Finite Group Databasebeta

← #11793962

Subgroups — #11793962

Order 1152.

605 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63831C211yesmaximal, characteristic
2C2×#63643C211yesmaximal, characteristic, complemented
3C3×#5110C211yesmaximal, characteristic
4C2×C3×#819C211yesmaximal, characteristic, complemented
5#10591088C211yesmaximal, characteristic
6C2×#63561C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70716—31nomaximal
9#70004—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3719—21no—
18#63831—22no—
19#63831—22no—
20C2×#3716—21no—
21#63643—22no—
22C3×(C2×D3)⋊C8—22no—
23C3×#819—22no—
24#63566—21no—
25#63563—21no—
26#63561—22no—
27C2×#951—31no—
28C2×#909—31no—
29C2×C3×#108—31no—
30C3×#408—31no—
31#5232—31no—
32C2×#824—31no—
33C2×#824—31no—
34#5133—31no—
35#5110D311yescharacteristic
36C2×#819D311yescharacteristic, complemented
37C2×#816—31no—
38C2×#816—31no—
39C2×#816—61no—
40#4554—31no—
41#4554—31no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634D412yes—
51C2×C3×#67—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×Dic6D411yescharacteristic
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8D412yes—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208D412yes—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3719—24no—
74#3716—24no—
75#2052—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C22×Dic6—31no—
79C22×Dic6—31no—
80C22×Dic6—61no—
81C2×C3×M16—31no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C22×C3×C8—21no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C2×D311yescharacteristic
87#951—62no—
88#951—62no—
89C2×#216—61no—
90C2×#214—61no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—61no—
94C2×#208C2×D311yescharacteristic
95C2×#208C2×D311yescharacteristic
96C2×#208C2×D311yescharacteristic
97#909—62no—
98#909—62no—
99C2×Dic12—61no—
100C2×#204—61no—
101C3×#108—62no—
102C3×C22⋊C8—62no—
103#835—61no—
104#832—61no—
105#824—62no—
106#824—62no—
107#821—61no—
108(C2×D3)⋊C8—22no—
109#819—22no—
110#816—64no—
111#816—61no—
112#816—62no—
113#816—62no—
114C23×C32#4111yescharacteristic
115C22×C3×D3—21no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—81no—
127#634—22no—
128#634—22no—
129#634—41no—
130#634—41no—
131C3×#67—41no—
132C3×#67—41no—
133C2×C3×Dic3—21no—
134C3×D12—21no—
135C3×D12—21no—
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3×Dic6—21no—
139C3×Dic6—21no—
140C32×C8—22no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144C2×#137—91no—
145C2×#108—31no—
146#417—91no—
147C2×#103—91no—
148C2×#101—91no—
149#408—31no—
150#343—91no—
151C3×#41—61no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—31no—
156C2×C3×D4—31no—
157C2×C3×D4—61no—
158C22×C3×C4—21no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—121no—
168C22×Dic3—121no—
169#235—21no—
170#235—21no—
171#235—21no—
172#235—21no—
173C2×D12D1211yescharacteristic
174C2×C4×D3—21no—
175C2×Dic6—32no—
176C2×Dic6—32no—
177C2×Dic6—62no—
178C2×Dic6—62no—
179C2×Dic6—62no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—61no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C2×Dic6—121no—
191C2×Dic6—121no—
192C2×Dic6—121no—
193C2×Dic6D1211yescharacteristic
194C3×M16—32no—
195C3×M16—61no—
196C3×M16—61no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—61no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8—22no—
205C2×C3×C8—41no—
206C2×C3×C8—41no—
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C2×C3×C8—61no—
210C2×C3×C8D1212yes—
211C2×C3×C8#6712yes—
212#216—64no—
213#214—64no—
214C4⋊Dic3—62no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—121no—
220#208—21no—
221#208—21no—
222#208—21no—
223#208—21no—
224#208—21no—
225#208#6712yes—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229Dic12—64no—
230#204—64no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32#12111yescharacteristic
234C22×C32#12311yescharacteristic
235C22×C32#12411yescharacteristic
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C32×C4#12011yescharacteristic
240C32×C4#12111yescharacteristic
241C32×C4#12111yescharacteristic
242C32×C4#12311yescharacteristic
243C3⋊Dic3—42no—
244C3⋊Dic3—81no—
245C3×Dic3—41no—
246C2×#41—31no—
247C22×Q8—91no—
248#137—182no—
249#137—182no—
250C2×Q16—181no—
251C2×SD16—181no—
252C2×M16—31no—
253C2×M16—31no—
254C2×M16—31no—
255C22×C8D3211yescharacteristic
256C2×C4⋊C4—91no—
257#108—62no—
258#103—181no—
259#103—182no—
260#102—181no—
261#101—182no—
