Finite Group Databasebeta

← #11778401

Subgroups — #11778401

Order 1152.

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

normal subgroups only

This group has 599 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#10595038C211yesmaximal, characteristic
2#10592926C211yesmaximal, characteristic, complemented
3C3×#5231C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5#10589153C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#70981—31nomaximal
9#69700—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3755—21no—
12#64139C2211yescharacteristic
13C2×C3×#216—21no—
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4C2211yescharacteristic
16C3×#924C2211yescharacteristic
17#63977—21no—
18#63952—21no—
19#63910—21no—
20#63907—21no—
21#63861—21no—
22#63854—21no—
23#63662—21no—
24#63657C2211yescharacteristic
25C3×#835—21no—
26C3×C3⋊#95—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5644—31no—
30#5494—31no—
31C3×#451—31no—
32C3×#393—31no—
33#5231D311yescharacteristic, complemented
34#5228D311yescharacteristic, complemented
35#5227—31no—
36#5227—31no—
37#5227—61no—
38#4538—31no—
39#4525—31no—
40#4470—31no—
41#4468—31no—
42#4452—31no—
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—42no—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×#638—21no—
51C2×C4⋊(C3⋊D3)D411yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×#626—21no—
56C2×#626—21no—
57C2×#624—21no—
58#3755—42no—
59#3752—21no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61C2×C3⋊(C3⋊C8)—21no—
62C3×#217—21no—
63C3×#216—42no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—42no—
67C3×C4⋊Dic3D411yescharacteristic
68C3×Dic3⋊C4—21no—
69C2×C3×C3⋊C8—21no—
70#3724—21no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74Dic32—21no—
75#1606—91noSylow
76C22×C3×Q8—21no—
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×Q8C2×D311yescharacteristic
79C2×C3×Q16—61no—
80C3×C22⋊Q8—31no—
81C2×C3×C22⋊C4—31no—
82C2×C3×C22⋊C4—61no—
83#953—61no—
84#947—61no—
85C2×#216—21no—
86C2×#215—61no—
87C2×#215—61no—
88C2×#215—62no—
89#930—31no—
90#930—31no—
91#930—61no—
92C4×#67—61no—
93C2×(C2×D3)⋊C4—21no—
94C2×(C2×D3)⋊C4C2×D311yescharacteristic
95#924C2×D311yescharacteristic
96#898—61no—
97#895—61no—
98#894—61no—
99#885—61no—
100#884—61no—
101#883—61no—
102#882—61no—
103#67⋊C4—61no—
104#879—61no—
105C3×#103—61no—
106C3×C22⋊C8—31no—
107C3×#95—31no—
108C3×#95—61no—
109#835—21no—
110#835—61no—
111#835—61no—
112#835—62no—
113C3⋊#95—21no—
114C3⋊#95C2×D311yescharacteristic
115#830—31no—
116#830—31no—
117#830—61no—
118#830C2×D311yescharacteristic
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—
126C32×Q8—22no—
127C32×Q8—22no—
128C32×Q8—41no—
129C32×Q8—41no—
130C2×C32×C4—22no—
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—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×Dic6—41no—
148#626—81no—
149#626—81no—
150#624—81no—
151C3⋊(C3⋊C8)—41no—
152C3×C3⋊C8—41no—
153#538—91no—
154#451—31no—
155#448—91no—
156#393—31no—
157#328—91no—
158#327—91no—
159#323—91no—
160C24×C3—31no—
161C23×D3#6711yescharacteristic
162C2×C3×Q8—22no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—31no—
168C2×C3×Q8—41no—
169C2×C3×Q8—42no—
170C2×C3×Q8—42no—
171C2×C3×Q8—44no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—41no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—61no—
181C2×#67—61no—
182C2×#67—61no—
183C2×#67—61no—
184C2×#67—121no—
185C22×Dic3—21no—
186C22×Dic3#6711yescharacteristic
187C2×D12—31no—
188C2×D12—31no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×Dic6#6711yescharacteristic
195C3×Q16—122no—
196C2×C3×C8—61no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—122no—
203#217—21no—
204#217—61no—
205#217—61no—
206#216—42no—
207#215—122no—
208#215—122no—
209#215—124no—
210(C2×D3)⋊C4—21no—
211(C2×D3)⋊C4—21no—
212(C2×D3)⋊C4—42no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—121no—
220C4⋊Dic3—31no—
221C4⋊Dic3—31no—
222C4⋊Dic3—61no—
223C4⋊Dic3#6711yescharacteristic
224Dic3⋊C4—21no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32#12011yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32#13711yescharacteristic
238C2×C3⋊D3—41no—
239C2×C3⋊D3—41no—
240C2×C3⋊D3—41no—
241C2×C3×D3—42no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—81no—
246C32×C4—21no—
247C32×C4—21no—
248C32×C4—42no—
249C3⋊Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—81no—
254C22×Q8D3211yescharacteristic
255C2×Q16—61no—
256C2×SD16—181no—
257#126—181no—
258#124—181no—
259#123—181no—
260C22⋊Q8—31no—
261#121—91no—
262#121—181no—
263#120—181no—
264C4×D4—181no—
