Finite Group Databasebeta

← #11884073

Subgroups — #11884073

Order 1152.

1482 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64124C211yesmaximal, characteristic, complemented
2C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
3Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4#10596025C211yesmaximal, characteristic
5C32×#440C211yesmaximal, characteristic, complemented
6#10592727C211yesmaximal, characteristic, complemented
7#10592718C211yesmaximal, characteristic, complemented
8#10592586C211yesmaximal, characteristic, complemented
9#10592585C211yesmaximal, characteristic, complemented
10#10592508C211yesmaximal, characteristic, complemented
11#10592505C211yesmaximal, characteristic, complemented
12#10592482C211yesmaximal, characteristic, complemented
13#10592475C211yesmaximal, characteristic, complemented
14#10592414C211yesmaximal, characteristic, complemented
15#10592405C211yesmaximal, characteristic, complemented
16#79795—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×#3830C2211yescharacteristic
20C2×D4×C3⋊D3C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24C2×#3756C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27C2×#3754C2211yescharacteristic
28#64139—21no—
29C2×#3752—21no—
30#64124—24no—
31SD16×C3⋊D3—24no—
32C2×#3746C2211yescharacteristic, complemented
33C2×#3746C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic
35C2×#3744C2211yescharacteristic
36C2×#3743C2211yescharacteristic, complemented
37C2×C8×C3⋊D3C2211yescharacteristic
38#64106—21no—
39#64106—21no—
40#64106C2211yescharacteristic
41#64106C2211yescharacteristic
42#64106C2211yescharacteristic, complemented
43#64104C2211yescharacteristic
44#64095—21no—
45#64091—21no—
46#64084C2211yescharacteristic
47C4×C4⋊(C3⋊D3)—21no—
48C4×C4⋊(C3⋊D3)C2211yescharacteristic
49#64078—21no—
50#64078C2211yescharacteristic, complemented
51C32×#107C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic
54C32×#97C2211yescharacteristic, complemented
55#63647C2211yescharacteristic
56#63647C2211yescharacteristic, complemented
57#63637C2211yescharacteristic, complemented
58#63637C2211yescharacteristic, complemented
59#63637C2211yescharacteristic, complemented
60#63636C2211yescharacteristic
61C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
62C2×#915—34no—
63C2×D3×SD16—34no—
64Q8×D12—34no—
65#5554—34no—
66C3×#440D314yescomplemented
67#5028—34no—
68#5019—34no—
69#4887—34no—
70#4886—34no—
71#4809—34no—
72#4806—34no—
73#4783—34no—
74#4776—34no—
75#4715—34no—
76#4706—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4C2311yescharacteristic
80C22×C32×C4—21no—
81C2×#638—21no—
82C2×#638—21no—
83C22×C3⋊Dic3—21no—
84Q8×C3⋊D3—22no—
85Q8×C3⋊D3—22no—
86Q8×C3⋊D3—41no—
87Q8×C3⋊D3—41no—
88#3830—22no—
89#3830—41no—
90D4×C3⋊D3—22no—
91D4×C3⋊D3—41no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)D411yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634—21no—
100C2×#634—21no—
101C2×#634C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C32×SD16D414yescomplemented
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C42—21no—
112C32×C42C2311yescharacteristic
113#3756—22no—
114#3755—22no—
115#3754—22no—
116#3754—22no—
117#3752—21no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752—21no—
122#3752—21no—
123#3752D411yescharacteristic
124#3752D411yescharacteristic
125C4⋊(C3⋊Dic3)—21no—
126C4⋊(C3⋊Dic3)—21no—
127C4⋊(C3⋊Dic3)—21no—
128C4⋊(C3⋊Dic3)—21no—
129C4⋊(C3⋊Dic3)—21no—