262C22⋊C8—62no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3#23511yescharacteristic
266C23×C3#23911yescharacteristic
267C22×D3—21no—
268C3×Q8—61no—
269C3×Q8—61no—
270C3×D4—61no—
271C3×D4—61no—
272C3×D4—121no—
273C3×D4—121no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—61no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4C2×D1211yescharacteristic
284C2×C3×C4C2×D1211yescharacteristic
285C2×C3×C4#23511yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4#23911yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295#67—41no—
296#67—41no—
297C2×Dic3—21no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—122no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—122no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—242no—
311C2×Dic3—241no—
312C2×Dic3—241no—
313D12—21no—
314D12—21no—
315C4×D3—41no—
316C4×D3—41no—
317Dic6—21no—
318Dic6—21no—
319Dic6—64no—
320Dic6—62no—
321Dic6—62no—
322Dic6—62no—
323Dic6—62no—
324Dic6—122no—
325Dic6—122no—
326Dic6—122no—
327Dic6—121no—
328Dic6—121no—
329Dic6—121no—
330Dic6—121no—
331C3×C8—22no—
332C3×C8—22no—
333C3×C8—42no—
334C3×C8—62no—
335C3×C8—121no—
336C3×C8—121no—
337C3⋊C8—22no—
338C3⋊C8—41no—
339C3⋊C8—41no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32#39411yescharacteristic
343C2×C32#47111yescharacteristic
344C2×C32#47311yescharacteristic
345C3×D3—81no—
346#41—61no—
347#41—61no—
348#41—61no—
349#41—61no—
350C2×Q8—31no—
351C2×Q8—92no—
352C2×Q8—181no—
353C2×Q8—181no—
354C2×Q8—181no—
355C2×Q8—181no—
356C2×Q8—181no—
357C2×D4—31no—
358C2×D4—61no—
359C22×C4—61no—
360C22×C4—181no—
361C22×C4—181no—
362C22×C4C2×D3211yescharacteristic
363Q16—184no—
364SD16—184no—
365M16—32no—
366M16—61no—
367M16—61no—
368M16—61no—
369M16—61no—
370M16—61no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8#62612yes—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—121no—
389C22×C3—121no—
390C22×C3—121no—
391C22×C3#88311yescharacteristic
392C22×C3#88511yescharacteristic
393C22×C3#89411yescharacteristic
394C22×C3#89511yescharacteristic
395C22×C3#93011yescharacteristic
396C22×C3#94711yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—121no—
405C3×C4#88211yescharacteristic
406C3×C4#88611yescharacteristic
407C3×C4#89411yescharacteristic
408C3×C4#89511yescharacteristic
409C3×C4#93011yescharacteristic
410C3×C4#93711yescharacteristic
411C3×C4#93811yescharacteristic
412C3×C4#93911yescharacteristic
413Dic3—41no—
414Dic3—124no—
415Dic3—122no—
416Dic3—122no—
417Dic3—242no—
418Dic3—241no—
419Dic3—241no—
420C32#205211yescharacteristic, complemented, Sylow
421C23—61no—
422C23#379911yescharacteristic
423Q8—61no—
424Q8—61no—
425Q8—182no—
426Q8—182no—
427Q8—361no—
428Q8—361no—
429D4—61no—
430D4—61no—
431D4—121no—
432D4—121no—
433C2×C4—61no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4—182no—
437C2×C4—361no—
438C2×C4—361no—
439C2×C4—361no—
440C2×C4—721no—
441C2×C4#379611yescharacteristic
442C2×C4D3×D1211yescharacteristic
443C2×C4#380211yescharacteristic
444C2×C4#380411yescharacteristic
445C2×C4C2×#62611yescharacteristic
446C2×C4D3×#6711yescharacteristic
447C8—22no—
448C8—62no—
449C8—121no—
450C8—121no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—241no—
461C2×C3#489611yescharacteristic
462C2×C3#489811yescharacteristic
463C2×C3#496111yescharacteristic
464C2×C3#499111yescharacteristic
465C2×C3#514111yescharacteristic
466C2×C3#514311yescharacteristic
467D3—81no—
468C22—21no—
469C22—21no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22#6385411yescharacteristic
474C22#6390711yescharacteristic
475C22#6390911yescharacteristic
476C4—121no—
477C4—362no—
478C4—721no—
479C4#6389011yescharacteristic
480C4#6391611yescharacteristic
481C4#6392211yescharacteristic
482C4#6397811yescharacteristic
483C3—21no—
484C3#7000411yescharacteristic, complemented
485C3#7071611yescharacteristic, complemented
486C2—21no—
487C2—21no—
488C2—241no—
489C2#1059093111yescharacteristic
490C2#1059093211yescharacteristic
491C2#1059139211yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC2×C3×#235C22
hypercenterC22×C8D32
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63643C2semidirect
4. C2×C3×#819C2semidirect
6. C2×#63561C2semidirect
7. #10589168C2semidirect
36. C2×#819D3semidirect
420. C32#2052semidirect
484. C3#70004semidirect
485. C3#70716semidirect

Maximal subgroups

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

subgroupindex
C2×#638312
C2×#636432
C3×#51102
C2×C3×#8192
#105910882
C2×#635612
#105891682
#707163
#700043