Finite Group Databasebeta

← #11792210

Subgroups — #11792210

Order 1152.

799 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5526C211yesmaximal, characteristic
2C2×#63866C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic
4#10592703C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic
6C2×#63560C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8#71868—31nomaximal
9#68768—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#897—22no—
18C3×#886—22no—
19C3×#875—21no—
20C3×#869—21no—
21C2×Dic3⋊Dic3—22no—
22#63866—22no—
23#63866—22no—
24C2×#3719—21no—
25#63831—22no—
26#63831—22no—
27C2×#3716—21no—
28#63637—22no—
29#63569—22no—
30#63560—22no—
31C3×#536—31no—
32C2×#951—31no—
33C2×#944—31no—
34C2×#909—31no—
35#5526D311yescharacteristic
36C2×#869—31no—
37C2×#837—31no—
38C2×#836—31no—
39C2×#824—31no—
40#5004—31no—
41#5004—31no—
42#5004—61no—
43C2×#805—31no—
44C3×#339—31no—
45#4532D311yescharacteristic, complemented
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634D412yes—
54C2×C3×#67—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D412yes—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6D411yescharacteristic
70C32×C4⋊C4D412yes—
71C32×C22⋊C4—21no—
72C32×C42—21no—
73#3748—21no—
74#3748—21no—
75C2×C3⋊(C3⋊C8)—21no—
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3—24no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3D412yes—
80C3×#208—21no—
81C3×#208D412yes—
82C2×C3×C3⋊C8—21no—
83Dic3⋊Dic3—28no—
84#3719—24no—
85#3716—24no—
86#2005—91noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—31no—
89C2×#235C2×D311yescharacteristic
90C22×Dic6—31no—
91C22×Dic6—31no—
92C22×Dic6—61no—
93C22×Dic6C2×D311yescharacteristic
94C2×C3×M16—31no—
95C3×C4⋊Q8—61no—
96C3×#124—61no—
97C3×#123—62no—
98C3×C22⋊Q8—62no—
99C3×#117—21no—
100C3×#117C2×D311yescharacteristic
101C3×#117C2×D311yescharacteristic
102C2×C3×C42—31no—
103#951—62no—
104#951—62no—
105#944—62no—
106#944—62no—
107C2×#216—61no—
108C2×#214—61no—
109C2×C4⋊Dic3—62no—
110C2×Dic3⋊C4—62no—
111C2×C4×Dic3C2×D311yescharacteristic
112C2×#208—31no—
113C2×#208—31no—
114C2×#208—61no—
115C2×#208C2×D311yescharacteristic
116#909—62no—
117#909—62no—
118C2×Dic12—61no—
119C2×#204—61no—
120#897—22no—
121#886—22no—
122#875—21no—
123#869—21no—
124#869—62no—
125#869—62no—
126#837—62no—
127#836—62no—
128#824—62no—
129#810—64no—
130#810—62no—
131#810—62no—
132#805—62no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—21no—
135C2×C32×C4—22no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—41no—
145#634—22no—
146#634—22no—
147#634—41no—
148#634—41no—
149C3×#67—41no—
150C3×#67—41no—
151C2×C3×Dic3—24no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—41no—
160C3×C4×D3—41no—
161C3×Dic6—21no—
162C3×Dic6—21no—
163C3×Dic6—41no—
164C3×Dic6—41no—
165C3×Dic6—41no—
166C3×Dic6—41no—
167C3⋊(C3⋊C8)—41no—
168C3×C3⋊C8—22no—
169C2×#137—91no—
170#536—31no—
171C2×C4⋊Q8—91no—
172C2×#104—91no—
173#419—91no—
174C2×#101—91no—
175#339—31no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—31no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×D4—31no—
188C2×C3×D4—61no—
189C22×C3×C4—21no—
190C22×C3×C4—32no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—21no—
