Finite Group Databasebeta

← #11778062

Subgroups — #11778062

Order 1152.

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

normal subgroups only

This group has 643 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#10594980C211yesmaximal, characteristic, complemented
2#10592916C211yesmaximal, characteristic
3C3×#5222C211yesmaximal, characteristic, complemented
4C3×#5218C211yesmaximal, characteristic, complemented
5#10589153C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#70978—31nomaximal
9#69702—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3753—21no—
12#64139C2211yescharacteristic
13C2×C3×#217—21no—
14C2×C3×#217—21no—
15C2×C3×#214—21no—
16C3×#924C2211yescharacteristic
17C2×C3×Dic3⋊C4C2211yescharacteristic
18#63966—21no—
19#63952—21no—
20#63897—21no—
21#63888—21no—
22#63848—21no—
23#63845—21no—
24#63659—21no—
25#63657C2211yescharacteristic
26C3×#832—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5645—31no—
30#5515—31no—
31C3×#450—31no—
32C3×#394—31no—
33#5222D311yescharacteristic, complemented
34#5218D311yescharacteristic, complemented
35#5217—31no—
36#5217—31no—
37#5217—61no—
38#4538—31no—
39#4528—31no—
40#4470—31no—
41#4469—31no—
42#4452—31no—
43#4451—31no—
44C24×C32—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—42no—
48C22×C32×C4C2311yescharacteristic
49C2×#638—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×#624—21no—
56#3753—42no—
57#3752—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#217—42no—
62C3×#217—42no—
63C3×#214—42no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C2×C3×C3⋊C8—21no—
69#3724—21no—
70Dic3⋊Dic3—21no—
71Dic3⋊Dic3—21no—
72#3722—21no—
73#3722—21no—
74#3722—21no—
75Dic32—21no—
76#1597—91noSylow
77C22×C3×D4—21no—
78C22×C3×D4C2×D311yescharacteristic
79C22×C3×D4C2×D311yescharacteristic
80C2×C3×SD16—61no—
81C3×C22⋊Q8—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C22⋊C4—61no—
84C2×C3×C22⋊C4—61no—
85C2×#217—21no—
86C2×#217—21no—
87#946—61no—
88C2×#214—21no—
89C2×#213—61no—
90C2×#213—61no—
91C2×#213—62no—
92#930—31no—
93#930—31no—
94#930—61no—
95#929—61no—
96C4×#67—61no—
97#924C2×D311yescharacteristic
98C2×Dic3⋊C4C2×D311yescharacteristic
99#898—61no—
100#898—61no—
101#896—61no—
102#894—61no—
103#894—61no—
104#890—61no—
105#889—61no—
106#886—61no—
107#67⋊C4—61no—
108C3×#102—61no—
109C3×C22⋊C8—31no—
110C3×#95—31no—
111#832—21no—
112#832—61no—
113#832—61no—
114#832—62no—
115C3⋊#95C2×D311yescharacteristic
116#830—31no—
117#830—31no—
118#830—61no—
119#830C2×D311yescharacteristic
120C23×C32—22no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—21no—
129C32×D4—22no—
130C32×D4—22no—
131C32×D4—41no—
132C32×D4—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—
140C2×C3×Dic3—21no—
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—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×Dic6—41no—
151#624—81no—
152C3⋊(C3⋊C8)—41no—
153C3×C3⋊C8—41no—
154#539—91no—
155#450—31no—
156#447—91no—
157#394—31no—
158#328—91no—
159#327—91no—
160#324—91no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—41no—
164C2×C3×Q8—31no—
165C2×C3×D4—22no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—41no—
171C2×C3×D4—42no—
172C2×C3×D4—42no—
173C2×C3×D4—44no—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—61no—
181C2×#67—61no—
182C2×#67—121no—
183C22×Dic3—21no—
184C22×Dic3#6711yescharacteristic
185C22×Dic3#6711yescharacteristic
186C2×D12—31no—
187C2×D12—31no—
188C2×D12—61no—
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×Dic6#6711yescharacteristic
192C3×SD16—122no—
193C2×C3×C8—61no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—122no—
200C3×C22⋊C4—122no—
201#217—21no—
202#217—42no—
203#217—42no—
204#214—42no—
205#213—122no—
206#213—122no—
207#213—124no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—121no—
217C4⋊Dic3—31no—
218C4⋊Dic3—31no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3#6711yescharacteristic
223Dic3⋊C4—21no—
224Dic3⋊C4—21no—
225Dic3⋊C4—21no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229Dic3⋊C4—61no—
230C4×Dic3—61no—
231C4×Dic3—61no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—62no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32—42no—
239C22×C32—42no—
240C22×C32—42no—
241C22×C32—81no—
242C22×C32—81no—
243C22×C32—81no—
244C22×C32—81no—
245C22×C32#12011yescharacteristic
246C22×C32#13511yescharacteristic
247C22×C32AGL(1,ℤ/8)11yescharacteristic
248C2×C3⋊D3—41no—
249C2×C3⋊D3—41no—
250C2×C3⋊D3—41no—
251C32×C4—21no—
252C32×C4—21no—
253C3⋊Dic3—41no—
254C3×Dic3—41no—
255C3×Dic3—41no—
256C3×Dic3—41no—
257C3×Dic3—41no—
258C3×Dic3—81no—
259C22×D4D3211yescharacteristic
260C2×SD16—61no—
261C2×D8—181no—
262#126—181no—
263#125—181no—
264#123—181no—
265#123—181no—
266C22⋊Q8—31no—
