Finite Group Databasebeta

← #11901972

Subgroups — #11901972

Order 1152.

3480 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2#10596275C212yesmaximal, complemented
3#10596262C212yesmaximal, complemented
4C2×C4×#638C212yesmaximal, complemented
5#10596035C214yesmaximal, complemented
6#10596031C214yesmaximal, complemented
7#10596018C214yesmaximal, complemented
8#10596009C214yesmaximal, complemented
9#10595986C212yesmaximal, complemented
10#10595965C212yesmaximal, complemented
11#10595964C211yesmaximal, characteristic, complemented
12#10595954C211yesmaximal, characteristic, complemented
13#10595950C212yesmaximal, complemented
14#85776—34nomaximal
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C23×C32×C4C2211yescharacteristic, complemented
18C22×#638C2212yes—
19C2×#3828C2212yescomplemented
20C22×C4×C3⋊D3C2212yescomplemented
21C32×C4×D4C2214yescomplemented
22C32×C4×D4C2214yescomplemented
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic, complemented
26C2×C32×C42C2211yescharacteristic, complemented
27#64162C2214yescomplemented
28C2×#3757C2212yes—
29#64148C2214yes—
30#64148C2214yes—
31#64146C2214yescomplemented
32#64144C2214yescomplemented
33#64139C2212yes—
34#64139C2212yes—
35#64139C2212yescomplemented
36#64138C2214yescomplemented
37#64138C2214yescomplemented
38C4×#638C2214yescomplemented
39C4×#638C2214yescomplemented
40C4×#638C2214yescomplemented
41C4×#638C2214yescomplemented
42C4×#638C2214yescomplemented
43C2×#3752C2212yescomplemented
44#64135C2212yescomplemented
45#64133C2212yescomplemented
46#64133C2212yescomplemented
47#64133C2212yescomplemented
48C2×#3750C2212yescomplemented
49C2×C4×C3⋊Dic3C2212yescomplemented
50#64107C2214yescomplemented
51#64105C2214yescomplemented
52#64103C2214yescomplemented
53#64098C2214yescomplemented
54#64095C2214yescomplemented
55#64094C2214yescomplemented
56#64093C2214yescomplemented
57#64092C2214yescomplemented
58#64091C2214yescomplemented
59#64088C2214yescomplemented
60#64087C2214yescomplemented
61#64087C2214yescomplemented
62#64085C2214yescomplemented
63#64084C2212yescomplemented
64C4×C4⋊(C3⋊D3)C2212yescomplemented
65#64081C2214yescomplemented
66#64079C2212yescomplemented
67C4×#634C2212yescomplemented
68C2×C3×C4×D4D314yescomplemented
69#5804—38no—
70#5791—38no—
71C2×C4×#67—38no—
72#5564—316no—
73#5560—316no—
74#5547—316no—
75#5538—316no—
76#5515—38no—
77#5494—38no—
78#5493—34no—
79#5483—34no—
80#5479—38no—
81C24×C32C2311yescharacteristic
82C24×C32C2311yescharacteristic
83C23×C3⋊D3C2312yes—
84C2×C32×D4—24no—
85C2×C32×D4C2314yes—
86C22×C32×C4—42no—
87C22×C32×C4—42no—
88C22×C32×C4C2312yes—
89C22×C32×C4C2312yes—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2312yes—
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2312yes—
96C22×C32×C4C2311yescharacteristic
97C2×#638—28no—
98C2×#638C2314yes—
99C2×#638C2314yes—
100C2×#638C2314yes—
101C2×#638C2314yes—
102C22×C3⋊Dic3C2312yes—
103C22×C3⋊Dic3C2312yes—
104C22×C3⋊Dic3C2312yes—
105#3828—44no—