196C22×Dic3—21no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—121no—
200C22×Dic3#6712yes—
201#235—21no—
202#235—21no—
203#235—21no—
204#235—21no—
205C2×D12#6711yescharacteristic
206C2×C4×D3—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—121no—
229C2×Dic6—121no—
230C2×Dic6—121no—
231C2×Dic6#6711yescharacteristic
232C3×M16—32no—
233C3×M16—61no—
234C2×C3×C8—61no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—64no—
237C3×C4⋊C4D1212yes—
238C3×C4⋊C4#6712yes—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—41no—
242C3×C22⋊C4—64no—
243C3×C42—21no—
244C3×C42—21no—
245C3×C42—32no—
246C3×C42—41no—
247C3×C42—61no—
248#216—64no—
249#214—64no—
250(C2×D3)⋊C4—24no—
251C4⋊Dic3—24no—
252C4⋊Dic3—68no—
253Dic3⋊C4—68no—
254C4×Dic3—21no—
255C4×Dic3D1212yes—
256#208—21no—
257#208—61no—
258#208—61no—
259#208—61no—
260#208—61no—
261#208—121no—
262#208—121no—
263#208D1212yes—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—61no—
268Dic12—64no—
269#204—64no—
270C22×C32—22no—
271C22×C32#12011yescharacteristic
272C22×C32#12011yescharacteristic
273C22×C32#12111yescharacteristic
274C2×C3×D3—41no—
275C2×C3×D3—42no—
276C32×C4—42no—
277C32×C4#12011yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4#12711yescharacteristic
281C3⋊Dic3—42no—
282C3×Dic3—24no—
283C3×Dic3—41no—
284C3×Dic3—42no—
285C2×#41—31no—
286C22×Q8—31no—
287C22×Q8—91no—
288#137—182no—
289#137—182no—
290C2×Q16—181no—
291C2×SD16—181no—
292C2×M16—31no—
293C2×M16—91no—
294C4⋊Q8—61no—
295C4⋊Q8—182no—
296C4⋊Q8—182no—
297#124—61no—
298#123—62no—
299C22⋊Q8—62no—
300#117D3211yescharacteristic
301C2×C4⋊C4—182no—
302C2×C42—31no—
303#104—182no—
304#103—182no—
305#101—182no—
306C23×C3—21no—
307C23×C3—61no—
308C23×C3D3×D411yescharacteristic
309C23×C3C2×#6711yescharacteristic
310C22×D3—21no—
311C3×Q8—61no—
312C3×Q8—61no—
313C3×Q8—121no—
314C3×Q8—121no—
315C3×Q8—121no—
316C3×Q8—121no—
317C3×D4—61no—
318C3×D4—61no—
319C3×D4—121no—
320C3×D4—121no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—42no—
330C2×C3×C4—64no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—61no—
335C2×C3×C4—62no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4#23911yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350#67—41no—
351#67—41no—
352C2×Dic3—24no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—122no—
362C2×Dic3—122no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367D12—21no—
368D12—21no—
369C4×D3—41no—
370C4×D3—41no—
371Dic6—21no—
372Dic6—21no—
373Dic6—41no—
374Dic6—41no—
375Dic6—41no—
376Dic6—41no—
377Dic6—64no—
378Dic6—62no—
379Dic6—62no—
380Dic6—62no—
381Dic6—62no—
382Dic6—122no—
383Dic6—122no—
384Dic6—122no—
385Dic6—121no—
386Dic6—121no—
387Dic6—121no—
388Dic6—121no—
389C3×C8—62no—
390C3⋊C8—22no—
391C3⋊C8—122no—
392C3⋊C8—121no—
393C3⋊C8—121no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32#39211yescharacteristic
397C2×C32#45612yes—
398C3×D3—81no—
399#41—61no—
400#41—61no—
401#41—61no—
402#41—61no—
403C2×Q8—31no—
404C2×Q8—61no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×Q8—61no—
409C2×Q8—61no—
410C2×Q8—92no—
411C2×Q8—181no—
412C2×Q8—181no—
413C2×Q8—181no—
414C2×Q8—181no—
