Finite Group Databasebeta

← #11798723

Subgroups — #11798723

Order 1152.

486 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×#5651C211yesmaximal, characteristic, complemented
2C3×#5053C211yesmaximal, characteristic
3#10591533C211yesmaximal, characteristic
4#10591512C211yesmaximal, characteristic
5#10589405C211yesmaximal, characteristic, complemented
6#10589180C211yesmaximal, characteristic, complemented
7#10589175C211yesmaximal, characteristic, complemented
8#71958—31nomaximal
9#71003—31nomaximal
10C3×#1004C2211yescharacteristic
11C32×#123C2211yescharacteristic
12C3×#936C2211yescharacteristic
13C3×#935C2211yescharacteristic
14C3×#929—21no—
15C3×#924—21no—
16C3×#889—21no—
17C3×#888—21no—
18C3×#879—21no—
19C3×#879—21no—
20C3×#878—21no—
21#63961—21no—
22#63827—21no—
23#63661C2211yescharacteristic
24#63660C2211yescharacteristic
25C3×#834C2211yescharacteristic
26C3×#806—21no—
27#63580—21no—
28#63569—21no—
29C3×#563—31no—
30#5651D311yescharacteristic, complemented
31C3×#458—31no—
32#5243—31no—
33#5242—31no—
34#5061—31no—
35#5053—31no—
36#5053D311yescharacteristic
37#4541—31no—
38#4539—31no—
39#4539—31no—
40#4539—31no—
41#4539—61no—
42#4473—31no—
43#4472—31no—
44C2×C32×D4C2311yescharacteristic
45C22×C32×C4D411yescharacteristic
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3D411yescharacteristic
49C3×#237—41no—
50C3×D3×D4—41no—
51C3×#235—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C22⋊C4—21no—
56C32×C22⋊C4D411yescharacteristic
57#3757—21no—
58#3748—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217D411yescharacteristic
64C3×(C2×D3)⋊C4—41no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—41no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3D411yescharacteristic
75#3724—41no—
76(C2×D3)⋊Dic3—41no—
77#3718—41no—
78#3715—41no—
79#2201—91noSylow
80C3×H(5,𝔽2)—31no—
81#1004C2×D311yescharacteristic
82C3×C4⋊Q8—61no—
83C3×#126—61no—
84C3×#126—61no—
85C3×#125—61no—
86C3×#124—31no—
87C3×#123—21no—
88C3×#123—31no—
89C3×#123—61no—
90C3×#123C2×D311yescharacteristic
91C3×#123C2×D311yescharacteristic
92C3×C22⋊Q8—61no—
93C3×C22⋊Q8—61no—
94#951—61no—
95#942—61no—
96#936C2×D311yescharacteristic
97#935—61no—
98#935C2×D311yescharacteristic
99#929—21no—
100#929—61no—
101#924—21no—
102#889—21no—
103#888—21no—
104#879—21no—
105#879—21no—
106#878—21no—
107C3×#99—31no—
108C3×#99—61no—
109#837—61no—
110#834—31no—
111#834—31no—
112#834—61no—
113#834—61no—
114#834C2×D311yescharacteristic
115#833—31no—
116#833—31no—
117#833—61no—
118#806—21no—
119#806—61no—
120#805—61no—
121C23×C32C2×D411yescharacteristic
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C32×D4—41no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C3⋊Dic3—41no—
131C3×#67—41no—
132C3×#67—41no—
133C3×#67—41no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×D12—21no—
143C3×C4×D3—41no—
144C3×Dic6—21no—
145C3×Dic6—41no—
146C3×Dic6—81no—
147C3⋊(C3⋊C8)—41no—
148#563—31no—
149#458—31no—
150#458—91no—
151#455—91no—
152#354—91no—
153#352—91no—
154#352—91no—
155C3×#41—61no—
156C3×#41—121no—
157C2×C3×Q8—31no—
158C2×C3×Q8—61no—
159C2×C3×D4—21no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—121no—
163C2×C3×D4C22×D311yescharacteristic
164C2×C3×D4C22×D311yescharacteristic
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4#6711yescharacteristic
168C22×C3×C4#6711yescharacteristic
169C2×#67—21no—
170C2×#67—21no—
171C22×Dic3#6711yescharacteristic
172#237—41no—
173D3×D4—41no—
174#235—21no—
175C2×Dic6—21no—
176C2×Dic6#6711yescharacteristic
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—121no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—31no—
192C3×C22⋊C4—41no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—121no—
198C3×C22⋊C4#6711yescharacteristic
199C3×C22⋊C4#6711yescharacteristic
200C3×C42—31no—
201C3×C42—61no—
202#217—21no—
203#217—21no—
204#217—21no—
205#217—21no—
206#217—61no—
207#217—61no—
208#217—121no—
209#217—121no—
210#217#6711yescharacteristic
211#216—121no—
212#216—121no—
213#215—121no—
214#214—121no—
215(C2×D3)⋊C4—41no—
216(C2×D3)⋊C4—121no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219Dic3⋊C4—21no—
220Dic3⋊C4—21no—
221Dic3⋊C4—21no—
222Dic3⋊C4—21no—
223Dic3⋊C4—21no—
224Dic3⋊C4—41no—
225Dic3⋊C4—121no—
226Dic3⋊C4—121no—
227C4×Dic3—21no—
228C4×Dic3#6711yescharacteristic
