Finite Group Databasebeta

← #11778145

Subgroups — #11778145

Order 1152.

571 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 571 conjugacy classes of subgroups — too many to draw. Only its 80 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#10594813C211yesmaximal, characteristic, complemented
2C3×#4731C211yesmaximal, characteristic
3#10591302C211yesmaximal, characteristic
4#10591169C211yesmaximal, characteristic
5#10589335C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589153C211yesmaximal, characteristic, complemented
8#70979—31nomaximal
9#68325—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×#3750C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×#204—21no—
15#63982—21no—
16C2×(C2×D3)⋊Dic3—21no—
17C2×(C2×D3)⋊Dic3—21no—
18#63957—21no—
19#63847—21no—
20#63847—21no—
21#63839—21no—
22#63839—21no—
23C2×#3715—21no—
24C32×C22⋊C8C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#821—21no—
28#63562—21no—
29#5623—31no—
30#5623—31no—
31C3×#450—31no—
32#5222—31no—
33#5218—31no—
34#5046—31no—
35#4731D311yescharacteristic
36#4672—31no—
37C3×#328—31no—
38#4538—31no—
39#4469—31no—
40#4469—31no—
41#4469—61no—
42#4467D311yescharacteristic, complemented
43#4452—31no—
44C23×C3×D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3×Dic3—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—42no—
52C2×C3×Dic6D411yescharacteristic
53C2×C3×Dic6D411yescharacteristic
54C2×#627—21no—
55C2×C32×C8—21no—
56#3750—21no—
57#3750—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×#204—42no—
66#3724—21no—
67#3724—21no—
68#3724—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71(C2×D3)⋊Dic3—42no—
72(C2×D3)⋊Dic3—42no—
73Dic32—21no—
74Dic32—21no—
75#3715—42no—
76#1599—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C2×C3×SD16—61no—
80C3×C22⋊Q8—31no—
81C3×C22⋊Q8—31no—
82C2×#217—61no—
83C2×#217—61no—
84#944—61no—
85#944—61no—
86C2×#215—61no—
87C2×#214—61no—
88C2×(C2×D3)⋊C4—61no—
89C2×(C2×D3)⋊C4—61no—
90#924C2×D311yescharacteristic
91#924C2×D311yescharacteristic
92C2×Dic3⋊C4—31no—
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—61no—
95C2×#204—21no—
96#889—61no—
97#889—61no—
98#889—61no—
99#889—61no—
100#888—61no—
101#888—61no—
102#878—61no—
103#878—61no—
104#877—61no—
105#877—61no—
106C3×#102—61no—
107C3×C22⋊C8—21no—
108C3×C22⋊C8C2×D311yescharacteristic
109C3×C22⋊C8C2×D311yescharacteristic
110C3×#95—31no—
111#832—61no—
112C3⋊#95C2×D311yescharacteristic
113#830—31no—
114#830—31no—
115#830—61no—
116#821—21no—
117#809—61no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—22no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3SD1612yescomplemented
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12—41no—
144C3×D12—41no—
145C3×Dic6—41no—
146C3×Dic6—41no—
147#627—81no—
148C32×C8—41no—
149C3⋊(C3⋊C8)—41no—
150#544—91no—
151#450—31no—
152#450—91no—
153#394—91no—
154#328—31no—
155#328—91no—
156#324—91no—
157C24×C3—61no—
158C23×D3—21no—
159C2×C3×Q8—31no—
160C2×C3×Q8—31no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—122no—
164C22×C3×C4—21no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×Dic3—21no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C2×D12—21no—
176C2×D12—21no—
177C2×D12—42no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6D1211yescharacteristic
181C2×Dic6#6711yescharacteristic
182C3×SD16—122no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—41no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192#217—21no—
193#217—21no—
194#217—122no—
195#217—122no—
196#215—122no—
197#214—122no—
198(C2×D3)⋊C4—122no—
199(C2×D3)⋊C4—122no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3D1211yescharacteristic
203C4⋊Dic3#6711yescharacteristic
204Dic3⋊C4—21no—
205Dic3⋊C4—21no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—121no—
219Dic3⋊C4—121no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227#204—42no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32#12011yescharacteristic
231C22×C32C2×SD1611yescharacteristic
232C22×C32#13711yescharacteristic
233C2×C3×D3—42no—
234C2×C3×D3—42no—
235C2×C3×D3—42no—
236C2×C3×D3—81no—
237C2×C3×D3—81no—
238C2×C3×D3—81no—
239C2×C3×D3—81no—
240C32×C4—21no—
241C32×C4—21no—
242C3⋊Dic3—22no—
243C3⋊Dic3—41no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C3×Dic3—41no—
247C3×Dic3—41no—
248C3×Dic3—81no—
249C22×D4—31no—
250C2×SD16—61no—
251C2×SD16—181no—
252C4⋊Q8—181no—
253C4⋊Q8—181no—
254#125—181no—
255#125—181no—
256C22⋊Q8—31no—
