Finite Group Databasebeta

← #11778228

Subgroups — #11778228

Order 1152.

661 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 661 conjugacy classes of subgroups — too many to draw. Only its 82 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#10595072C211yesmaximal, characteristic
2C3×#4673C211yesmaximal, characteristic, complemented
3#10591174C211yesmaximal, characteristic, complemented
4#10591171C211yesmaximal, characteristic, complemented
5#10589317C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#69699—31nomaximal
9#68286—31nomaximal
10C22×C3×Dic6C2211yescharacteristic, complemented
11C2×D3×#67—21no—
12#64139C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4C2211yescharacteristic
16#63978—21no—
17#63923—21no—
18#63922—21no—
19#63891—21no—
20#63890—21no—
21C2×#3717—21no—
22C2×#3715—21no—
23C32×#95C2211yescharacteristic, complemented
24#63657C2211yescharacteristic, complemented
25C3×C3⋊#95—21no—
26C3×#830C2211yescharacteristic, complemented
27#63566—21no—
28#63565—21no—
29#5605—31no—
30#5493—31no—
31C3×#393—31no—
32#5227—31no—
33#5227—31no—
34#5040—31no—
35#4738—31no—
36#4673D311yescharacteristic, complemented
37C3×#327—31no—
38#4525—31no—
39#4468—31no—
40#4451—31no—
41#4451—31no—
42#4451—61no—
43#4451D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×D32—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×#638—21no—
49C2×C4⋊(C3⋊D3)D411yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C2×C3×D12D411yescharacteristic
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—42no—
57D3×#67—42no—
58D3×#67—42no—
59C2×#626—21no—
60C2×#626—21no—
61C2×#625—21no—
62C2×D3×Dic3—21no—
63#3752—21no—
64C4⋊(C3⋊Dic3)D411yescharacteristic
65C2×C3⋊(C3⋊C8)—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—42no—
70C3×C4⋊Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72Dic3⋊Dic3—21no—
73#3722—21no—
74(C2×D3)⋊Dic3—21no—
75#3717—42no—
76#3715—42no—
77#1601—91noSylow
78C22×C3×Q8—31no—
79C22×#67—61no—
80C2×D3×D4—61no—
81C22×Dic6C2×D311yescharacteristic, complemented
82C3×#121—31no—
83C2×C3×C22⋊C4—31no—
84C2×C3×C22⋊C4—61no—
85C2×#215—61no—
86C2×#215—61no—
87#939—61no—
88#937—61no—
89C2×#214—61no—
90#930—31no—
91#930—31no—
92#930—61no—
93#930—61no—
94#930C2×D311yescharacteristic
95C2×(C2×D3)⋊C4—21no—
96C2×(C2×D3)⋊C4C2×D311yescharacteristic
97C2×#204—61no—
98#894—61no—
99#886—61no—
100#886—61no—
101#883—61no—
102#882—61no—
103#882—61no—
104#882—61no—
105C3×C22⋊C8—31no—
106C3×#95—21no—
107C3×#95—61no—
108C3×#95C2×D311yescharacteristic, complemented
109C3×#95C2×D311yescharacteristic, complemented
110#835—61no—
111#835—61no—
112C3⋊#95—21no—
113#830—31no—
114#830—31no—
115#830—61no—
116#830C2×D311yescharacteristic, complemented
117#816—61no—
118#810—61no—
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3SD1612yescomplemented
127C2×D32—42no—
128C2×D32—81no—
129C2×D32—81no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136#638—41no—
137#638—41no—
138C2×C3⋊Dic3—21no—
139C4⋊(C3⋊D3)—41no—
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C3×D12—41no—
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—41no—
152C3×Dic6—41no—
153#626—42no—
154#626—81no—
155#625—42no—
156D3×Dic3—42no—
157C3⋊(C3⋊C8)—41no—
158C3×C3⋊C8—41no—
159#534—91no—
160#448—91no—
161#448—91no—
162#393—31no—
163#327—31no—
164#327—91no—
165#323—91no—
166C24×C3—31no—
167C23×D3—61no—
168C23×D3—61no—
169C23×D3#6711yescharacteristic
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—122no—
173C2×C3×D4—31no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—41no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—21no—
