Finite Group Databasebeta

← #11909349

Subgroups — #11909349

Order 1152.

2394 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596022C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic, complemented
3C3×#5542C211yesmaximal, characteristic, complemented
4#10595229C212yesmaximal, complemented
5#10595121C212yesmaximal, complemented
6#10595023C212yesmaximal, complemented
7#10594939C212yesmaximal, complemented
8#10594916C212yesmaximal, complemented
9D3×#924C212yesmaximal, complemented
10#10594536C212yesmaximal, complemented
11#10594361C212yesmaximal, complemented
12#10594093C214yesmaximal, complemented
13#10594090C214yesmaximal, complemented
14Dic6×D12C211yesmaximal, characteristic, complemented
15#10593896C211yesmaximal, characteristic, complemented
16#10593870C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86990—31nomaximal
19#85767—31nomaximal
20C2×#3828C2212yescomplemented
21C2×C3×D3×D4C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C2×#3796C2212yes—
24C2×D3×Dic6C2212yescomplemented
25C32×C4×D4C2211yescharacteristic
26#64147C2212yes—
27#64133C2212yescomplemented
28C4⋊C4×C3⋊D3C2212yescomplemented
29#64092C2214yescomplemented
30C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
31#64078C2211yescharacteristic, complemented
32C3×#936C2212yes—
33C3×D4×Dic3C2211yescharacteristic
34C3×C4×#67C2212yes—
35C3×#926C2212yescomplemented
36C3×#924C2212yescomplemented
37C3×#893C2211yescharacteristic
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×#887C2212yescomplemented
40C3×#67⋊C4C2212yes—
41C3×D3×C22⋊C4C2212yes—
42C3×#879C2214yescomplemented
43C3×C4×D12C2211yescharacteristic
44C3×C42×D3C2211yescharacteristic
45C3×#869C2211yescharacteristic, complemented
46C3×C4×Dic6C2211yescharacteristic, complemented
47#63977C2214yes—
48#63971C2214yes—
49#63969C2214yes—
50D3×#217C2214yes—
51#63966C2214yescomplemented
52#63964C2214yescomplemented
53#63956C2214yescomplemented
54#63953C2214yescomplemented
55#63918C2212yescomplemented
56#63909C2211yescharacteristic
57#63909C2212yescomplemented
58C4×#626C2214yes—
59C4×#626C2212yes—
60C4×#626C2214yescomplemented
61#63893C2214yescomplemented
62Dic3×D12C2212yes—
63#63890C2214yescomplemented
64D3×C4⋊Dic3C2212yescomplemented
65#63881C2214yescomplemented
66#63877C2214yescomplemented
67D3×Dic3⋊C4C2214yescomplemented
68#63874C2212yescomplemented
69#63871C2212yescomplemented
70#63869C2212yescomplemented
71#63869C2211yescharacteristic, complemented
72#63868C2212yescomplemented
73#63867C2214yescomplemented
74#63865C2214yescomplemented
75#63864C2211yescharacteristic, complemented
76#63857C2212yes—
77#63857C2212yescomplemented
78#63856C2212yes—
79#63856C2211yescharacteristic
80#63851C2214yes—
81#63850C2212yes—
82#63844C2212yescomplemented
83Dic3×Dic6C2212yescomplemented
84#63841C2212yes—
85C3×#556—31no—
86C2×C3×C4×D4—31no—
87#5806—32no—
88#5791—32no—
89C2×#924—32no—
90#5728—31no—
91#5726—31no—
92#5707—34no—
93#5705—34no—
94#5682—32no—
95#5676—32no—
96#5633—32no—
97D3×C22⋊Q8—32no—
98#5580—31no—
99#5579—32no—
