no—
301C23×C3D3×D411yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C22×D3—22no—
304C22×D3—21no—
305C22×D3—21no—
306C22×D3—21no—
307C22×D3—21no—
308C22×D3—41no—
309C22×D3—41no—
310C22×D3—41no—
311C22×D3—41no—
312C22×D3—41no—
313C22×D3—41no—
314C22×D3—41no—
315C22×D3—41no—
316C3×D4—62no—
317C3×D4—62no—
318C3×D4—121no—
319C3×D4—121no—
320C3×D4—121no—
321C3×D4—128no—
322C3×D4—121no—
323C3×D4—121no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—42no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—81no—
338C2×C3×C4—81no—
339C2×C3×C4—81no—
340C2×C3×C4—121no—
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345#67—41no—
346#67—41no—
347#67—241no—
348#67—241no—
349#67—241no—
350#67—241no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—41no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—241no—
361D12—22no—
362D12—22no—
363D12—41no—
364D12—41no—
365D12—41no—
366D12—48no—
367C4×D3—241no—
368Dic6—121no—
369Dic6—121no—
370Dic6—241no—
371C3×C8—121no—
372C3⋊C8—41no—
373C3⋊C8—121no—
374C3⋊C8—121no—
375C3⋊C8—241no—
376C2×C32—21no—
377C2×C32—21no—
378C2×C32#44911yescharacteristic
379C2×C32#45311yescharacteristic
380C2×C32B(4,𝔽2)11yescharacteristic
381C3×D3—81no—
382C3×D3—81no—
383C3×D3—82no—
384C24—31no—
385C24—61no—
386C2×Q8—91no—
387C2×D4—31no—
388C2×D4—61no—
389C2×D4—61no—
390C2×D4—61no—
391C2×D4—122no—
392C2×D4—122no—
393C2×D4—122no—
394C2×D4—122no—
395C2×D4—181no—
396C2×D4—181no—
397C22×C4—21no—
398C22×C4—31no—
399C22×C4—181no—
400C22×C4C2×D3211yescharacteristic
401SD16—362no—
402D8—362no—
403C2×C8—61no—
404C2×C8—181no—
405C4⋊C4—31no—
406C4⋊C4—91no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C22⋊C4—61no—
410C22⋊C4—61no—
411C22⋊C4—61no—
412C22⋊C4—122no—
413C22⋊C4—181no—
414C22⋊C4—181no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C42—181no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—121no—
431C22×C3—122no—
432C22×C3—121no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3—241no—
438C22×C3—241no—
439C22×C3—241no—
440C22×C3—241no—
441C22×C3—241no—
442C22×C3#88211yescharacteristic
443C22×C3#91111yescharacteristic
444C22×C3#91611yescharacteristic
445C22×C3#93211yescharacteristic
446C22×C3#93711yescharacteristic
447C22×C3#95011yescharacteristic
448C2×D3—42no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—41no—
452C2×D3—42no—
453C2×D3—41no—
454C2×D3—41no—
455C2×D3—41no—
456C2×D3—41no—
457C2×D3—41no—
458C2×D3—81no—
459C2×D3—81no—
460C2×D3—81no—
461C2×D3—81no—
462C2×D3—81no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—42no—
470C3×C4—42no—
471C3×C4—82no—
472C3×C4—121no—
473C3×C4—121no—
474Dic3—41no—
475Dic3—41no—
476Dic3—121no—
477Dic3—121no—
478Dic3—121no—
479Dic3—121no—
480Dic3—241no—
481Dic3—241no—
482C32#160011yescharacteristic, complemented, Sylow
483C23—62no—
484C23—61no—
485C23—61no—
486C23—61no—
487C23—61no—
488C23—121no—
489C23—121no—
490C23—121no—
491C23—121no—
492C23—121no—
493C23—121no—
494C23—121no—
495C23—121no—
496C23D3×#6711yescharacteristic
497Q8—361no—
498D4—62no—
499D4—62no—
500D4—121no—
501D4—121no—
502D4—121no—
503D4—128no—
504D4—121no—
505D4—121no—
506D4—721no—
507D4—721no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—121no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—721no—
518C2×C4D3×D1211yescharacteristic
519C2×C4#380211yescharacteristic
520C8—121no—
521C8—361no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—41no—
530C2×C3—41no—
531C2×C3—241no—
532C2×C3—241no—
533C2×C3—242no—
534C2×C3#474111yescharacteristic
535C2×C3#478111yescharacteristic
536C2×C3#482211yescharacteristic
537C2×C3#503211yescharacteristic
538C2×C3#503711yescharacteristic
539C2×C3#507711yescharacteristic
540D3—81no—
541D3—82no—
542D3—81no—
543C22—21no—
544C22—21no—
545C22—122no—
546C22—122no—
547C22—122no—
548C22—121no—
549C22—121no—
550C22—121no—
551C22—121no—
552C22—122no—
553C22—121no—
554C22—121no—
555C22—241no—
556C22—241no—
557C22—241no—
558C22—241no—
559C22—241no—
560C22#6392211yescharacteristic
561C22#6393211yescharacteristic
562C22#6394711yescharacteristic
563C4—21no—
564C4—21no—
565C4—42no—
566C4—121no—
567C4—121no—
568C4—361no—
569C4—361no—
570C3—21no—
571C3#6828511yescharacteristic, complemented
572C3#6969711yescharacteristic, complemented
573C2—21no—
574C2—21no—
575C2—241no—
576C2—242no—
577C2—241no—
578C2#1059039511yescharacteristic
579C2#1059040711yescharacteristic
580C2#1059061311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
hypercenter#95D32
hypocenterC32#1600
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #10594977C2semidirect
2. C3×#4671C2semidirect
3. #10591172C2semidirect
4. #10591160C2semidirect
5. #10589318C2semidirect
6. C3×#4451C2semidirect
7. #10589145C2semidirect
36. #4671D3semidirect
43. #4451D3semidirect
48. C2×#634D4semidirect
57. C2×C3×D12D4semidirect
62. C4⋊(C3⋊Dic3)D4semidirect
69. C3×C4⋊Dic3D4semidirect
198. C2×D12D12semidirect
229. C4⋊Dic3D12semidirect
482. C32#1600semidirect
571. C3#68285semidirect
572. C3#69697semidirect

Maximal subgroups

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

subgroupindex
#105949772
C3×#46712
#105911722
#105911602
#105893182
C3×#44512
#105891452
#696973
#682853