257C22⋊Q8—31no—
258C22⋊Q8—181no—
259#117—181no—
260C2×C4⋊C4—91no—
261C2×C22⋊C4—181no—
262C2×C22⋊C4—181no—
263#102—61no—
264#102—181no—
265C22⋊C8—91no—
266C22⋊C8D3211yescharacteristic
267#95—31no—
268C23×C3—21no—
269C23×C3—62no—
270C23×C3—121no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3—121no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3D3×D411yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—22no—
279C22×D3—41no—
280C22×D3—41no—
281C22×D3—41no—
282C22×D3—41no—
283C22×D3—41no—
284C22×D3—41no—
285C3×Q8—121no—
286C3×Q8—121no—
287C3×D4—62no—
288C3×D4—62no—
289C3×D4—121no—
290C3×D4—121no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—81no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—32no—
312C2×Dic3—32no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—62no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—241no—
329D12—22no—
330D12—22no—
331D12—41no—
332D12—41no—
333Dic6—41no—
334Dic6—41no—
335Dic6—241no—
336Dic6—241no—
337C3×C8—41no—
338C3×C8—41no—
339C3×C8—81no—
340C3⋊C8—121no—
341C3⋊C8—121no—
342C3⋊C8—241no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32#44811yescharacteristic
346C2×C32#45411yescharacteristic
347C2×C32B(4,𝔽2)11yescharacteristic
348C3×D3—82no—
349C24—61no—
350C2×Q8—31no—
351C2×Q8—31no—
352C2×Q8—181no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—122no—
356C22×C4—61no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4C2×D3211yescharacteristic
360SD16—122no—
361SD16—362no—
362C2×C8—21no—
363C2×C8—181no—
364C4⋊C4—31no—
365C4⋊C4—31no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—181no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C4⋊C4—181no—
373C4⋊C4—181no—
374C4⋊C4—181no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—362no—
378C22⋊C4—362no—
379C42—181no—
380C42—181no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—122no—
391C22×C3—122no—
392C22×C3—122no—
393C22×C3—241no—
394C22×C3—241no—
395C22×C3—241no—
396C22×C3—241no—
397C22×C3#88211yescharacteristic
398C22×C3D3×SD1611yescharacteristic
399C22×C3D3×SD1611yescharacteristic
400C22×C3#91511yescharacteristic
401C22×C3#91811yescharacteristic
402C22×C3#93711yescharacteristic
403C2×D3—42no—
404C2×D3—42no—
405C2×D3—42no—
406C2×D3—81no—
407C2×D3—81no—
408C2×D3—81no—
409C2×D3—81no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—121no—
417C3×C4—121no—
418C3×C4—121no—
419C3×C4—121no—
420C3×C4—241no—
421Dic3—41no—
422Dic3—41no—
423Dic3—41no—
424Dic3—41no—
425Dic3—62no—
426Dic3—62no—
427Dic3—81no—
428Dic3—122no—
429Dic3—121no—
430Dic3—121no—
431Dic3—241no—
432C32#159911yescharacteristic, complemented, Sylow
433C23—62no—
434C23—121no—
435C23—121no—
436C23—121no—
437C23—121no—
438C23—121no—
439C23—121no—
440C23#380211yescharacteristic
441Q8—121no—
442Q8—121no—
443Q8—721no—
444D4—62no—
445D4—62no—
446D4—121no—
447D4—121no—
448C2×C4—41no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—92no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—361no—
461C2×C4D3×D1211yescharacteristic
462C2×C4D3×#6711yescharacteristic
463C8—41no—
464C8—361no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—41no—
473C2×C3—41no—
474C2×C3—242no—
475C2×C3#474111yescharacteristic
476C2×C3#480611yescharacteristic
477C2×C3#482711yescharacteristic
478C2×C3#503211yescharacteristic
479C2×C3#517011yescharacteristic
480C2×C3#520111yescharacteristic
481D3—82no—
482C22—21no—
483C22—21no—
484C22—122no—
485C22—122no—
486C22—122no—
487C22—241no—
488C22—241no—
489C22—241no—
490C22—241no—
491C22#6379611yescharacteristic
492C22#6381111yescharacteristic
493C22#6392211yescharacteristic
494C4—21no—
495C4—21no—
496C4—121no—
497C4—121no—
498C4—121no—
499C4—121no—
500C4—182no—
501C4—241no—
502C4—361no—
503C3—21no—
504C3#6832511yescharacteristic, complemented
505C3#7097911yescharacteristic, complemented
506C2—21no—
507C2—21no—
508C2—242no—
509C2#1059040711yescharacteristic
510C2#1059082411yescharacteristic
511C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC22×C3×D12C22
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. #10594813C2semidirect
5. #10589335C2semidirect
6. C3×#4467C2semidirect
7. #10589153C2semidirect
42. #4467D3semidirect
133. C2×C3⋊Dic3SD16semidirect
432. C32#1599semidirect
504. C3#68325semidirect
505. C3#70979semidirect

Maximal subgroups

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

subgroupindex
#105948132
C3×#47312
#105913022
#105911692
#105893352
C3×#44672
#105891532
#709793
#683253