130C4⋊(C3⋊Dic3)D411yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3746—22no—
134#3746—41no—
135#3744—22no—
136#3744—41no—
137#3743—22no—
138C8×C3⋊D3—22no—
139#3266—91noSylow
140C2×D3×Q8—34no—
141C2×D3×Q8—34no—
142C2×#237—34no—
143C2×D3×D4—34no—
144C2×C3×SD16C2×D314yes—
145C3×C4×Q8C2×D314yescomplemented
146C3×C4×D4C2×D314yes—
147C2×#216—34no—
148C2×#215—34no—
149C2×#214—34no—
150C2×#214—34no—
151#930—64no—
152C2×(C2×D3)⋊C4—64no—
153#915—616no—
154D3×SD16—616no—
155C2×Dic12—34no—
156C2×Dic12—34no—
157C2×#204—34no—
158C2×#204—34no—
159C2×ΓL(1,𝔽25)—34no—
160C2×D3×C8—34no—
161#897—34no—
162#897—34no—
163#897—34no—
164#897—64no—
165#897—64no—
166#895—34no—
167#886—64no—
168#882—64no—
169#875—34no—
170C4×D12—34no—
171C4×D12—64no—
172#869—34no—
173#869—64no—
174C3×#107C2×D314yescomplemented
175C3×#103C2×D314yescomplemented
176C3×#102C2×D314yes—
177C3×#97C2×D314yescomplemented
178(C2×D3)⋊C8—34no—
179(C2×D3)⋊C8—34no—
180#810—34no—
181#810—34no—
182#810—34no—
183#809—34no—
184C4⋊(C3⋊C8)—34no—
185C23×C32—21no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—42no—
188C22×C3⋊D3—42no—
189C22×C3⋊D3—81no—
190C22×C3⋊D3C2×D411yescharacteristic
191C22×C3⋊D3C2×D411yescharacteristic
192C32×Q8—21no—
193C32×Q8C2×D412yes—
194C32×D4—21no—
195C32×D4C2×D412yes—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—81no—
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2×D411yescharacteristic
202C2×C32×C4C2411yescharacteristic
203#638—42no—
204#638—42no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—42no—
209C2×C3⋊Dic3C2×D411yescharacteristic
210C2×C3⋊Dic3C2×D411yescharacteristic
211C4⋊(C3⋊D3)—22no—
212C4⋊(C3⋊D3)—21no—
213C4⋊(C3⋊D3)—21no—
214C4⋊(C3⋊D3)—81no—
215C4×C3⋊D3—21no—
216C4×C3⋊D3—21no—
217C4×C3⋊D3—21no—
218C4×C3⋊D3—21no—
219C4×C3⋊D3—42no—
220C4×C3⋊D3—42no—
221#634—21no—
222#634—21no—
223#634—21no—
224#634—21no—
225#634—21no—
226#634—21no—
227#634—42no—
228#634—42no—
229C32×C8—21no—
230C32×C8C2×D412yes—
231C3⋊(C3⋊C8)—21no—
232C3⋊(C3⋊C8)—21no—
233C2×#137—91no—
234C22×SD16—91no—
235D4×Q8—91no—
236#546—91no—
237#497—91no—
238#468—91no—
239#467—91no—
240#464—91no—
241#461—91no—
242#452—91no—
243#451—91no—
244#450—91no—
245#448—91no—
246#440C3⋊D311yescharacteristic, complemented
247#435—91no—
248C23×D3—64no—
249C2×C3×Q8C22×D314yes—
250C2×C3×D4C22×D314yes—
251C22×C3×C4—24no—
252C2×#67—64no—
253C2×#67—64no—
254C22×Dic3—64no—
255D3×Q8—68no—
256D3×Q8—68no—
257D3×Q8—124no—
258D3×Q8—124no—
259#237—68no—
260#237—124no—
261D3×D4—68no—
262D3×D4—124no—
263C2×D12—34no—
264C2×D12—34no—
265C2×D12—64no—
266C2×C4×D3—34no—
267C2×C4×D3—34no—
268C2×C4×D3—64no—
269C2×C4×D3—64no—
270C2×Dic6—34no—
271C2×Dic6—34no—
272C2×Dic6—34no—
273C2×Dic6—64no—
274C2×Dic6—64no—
275C3×SD16D12116yescomplemented
276C2×C3×C8C22×D314yes—
277C2×C3×C8C22×D314yes—
278C3×C4⋊C4—24no—
279C3×C4⋊C4C22×D314yes—
280C3×C4⋊C4C22×D314yes—
281C3×C22⋊C4—24no—
282C3×C42—24no—
283C3×C42C22×D314yes—
284#216—68no—
285#215—68no—
286#214—68no—
287#214—68no—
288(C2×D3)⋊C4—34no—
289(C2×D3)⋊C4—34no—
290(C2×D3)⋊C4—64no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296C4⋊Dic3—34no—
297C4⋊Dic3—64no—
298C4⋊Dic3—64no—
299C4⋊Dic3—64no—
300C4⋊Dic3—64no—
301C4⋊Dic3—64no—
302C2×C3⋊C8—34no—
303C2×C3⋊C8—34no—
304Dic12—68no—
305Dic12—124no—
306#204—68no—
307#204—124no—
308ΓL(1,𝔽25)—68no—
309D3×C8—68no—
310C22×C32—22no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32C22×D411yescharacteristic
314C2×C3⋊D3—21no—
315C2×C3⋊D3—21no—
316C2×C3⋊D3—21no—