265C2×C22⋊C4—31no—
266C2×C22⋊C4—61no—
267#103—61no—
268#103—181no—
269C22⋊C8—31no—
270C22⋊C8—91no—
271#95—31no—
272#95—61no—
273C23×C3—21no—
274C23×C3—61no—
275C23×C3—61no—
276C23×C3—61no—
277C23×C3—121no—
278C23×C3—121no—
279C23×C3D3×D411yescharacteristic
280C23×C3C2×#6711yescharacteristic
281C22×D3—21no—
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—41no—
285C22×D3—41no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—121no—
289C3×Q8—24no—
290C3×Q8—22no—
291C3×Q8—22no—
292C3×Q8—22no—
293C3×Q8—22no—
294C3×Q8—42no—
295C3×Q8—42no—
296C3×Q8—41no—
297C3×Q8—41no—
298C3×Q8—41no—
299C3×Q8—41no—
300C3×Q8—42no—
301C3×Q8—121no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—42no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327#67—121no—
328#67—121no—
329#67—121no—
330#67—121no—
331#67—241no—
332#67—241no—
333#67—241no—
334#67—241no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—41no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—121no—
345D12—121no—
346D12—121no—
347D12—122no—
348D12—241no—
349D12—241no—
350C4×D3—241no—
351C4×D3—241no—
352Dic6—41no—
353C3×C8—121no—
354C3⋊C8—41no—
355C3⋊C8—122no—
356C3⋊C8—121no—
357C3⋊C8—121no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32#45211yescharacteristic
361C2×C32#45511yescharacteristic
362C2×C32B(4,𝔽2)11yescharacteristic
363C3⋊D3—81no—
364C3×D3—81no—
365C24—31no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—31no—
369C2×Q8—42no—
370C2×D4—91no—
371C2×D4—181no—
372C2×D4—181no—
373C2×D4—181no—
374C22×C4—21no—
375C22×C4—31no—
376C22×C4—61no—
377C22×C4—181no—
378C22×C4C2×D3211yescharacteristic
379Q16—122no—
380SD16—362no—
381C2×C8—61no—
382C2×C8—181no—
383C4⋊C4—31no—
384C4⋊C4—61no—
385C4⋊C4—91no—
386C4⋊C4—181no—
387C22⋊C4—61no—
388C22⋊C4—61no—
389C22⋊C4—61no—
390C22⋊C4—122no—
391C22⋊C4—181no—
392C22⋊C4—181no—
393C22⋊C4—181no—
394C22⋊C4—181no—
395C42—181no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—122no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—241no—
410C22×C3#91811yescharacteristic
411C22×C3#91911yescharacteristic
412C22×C3#93711yescharacteristic
413C22×C3#93711yescharacteristic
414C22×C3#94211yescharacteristic
415C22×C3#95011yescharacteristic
416C2×D3—42no—
417C2×D3—41no—
418C2×D3—41no—
419C2×D3—41no—
420C2×D3—81no—
421C2×D3—121no—
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—241no—
428C2×D3—241no—
429C2×D3—241no—
430C3×C4—22no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—41no—
436C3×C4—44no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4—121no—
442C3×C4—241no—
443Dic3—41no—
444Dic3—41no—
445Dic3—41no—
446Dic3—81no—
447Dic3—121no—
448Dic3—121no—
449Dic3—241no—
450C32#160611yescharacteristic, complemented, Sylow
451C23—61no—
452C23—61no—
453C23—61no—
454C23—121no—
455C23—121no—
456C23—181no—
457C23D3×#6711yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—41no—
461Q8—41no—
462Q8—121no—
463D4—361no—
464D4—361no—
465D4—361no—
466D4—721no—
467D4—721no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4D3×#6711yescharacteristic
482C2×C4#381111yescharacteristic
483C8—121no—
484C8—361no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—241no—
495C2×C3#503211yescharacteristic
496C2×C3#503211yescharacteristic
497C2×C3#504711yescharacteristic
498C2×C3#506111yescharacteristic
499C2×C3#518711yescharacteristic
500C2×C3#520211yescharacteristic
501D3—81no—
502D3—241no—
503D3—241no—
504D3—481no—
505C22—21no—
506C22—21no—
507C22—122no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22—241no—
512C22—361no—
513C22—361no—
514C22—361no—
515C22#6394811yescharacteristic
516C22#6394911yescharacteristic
517C22#6398311yescharacteristic
518C4—21no—
519C4—21no—
520C4—42no—
521C4—121no—
522C4—121no—
523C4—121no—
524C4—241no—
525C4—361no—
526C3—21no—
527C3#6970011yescharacteristic, complemented
528C3#7098111yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—241no—
532C2—721no—
533C2#1059165711yescharacteristic
534C2#1059165911yescharacteristic
535C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radical#10595038C2
hypercenterC22×Q8D32
hypocenterC32#1606
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #10592926C2semidirect
3. C3×#5231C2semidirect
4. C3×#5228C2semidirect
5. #10589153C2semidirect
6. #10589151C2semidirect
7. #10589145C2semidirect
33. #5231D3semidirect
34. #5228D3semidirect
450. C32#1606semidirect
527. C3#69700semidirect
528. C3#70981semidirect

Maximal subgroups

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

subgroupindex
#105950382
#105929262
C3×#52312
C3×#52282
#105891532
#105891512
#105891452
#709813
#697003