106C2×C4⋊(C3⋊D3)C2312yes—
107C2×C4⋊(C3⋊D3)C2312yes—
108C2×C4×C3⋊D3—44no—
109C2×C4×C3⋊D3C2314yes—
110C2×C4×C3⋊D3C2314yes—
111C2×#634C2312yes—
112C2×#634C2312yes—
113C32×C4⋊C4C2314yes—
114C32×C22⋊C4C2314yes—
115C32×C22⋊C4C2314yes—
116C32×C42C2312yes—
117C32×C42C2312yes—
118#3757C2314yes—
119#3757C2314yes—
120#3757C2314yes—
121#3757C2314yes—
122#3752C2314yes—
123#3752C2314yes—
124#3752C2314yes—
125#3752C2314yes—
126#3752C2314yes—
127#3752C2314yes—
128C4⋊(C3⋊Dic3)C2312yes—
129C4⋊(C3⋊Dic3)C2312yes—
130C4⋊(C3⋊Dic3)C2312yes—
131C4⋊(C3⋊Dic3)C2312yes—
132#3750C2314yes—
133#3750C2314yes—
134#3750C2314yes—
135#3750C2314yes—
136#3750C2314yes—
137#3750C2314yes—
138C4×C3⋊Dic3C2314yes—
139C4×C3⋊Dic3C2314yes—
140#3459—91noSylow
141C22×C3×D4C2×D314yes—
142C23×C3×C4C2×D314yes—
143C23×C3×C4C2×D314yescomplemented
144C22×#67—38no—
145C2×#235—38no—
146C22×C4×D3—38no—
147C3×C4×D4C2×D3116yescomplemented
148C3×C4×D4C2×D3116yescomplemented
149C2×C3×C4⋊C4C2×D314yescomplemented
150C2×C3×C22⋊C4C2×D314yes—
151C2×C3×C22⋊C4C2×D314yescomplemented
152C2×C3×C42C2×D314yescomplemented
153#953—316no—
154C2×#217—38no—
155#939—316no—
156#939—316no—
157#937—316no—
158#935—316no—
159#930—38no—
160#930—38no—
161#930—38no—
162#929—316no—
163#929—316no—
164C4×#67—316no—
165C4×#67—316no—
166C4×#67—316no—
167C4×#67—316no—
168C4×#67—316no—
169C2×(C2×D3)⋊C4—38no—
170#926—38no—
171#924—38no—
172#924—38no—
173#924—38no—
174C2×Dic3⋊C4—38no—
175C2×C4×Dic3—38no—
176#898—316no—
177#896—316no—
178#894—316no—
179#889—316no—
180#886—316no—
181#885—316no—
182#884—316no—
183#883—316no—
184#882—316no—
185#879—316no—
186#878—316no—
187#878—316no—
188#876—316no—
189#875—38no—
190C4×D12—38no—
191#872—316no—
192#870—38no—
193C4×Dic6—38no—
194C23×C32—22no—
195C23×C32—41no—
196C23×C32—41no—
197C23×C32—41no—
198C23×C32—41no—
199C23×C32#4114yescomplemented
200C23×C32C2412yes—
201C23×C32C2412yes—
202C23×C32C2411yescharacteristic
203C22×C3⋊D3—24no—
204C22×C3⋊D3—42no—
205C22×C3⋊D3—42no—
206C22×C3⋊D3C2414yes—
207C32×D4—28no—
208C2×C32×C4—22no—
209C2×C32×C4—24no—
210C2×C32×C4—24no—
211C2×C32×C4—22no—
212C2×C32×C4—41no—
213C2×C32×C4—42no—
214C2×C32×C4—41no—
215C2×C32×C4—42no—
216C2×C32×C4—41no—
217C2×C32×C4C2412yes—
218C2×C32×C4C2412yes—
219C2×C32×C4C2411yescharacteristic
220C2×C32×C4C2412yes—
221C2×C32×C4C2412yes—
222C2×C32×C4C2411yescharacteristic
223#638—28no—
224#638—28no—
225#638—44no—
226#638—44no—
227C2×C3⋊Dic3—24no—
228C2×C3⋊Dic3—42no—
229C2×C3⋊Dic3—42no—
230C2×C3⋊Dic3C2414yes—
231C2×C3⋊Dic3C2414yes—
232C2×C3⋊Dic3C2414yes—
233C4⋊(C3⋊D3)—42no—
234C4⋊(C3⋊D3)—42no—
235C4×C3⋊D3—28no—
236C4×C3⋊D3—44no—
237#634—42no—
238#634—42no—
239#543—91no—
240#539—94no—
241#539—92no—
242#538—94no—
243#538—92no—
244#534—92no—
245#534—91no—
246#529—94no—
247#529—92no—
248#525—92no—
249#525—94no—
250C2×C4×D4—92no—
251C2×C4×D4C3⋊D311yescharacteristic, complemented
252C24×C3C22×D314yes—
253C24×C3C22×D314yes—
254C23×D3—38no—
255C2×C3×D4—216no—
256C2×C3×D4C22×D3116yes—
257C22×C3×C4—48no—