100Q8×D12—31no—
101#5574—32no—
102#5564—34no—
103#5561—32no—
104#5555—31no—
105#5552—32no—
106#5551—31no—
107#5551—31no—
108#5551—61no—
109#5546—32no—
110C4×D3×D4D311yescharacteristic, complemented
111#5542D311yescharacteristic, complemented
112#5541—32no—
113D4×Dic6—31no—
114#5529—32no—
115#5524—32no—
116#5511—32no—
117#5495—34no—
118#5479—31no—
119#5470—31no—
120C23×C3×D3C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#638C2314yes—
124#3828—44no—
125C2×C4⋊(C3⋊D3)C2311yescharacteristic
126C2×C4×C3⋊D3C2312yes—
127C2×C4×C3⋊D3C2314yes—
128C2×#634C2312yes—
129C2×C3×#67C2312yes—
130C22×C3×Dic3C2312yes—
131C3×D3×D4—24no—
132C2×C3×D12C2311yescharacteristic
133C2×C3×C4×D3—44no—
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2312yes—
140C2×C3×Dic6C2312yes—
141C2×C3×Dic6C2311yescharacteristic
142C2×#627C2314yes—
143C2×#626C2314yes—
144C2×#626C2312yes—
145C2×D3×Dic3C2314yes—
146C2×D3×Dic3C2314yes—
147#3796—28no—
148D3×Dic6—44no—
149C32×C4⋊C4C2311yescharacteristic
150C32×C22⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152#3757C2314yes—
153#3752C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2312yes—
156C4⋊(C3⋊Dic3)C2311yescharacteristic
157#3750C2314yes—
158C3×#217C2314yes—
159C3×#217C2314yes—
160C3×#217C2312yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2312yes—
170C3×C4×Dic3C2314yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2312yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2311yescharacteristic
175#3724C2314yes—
176#3724C2312yes—
177#3724C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182#3722C2312yes—
183#3722C2312yes—
184#3722C2314yes—
185#3722C2312yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2312yes—
188(C2×D3)⋊Dic3C2314yes—
189Dic32C2314yes—
190#3520—91noSylow
191C22×C3×D4—31no—
192C23×C3×C4—32no—
193C2×#239—32no—
194C2×D3×Q8—32no—
195C2×#237—32no—
196C2×D3×D4C2×D311yescharacteristic
197C2×#235—32no—
198C2×#235—32no—
199C2×#235—62no—
200C22×C4×D3C2×D312yes—
201C22×Dic6—32no—
202C3×C4⋊Q8—31no—
203C3×#126—34no—
204C3×#124—32no—
205C3×C22⋊Q8—32no—
206C3×C4×Q8—32no—
207C3×C4×Q8—31no—
208C3×C4×D4—21no—
209C3×C4×D4—31no—
210C3×C4×D4—32no—
211C3×C4×D4—31no—
212C3×C4×D4—32no—
213C3×C4×D4—31no—
214C3×C4×D4C2×D311yescharacteristic
215C3×C4×D4C2×D311yescharacteristic
216C3×#117—32no—
217C2×C3×C4⋊C4—31no—
218C2×C3×C22⋊C4—32no—
219C2×C3×C42—31no—
220#953—34no—
221C2×#217—34no—
222#947—31no—
223#946—32no—
224#946—31no—
225#946—32no—
226Q8×Dic3—32no—
227#939—34no—
228#938—32no—
229#938—32no—
230#938—62no—
231#936C2×D312yes—
232#935—34no—
233D4×Dic3—32no—
234D4×Dic3C2×D311yescharacteristic
235#930—31no—
236#930—32no—
237#929—34no—
238#929—32no—
239C4×#67—32no—
240C4×#67—34no—
241C4×#67—34no—
242C4×#67C2×D312yes—
243#926—32no—
244#926C2×D312yescomplemented
245C2×C4⋊Dic3—32no—
246#924—32no—
247#924—32no—
248#924—32no—
249#924—31no—
250#924—34no—
251#924—32no—
252#924—32no—
253#924—34no—
254#924—62no—
255#924C2×D312yescomplemented
256C2×Dic3⋊C4—34no—
257#898—32no—
258#897—32no—
259#897—32no—