184C2×#67—61no—
185C2×#67—61no—
186C2×#67—61no—
187C2×#67—61no—
188C2×#67—61no—
189C2×#67—61no—
190C2×#67—121no—
191C2×#67—122no—
192C2×#67—122no—
193C22×Dic3—21no—
194C22×Dic3—61no—
195C22×Dic3#6711yescharacteristic
196D3×D4—122no—
197D3×D4—122no—
198C2×D12—31no—
199C2×D12—31no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12D1211yescharacteristic
204C2×C4×D3—61no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—42no—
208C2×C3×C8—61no—
209C3×C4⋊C4—31no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—122no—
214#217—61no—
215#215—122no—
216#215—122no—
217#214—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—
225(C2×D3)⋊C4—61no—
226(C2×D3)⋊C4—61no—
227(C2×D3)⋊C4—121no—
228C4⋊Dic3—31no—
229C4⋊Dic3—31no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3D1211yescharacteristic
233Dic3⋊C4—61no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—121no—
238#204—122no—
239C22×C32—21no—
240C22×C32—21no—
241C22×C32#12011yescharacteristic
242C22×C32C2×SD1611yescharacteristic
243C22×C32AGL(1,ℤ/8)11yescharacteristic
244C2×C3⋊D3—41no—
245C2×C3⋊D3—41no—
246C2×C3⋊D3—41no—
247C2×C3×D3—22no—
248C2×C3×D3—41no—
249C2×C3×D3—41no—
250C2×C3×D3—42no—
251C2×C3×D3—41no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C2×C3×D3—81no—
255D32—84no—
256C32×C4—21no—
257C32×C4—21no—
258C32×C4—81no—
259C3⋊Dic3—41no—
260C3×Dic3—41no—
261C3×Dic3—41no—
262C3×Dic3—42no—
263C22×Q8—31no—
264C22×D4—181no—
265C2×SD16—181no—
266C2×SD16—181no—
267#123—181no—
268#123—181no—
269#121—31no—
270#121—91no—
271#121—181no—
272#120—181no—
273#120—181no—
274C2×C22⋊C4—31no—
275C2×C22⋊C4—61no—
276#103—181no—
277#103—181no—
278C22⋊C8—31no—
279C22⋊C8—91no—
280#95—61no—
281#95D3211yescharacteristic, complemented
282C23×C3—21no—
283C23×C3—32no—
284C23×C3—61no—
285C23×C3—61no—
286C23×C3—61no—
287C23×C3—121no—
288C23×C3—121no—
289C23×C3D3×D411yescharacteristic
290C23×C3C2×#6711yescharacteristic
291C22×D3—21no—
292C22×D3—21no—
293C22×D3—21no—
294C22×D3—41no—
295C22×D3—41no—
296C22×D3—61no—
297C22×D3—61no—
298C22×D3—121no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—241no—
302C22×D3—241no—
303C22×D3—241no—
304C22×D3—241no—
305C22×D3#21512yescomplemented
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—121no—
309C3×Q8—121no—
310C3×D4—121no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—42no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—62no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—81no—
328C2×C3×C4—81no—
329C2×C3×C4—81no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337#67—41no—
338#67—41no—
339#67—122no—
340#67—122no—
341#67—122no—
342#67—121no—
343#67—121no—
344#67—121no—
345#67—121no—
346#67—241no—
347#67—241no—
348#67—241no—
349C2×Dic3—22no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—121no—
358C2×Dic3—122no—
359D12—41no—
360D12—121no—
361D12—121no—
362D12—122no—
363D12—241no—
364D12—241no—
365C4×D3—122no—
366Dic6—22no—
367Dic6—22no—
368Dic6—41no—
369Dic6—41no—
370C3×C8—121no—
371C3⋊C8—41no—
372C3⋊C8—121no—
373C3⋊C8—121no—
374C3⋊C8—241no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32#45011yescharacteristic
378C2×C32#45511yescharacteristic
379C2×C32B(4,𝔽2)11yescharacteristic
380C3⋊D3—81no—
381C3×D3—42no—
382C3×D3—81no—
383C24—31no—
384C24—181no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—122no—
388C2×D4—31no—
389C2×D4—61no—
390C2×D4—91no—
391C2×D4—181no—
392C2×D4—181no—
393C2×D4—181no—
394C2×D4—181no—
395C2×D4—362no—
396C2×D4—362no—
397C22×C4—21no—
398C22×C4—31no—
399C22×C4—61no—
400C22×C4—181no—
401C22×C4C2×D3211yescharacteristic
402SD16—362no—