258C22×C3×C4—48no—
259C22×C3×C4C22×D318yes—
260C22×C3×C4C22×D318yes—
261C22×C3×C4C22×D314yes—
262C22×C3×C4C22×D314yes—
263C22×C3×C4C22×D318yes—
264C22×C3×C4C22×D314yes—
265C22×C3×C4C22×D314yes—
266C22×C3×C4C22×D318yes—
267C22×C3×C4C22×D314yes—
268C2×#67—316no—
269C2×#67—316no—
270C2×#67—316no—
271C2×#67—316no—
272C2×#67—632no—
273C22×Dic3—38no—
274C22×Dic3—38no—
275C22×Dic3—38no—
276#235—1216no—
277C2×D12—38no—
278C2×D12—38no—
279C2×C4×D3—316no—
280C2×C4×D3—316no—
281C2×C4×D3—1216no—
282C2×Dic6—38no—
283C2×Dic6—38no—
284C3×C4⋊C4C22×D3116yes—
285C3×C22⋊C4C22×D3116yes—
286C3×C22⋊C4C22×D3116yes—
287C3×C42C22×D318yes—
288C3×C42C22×D318yes—
289#217—316no—
290#217—316no—
291#217—316no—
292#217—316no—
293(C2×D3)⋊C4—316no—
294(C2×D3)⋊C4—316no—
295(C2×D3)⋊C4—316no—
296(C2×D3)⋊C4—316no—
297(C2×D3)⋊C4—316no—
298(C2×D3)⋊C4—316no—
299C4⋊Dic3—38no—
300C4⋊Dic3—38no—
301C4⋊Dic3—38no—
302C4⋊Dic3—38no—
303Dic3⋊C4—316no—
304Dic3⋊C4—316no—
305Dic3⋊C4—316no—
306Dic3⋊C4—316no—
307Dic3⋊C4—316no—
308Dic3⋊C4—316no—
309C4×Dic3—316no—
310C4×Dic3—316no—
311C22×C32—22no—
312C22×C32—21no—
313C22×C32—22no—
314C22×C32—21no—
315C22×C32—22no—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—44no—
319C22×C32—44no—
320C22×C32C2×#4114yes—
321C22×C32C2×#4112yes—
322C22×C32C2511yescharacteristic
323C2×C3⋊D3—24no—
324C2×C3⋊D3—24no—
325C2×C3⋊D3—24no—
326C2×C3⋊D3—48no—
327C32×C4—22no—
328C32×C4—22no—
329C32×C4—22no—
330C32×C4—21no—
331C32×C4—22no—
332C32×C4H(5,𝔽2)12yes—
333C3⋊Dic3—24no—
334C3⋊Dic3—24no—
335C3⋊Dic3—24no—
336C2×#41—92no—
337C22×D4—92no—
338C22×D4C2×C3⋊D311yescharacteristic
339C23×C4—92no—
340C23×C4C2×C3⋊D311yescharacteristic
341C23×C4C2×C3⋊D311yescharacteristic, complemented
342#126—94no—
343#126—94no—
344#126—94no—
345#125—94no—
346#125—92no—
347#124—94no—
348#124—92no—
349#123—94no—
350#123—94no—
351#123—94no—
352#123—94no—
353#123—94no—
354#123—94no—
355C22⋊Q8—92no—
356C22⋊Q8—92no—
357C22⋊Q8—92no—
358C22⋊Q8—94no—
359C22⋊Q8—94no—
360C22⋊Q8—94no—
361#121—94no—
362#121—94no—
363#121—92no—
364#121—92no—
365#121—92no—
366#121—94no—
367#120—94no—
368#120—94no—
369#120—94no—
370C4×Q8—92no—
371C4×D4—94no—
372C4×D4—94no—
373C4×D4—94no—
374C4×D4—94no—
375C4×D4—94no—
376C4×D4—92no—
377C4×D4C2×C3⋊D314yescomplemented
378C4×D4C2×C3⋊D314yescomplemented
379#117—92no—
380#117—94no—
381C2×C4⋊C4—92no—
382C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
383C2×C22⋊C4—92no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4C2×C3⋊D311yescharacteristic
386C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
387C2×C42—92no—
388C2×C42C2×C3⋊D311yescharacteristic, complemented
389C23×C3—28no—
390C23×C3—44no—
391C23×C3—44no—
392C23×C3—44no—
393C23×C3—44no—
394C23×C3#235116yescomplemented
395C23×C3C23×D318yes—
396C23×C3C23×D314yes—
397C23×C3C23×D318yes—
398C22×D3—316no—
399C22×D3—616no—
400C22×D3—128no—
401C22×D3—128no—
402C3×D4—232no—
403C2×C3×C4—28no—
404C2×C3×C4—216no—
405C2×C3×C4—216no—
406C2×C3×C4—28no—
407C2×C3×C4—44no—