260#897—32no—
261#897—34no—
262#896—34no—
263#896—34no—
264#896—34no—
265#895—32no—
266#895—31no—
267#894—32no—
268#894—34no—
269#893—34no—
270#893C2×D311yescharacteristic
271#892—32no—
272D3×C4⋊C4—34no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—32no—
275D3×C4⋊C4—32no—
276D3×C4⋊C4—62no—
277D3×C4⋊C4C2×D311yescharacteristic
278#890—32no—
279#890—31no—
280#889—34no—
281#888—32no—
282#887—32no—
283#887C2×D312yescomplemented
284#886—34no—
285#886—34no—
286#885—34no—
287#885—34no—
288#884—34no—
289#883—34no—
290#883—34no—
291#883—34no—
292#883—64no—
293#882—34no—
294#67⋊C4—34no—
295#67⋊C4C2×D312yes—
296D3×C22⋊C4—34no—
297D3×C22⋊C4C2×D312yes—
298#879—34no—
299#879—34no—
300#879C2×D314yescomplemented
301#878—34no—
302#878—34no—
303#877—34no—
304#876—32no—
305#875—31no—
306C4×D12—32no—
307C4×D12—32no—
308C4×D12—34no—
309C4×D12—34no—
310C4×D12—31no—
311C4×D12—31no—
312C4×D12—61no—
313C4×D12C2×D311yescharacteristic
314#872—34no—
315#872—32no—
316#872—32no—
317C42×D3C2×D311yescharacteristic
318#870—32no—
319#870—31no—
320#870—34no—
321#869—31no—
322#869—31no—
323#869—32no—
324#869—61no—
325#869C2×D311yescharacteristic, complemented
326C4×Dic6—32no—
327C4×Dic6—32no—
328C4×Dic6C2×D311yescharacteristic, complemented
329C23×C32C2412yes—
330C22×C3⋊D3C2412yes—
331C22×C3×D3—24no—
332C22×C3×D3—24no—
333C22×C3×D3—42no—
334C22×C3×D3C2412yes—
335C22×C3×D3C2411yescharacteristic
336C32×D4—22no—
337C2×C32×C4—24no—
338C2×C32×C4C2412yes—
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C32×C4C2411yescharacteristic
342#638—44no—
343C2×C3⋊Dic3C2414yes—
344C2×C3⋊Dic3C2412yes—
345C4⋊(C3⋊D3)—22no—
346C4×C3⋊D3—24no—
347C4×C3⋊D3—44no—
348#634—24no—
349C3×#67—24no—
350C2×C3×Dic3—42no—
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2414yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2411yescharacteristic
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2411yescharacteristic
358C3×D12#4114yescomplemented
359C3×C4×D3—22no—
360C3×C4×D3—22no—
361C3×C4×D3—24no—
362C3×C4×D3—22no—
363C3×C4×D3—42no—
364C3×C4×D3—42no—
365C3×Dic6—24no—
366C3×Dic6—22no—
367#627—44no—
368#626—28no—
369#626—24no—
370D3×Dic3—28no—
371D3×Dic3—44no—
372#556—31no—
373#554—92no—
374#552—92no—
375#551—94no—
376D4×Q8—91no—
377#548—92no—
378#547—91no—
379#547—91no—
380#546—92no—
381#542—92no—
382#539—94no—
383#533—91no—
384#529—91no—
385#525—92no—
386C2×C22⋊Q8—92no—
387#520—92no—
388C2×C4×D4—31no—
389C24×C3—32no—
390C23×D3C22×D312yes—
391C2×C3×Q8—32no—
392C2×C3×Q8—31no—
393C2×C3×D4—21no—
394C2×C3×D4—32no—
395C2×C3×D4—31no—
396C2×C3×D4—64no—
397C2×C3×D4C22×D311yescharacteristic
398C2×C3×D4C22×D311yescharacteristic
399C22×C3×C4—22no—
400C22×C3×C4—32no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—32no—
404C22×C3×C4—31no—
405C22×C3×C4—32no—
406C22×C3×C4—32no—
407C22×C3×C4—124no—
408C22×C3×C4C22×D312yes—
409C22×C3×C4C22×D312yes—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—32no—
414C2×#67—64no—
415C2×#67C22×D312yes—
416C22×Dic3—34no—
417C22×Dic3—34no—
418C22×Dic3C22×D312yes—