267C22⋊Q8—181no—
268#121—91no—
269C4×D4—181no—
270C2×C4⋊C4—31no—
271C2×C22⋊C4—61no—
272C2×C22⋊C4—61no—
273#102—61no—
274#102—181no—
275C22⋊C8—31no—
276C22⋊C8—91no—
277#95—31no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—21no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—41no—
288C23×C3—41no—
289C23×C3—42no—
290C23×C3—41no—
291C23×C3—41no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3—81no—
297C23×C3—81no—
298C23×C3—81no—
299C23×C3—81no—
300C23×C3D3×D411yescharacteristic
301C23×C3C2×#6711yescharacteristic
302C22×D3—61no—
303C22×D3—61no—
304C22×D3—121no—
305C3×Q8—121no—
306C3×D4—24no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—42no—
312C3×D4—42no—
313C3×D4—41no—
314C3×D4—41no—
315C3×D4—41no—
316C3×D4—41no—
317C3×D4—42no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—42no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337#67—121no—
338#67—121no—
339#67—121no—
340#67—121no—
341#67—241no—
342#67—241no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—121no—
356D12—121no—
357D12—121no—
358D12—122no—
359C4×D3—241no—
360C4×D3—241no—
361Dic6—41no—
362C3×C8—121no—
363C3⋊C8—41no—
364C3⋊C8—122no—
365C3⋊C8—121no—
366C3⋊C8—121no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32—82no—
370C2×C32#44911yescharacteristic
371C2×C32#45411yescharacteristic
372C2×C32B(4,𝔽2)11yescharacteristic
373C3⋊D3—81no—
374C24—21no—
375C2×Q8—31no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—42no—
379C2×D4—91no—
380C2×D4—181no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—61no—
384C22×C4—181no—
385C22×C4C2×D3211yescharacteristic
386SD16—122no—
387D8—362no—
388C2×C8—61no—
389C2×C8—181no—
390C4⋊C4—31no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C4⋊C4—61no—
394C4⋊C4—91no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C22⋊C4—61no—
399C22⋊C4—122no—
400C22⋊C4—122no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C42—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—44no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—82no—
423C22×C3—82no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3—81no—
428C22×C3—82no—
429C22×C3—82no—
430C22×C3—82no—
431C22×C3—82no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3—81no—
436C22×C3#91411yescharacteristic
437C22×C3#91611yescharacteristic
438C22×C3#93211yescharacteristic
439C22×C3#93711yescharacteristic
440C22×C3#93711yescharacteristic
441C22×C3#95011yescharacteristic
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—241no—
449C2×D3—241no—
450C2×D3—241no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—41no—
457C3×C4—121no—
458C3×C4—121no—
459C3×C4—121no—
460C3×C4—121no—
461C3×C4—241no—
462Dic3—41no—
463Dic3—41no—
464Dic3—41no—
465Dic3—41no—
466Dic3—81no—
467Dic3—121no—
468Dic3—121no—
469Dic3—241no—
470C32#159711yescharacteristic, complemented, Sylow
471C23—22no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—181no—
479C23D3×#6711yescharacteristic
480Q8—121no—
481D4—22no—
482D4—22no—
483D4—41no—
484D4—41no—
485D4—361no—
486D4—361no—
487D4—361no—
488C2×C4—41no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—181no—
500C2×C4—721no—
501C2×C4D3×#6711yescharacteristic
502C2×C4#381111yescharacteristic
503C8—121no—
504C8—361no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—41no—
513C2×C3—41no—
514C2×C3—84no—
515C2×C3—82no—
516C2×C3—82no—
517C2×C3#503211yescharacteristic
518C2×C3#503211yescharacteristic
519C2×C3#503711yescharacteristic
520C2×C3#506211yescharacteristic
521C2×C3#517211yescharacteristic
522C2×C3#520111yescharacteristic
523D3—241no—
524D3—241no—
525D3—481no—
526C22—21no—
527C22—21no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—361no—
536C22—361no—
537C22—361no—
538C22#6393411yescharacteristic
539C22#6393511yescharacteristic
540C22#6398311yescharacteristic
541C4—21no—
542C4—21no—
543C4—121no—
544C4—121no—
545C4—121no—
546C4—121no—
547C4—241no—
548C4—361no—
549C3—21no—
550C3#6970211yescharacteristic, complemented
551C3#7097811yescharacteristic, complemented
552C2—21no—
553C2—21no—
554C2—82no—
555C2—721no—
556C2#1059152111yescharacteristic
557C2#1059152511yescharacteristic
558C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radical#10592916C2
hypercenterC22×D4D32
hypocenterC32#1597
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10594980C2semidirect
3. C3×#5222C2semidirect
4. C3×#5218C2semidirect
5. #10589153C2semidirect
6. #10589151C2semidirect
7. #10589147C2semidirect
33. #5222D3semidirect
34. #5218D3semidirect
470. C32#1597semidirect
550. C3#69702semidirect
551. C3#70978semidirect

Maximal subgroups

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

subgroupindex
#105949802
#105929162
C3×#52222
C3×#52182
#105891532
#105891512
#105891472
#709783
#697023