408C2×C3×C4—48no—
409C2×C3×C4—44no—
410C2×C3×C4—48no—
411C2×C3×C4—44no—
412C2×C3×C4C23×D318yes—
413C2×C3×C4C23×D318yes—
414C2×C3×C4C23×D314yes—
415C2×C3×C4C23×D318yes—
416C2×C3×C4C23×D318yes—
417C2×C3×C4C23×D314yes—
418#67—632no—
419#67—632no—
420#67—1216no—
421#67—1216no—
422C2×Dic3—316no—
423C2×Dic3—316no—
424C2×Dic3—316no—
425C2×Dic3—616no—
426C2×Dic3—128no—
427C2×Dic3—128no—
428D12—128no—
429D12—128no—
430C4×D3—632no—
431C4×D3—1216no—
432Dic6—128no—
433Dic6—128no—
434C2×C32—24no—
435C2×C32—22no—
436C2×C32—42no—
437C2×C32C22×#4111yescharacteristic
438C2×C32C2×H(5,𝔽2)11yescharacteristic
439C2×C32#58511yescharacteristic
440C3⋊D3—44no—
441C24—92no—
442C24C22×C3⋊D311yescharacteristic
443C24C22×C3⋊D311yescharacteristic
444#41—364no—
445C2×Q8—92no—
446C2×Q8—92no—
447C2×D4—24no—
448C2×D4—94no—
449C2×D4—94no—
450C2×D4—94no—
451C2×D4—94no—
452C2×D4—92no—
453C2×D4—92no—
454C2×D4—188no—
455C2×D4C22×C3⋊D314yes—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—92no—
459C22×C4—92no—
460C22×C4—92no—
461C22×C4—94no—
462C22×C4—94no—
463C22×C4—364no—
464C22×C4C22×C3⋊D311yescharacteristic
465C22×C4C22×C3⋊D312yes—
466C22×C4C22×C3⋊D311yescharacteristic
467C22×C4C22×C3⋊D312yes—
468C22×C4C22×C3⋊D311yescharacteristic
469C22×C4C22×C3⋊D312yes—
470C22×C4C22×C3⋊D311yescharacteristic
471C22×C4C22×C3⋊D311yescharacteristic
472C22×C4C22×C3⋊D312yes—
473C4⋊C4—94no—
474C4⋊C4—94no—
475C4⋊C4—94no—
476C4⋊C4—92no—
477C4⋊C4—94no—
478C4⋊C4—92no—
479C4⋊C4—94no—
480C4⋊C4—92no—
481C4⋊C4—94no—
482C4⋊C4—92no—
483C4⋊C4C22×C3⋊D314yes—
484C22⋊C4—94no—
485C22⋊C4—94no—
486C22⋊C4—94no—
487C22⋊C4—94no—
488C22⋊C4—94no—
489C22⋊C4—94no—
490C22⋊C4—94no—
491C22⋊C4—94no—
492C22⋊C4—94no—
493C22⋊C4—94no—
494C22⋊C4C22×C3⋊D314yes—
495C22⋊C4C22×C3⋊D314yes—
496C42—94no—
497C42—94no—
498C42C22×C3⋊D312yes—
499C42C22×C3⋊D312yes—
500C22×C3—28no—
501C22×C3—24no—
502C22×C3—28no—
503C22×C3—24no—
504C22×C3—28no—
505C22×C3—28no—
506C22×C3—28no—
507C22×C3—416no—
508C22×C3—416no—
509C22×C3C2×#235116yes—
510C22×C3C2×#23518yes—
511C22×C3C24×D314yes—
512C2×D3—616no—
513C2×D3—616no—
514C2×D3—616no—
515C2×D3—1232no—
516C3×C4—28no—
517C3×C4—28no—
518C3×C4—28no—
519C3×C4—24no—
520C3×C4—28no—
521C3×C4#100418yes—
522Dic3—616no—
523Dic3—616no—
524Dic3—616no—
525C32#345911yescharacteristic, complemented, Sylow
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—94no—
532C23—184no—
533C23—362no—
534C23—362no—
535C23#382814yescomplemented
536C23C23×C3⋊D312yes—
537C23C23×C3⋊D311yescharacteristic
538C23C23×C3⋊D312yes—
539Q8—362no—
540Q8—362no—
541D4—28no—
542D4—188no—
543D4—188no—
544D4—362no—
545D4—362no—
546D4—364no—
547D4—364no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—94no—
558C2×C4—94no—
559C2×C4—94no—
560C2×C4—184no—
561C2×C4—188no—
562C2×C4—364no—
563C2×C4—362no—
564C2×C4—362no—
565C2×C4C23×C3⋊D312yes—
566C2×C4C23×C3⋊D312yes—
567C2×C4C23×C3⋊D311yescharacteristic
568C2×C4C23×C3⋊D312yes—
569C2×C4C23×C3⋊D312yes—
570C2×C4C23×C3⋊D311yescharacteristic
571C2×C3—216no—
