Finite Group Databasebeta

← #11792216

Subgroups — #11792216

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
1C2×#63866C211yesmaximal, characteristic, complemented
2#10594855C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic
4#10592819C211yesmaximal, characteristic, complemented
5C2×C3×#825C211yesmaximal, characteristic
6C2×C3×#824C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70389—31nomaximal
9#70119—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×Dic3⋊Dic3—22no—
18#63961—22no—
19#63873—21no—
20#63866—22no—
21#63866—22no—
22#63863—21no—
23#63856—22no—
24C2×#3719—21no—
25#63831—22no—
26#63831—22no—
27C2×#3716—21no—
28#63643—22no—
29C3×#825—22no—
30C3×#824—22no—
31#5825—31no—
32C2×#951—31no—
33#5816—31no—
34C2×#944—31no—
35C2×#909—31no—
36C2×#869—31no—
37C2×C3×#104—31no—
38C2×C3×#101—31no—
39C2×#825D311yescharacteristic
40C2×#824D311yescharacteristic, complemented
41#5120—31no—
42#5120—31no—
43#5120—61no—
44#4555—31no—
45#4523—31no—
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×M16—21no—
71C32×M16—21no—
72C2×C32×C8—21no—
73#3757—21no—
74C4⋊(C3⋊Dic3)D412yes—
75C4×C3⋊Dic3—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3D412yes—
78C3×#208—21no—
79C3×#208D412yes—
80C2×C3×C3⋊C8—21no—
81#3724—24no—
82Dic3⋊Dic3—28no—
83(C2×D3)⋊Dic3—24no—
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—21no—
95C2×C3×M16—31no—
96C2×C3×M16C2×D311yescharacteristic
97C2×C3×M16C2×D311yescharacteristic
98C2×C3×C42—31no—
99#951—62no—
100#951—62no—
101#947—61no—
102#946—62no—
103#944—62no—
104#944—61no—
105#944—61no—
106#944—62no—
107C2×#216—61no—
108#936—61no—
109#935—62no—
110C2×#214—61no—
111#929—62no—
112#926—31no—
113#926—31no—
114#926—61no—
115C2×C4⋊Dic3—62no—
116#924—62no—
117C2×Dic3⋊C4—62no—
118C2×C4×Dic3C2×D311yescharacteristic
119C2×#208C2×D311yescharacteristic
120#909—62no—
121#909—62no—
122C2×Dic12—61no—
123C2×#204—61no—
124#869—62no—
125#869—62no—
126C3×#104—62no—
127C3×#101—62no—
128#825—22no—
129#824—22no—
130#816—62no—
131#816—62no—
132#816—64no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—21no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3⋊Dic3—22no—
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—22no—
155C2×C3×Dic3—21no—
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—
167C32×C8—41no—
168C3×C3⋊C8—22no—
169C2×#137—91no—
170#536—91no—
171C2×C4⋊Q8—91no—
172C2×#104—31no—
173#419—91no—
174C2×#101—31no—
175#339—91no—
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×Dic3D1212yes—
201#235—21no—
202#235—21no—
203#235—21no—
204#235—21no—
205C2×D12D1211yescharacteristic
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×Dic6D1211yescharacteristic
232C3×M16—21no—
233C3×M16—21no—
234C3×M16—21no—
235C3×M16—21no—
236C3×M16—32no—
237C3×M16—41no—
238C3×M16—41no—
239C3×M16—61no—
240C2×C3×C8—22no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—61no—
244C3×C42—32no—
245C3×C42—61no—
246#217—64no—
247#217—61no—
248#217—61no—
249#217—121no—
250#216—64no—
251#214—64no—
252(C2×D3)⋊C4—64no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—62no—
256C4⋊Dic3—68no—
257Dic3⋊C4—68no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260C4×Dic3—21no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—121no—
264C4×Dic3#6712yes—
265#208—21no—
266#208#6712yes—
267C2×C3⋊C8—21no—
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#12011yescharacteristic
277C32×C4#12111yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12711yescharacteristic
280C3⋊Dic3—42no—
