Finite Group Databasebeta

← #11778144

Subgroups — #11778144

Order 1152.

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

normal subgroups only

This group has 626 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#10594812C211yesmaximal, characteristic, complemented
2#10592430C211yesmaximal, characteristic
3#10591321C211yesmaximal, characteristic
4#10591183C211yesmaximal, characteristic
5C3×#4469C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589154C211yesmaximal, characteristic, complemented
8#68325—31nomaximal
9#68138—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11#64133C2211yescharacteristic
12C2×#3744—21no—
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15#63964—21no—
16C2×#3722—21no—
17C2×#3722—21no—
18#63955—21no—
19#63846—21no—
20#63845—21no—
21#63840—21no—
22#63839—21no—
23C2×#3717—21no—
24C32×C22⋊C8C2211yescharacteristic
25#63648—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28#63564—21no—
29#5623—31no—
30#5500—31no—
31#5046—31no—
32#4991—31no—
33#4731—31no—
34#4731—31no—
35#4731—31no—
36#4731—61no—
37#4672—31no—
38C3×#328—31no—
39C3×#324—31no—
40#4469D311yescharacteristic, complemented
41#4467—31no—
42#4467D311yescharacteristic, complemented
43#4452—31no—
44C23×C3⋊D3—21no—
45C22×C32×C4C2311yescharacteristic
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—42no—
49C2×#634D411yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3D411yescharacteristic
52C22×C3×Dic3D411yescharacteristic
53C2×C3×Dic6D411yescharacteristic
54C2×#627—21no—
55C2×C32×C8—21no—
56#3757—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59#3744—42no—
60C3×#217—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71#3722—42no—
72#3722—42no—
73Dic32—21no—
74Dic32—21no—
75#3717—42no—
76#1599—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C3×C22⋊Q8—31no—
81C2×C3×C4⋊C4—31no—
82#944—61no—
83C2×#215—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×(C2×D3)⋊C4—61no—
87C2×(C2×D3)⋊C4—61no—
88#926—61no—
89#924—31no—
90#924—31no—
91#924—61no—
92#924—61no—
93#924C2×D311yescharacteristic
94C2×Dic3⋊C4C2×D311yescharacteristic
95C2×#204—61no—
96C2×#204—61no—
97C2×#204—62no—
98C2×#204—61no—
99#890—61no—
100#890—61no—
101#889—61no—
102#889—61no—
103#888—61no—
104#888—61no—
105#888—61no—
106#878—61no—
107#877—61no—
108C3×C22⋊C8—21no—
109C3×C22⋊C8—31no—
110C3×C22⋊C8C2×D311yescharacteristic
111C3×C22⋊C8C2×D311yescharacteristic
112C3×#95—31no—
113C3⋊#95C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#821—61no—
116#821—61no—
117#821—62no—
118#821—61no—
119#809—61no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—22no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—41no—
136C4⋊(C3⋊D3)—41no—
137#634—41no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
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—
147C2×C3×Dic3SD1612yescomplemented
148C3×Dic6—41no—
149#627—81no—
150C32×C8—41no—
151C3×C3⋊C8—41no—
152#544—91no—
153#450—91no—
154#450—91no—
155#394—91no—
156#328—31no—
157#328—91no—
158#324—31no—
159C23×D3—61no—
160C23×D3—61no—
161C23×D3—121no—
162C2×C3×Q8—31no—
163C22×C3×C4—21no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3—21no—
170C22×Dic3D1211yescharacteristic
171C22×Dic3D1211yescharacteristic
172C2×D12—62no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—121no—
178C2×D12—122no—
179C2×D12—122no—
180C2×D12—124no—
181C2×Dic6—31no—
182C2×Dic6—31no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—61no—
186C2×Dic6D1211yescharacteristic
187C2×C3×C8—22no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—61no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C22⋊C4—61no—
196#217—21no—
197#217—61no—
198#217—61no—
199#217—121no—
200#215—122no—
201(C2×D3)⋊C4—122no—
202(C2×D3)⋊C4—122no—
203(C2×D3)⋊C4—122no—
204(C2×D3)⋊C4—122no—
205C4⋊Dic3—31no—
206C4⋊Dic3—31no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3D1211yescharacteristic
213Dic3⋊C4—21no—
214Dic3⋊C4—21no—
215Dic3⋊C4—21no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—121no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C2×C3⋊C8—21no—
230#204—122no—
231#204—122no—
232#204—124no—
233#204—122no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32#12011yescharacteristic
237C22×C32C2×SD1611yescharacteristic
238C22×C32#13711yescharacteristic
239C2×C3⋊D3—42no—
240C2×C3⋊D3—42no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—81no—
243C2×C3⋊D3—81no—
244C2×C3⋊D3—81no—
245C2×C3⋊D3—81no—
246C32×C4—21no—
247C32×C4—21no—
248C3⋊Dic3—41no—
249C3⋊Dic3—41no—
250C3×Dic3—22no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—41no—
254C3×Dic3—81no—
255C22×D4—91no—
256C2×SD16—181no—
257C2×SD16—181no—
258C4⋊Q8—181no—
259C4⋊Q8—181no—
260#125—181no—
261#125—181no—