415C2×Q8—181no—
416C2×D4—31no—
417C2×D4—61no—
418C22×C4—32no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—181no—
422C22×C4C2×D3211yescharacteristic
423Q16—184no—
424SD16—184no—
425M16—32no—
426M16—61no—
427M16—181no—
428M16—181no—
429C2×C8—61no—
430C2×C8—181no—
431C4⋊C4—64no—
432C4⋊C4—188no—
433C4⋊C4#62612yes—
434C22⋊C4—21no—
435C22⋊C4—64no—
436C42—21no—
437C42—32no—
438C42—61no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—42no—
445C22×C3—121no—
446C22×C3—122no—
447C22×C3#88211yescharacteristic
448C22×C3#88211yescharacteristic
449C22×C3#89511yescharacteristic
450C22×C3#93711yescharacteristic
451C22×C3#93911yescharacteristic
452C22×C3#95311yescharacteristic
453C2×D3—41no—
454C2×D3—42no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—42no—
460C3×C4—42no—
461C3×C4—64no—
462C3×C4—82no—
463C3×C4—122no—
464C3×C4—121no—
465C3×C4#87411yescharacteristic
466C3×C4#88211yescharacteristic
467C3×C4#89511yescharacteristic
468C3×C4#89511yescharacteristic
469C3×C4#93711yescharacteristic
470C3×C4#93811yescharacteristic
471C3×C4#93911yescharacteristic
472C3×C4#94011yescharacteristic
473Dic3—24no—
474Dic3—41no—
475Dic3—42no—
476Dic3—124no—
477Dic3—122no—
478Dic3—122no—
479C32#200511yescharacteristic, complemented, Sylow
480C23—61no—
481C23D3×#6711yescharacteristic
482Q8—61no—
483Q8—61no—
484Q8—121no—
485Q8—121no—
486Q8—121no—
487Q8—121no—
488Q8—182no—
489Q8—182no—
490Q8—361no—
491Q8—361no—
492D4—61no—
493D4—61no—
494D4—121no—
495D4—121no—
496C2×C4—22no—
497C2×C4—64no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—61no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—182no—
506C2×C4—361no—
507C2×C4—361no—
508C2×C4#379611yescharacteristic
509C2×C4D3×D1211yescharacteristic
510C2×C4D3×D1211yescharacteristic
511C2×C4#380211yescharacteristic
512C2×C4C2×#62611yescharacteristic
513C2×C4D3×#6711yescharacteristic
514C8—62no—
515C8—361no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—22no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3—241no—
525C2×C3#467111yescharacteristic
526C2×C3#482612yes—
527C2×C3#522311yescharacteristic
528C2×C3#524612yes—
529D3—81no—
530C22—22no—
531C22—121no—
532C22—122no—
533C22#6388611yescharacteristic
534C22#6392211yescharacteristic
535C22#6397711yescharacteristic
536C4—42no—
537C4—64no—
538C4—122no—
539C4—121no—
540C4—362no—
541C4#6388611yescharacteristic
542C4#6391111yescharacteristic
543C4#6391611yescharacteristic
544C4#6392211yescharacteristic
545C3—21no—
546C3#6876811yescharacteristic, complemented
547C3#7186811yescharacteristic, complemented
548C2—21no—
549C2—21no—
550C2—241no—
551C2#1059139111yescharacteristic
552C2#1059168912yes—
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenter#117D32
hypocenterC32#2005
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63866C2semidirect
4. #10592703C2semidirect
6. C2×#63560C2semidirect
7. C3×#4532C2semidirect
45. #4532D3semidirect
479. C32#2005semidirect
546. C3#68768semidirect
547. C3#71868semidirect

Maximal subgroups

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

subgroupindex
C3×#55262
C2×#638662
C2×#638312
#105927032
C2×#635692
C2×#635602
C3×#45322
#718683
#687683