419#239—68no—
420D3×Q8—124no—
421#237—68no—
422D3×D4—24no—
423#235—124no—
424#235—124no—
425#235—128no—
426C2×D12—32no—
427C2×D12—34no—
428C2×D12—31no—
429C2×D12—31no—
430C2×D12—61no—
431C2×D12C22×D311yescharacteristic
432C2×C4×D3—34no—
433C2×C4×D3—32no—
434C2×C4×D3—32no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—44no—
439C2×C4×D3—62no—
440C2×C4×D3—64no—
441C2×C4×D3C22×D311yescharacteristic
442C2×C4×D3C22×D311yescharacteristic
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D312yes—
445C2×C4×D3C22×D312yes—
446C2×C4×D3C22×D312yes—
447C2×Dic6—32no—
448C2×Dic6—32no—
449C2×Dic6—34no—
450C2×Dic6—34no—
451C2×Dic6—62no—
452C2×Dic6—124no—
453C2×Dic6C22×D312yes—
454C2×Dic6C22×D311yescharacteristic
455C3×C4⋊C4—21no—
456C3×C4⋊C4—32no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—34no—
462C3×C4⋊C4—32no—
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C22⋊C4—22no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—32no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—32no—
470C3×C22⋊C4—32no—
471C3×C22⋊C4C22×D312yes—
472C3×C22⋊C4C22×D312yes—
473C3×C42—21no—
474C3×C42—31no—
475C3×C42—31no—
476C3×C42—32no—
477C3×C42—31no—
478C3×C42—34no—
479C3×C42C22×D311yescharacteristic
480C3×C42C22×D311yescharacteristic
481#217—34no—
482#217—34no—
483#217—34no—
484#217—34no—
485#217—32no—
486#217—64no—
487#217C22×D312yes—
488#217C22×D314yes—
489#217C22×D314yes—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—32no—
496(C2×D3)⋊C4—32no—
497(C2×D3)⋊C4—32no—
498(C2×D3)⋊C4—32no—
499(C2×D3)⋊C4—32no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—32no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—62no—
504(C2×D3)⋊C4C22×D312yes—
505(C2×D3)⋊C4C22×D312yes—
506C4⋊Dic3—32no—
507C4⋊Dic3—32no—
508C4⋊Dic3—32no—
509C4⋊Dic3—32no—
510C4⋊Dic3—31no—
511C4⋊Dic3—31no—
512C4⋊Dic3—34no—
513C4⋊Dic3—32no—
514C4⋊Dic3—34no—
515C4⋊Dic3—34no—
516C4⋊Dic3—62no—
517C4⋊Dic3—62no—
518C4⋊Dic3—61no—
519C4⋊Dic3C22×D312yes—
520C4⋊Dic3C22×D311yescharacteristic
521C4⋊Dic3C22×D311yescharacteristic
522C4⋊Dic3C22×D312yes—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—32no—
528Dic3⋊C4—32no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—32no—
532Dic3⋊C4—32no—
533Dic3⋊C4—32no—
534Dic3⋊C4—34no—
535Dic3⋊C4—64no—
536Dic3⋊C4C22×D312yes—
537Dic3⋊C4C22×D312yes—
538Dic3⋊C4C22×D314yes—
539C4×Dic3—34no—
540C4×Dic3—34no—
541C4×Dic3C22×D312yes—
542C4×Dic3C22×D311yescharacteristic
543C4×Dic3C22×D311yescharacteristic
544C4×Dic3C22×D311yescharacteristic
545C4×Dic3C22×D314yes—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32—22no—
549C22×C32C2511yescharacteristic
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—22no—
553C2×C3×D3—21no—
554C2×C3×D3—22no—
555C2×C3×D3—21no—
556C2×C3×D3—22no—
557C2×C3×D3—48no—
558C2×C3×D3C2×#4114yes—
559C2×C3×D32−1+412yes—
560C32×C4—22no—
561C32×C4—21no—
562C32×C4C2×#4112yes—
563C32×C4H(5,𝔽2)12yes—
564C3⋊Dic3—22no—
565C3⋊Dic3—24no—
566C3×Dic3—24no—
567C3×Dic3—21no—
568C3×Dic3—22no—
569C3×Dic3—22no—
570C3×Dic3—21no—
571C3×Dic3—22no—