262C22⋊Q8—31no—
263C22⋊Q8—91no—
264C22⋊Q8—181no—
265#117—181no—
266C2×C4⋊C4—31no—
267C2×C22⋊C4—181no—
268C2×C22⋊C4—181no—
269#102—181no—
270#102—181no—
271C22⋊C8—31no—
272C22⋊C8D3211yescharacteristic
273#95—31no—
274C23×C3—21no—
275C23×C3C2×D1211yescharacteristic
276C23×C3D3×D411yescharacteristic
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—122no—
280C22×D3—122no—
281C22×D3—121no—
282C22×D3—121no—
283C22×D3—121no—
284C22×D3—121no—
285C22×D3—121no—
286C22×D3—121no—
287C22×D3—122no—
288C22×D3—121no—
289C22×D3—121no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—241no—
295C22×D3—241no—
296C22×D3—241no—
297C22×D3—241no—
298C3×Q8—121no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—32no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—42no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4C2×D1211yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×Dic3—21no—
319C2×Dic3—21no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3#20412yescomplemented
334D12—64no—
335D12—62no—
336D12—62no—
337D12—62no—
338D12—62no—
339D12—122no—
340D12—122no—
341D12—121no—
342D12—121no—
343D12—121no—
344D12—121no—
345D12—122no—
346Dic6—41no—
347Dic6—121no—
348Dic6—121no—
349Dic6—122no—
350Dic6—241no—
351Dic6—241no—
352C3×C8—42no—
353C3×C8—41no—
354C3×C8—41no—
355C3×C8—121no—
356C3⋊C8—41no—
357C2×C32—21no—
358C2×C32—21no—
359C2×C32#44811yescharacteristic
360C2×C32#45411yescharacteristic
361C2×C32B(4,𝔽2)11yescharacteristic
362C3⋊D3—82no—
363C24—181no—
364C2×Q8—31no—
365C2×Q8—91no—
366C2×Q8—181no—
367C2×D4—181no—
368C2×D4—181no—
369C2×D4—362no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—61no—
373C22×C4C2×D3211yescharacteristic
374SD16—362no—
375SD16—362no—
376C2×C8—21no—
377C2×C8—61no—
378C4⋊C4—31no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—91no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C22⋊C4—61no—
390C22⋊C4—181no—
391C22⋊C4—362no—
392C22⋊C4—362no—
393C42—181no—
394C42—181no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3#88211yescharacteristic
405C22×C3#88211yescharacteristic
406C22×C3C2×#20411yescharacteristic
407C22×C3#90911yescharacteristic
408C22×C3D3×SD1611yescharacteristic
409C22×C3#91811yescharacteristic
410C2×D3—124no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—242no—
418C2×D3—242no—
419C2×D3—241no—
420C2×D3—241no—
421C2×D3—241no—
422C2×D3—241no—
423C2×D3—242no—
424C2×D3—242no—
425C2×D3—242no—
426C2×D3—242no—
427C2×D3—241no—
428C2×D3—241no—
429C2×D3—241no—
430C2×D3—241no—
431C3×C4—22no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—41no—
437C3×C4—62no—
438C3×C4—121no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4—241no—
442Dic3—22no—
443Dic3—41no—
444Dic3—41no—
445Dic3—41no—
446Dic3—81no—
447Dic3—121no—
448Dic3—121no—
449Dic3—121no—
450Dic3—121no—
451Dic3—241no—
452Dic3—241no—
453C32#159911yescharacteristic, complemented, Sylow
454C23—182no—
455C23—361no—
456C23—361no—
457C23—361no—
458C23—361no—
459C23—361no—
460C23—361no—
461C23D3×D1211yescharacteristic
462Q8—121no—
463Q8—361no—
464Q8—721no—
465D4—182no—
466D4—182no—
467D4—361no—
468D4—361no—
469C2×C4—32no—
470C2×C4—41no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4D3×D1211yescharacteristic
483C2×C4#381111yescharacteristic
484C8—41no—
485C8—121no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—41no—
494C2×C3—41no—
495C2×C3#473811yescharacteristic
496C2×C3#474111yescharacteristic
497C2×C3#474111yescharacteristic
498C2×C3#475311yescharacteristic
499C2×C3#480611yescharacteristic
500C2×C3#482711yescharacteristic
501D3—244no—
502D3—242no—
503D3—242no—
504C22—21no—
505C22—21no—
506C22—362no—
507C22—362no—
508C22—362no—
509C22—721no—
510C22—721no—
511C22—721no—
512C22—721no—
513C22D3×#20411yescharacteristic
514C22#6380111yescharacteristic
515C22#6392311yescharacteristic
516C4—21no—
517C4—21no—
518C4—62no—
519C4—121no—
520C4—121no—
521C4—121no—
522C4—241no—
523C4—361no—
524C4—361no—
525C3—21no—
526C3#6813811yescharacteristic, complemented
527C3#6832511yescharacteristic, complemented
528C2—21no—
529C2—21no—
530C2—722no—
531C2#1059041011yescharacteristic
532C2#1059095111yescharacteristic
533C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22⋊C8D32
hypocenterC32#1599
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594812C2semidirect
5. C3×#4469C2semidirect
6. C3×#4467C2semidirect
7. #10589154C2semidirect
40. #4469D3semidirect
42. #4467D3semidirect
147. C2×C3×Dic3SD16semidirect
333. C2×Dic3#204semidirect
453. C32#1599semidirect
526. C3#68138semidirect
527. C3#68325semidirect

Maximal subgroups

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

subgroupindex
#105948122
#105924302
#105913212
#105911832
C3×#44692
C3×#44672
#105891542
#683253
#681383