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×M16D3211yescharacteristic
294C4⋊Q8—182no—
295C4⋊Q8—182no—
296C4⋊Q8—181no—
297#124—181no—
298#123—182no—
299C22⋊Q8—182no—
300#117—91no—
301C2×C4⋊C4—182no—
302C2×C42—31no—
303#104—62no—
304#103—182no—
305#101—62no—
306C23×C3—21no—
307C23×C3—61no—
308C23×C3C2×D1211yescharacteristic
309C23×C3D3×D411yescharacteristic
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—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—64no—
328C2×C3×C4—62no—
329C2×C3×C4—61no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4#23511yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347#67—41no—
348#67—41no—
349C2×Dic3—24no—
350C2×Dic3—22no—
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—122no—
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—42no—
390C3×C8—41no—
391C3×C8—41no—
392C3×C8—62no—
393C3⋊C8—22no—
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—21no—
426M16—21no—
427M16—32no—
428M16—61no—
429C2×C8—21no—
430C2×C8—61no—
431C4⋊C4—92no—
432C4⋊C4—188no—
433C4⋊C4—184no—
434C22⋊C4—184no—
435C22⋊C4—181no—
436C42—32no—
437C42—61no—
438C42—181no—
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#88211yescharacteristic
450C22×C3#88411yescharacteristic
451C22×C3#93011yescharacteristic
452C22×C3#93711yescharacteristic
453C2×D3—41no—
454C2×D3—42no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—64no—
460C3×C4—122no—
461C3×C4—121no—
462C3×C4#88211yescharacteristic
463C3×C4#88411yescharacteristic
464C3×C4#88411yescharacteristic
465C3×C4#88411yescharacteristic
466C3×C4#93011yescharacteristic
467C3×C4#93711yescharacteristic
468C3×C4#94011yescharacteristic
469C3×C4#94011yescharacteristic
470Dic3—24no—
471Dic3—41no—
472Dic3—42no—
473Dic3—124no—
474Dic3—122no—
475Dic3—122no—
476Dic3—122no—
477Dic3—122no—
478Dic3—242no—
479C32#200511yescharacteristic, complemented, Sylow
480C23—61no—
481C23D3×D1211yescharacteristic
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—64no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—61no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—361no—
507C2×C4—361no—
508C2×C4#379811yescharacteristic
509C2×C4D3×D1211yescharacteristic
510C2×C4#380211yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4D3×#6711yescharacteristic
513C2×C4#381111yescharacteristic
514C8—41no—
515C8—62no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3—241no—
525C2×C3#475212yes—
526C2×C3#482612yes—
527C2×C3#496011yescharacteristic
528C2×C3#496011yescharacteristic
529D3—81no—
530C22—22no—
531C22—122no—
532C22—121no—
533C22#6390611yescharacteristic
534C22#6392211yescharacteristic
535C22#6392311yescharacteristic
536C4—64no—
537C4—122no—
538C4—121no—
539C4—362no—
540C4—362no—
541C4#6390611yescharacteristic
542C4#6391211yescharacteristic
543C4#6392211yescharacteristic
544C4#6397911yescharacteristic
545C3—21no—
546C3#7011911yescharacteristic, complemented
547C3#7038911yescharacteristic, complemented
548C2—21no—
549C2—21no—
550C2—241no—
551C2#1059102112yes—
552C2#1059139311yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenterC2×M16D32
hypocenterC32#2005
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#63866C2semidirect
4. #10592819C2semidirect
6. C2×C3×#824C2semidirect
7. #10589162C2semidirect
40. C2×#824D3semidirect
479. C32#2005semidirect
546. C3#70119semidirect
547. C3#70389semidirect

Maximal subgroups

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

subgroupindex
C2×#638662
#105948552
C2×#638312
#105928192
C2×C3×#8252
C2×C3×#8242
#105891622
#703893
#701193