572C3×Dic3—21no—
573C2×#41—92no—
574C2×#41—92no—
575C22×Q8—92no—
576C22×D4—31no—
577C23×C4—32no—
578C4⋊Q8—31no—
579C4⋊Q8—92no—
580C4⋊Q8—91no—
581#126—34no—
582#126—92no—
583#126—94no—
584#125—91no—
585#125—92no—
586#125—94no—
587#124—32no—
588#124—91no—
589#124—94no—
590#123—94no—
591#123—94no—
592#123—94no—
593#123—92no—
594#123—94no—
595C22⋊Q8—32no—
596C22⋊Q8—94no—
597C22⋊Q8—94no—
598C22⋊Q8—94no—
599C22⋊Q8—92no—
600C22⋊Q8—94no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—91no—
604C22⋊Q8—92no—
605C22⋊Q8—92no—
606#121—94no—
607#121—91no—
608#121—92no—
609#121—92no—
610#120—94no—
611C4×Q8—32no—
612C4×Q8—31no—
613C4×Q8—92no—
614C4×Q8—92no—
615C4×D4—31no—
616C4×D4—32no—
617C4×D4—31no—
618C4×D4—32no—
619C4×D4—31no—
620C4×D4—94no—
621C4×D4—94no—
622C4×D4—92no—
623C4×D4—92no—
624C4×D4—94no—
625C4×D4—91no—
626C4×D4D3211yescharacteristic
627#117—32no—
628#117—92no—
629#117—94no—
630#117—92no—
631C2×C4⋊C4—31no—
632C2×C4⋊C4—94no—
633C2×C4⋊C4—92no—
634C2×C4⋊C4—92no—
635C2×C22⋊C4—32no—
636C2×C22⋊C4—94no—
637C2×C42—31no—
638C23×C3—22no—
639C23×C3—31no—
640C23×C3—32no—
641C23×C3—64no—
642C23×C3—64no—
643C23×C3—122no—
644C23×C3C23×D312yes—
645C23×C3C23×D312yes—
646C22×D3—24no—
647C22×D3—24no—
648C22×D3—32no—
649C22×D3—32no—
650C22×D3—42no—
651C22×D3—62no—
652C22×D3C23×D312yes—
653C22×D3C23×D311yescharacteristic
654C3×Q8—64no—
655C3×Q8—62no—
656C3×D4—22no—
657C3×D4—22no—
658C3×D4—34no—
659C3×D4—42no—
660C3×D4—64no—
661C2×C3×C4—24no—
662C2×C3×C4—24no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—22no—
666C2×C3×C4—21no—
667C2×C3×C4—31no—
668C2×C3×C4—34no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—32no—
672C2×C3×C4—32no—
673C2×C3×C4—32no—
674C2×C3×C4—44no—
675C2×C3×C4—62no—
676C2×C3×C4—62no—
677C2×C3×C4—64no—
678C2×C3×C4—62no—
679C2×C3×C4—122no—
680C2×C3×C4—122no—
681C2×C3×C4—122no—
682C2×C3×C4C23×D312yes—
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D312yes—
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D311yescharacteristic
687C2×C3×C4C23×D311yescharacteristic
688C2×C3×C4C23×D311yescharacteristic
689C2×C3×C4C23×D311yescharacteristic
690#67—24no—
691#67—68no—
692#67—64no—
693#67—124no—
694#67—124no—
695#67—128no—
696C2×Dic3—34no—
697C2×Dic3—34no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—42no—
701C2×Dic3—62no—
702C2×Dic3—64no—
703C2×Dic3—68no—
704C2×Dic3—124no—
705C2×Dic3C23×D311yescharacteristic
706C2×Dic3C23×D314yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D311yescharacteristic
709C2×Dic3C23×D311yescharacteristic
710C2×Dic3C23×D312yes—
711C2×Dic3C23×D312yes—
712D12—64no—
713D12—68no—
714D12—64no—
715D12—62no—
716D12—62no—
717D12#23514yescomplemented
718C4×D3—22no—
719C4×D3—22no—
720C4×D3—22no—
721C4×D3—24no—
722C4×D3—42no—
723C4×D3—42no—
724C4×D3—68no—
725C4×D3—64no—
726C4×D3—64no—
727C4×D3—124no—
728C4×D3—124no—
729C4×D3—124no—
730C4×D3—124no—
731C4×D3—128no—
732Dic6—24no—
733Dic6—22no—
734Dic6—64no—
735Dic6—64no—
736Dic6—124no—
737Dic6—124no—
738Dic6—124no—
739C2×C32—42no—
740C2×C32C22×#4111yescharacteristic