229#208—61no—
230#208—61no—
231#208—121no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32—41no—
235C22×C32—41no—
236C22×C32#12011yescharacteristic
237C2×C3×D3—41no—
238C2×C3×D3—81no—
239C2×C3×D3—81no—
240C32×C4—21no—
241C32×C4—41no—
242C32×C4—41no—
243C3⋊Dic3—81no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C3×Dic3—41no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C3×Dic3—81no—
250H(5,𝔽2)—31no—
251#137—181no—
252C4⋊Q8—61no—
253#126—61no—
254#126—61no—
255#125—61no—
256#124—31no—
257#123—31no—
258#123—61no—
259#123—181no—
260#123D3211yescharacteristic
261C22⋊Q8—61no—
262C22⋊Q8—61no—
263#104—181no—
264#100—91no—
265#99—31no—
266#99—61no—
267#99—91no—
268#99—181no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3D3×D411yescharacteristic
274C23×C3C2×#6711yescharacteristic
275C23×C3C2×#6711yescharacteristic
276C23×C3C2×#6711yescharacteristic
277C22×D3—21no—
278C22×D3—21no—
279C3×Q8—61no—
280C3×Q8—121no—
281C3×Q8—241no—
282C3×D4—41no—
283C3×D4—41no—
284C3×D4—61no—
285C3×D4—81no—
286C3×D4—121no—
287C3×D4—121no—
288C3×D4—121no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—81no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310#67—41no—
311#67—41no—
312#67—41no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—21no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—241no—
324D12—21no—
325C4×D3—41no—
326Dic6—21no—
327Dic6—41no—
328Dic6—81no—
329C3⋊C8—121no—
330C3⋊C8—121no—
331C3⋊C8—241no—
332C2×C32—21no—
333C2×C32—41no—
334C2×C32—41no—
335C2×C32B(4,𝔽2)11yescharacteristic
336C3×D3—81no—
337#41—61no—
338#41—121no—
339C2×Q8—31no—
340C2×Q8—61no—
341C2×D4—61no—
342C2×D4—61no—
343C2×D4—121no—
344C2×D4C2×D3211yescharacteristic
345C22×C4—31no—
346C22×C4#62511yescharacteristic
347Q16—361no—
348SD16—361no—
349M16—181no—
350C4⋊C4—21no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—121no—
359C4⋊C4—361no—
360C22⋊C4—21no—
361C22⋊C4—31no—
362C22⋊C4—61no—
363C22⋊C4—61no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4—121no—
367C22⋊C4—181no—
368C22⋊C4—361no—
369C22⋊C4#62511yescharacteristic
370C42—31no—
371C42—61no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—81no—
384C22×C3—81no—
385C22×C3—121no—
386C22×C3—241no—
387C22×C3—241no—
388C22×C3#93711yescharacteristic
389C22×C3#95311yescharacteristic
390C2×D3—41no—
391C2×D3—81no—
392C2×D3—81no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—81no—
401C3×C4—81no—
402C3×C4—121no—
403C3×C4—121no—
404C3×C4—121no—
405C3×C4—121no—
406C3×C4—121no—
407C3×C4—241no—
408Dic3—41no—
409Dic3—41no—
410Dic3—41no—
411Dic3—41no—
412Dic3—41no—
413Dic3—81no—
414Dic3—241no—
415Dic3—241no—
416Dic3—481no—
417C32#220111yescharacteristic, complemented, Sylow
418C23—61no—
419C23—61no—
420C23C2×#62511yescharacteristic
421C23D3×#6711yescharacteristic
422Q8—61no—
423Q8—121no—
424Q8—241no—
425D4—41no—
426D4—61no—
427D4—121no—
428D4—121no—
429D4—121no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—41no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4—361no—
443C2×C4D3×#6711yescharacteristic
444C8—361no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—81no—
454C2×C3—81no—
455C2×C3—241no—
456C2×C3#503211yescharacteristic
457C2×C3#524411yescharacteristic
458D3—81no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—121no—
464C22—241no—
465C22—241no—
466C22#6397611yescharacteristic
467C4—21no—
468C4—41no—
469C4—41no—
470C4—121no—
471C4—121no—
472C4—121no—
473C4—121no—
474C4—121no—
475C4—241no—
476C4—721no—
477C3—21no—
478C3#7100311yescharacteristic, complemented
479C3#7195811yescharacteristic, complemented
480C2—21no—
481C2—41no—
482C2—41no—
483C2—241no—
484C2#1059153011yescharacteristic
subgroupG/H
centerC2#10591530
commutator, cosocleC2×C32×D4C23
FrattiniC2×D4C2×D32
FittingC32×#123C22
socleC2×C32B(4,𝔽2)
prime radicalC3×#1004C22
hypercenter#123D32
hypocenterC32#2201
LCSG ▷ C2×C32×D4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C3×#5651C2semidirect
5. #10589405C2semidirect
6. #10589180C2semidirect
7. #10589175C2semidirect
30. #5651D3semidirect
417. C32#2201semidirect
478. C3#71003semidirect
479. C3#71958semidirect

Maximal subgroups

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

subgroupindex
C3×#56512
C3×#50532
#105915332
#105915122
#105894052
#105891802
#105891752
#719583
#710033