403SD16—362no—
404C2×C8—61no—
405C2×C8—181no—
406C4⋊C4—31no—
407C4⋊C4—91no—
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×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—62no—
426C22×C3—122no—
427C22×C3—121no—
428C22×C3—121no—
429C22×C3—121no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3—241no—
433C22×C3#88211yescharacteristic
434C22×C3#91111yescharacteristic
435C22×C3D3×SD1611yescharacteristic
436C22×C3#93711yescharacteristic
437C22×C3C2×#21511yescharacteristic
438C22×C3#94911yescharacteristic
439C2×D3—22no—
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—42no—
443C2×D3—41no—
444C2×D3—41no—
445C2×D3—41no—
446C2×D3—81no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—241no—
454C2×D3—241no—
455C2×D3—241no—
456C2×D3—244no—
457C2×D3—244no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—81no—
465C3×C4—81no—
466C3×C4—82no—
467C3×C4—122no—
468C3×C4—121no—
469C3×C4—121no—
470Dic3—41no—
471Dic3—42no—
472Dic3—41no—
473Dic3—121no—
474Dic3—121no—
475Dic3—241no—
476C32#160111yescharacteristic, complemented, Sylow
477C23—32no—
478C23—61no—
479C23—61no—
480C23—61no—
481C23—121no—
482C23—121no—
483C23—181no—
484C23—362no—
485C23—721no—
486C23—721no—
487C23D3×#6711yescharacteristic
488Q8—62no—
489Q8—62no—
490Q8—121no—
491Q8—121no—
492D4—121no—
493D4—121no—
494D4—121no—
495D4—361no—
496D4—362no—
497D4—362no—
498D4—361no—
499D4—361no—
500D4—721no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—62no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—121no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—181no—
512C2×C4—362no—
513C2×C4D3×D1211yescharacteristic
514C2×C4#380211yescharacteristic
515C8—121no—
516C8—361no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—41no—
525C2×C3—41no—
526C2×C3—122no—
527C2×C3—241no—
528C2×C3#474111yescharacteristic
529C2×C3#477611yescharacteristic
530C2×C3#482511yescharacteristic
531C2×C3#503211yescharacteristic
532C2×C3#504611yescharacteristic
533C2×C3#506111yescharacteristic
534D3—42no—
535D3—81no—
536D3—241no—
537D3—241no—
538D3—481no—
539C22—21no—
540C22—21no—
541C22—62no—
542C22—122no—
543C22—121no—
544C22—121no—
545C22—121no—
546C22—121no—
547C22—121no—
548C22—241no—
549C22—361no—
550C22—361no—
551C22—361no—
552C22—724no—
553C22#6392211yescharacteristic
554C22#6392511yescharacteristic
555C22D3×#21511yescharacteristic
556C4—21no—
557C4—21no—
558C4—81no—
559C4—121no—
560C4—121no—
561C4—122no—
562C4—361no—
563C3—21no—
564C3#6828611yescharacteristic, complemented
565C3#6969911yescharacteristic, complemented
566C2—21no—
567C2—21no—
568C2—122no—
569C2—241no—
570C2—721no—
571C2#1059039611yescharacteristic
572C2#1059040711yescharacteristic
573C2#1059059611yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#10595072C2
hypercenter#95D32
hypocenterC32#1601
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
2. C3×#4673C2semidirect
3. #10591174C2semidirect
4. #10591171C2semidirect
5. #10589317C2semidirect
6. C3×#4451C2semidirect
7. #10589145C2semidirect
10. C22×C3×Dic6C22semidirect
23. C32×#95C22semidirect
24. #63657C22semidirect
26. C3×#830C22semidirect
36. #4673D3semidirect
43. #4451D3semidirect
81. C22×Dic6C2×D3semidirect
108. C3×#95C2×D3semidirect
109. C3×#95C2×D3semidirect
116. #830C2×D3semidirect
126. C22×C3×D3SD16semidirect
281. #95D32semidirect
305. C22×D3#215semidirect
476. C32#1601semidirect
564. C3#68286semidirect
565. C3#69699semidirect

Maximal subgroups

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

subgroupindex
#105950722
C3×#46732
#105911742
#105911712
#105893172
C3×#44512
#105891452
#696993
#682863