Finite Group Databasebeta

← #11778115

Subgroups — #11778115

Order 1152.

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

normal subgroups only

This group has 665 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#10594911C211yesmaximal, characteristic, complemented
2C3×#4672C211yesmaximal, characteristic, complemented
3#10591162C211yesmaximal, characteristic, complemented
4#10591160C211yesmaximal, characteristic, complemented
5#10589317C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#69703—31nomaximal
9#68293—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×#3804—21no—
12#64139C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×Dic3⋊C4C2211yescharacteristic
17#63978—21no—
18#63910—21no—
19#63895—21no—
20#63893—21no—
21#63886—21no—
22C2×#3714—21no—
23C2×#3713—21no—
24C32×#95C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63563—21no—
28#63562—21no—
29#5597—31no—
30#5510—31no—
31C3×#394—31no—
32#5217—31no—
33#5217—31no—
34#5036—31no—
35#4732—31no—
36#4672D311yescharacteristic, complemented
37C3×#327—31no—
38#4528—31no—
39#4469—31no—
40#4451—31no—
41#4451—31no—
42#4451—61no—
43#4451D311yescharacteristic, complemented
44C23×C3×D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C2×C3×#67—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—42no—
55C2×C3×D12D411yescharacteristic
56C2×#627—21no—
57C2×#626—21no—
58C2×#626—21no—
59C2×#624—21no—
60#3804—42no—
61#3804—42no—
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—42no—
68C3×(C2×D3)⋊C4—42no—
69C3×C4⋊Dic3D411yescharacteristic
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—21no—
74#3722—21no—
75(C2×D3)⋊Dic3—21no—
76#3714—42no—
77#3713—42no—
78#1598—91noSylow
79C22×C3×D4—31no—
80C2×#237—61no—
81C2×#235—61no—
82C22×D12C2×D311yescharacteristic
83C3×#121—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C22⋊C4—61no—
86C2×C3×C22⋊C4—61no—
87#939—61no—
88#939—61no—
89C2×#213—61no—
90C2×#213—61no—
91C2×#213—61no—
92#930—31no—
93#930—31no—
94#930—61no—
95#930—61no—
96#930C2×D311yescharacteristic
97C2×(C2×D3)⋊C4—21no—
98C2×(C2×D3)⋊C4—21no—
99C2×Dic3⋊C4C2×D311yescharacteristic
100C2×D24—61no—
101#897—61no—
102#897—61no—
103#896—61no—
104#895—61no—
105#895—61no—
106#884—61no—
107#878—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—21no—
122C22×C3×D3—22no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
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—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3D812yescomplemented
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C3×D12—41no—
153#627—42no—
154#626—42no—
155#626—81no—
156#624—42no—
157D3×Dic3—42no—
158C3⋊(C3⋊C8)—41no—
159C3×C3⋊C8—41no—
160#537—91no—
161#447—91no—
162#447—91no—
163#394—31no—
164#327—31no—
165#327—91no—
166#324—91no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×D4—31no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—122no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—41no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×#67—21no—
183C2×#67—61no—
184C2×#67—61no—
185C2×#67—61no—
186C2×#67—61no—
187C2×#67—121no—
188C22×Dic3—61no—
189C22×Dic3#6711yescharacteristic
190C22×Dic3#6711yescharacteristic
191#237—122no—
192#237—122no—
193#235—122no—
194#235—122no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—31no—
198C2×D12—31no—
199C2×D12—42no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12D1211yescharacteristic
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×C3×C8—61no—
210C3×C4⋊C4—31no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C22⋊C4—122no—
215C3×C22⋊C4—122no—
216#217—61no—
217#213—122no—
218#213—122no—
219#213—122no—
220(C2×D3)⋊C4—21no—
221(C2×D3)⋊C4—42no—
222(C2×D3)⋊C4—42no—
223(C2×D3)⋊C4—61no—
224(C2×D3)⋊C4—61no—
225(C2×D3)⋊C4—61no—
226(C2×D3)⋊C4—61no—
227(C2×D3)⋊C4—61no—
228(C2×D3)⋊C4—121no—
229C4⋊Dic3—31no—
230C4⋊Dic3—31no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3D1211yescharacteristic
234Dic3⋊C4—21no—
235Dic3⋊C4—21no—
236Dic3⋊C4—61no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—121no—
241D24—122no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32#12011yescharacteristic
245C22×C32C2×D811yescharacteristic
246C22×C32AGL(1,ℤ/8)11yescharacteristic
247C2×C3⋊D3—41no—
248C2×C3⋊D3—41no—
249C2×C3⋊D3—41no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
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—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—81no—
263C3⋊Dic3—41no—
264C3×Dic3—22no—
265C3×Dic3—41no—
266C3×Dic3—41no—
267C2×#41—181no—
268C22×D4—31no—
269C2×D8—181no—
270C2×D8—181no—
271C22⋊Q8—181no—
272C22⋊Q8—181no—
273#121—31no—
274#121—91no—
275#121—181no—
276#121—181no—
277#121—181no—
278C2×C4⋊C4—31no—
279C2×C22⋊C4—61no—
280C2×C22⋊C4—61no—
281#102—181no—
282#102—181no—
283C22⋊C8—31no—
284C22⋊C8—91no—
285#95D3211yescharacteristic
286C23×C3—21no—
287C23×C3—62no—
288C23×C3—61no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3D3×D411yescharacteristic
296C23×C3C2×#6711yescharacteristic
