Finite Group Databasebeta

← #11778064

Subgroups — #11778064

Order 1152.

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

normal subgroups only

This group has 638 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#10594973C211yesmaximal, characteristic, complemented
2#10592917C211yesmaximal, characteristic, complemented
3C3×#5222C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic
5#10589154C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#70970—31nomaximal
9#69702—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3754—21no—
12#64133C2211yescharacteristic
13C2×C3×#217—21no—
14C2×C3×#217—21no—
15C2×C3×#213—21no—
16C3×#930C2211yescharacteristic
17C2×C3×Dic3⋊C4C2211yescharacteristic
18Dic3×#67—21no—
19#63961—21no—
20#63896—21no—
21#63884—21no—
22#63861—21no—
23#63847—21no—
24#63659—21no—
25#63657C2211yescharacteristic
26C3×#832—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5602—31no—
30#5515—31no—
31C3×#447—31no—
32C3×#394—31no—
33#5222D311yescharacteristic, complemented
34#5218—31no—
35#5218—31no—
36#5218—61no—
37#5217D311yescharacteristic
38#4537—31no—
39#4528—31no—
40#4469—31no—
41#4467—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×#634D411yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×C3×D12D411yescharacteristic
55C2×D3×Dic3—21no—
56#3757—21no—
57#3754—42no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—42no—
62C3×#217—42no—
63C3×#213—42no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C2×C3×C3⋊C8—21no—
69#3724—21no—
70#3724—21no—
71Dic3⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74(C2×D3)⋊Dic3—21no—
75Dic32—21no—
76#1597—91noSylow
77C22×C3×D4—21no—
78C22×C3×D4C2×D311yescharacteristic
79C22×C3×D4C2×D311yescharacteristic
80C2×C3×D8—61no—
81C3×#121—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C22⋊C4—61no—
84C2×C3×C22⋊C4—61no—
85C2×#217—21no—
86C2×#217—21no—
87#935—61no—
88#935—61no—
89D4×Dic3—61no—
90C2×#214—61no—
91C2×#214—61no—
92C2×#214—62no—
93C2×#213—21no—
94#930C2×D311yescharacteristic
95#929—61no—
96C4×#67—61no—
97#924—31no—
98#924—31no—
99#924—61no—
100C2×Dic3⋊C4C2×D311yescharacteristic
101#898—61no—
102#896—61no—
103#894—61no—
104#889—61no—
105#889—61no—
106#879—61no—
107#878—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
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138#634—41no—
139C3×#67—41no—
140C3×#67—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—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×D12—41no—
151D3×Dic3—81no—
152C3⋊(C3⋊C8)—41no—
153C3×C3⋊C8—41no—
154#539—91no—
155#450—91no—
156#447—31no—
157#394—31no—
158#328—91no—
159#327—91no—
160#324—91no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—41no—
164C2×C3×D4—22no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—31no—
170C2×C3×D4—41no—
171C2×C3×D4—42no—
172C2×C3×D4—42no—
173C2×C3×D4—44no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—21no—
182C22×Dic3—21no—
183C22×Dic3—61no—
184C22×Dic3#6711yescharacteristic
185C22×Dic3#6711yescharacteristic
186C2×D12#6711yescharacteristic
187C2×C4×D3—61no—
188C2×Dic6—31no—
189C2×Dic6—31no—
190C2×Dic6—61no—
191C3×D8—122no—
192C2×C3×C8—61no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—122no—
198C3×C22⋊C4—122no—
199#217—42no—
200#217—42no—
201#217—61no—
202#217—61no—
203#217—61no—
204#217—61no—
205#217—61no—
206#217—121no—
207#214—122no—
208#214—122no—
209#214—124no—
210#213—42no—
211(C2×D3)⋊C4—21no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215C4⋊Dic3—31no—
216C4⋊Dic3—31no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3#6711yescharacteristic
220Dic3⋊C4—21no—
221Dic3⋊C4—21no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229Dic3⋊C4—121no—
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—181no—
261C2×D8—61no—
262#126—181no—
263#125—181no—
264#123—181no—
265#123—181no—
266C22⋊Q8—91no—
267C22⋊Q8—181no—
268#121—31no—
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—61no—
297C23×C3—81no—
298C23×C3—81no—
299C23×C3—81no—
300C23×C3—81no—
301C23×C3D3×D411yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C22×D3—21no—