741C2×C32C2×H(5,𝔽2)11yescharacteristic
742C2×C32C2×2−1+411yescharacteristic
743C3⋊D3—42no—
744C3×D3—22no—
745C3×D3—24no—
746C24—32no—
747#41—188no—
748#41—364no—
749C2×Q8—32no—
750C2×Q8—31no—
751C2×Q8—94no—
752C2×Q8—92no—
753C2×Q8—364no—
754C2×D4—32no—
755C2×D4—31no—
756C2×D4—64no—
757C2×D4—92no—
758C2×D4—94no—
759C2×D4—94no—
760C2×D4—91no—
761C2×D4C2×D3211yescharacteristic
762C22×C4—32no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—32no—
767C22×C4—32no—
768C22×C4—32no—
769C22×C4—94no—
770C22×C4—94no—
771C22×C4—92no—
772C22×C4—94no—
773C22×C4—124no—
774C22×C4C2×D3212yes—
775C4⋊C4—32no—
776C4⋊C4—31no—
777C4⋊C4—32no—
778C4⋊C4—34no—
779C4⋊C4—31no—
780C4⋊C4—32no—
781C4⋊C4—32no—
782C4⋊C4—92no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—92no—
786C4⋊C4—94no—
787C4⋊C4—92no—
788C4⋊C4—94no—
789C4⋊C4—94no—
790C4⋊C4—91no—
791C4⋊C4—92no—
792C4⋊C4—92no—
793C4⋊C4C2×D3211yescharacteristic
794C22⋊C4—32no—
795C22⋊C4—34no—
796C22⋊C4—34no—
797C22⋊C4—32no—
798C22⋊C4—32no—
799C22⋊C4—92no—
800C22⋊C4—92no—
801C22⋊C4—92no—
802C22⋊C4—94no—
803C22⋊C4—92no—
804C22⋊C4—94no—
805C22⋊C4—94no—
806C22⋊C4—94no—
807C22⋊C4—92no—
808C22⋊C4C2×D3212yes—
809C42—31no—
810C42—31no—
811C42—31no—
812C42—34no—
813C42—32no—
814C42—94no—
815C42C2×D3211yescharacteristic
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—21no—
823C22×C3—34no—
824C22×C3—32no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—61no—
829C22×C3—62no—
830C22×C3—61no—
831C22×C3—62no—
832C22×C3—128no—
833C22×C3C24×D311yescharacteristic
834C22×C3C24×D311yescharacteristic
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—48no—
840C2×D3—64no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—122no—
848C2×D3—122no—
849C2×D3C2×#23514yes—
850C2×D3#101012yes—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—42no—
858C3×C4—41no—
859C3×C4—64no—
860C3×C4—62no—
861C3×C4—61no—
862C3×C4—62no—
863C3×C4—61no—
864C3×C4—62no—
865C3×C4—61no—
866C3×C4C2×#23512yes—
867C3×C4#100412yes—
868C3×C4D3×#4112yes—
869C3×C4#100912yes—
870Dic3—21no—
871Dic3—22no—
872Dic3—21no—
873Dic3—24no—
874Dic3—22no—
875Dic3—21no—
876Dic3—22no—
877Dic3—62no—
878Dic3—64no—
879Dic3—62no—
880Dic3—64no—
881Dic3—124no—
882Dic3—122no—
883C32#352011yescharacteristic, complemented, Sylow
884C23—32no—
885C23—31no—
886C23—64no—
887C23—64no—
888C23—92no—
889C23—122no—
890C23C22×D3212yes—
891Q8—64no—
892Q8—62no—
893Q8—184no—
894Q8—364no—
895D4—22no—
896D4—34no—
897D4—64no—
898D4—188no—
899D4—184no—
900D4—182no—
901D4—364no—
902C2×C4—24no—
903C2×C4—32no—
904C2×C4—31no—
905C2×C4—31no—
906C2×C4—31no—
907C2×C4—34no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—64no—
914C2×C4—94no—
915C2×C4—92no—
916C2×C4—122no—
917C2×C4—122no—
918C2×C4—122no—
919C2×C4—188no—
920C2×C4—184no—
921C2×C4—364no—
922C2×C4—364no—
923C2×C4C22×D3212yes—
924C2×C4C22×D3211yescharacteristic
925C2×C4C22×D3211yescharacteristic
926C2×C4C22×D3211yescharacteristic
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—42no—
931C2×C3—42no—
932C2×C3—62no—