297C22×D3—22no—
298C22×D3—21no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—41no—
305C22×D3—61no—
306C22×D3—61no—
307C22×D3—121no—
308C3×D4—62no—
309C3×D4—62no—
310C3×D4—121no—
311C3×D4—121no—
312C3×D4—121no—
313C3×D4—121no—
314C3×D4—121no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—32no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—42no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—81no—
332C2×C3×C4—81no—
333C2×C3×C4—81no—
334C2×C3×C4—121no—
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339#67—41no—
340#67—41no—
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—21no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—41no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—121no—
357C2×Dic3—122no—
358C2×Dic3#21312yescomplemented
359D12—22no—
360D12—22no—
361D12—41no—
362D12—41no—
363D12—41no—
364D12—121no—
365D12—121no—
366D12—122no—
367D12—241no—
368D12—241no—
369C4×D3—122no—
370C4×D3—122no—
371C4×D3—122no—
372Dic6—122no—
373Dic6—122no—
374C3×C8—121no—
375C3⋊C8—41no—
376C3⋊C8—121no—
377C3⋊C8—121no—
378C3⋊C8—241no—
379C2×C32—21no—
380C2×C32—21no—
381C2×C32#44711yescharacteristic
382C2×C32#45411yescharacteristic
383C2×C32B(4,𝔽2)11yescharacteristic
384C3⋊D3—81no—
385C3×D3—81no—
386C3×D3—82no—
387C24—61no—
388#41—362no—
389#41—362no—
390C2×Q8—181no—
391C2×D4—31no—
392C2×D4—61no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—91no—
396C2×D4—122no—
397C2×D4—181no—
398C2×D4—181no—
399C2×D4—181no—
400C22×C4—21no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4C2×D3211yescharacteristic
406D8—362no—
407D8—362no—
408C2×C8—61no—
409C2×C8—181no—
410C4⋊C4—31no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—91no—
414C4⋊C4—181no—
415C22⋊C4—61no—
416C22⋊C4—122no—
417C22⋊C4—122no—
418C22⋊C4—181no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—122no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3—241no—
437C22×C3—241no—
438C22×C3—241no—
439C22×C3—241no—
440C22×C3#88211yescharacteristic
441C22×C3D3×D811yescharacteristic
442C22×C3#91411yescharacteristic
443C22×C3C2×#21311yescharacteristic
444C22×C3#93711yescharacteristic
445C22×C3#94911yescharacteristic
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—41no—
449C2×D3—41no—
450C2×D3—42no—
451C2×D3—41no—
452C2×D3—81no—
453C2×D3—81no—
454C2×D3—81no—
455C2×D3—81no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—121no—
462C2×D3—241no—
463C2×D3—241no—
464C2×D3—241no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—41no—
470C3×C4—41no—
471C3×C4—62no—
472C3×C4—81no—
473C3×C4—81no—
474C3×C4—82no—
475C3×C4—121no—
476C3×C4—121no—
477Dic3—22no—
478Dic3—41no—
479Dic3—41no—
480Dic3—121no—
481Dic3—121no—
482Dic3—241no—
483C32#159811yescharacteristic, complemented, Sylow
484C23—62no—
485C23—61no—
486C23—121no—
487C23—121no—
488C23—121no—
489C23—121no—
490C23—121no—
491C23—121no—
492C23—181no—
493C23D3×#6711yescharacteristic
494Q8—362no—
495D4—62no—
496D4—62no—
497D4—121no—
498D4—121no—
499D4—121no—
500D4—121no—
501D4—121no—
502D4—361no—
503D4—362no—
504D4—361no—
505D4—361no—
506D4—721no—
507C2×C4—32no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—121no—
517C2×C4—181no—
518C2×C4—362no—
519C2×C4—362no—
520C2×C4D3×D1211yescharacteristic
521C2×C4#380211yescharacteristic
522C8—121no—
523C8—361no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—41no—
532C2×C3—41no—
533C2×C3—241no—
534C2×C3—242no—
535C2×C3#474111yescharacteristic
536C2×C3#477311yescharacteristic
537C2×C3#482711yescharacteristic
538C2×C3#503211yescharacteristic
539C2×C3#503611yescharacteristic
540C2×C3#506211yescharacteristic
541D3—82no—
542D3—81no—
543D3—241no—
544D3—241no—
545D3—481no—
546C22—21no—
547C22—21no—
548C22—122no—
549C22—122no—
550C22—121no—
551C22—121no—
552C22—122no—
553C22—121no—
554C22—241no—
555C22—241no—
556C22—241no—
557C22—241no—
558C22—361no—
559C22—361no—
560C22—361no—
561C22#6392211yescharacteristic
562C22D3×#21311yescharacteristic
563C22#6393911yescharacteristic
564C4—21no—
565C4—21no—
566C4—62no—
567C4—81no—
568C4—121no—
569C4—121no—
570C4—361no—
571C3—21no—
572C3#6829311yescharacteristic, complemented
573C3#6970311yescharacteristic, complemented
574C2—21no—
575C2—21no—
576C2—242no—
577C2—241no—
578C2—721no—
579C2#1059040011yescharacteristic
580C2#1059040711yescharacteristic
581C2#1059059511yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
hypercenter#95D32
hypocenterC32#1598
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. #10594911C2semidirect
2. C3×#4672C2semidirect
3. #10591162C2semidirect
4. #10591160C2semidirect
5. #10589317C2semidirect
6. C3×#4451C2semidirect
7. #10589147C2semidirect
36. #4672D3semidirect
43. #4451D3semidirect
147. C2×C3×Dic3D8semidirect
358. C2×Dic3#213semidirect
483. C32#1598semidirect
572. C3#68293semidirect
573. C3#69703semidirect

Maximal subgroups

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

subgroupindex
#105949112
C3×#46722
#105911622
#105911602
#105893172
C3×#44512
#105891472
#697033
#682933