572C2×C3—28no—
573C2×C3—48no—
574C2×C3C22×#23514yes—
575C2×C3C2×#100414yes—
576C2×C3#596414yes—
577D3—1216no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—44no—
586C22—44no—
587C22—184no—
588C22—184no—
589C22—184no—
590C22—368no—
591C22C2×#382812yes—
592C22C2×#382814yes—
593C22C24×C3⋊D311yescharacteristic
594C4—22no—
595C4—21no—
596C4—22no—
597C4—22no—
598C4—22no—
599C4—184no—
600C4—184no—
601C4—184no—
602C4#6436112yes—
603C3#8577614yescomplemented
604C2—22no—
605C2—24no—
606C2—42no—
607C2—364no—
608C2C22×#382811yescharacteristic
609C2C2×#6436111yescharacteristic
610C2#1059675611yescharacteristic
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×C4×D4C2
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#3459
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. #10596275C2semidirect
3. #10596262C2semidirect
4. C2×C4×#638C2semidirect
5. #10596035C2semidirect
6. #10596031C2semidirect
7. #10596018C2semidirect
8. #10596009C2semidirect
9. #10595986C2semidirect
10. #10595965C2semidirect
11. #10595964C2semidirect
12. #10595954C2semidirect
13. #10595950C2semidirect
17. C23×C32×C4C22semidirect
19. C2×#3828C22semidirect
20. C22×C4×C3⋊D3C22semidirect
21. C32×C4×D4C22semidirect
22. C32×C4×D4C22semidirect
23. C2×C32×C4⋊C4C22semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×C32×C42C22semidirect
27. #64162C22semidirect
31. #64146C22semidirect
32. #64144C22semidirect
35. #64139C22semidirect
36. #64138C22semidirect
37. #64138C22semidirect
38. C4×#638C22semidirect
39. C4×#638C22semidirect
40. C4×#638C22semidirect
41. C4×#638C22semidirect
42. C4×#638C22semidirect
43. C2×#3752C22semidirect
44. #64135C22semidirect
45. #64133C22semidirect
46. #64133C22semidirect
47. #64133C22semidirect
48. C2×#3750C22semidirect
49. C2×C4×C3⋊Dic3C22semidirect
50. #64107C22semidirect
51. #64105C22semidirect
52. #64103C22semidirect
53. #64098C22semidirect
54. #64095C22semidirect
55. #64094C22semidirect
56. #64093C22semidirect
57. #64092C22semidirect
58. #64091C22semidirect
59. #64088C22semidirect
60. #64087C22semidirect
61. #64087C22semidirect
62. #64085C22semidirect
63. #64084C22semidirect
64. C4×C4⋊(C3⋊D3)C22semidirect
65. #64081C22semidirect
66. #64079C22semidirect
67. C4×#634C22semidirect
68. C2×C3×C4×D4D3semidirect
143. C23×C3×C4C2×D3semidirect
147. C3×C4×D4C2×D3semidirect
148. C3×C4×D4C2×D3semidirect
149. C2×C3×C4⋊C4C2×D3semidirect
151. C2×C3×C22⋊C4C2×D3semidirect
152. C2×C3×C42C2×D3semidirect
199. C23×C32#41semidirect
251. C2×C4×D4C3⋊D3semidirect
341. C23×C4C2×C3⋊D3semidirect
377. C4×D4C2×C3⋊D3semidirect
378. C4×D4C2×C3⋊D3semidirect
382. C2×C4⋊C4C2×C3⋊D3semidirect
386. C2×C22⋊C4C2×C3⋊D3semidirect
388. C2×C42C2×C3⋊D3semidirect
394. C23×C3#235semidirect
525. C32#3459semidirect
535. C23#3828semidirect
603. C3#85776semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
#105962752
#105962622
C2×C4×#6382
#105960352
#105960312
#105960182
#105960092
#105959862
#105959652
#105959642
#105959542
#105959502
#857763