933C2×C3—64no—
934C2×C3—82no—
935C2×C3C22×#23511yescharacteristic
936C2×C3C2×#100411yescharacteristic
937C2×C3C2×D3×#4111yescharacteristic
938C2×C3C2×#100911yescharacteristic
939C2×C3C2×#101011yescharacteristic
940C2×C3D3×2−1+411yescharacteristic
941D3—22no—
942D3—24no—
943D3—124no—
944D3—122no—
945D3—122no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—34no—
950C22—32no—
951C22—61no—
952C22—61no—
953C22—62no—
954C22—62no—
955C22—128no—
956C22—182no—
957C22—182no—
958C22—182no—
959C22C23×D3211yescharacteristic
960C4—22no—
961C4—21no—
962C4—61no—
963C4—64no—
964C4—61no—
965C4—62no—
966C4—62no—
967C4—61no—
968C4—62no—
969C4—182no—
970C4—184no—
971C4D3×#23512yes—
972C4#6431412yes—
973C3—21no—
974C3#8576711yescharacteristic, complemented
975C3#8699011yescharacteristic, complemented
976C2—42no—
977C2—62no—
978C2—64no—
979C2—362no—
980C2C2×D3×#23511yescharacteristic
981C2C2×#6431411yescharacteristic
982C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3520
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596022C2semidirect
2. C3×C4×D3×D4C2semidirect
3. C3×#5542C2semidirect
4. #10595229C2semidirect
5. #10595121C2semidirect
6. #10595023C2semidirect
7. #10594939C2semidirect
8. #10594916C2semidirect
9. D3×#924C2semidirect
10. #10594536C2semidirect
11. #10594361C2semidirect
12. #10594093C2semidirect
13. #10594090C2semidirect
14. Dic6×D12C2semidirect
15. #10593896C2semidirect
16. #10593870C2semidirect
17. #10593859C2semidirect
20. C2×#3828C22semidirect
24. C2×D3×Dic6C22semidirect
27. #64133C22semidirect
28. C4⋊C4×C3⋊D3C22semidirect
29. #64092C22semidirect
30. C4×C4⋊(C3⋊D3)C22semidirect
31. #64078C22semidirect
35. C3×#926C22semidirect
36. C3×#924C22semidirect
39. C3×#887C22semidirect
42. C3×#879C22semidirect
45. C3×#869C22semidirect
46. C3×C4×Dic6C22semidirect
51. #63966C22semidirect
52. #63964C22semidirect
53. #63956C22semidirect
54. #63953C22semidirect
55. #63918C22semidirect
57. #63909C22semidirect
60. C4×#626C22semidirect
61. #63893C22semidirect
63. #63890C22semidirect
64. D3×C4⋊Dic3C22semidirect
65. #63881C22semidirect
66. #63877C22semidirect
67. D3×Dic3⋊C4C22semidirect
68. #63874C22semidirect
69. #63871C22semidirect
70. #63869C22semidirect
71. #63869C22semidirect
72. #63868C22semidirect
73. #63867C22semidirect
74. #63865C22semidirect
75. #63864C22semidirect
77. #63857C22semidirect
82. #63844C22semidirect
83. Dic3×Dic6C22semidirect
110. C4×D3×D4D3semidirect
111. #5542D3semidirect
244. #926C2×D3semidirect
255. #924C2×D3semidirect
283. #887C2×D3semidirect
300. #879C2×D3semidirect
325. #869C2×D3semidirect
328. C4×Dic6C2×D3semidirect
358. C3×D12#41semidirect
717. D12#235semidirect
883. C32#3520semidirect
974. C3#85767semidirect
975. C3#86990semidirect

Maximal subgroups

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

subgroupindex
#105960222
C3×C4×D3×D42
C3×#55422
#105952292
#105951212
#105950232
#105949392
#105949162
D3×#9242
#105945362
#105943612
#105940932
#105940902
Dic6×D122
#105938962
#105938702
#105938592
#869903
#857673