317C2×C3⋊D3—21no—
318C2×C3⋊D3—21no—
319C2×C3⋊D3—41no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—84no—
323C2×C3⋊D3#13712yescomplemented
324C32×C4—22no—
325C32×C4—21no—
326C32×C4—21no—
327C32×C4—41no—
328C32×C4—41no—
329C32×C4C22×D411yescharacteristic
330C32×C4H(5,𝔽2)11yescharacteristic
331C3⋊Dic3—21no—
332C3⋊Dic3—21no—
333C3⋊Dic3—41no—
334C3⋊Dic3—41no—
335C3⋊Dic3—41no—
336C2×#41—91no—
337C22×Q8—91no—
338C22×Q8—91no—
339C22×D4—91no—
340#137—184no—
341C2×Q16—91no—
342C2×Q16—91no—
343C2×Q16—91no—
344C2×SD16—91no—
345C2×SD16—91no—
346C2×SD16—91no—
347C2×SD16—91no—
348C2×SD16—91no—
349C2×SD16—184no—
350C2×SD16C2×C3⋊D311yescharacteristic
351C2×M16—91no—
352C22×C8—91no—
353C4⋊Q8—91no—
354C4⋊Q8—181no—
355#124—91no—
356#123—181no—
357C22⋊Q8—91no—
358C22⋊Q8—91no—
359C22⋊Q8—91no—
360C22⋊Q8—181no—
361C22⋊Q8—181no—
362#121—91no—
363#121—181no—
364#120—181no—
365C4×Q8C2×C3⋊D311yescharacteristic, complemented
366C4×D4—91no—
367C4×D4—181no—
368C4×D4C2×C3⋊D311yescharacteristic
369C2×C22⋊C4—181no—
370#107C2×C3⋊D311yescharacteristic, complemented
371C4⋊C8—91no—
372#103—91no—
373#103—91no—
374#103—91no—
375#103C2×C3⋊D311yescharacteristic, complemented
376#102—91no—
377#102C2×C3⋊D311yescharacteristic
378C22⋊C8—91no—
379C22⋊C8—91no—
380#97C2×C3⋊D311yescharacteristic, complemented
381C23×C3—24no—
382C22×D3—34no—
383C22×D3—34no—
384C22×D3—64no—
385C22×D3—128no—
386C22×D3—128no—
387C22×D3—244no—
388C3×Q8—24no—
389C3×Q8C2×D1218yes—
390C3×D4—24no—
391C3×D4C2×D1218yes—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—84no—
396C2×C3×C4D3×D414yes—
397C2×C3×C4D3×D414yes—
398C2×C3×C4C23×D314yes—
399#67—128no—
400#67—128no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—64no—
404C2×Dic3—64no—
405C2×Dic3—64no—
406C2×Dic3—128no—
407D12—68no—
408D12—64no—
409D12—64no—
410D12—244no—
411C4×D3—64no—
412C4×D3—64no—
413C4×D3—64no—
414C4×D3—64no—
415C4×D3—128no—
416C4×D3—128no—
417Dic6—64no—
418Dic6—64no—
419Dic6—64no—
420Dic6—64no—
421Dic6—64no—
422Dic6—64no—
423Dic6—128no—
424Dic6—128no—
425C3×C8—24no—
426C3×C8C2×D1218yes—
427C3⋊C8—64no—
428C3⋊C8—64no—
429C2×C32—42no—
430C2×C32D4211yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C2×C32#57711yescharacteristic
433C3⋊D3—22no—
434C3⋊D3—41no—
435C3⋊D3—81no—
436C24—181no—
437#41—182no—
438#41—361no—
439C2×Q8—91no—
440C2×Q8—91no—
441C2×Q8—91no—
442C2×Q8—181no—
443C2×Q8—181no—
444C2×Q8—182no—
445C2×Q8—182no—
446C2×Q8—361no—
447C2×Q8—361no—
448C2×Q8C22×C3⋊D311yescharacteristic
449C2×D4—91no—
450C2×D4—91no—
451C2×D4—181no—
452C2×D4—181no—
453C2×D4—182no—
454C2×D4—181no—
455C2×D4—361no—
456C2×D4C22×C3⋊D311yescharacteristic
457C22×C4—21no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—181no—
461C22×C4—181no—
462C22×C4—181no—
463Q16—182no—
464Q16—182no—
465Q16—361no—
466SD16—182no—
467SD16—182no—
468SD16—182no—
469SD16—182no—
470SD16—361no—
471SD16C4⋊(C3⋊D3)14yescomplemented
472M16—182no—
473C2×C8—91no—
474C2×C8—91no—
475C2×C8—182no—
476C2×C8C22×C3⋊D311yescharacteristic
477C2×C8C22×C3⋊D311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—91no—
480C4⋊C4—181no—
481C4⋊C4—181no—
482C4⋊C4—181no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4C22×C3⋊D311yescharacteristic
486C4⋊C4C22×C3⋊D311yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—91no—
489C22⋊C4—91no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C22⋊C4—181no—
496C42—21no—
497C42C22×C3⋊D311yescharacteristic
498C22×C3—28no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3C2×D3×D414yes—