304C3×D4—22no—
305C3×D4—24no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—42no—
310C3×D4—42no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—41no—
315C3×D4—42no—
316C3×D4—121no—
317C3×D4—121no—
318C3×D4—121no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—42no—
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—41no—
338#67—41no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—241no—
355D12—41no—
356C4×D3—241no—
357Dic6—121no—
358Dic6—121no—
359Dic6—122no—
360C3×C8—121no—
361C3⋊C8—41no—
362C3⋊C8—122no—
363C3⋊C8—121no—
364C3⋊C8—121no—
365C2×C32—21no—
366C2×C32—21no—
367C2×C32—82no—
368C2×C32#44911yescharacteristic
369C2×C32#45411yescharacteristic
370C2×C32B(4,𝔽2)11yescharacteristic
371C3×D3—81no—
372C24—21no—
373C2×Q8—91no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—31no—
377C2×D4—42no—
378C2×D4—61no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—61no—
382C22×C4—181no—
383C22×C4C2×D3211yescharacteristic
384SD16—362no—
385D8—122no—
386C2×C8—61no—
387C2×C8—181no—
388C4⋊C4—31no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—91no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C22⋊C4—61no—
397C22⋊C4—122no—
398C22⋊C4—122no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C42—181no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—44no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—82no—
421C22×C3—82no—
422C22×C3—81no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—82no—
427C22×C3—82no—
428C22×C3—82no—
429C22×C3—82no—
430C22×C3—81no—
431C22×C3—81no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3#91111yescharacteristic
438C22×C3#91211yescharacteristic
439C22×C3#93211yescharacteristic
440C22×C3#93711yescharacteristic
441C22×C3#93711yescharacteristic
442C22×C3#95011yescharacteristic
443C2×D3—41no—
444C2×D3—41no—
445C2×D3—41no—
446C3×C4—22no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—41no—
452C3×C4—121no—
453C3×C4—121no—
454C3×C4—121no—
455C3×C4—241no—
456Dic3—41no—
457Dic3—41no—
458Dic3—41no—
459Dic3—81no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463Dic3—121no—
464Dic3—241no—
465Dic3—241no—
466C32#159711yescharacteristic, complemented, Sylow
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—61no—
475C23D3×#6711yescharacteristic
476Q8—361no—
477D4—22no—
478D4—22no—
479D4—41no—
480D4—41no—
481D4—121no—
482D4—121no—
483D4—121no—
484C2×C4—41no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—121no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—721no—
497C2×C4D3×#6711yescharacteristic
498C2×C4#381111yescharacteristic
499C8—121no—
500C8—361no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—41no—
509C2×C3—41no—
510C2×C3—84no—
511C2×C3—82no—
512C2×C3—82no—
513C2×C3—241no—
514C2×C3#503211yescharacteristic
515C2×C3#503211yescharacteristic
516C2×C3#503711yescharacteristic
517C2×C3#506211yescharacteristic
518C2×C3#515811yescharacteristic
519C2×C3#520111yescharacteristic
520D3—81no—
521C22—21no—
522C22—21no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—121no—
531C22—121no—
532C22—121no—
533C22#6393211yescharacteristic
534C22#6393311yescharacteristic
535C22#6398311yescharacteristic
536C4—21no—
537C4—21no—
538C4—121no—
539C4—121no—
540C4—121no—
541C4—241no—
542C4—361no—
543C4—361no—
544C3—21no—
545C3#6970211yescharacteristic, complemented
546C3#7097011yescharacteristic, complemented
547C2—21no—
548C2—21no—
549C2—82no—
550C2—241no—
551C2#1059151911yescharacteristic
552C2#1059152511yescharacteristic
553C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC3×#5217C2
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. #10594973C2semidirect
2. #10592917C2semidirect
3. C3×#5222C2semidirect
5. #10589154C2semidirect
6. #10589149C2semidirect
7. #10589147C2semidirect
33. #5222D3semidirect
466. C32#1597semidirect
545. C3#69702semidirect
546. C3#70970semidirect

Maximal subgroups

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

subgroupindex
#105949732
#105929172
C3×#52222
C3×#52172
#105891542
#105891492
#105891472
#709703
#697023