502C2×D3—38no—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—64no—
508C2×D3—124no—
509C2×D3—124no—
510C2×D3—124no—
511C2×D3—2416no—
512C3×C4—24no—
513C3×C4—24no—
514C3×C4—28no—
515C3×C4—44no—
516C3×C4—44no—
517C3×C4C22×D1214yes—
518C3×C4#100914yes—
519Dic3—64no—
520Dic3—64no—
521Dic3—124no—
522Dic3—124no—
523Dic3—124no—
524C32#326611yescharacteristic, complemented, Sylow
525C23—21no—
526C23—91no—
527C23—91no—
528C23—181no—
529C23—362no—
530C23—362no—
531C23—721no—
532Q8—21no—
533Q8—181no—
534Q8—181no—
535Q8—181no—
536Q8—181no—
537Q8—181no—
538Q8—181no—
539Q8—362no—
540Q8—362no—
541Q8C2×C4⋊(C3⋊D3)12yes—
542D4—21no—
543D4—182no—
544D4—181no—
545D4—181no—
546D4—362no—
547D4—362no—
548D4—721no—
549D4C2×C4⋊(C3⋊D3)12yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—81no—
554C2×C4—91no—
555C2×C4—91no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—362no—
564C2×C4—362no—
565C2×C4—362no—
566C2×C4D4×C3⋊D311yescharacteristic
567C2×C4D4×C3⋊D311yescharacteristic
568C2×C4C23×C3⋊D311yescharacteristic
569C8—21no—
570C8—181no—
571C8—181no—
572C8C2×C4⋊(C3⋊D3)12yes—
573C2×C3—48no—
574C2×C3D4×D1214yes—
575C2×C3#577514yes—
576C2×C3D3×#13714yes—
577D3—68no—
578D3—124no—
579D3—244no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—92no—
584C22—181no—
585C22—181no—
586C22—181no—
587C22—181no—
588C22—181no—
589C22—361no—
590C22—361no—
591C22—361no—
592C22—724no—
593C22C2×D4×C3⋊D311yescharacteristic
594C4—21no—
595C4—21no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—181no—
600C4—181no—
601C4—361no—
602C4—361no—
603C4—361no—
604C4C22×C4⋊(C3⋊D3)11yescharacteristic
605C4#6436611yescharacteristic
606C3#7979514yescomplemented
607C2—42no—
608C2—182no—
609C2—361no—
610C2—721no—
611C2D4×C4⋊(C3⋊D3)11yescharacteristic
612C2#1059624611yescharacteristic
613C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radical#10596025C2
hypercenter#440C3⋊D3
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#64124C2semidirect
2. C2×SD16×C3⋊D3C2semidirect
3. Q8×C4⋊(C3⋊D3)C2semidirect
5. C32×#440C2semidirect
6. #10592727C2semidirect
7. #10592718C2semidirect
8. #10592586C2semidirect
9. #10592585C2semidirect
10. #10592508C2semidirect
11. #10592505C2semidirect
12. #10592482C2semidirect
13. #10592475C2semidirect
14. #10592414C2semidirect
15. #10592405C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
22. C32×C4×Q8C22semidirect
24. C2×#3756C22semidirect
32. C2×#3746C22semidirect
33. C2×#3746C22semidirect
36. C2×#3743C22semidirect
42. #64106C22semidirect
50. #64078C22semidirect
51. C32×#107C22semidirect
52. C32×#103C22semidirect
54. C32×#97C22semidirect
56. #63647C22semidirect
57. #63637C22semidirect
58. #63637C22semidirect
59. #63637C22semidirect
61. C4⋊(C3⋊(C3⋊C8))C22semidirect
66. C3×#440D3semidirect
104. C32×SD16D4semidirect
145. C3×C4×Q8C2×D3semidirect
174. C3×#107C2×D3semidirect
175. C3×#103C2×D3semidirect
177. C3×#97C2×D3semidirect
246. #440C3⋊D3semidirect
275. C3×SD16D12semidirect
323. C2×C3⋊D3#137semidirect
365. C4×Q8C2×C3⋊D3semidirect
370. #107C2×C3⋊D3semidirect
375. #103C2×C3⋊D3semidirect
380. #97C2×C3⋊D3semidirect
471. SD16C4⋊(C3⋊D3)semidirect
524. C32#3266semidirect
606. C3#79795semidirect

Maximal subgroups

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

subgroupindex
C2×#641242
C2×SD16×C3⋊D32
Q8×C4⋊(C3⋊D3)2
#105960252
C32×#4402
#105927272
#105927182
#105925862
#105925852
#105925082
#105925052
#105924822
#105924752
#105924142
#105924052
#797953