Finite Group Databasebeta

← #11903624

Subgroups — #11903624

Order 1152.

2378 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic, complemented
3C3×C4×D3×D4C211yesmaximal, characteristic, complemented
4#10595244C212yesmaximal, complemented
5Dic3×#237C212yesmaximal, complemented
6#10594995C212yesmaximal, complemented
7#10594892C212yesmaximal, complemented
8#10594849C212yesmaximal, complemented
9C2×#63841C212yesmaximal, complemented
10#10594551C212yesmaximal, complemented
11#10594444C212yesmaximal, complemented
12#10594211C214yesmaximal, complemented
13#10594131C214yesmaximal, complemented
14#10593988C211yesmaximal, characteristic, complemented
15C4×#3795C211yesmaximal, characteristic, complemented
16#10593863C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86675—31nomaximal
19#85764—31nomaximal
20C2×C3×#237C2212yes—
21C2×C3×D3×D4C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C2×#3795C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25D4×C3⋊Dic3C2212yes—
26C2×C4⋊(C3⋊Dic3)C2212yescomplemented
27#64133C2212yescomplemented
28#64099C2212yescomplemented
29#64087C2214yescomplemented
30#64078C2211yescharacteristic, complemented
31C4×#634C2211yescharacteristic, complemented
32C3×D4×Dic3C2211yescharacteristic
33C3×#930C2212yescomplemented
34C3×C4×#67C2212yes—
35C2×C3×C4⋊Dic3C2212yescomplemented
36C3×#897C2212yescomplemented
37C3×#893C2211yescharacteristic
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×#886C2214yescomplemented
40C3×#67⋊C4C2212yes—
41C3×D3×C22⋊C4C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic, complemented
44C3×C42×D3C2211yescharacteristic
45C3×#869C2211yescharacteristic, complemented
46#63980C2214yes—
47#63976C2214yes—
48#67⋊Dic3C2214yescomplemented
49Dic3×#67C2214yescomplemented
50#63961C2214yes—
51C2×(C2×D3)⋊Dic3C2214yes—
52#63955C2214yescomplemented
53C2×Dic32C2214yescomplemented
54#63913C2214yescomplemented
55#63908C2212yes—
56#63908C2212yescomplemented
57#63905C2214yes—
58C4×#625C2212yes—
59Dic3×D12C2211yescharacteristic, complemented
60#63891C2214yescomplemented
61#63879C2212yes—
62#63879C2214yescomplemented
63#63877C2212yescomplemented
64C4×D3×Dic3C2212yescomplemented
65#63869C2212yescomplemented
66#63863C2212yes—
67#63861C2214yescomplemented
68#63858C2214yescomplemented
69#63858C2214yescomplemented
70#63857C2212yes—
71#63857C2212yescomplemented
72#63856C2212yes—
73#63847C2214yescomplemented
74#63844C2211yescharacteristic, complemented
75#63844C2212yescomplemented
76#63843C2212yescomplemented
77Dic3×Dic6C2212yescomplemented
78#63841C2212yes—
79#63841C2211yescharacteristic
80#63841C2214yes—
81#63841C2212yescomplemented
82#63841C2212yescomplemented
83#63841C2214yescomplemented
84#63841C2212yescomplemented
85C3×#547—31no—
86C2×C3×C4×D4—31no—
87#5829—32no—
88Dic3×#41—32no—
89#5806—32no—
90#5791—32no—
91C2×#926—32no—
92#5732—31no—
93#5728—31no—
94#5658—34no—
95#5649—34no—
96#5639—32no—
97#5624—32no—
98#5618—32no—
99#5606—32no—
100#5565—32no—
101#5563—31no—
102#5563—31no—
103#5557—32no—
104#5555D311yescharacteristic, complemented
105C4×D3×D4D311yescharacteristic, complemented
106#5543—31no—
107#5543—31no—
108#5543—61no—
109#5542—31no—
110#5541—32no—
111#5538—34no—
112C4×#237—32no—
113C4×#237—31no—
114#5513—32no—
115#5513—32no—
116C2×#892—32no—
117#5495—34no—
118C4×#235—31no—
119#5470—31no—
120C23×C3×D3C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C22×C3⋊Dic3C2314yes—
124C2×#634C2311yescharacteristic
125C2×#634C2312yes—
126C2×C3×#67C2312yes—
127C2×C3×#67C2314yes—
128C22×C3×Dic3C2312yes—
129C22×C3×Dic3C2314yes—
130C3×#237—28no—
131C3×D3×D4—24no—
132C2×C3×D12C2311yescharacteristic
133C2×C3×D12C2311yescharacteristic
134C2×C3×C4×D3—28no—
135C2×C3×C4×D3C2312yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2312yes—
140C2×C3×C4×D3C2311yescharacteristic
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×Dic6C2312yes—
143C2×#625C2312yes—
144C2×#625C2314yes—
145C2×D3×Dic3C2312yes—
146C2×D3×Dic3C2312yes—
147#3795—24no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C22⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151#3757C2314yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2314yes—
156#3750C2312yes—
157#3750C2314yes—
158C4×C3⋊Dic3C2312yes—
159C3×#217C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2314yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173#3724C2312yes—
174#3724C2314yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177(C2×D3)⋊Dic3C2312yes—
178(C2×D3)⋊Dic3C2314yes—
179(C2×D3)⋊Dic3C2314yes—
180(C2×D3)⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184Dic32C2314yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2314yes—
188Dic32C2312yes—
189#3475—91noSylow
190C2×C3×#41—32no—
191C22×C3×D4—31no—
192C23×C3×C4—32no—
193C2×#237—31no—
194C2×#237C2×D312yes—
195C2×D3×D4C2×D311yescharacteristic
196C2×#235—31no—
197C22×C4×D3C2×D312yes—
198C3×C4⋊Q8—31no—
199C3×#123—34no—
200C3×C22⋊Q8—32no—
201C3×#121—32no—
202C3×C4×D4—21no—
203C3×C4×D4—31no—
204C3×C4×D4—32no—
205C3×C4×D4—31no—
206C3×C4×D4—32no—
207C3×C4×D4—31no—
208C3×C4×D4—31no—
209C3×C4×D4C2×D311yescharacteristic
210C3×C4×D4C2×D311yescharacteristic
211C2×C3×C4⋊C4—32no—
212C2×C3×C4⋊C4—31no—
213C2×C3×C22⋊C4—32no—
214C2×C3×C42—31no—
215#953—34no—
216C2×#217—34no—
217#947—32no—
218#946—32no—
219Q8×Dic3—32no—
220Q8×Dic3—32no—
221#939—34no—
222#939—34no—
223#938—32no—
224#938—32no—
225#937—34no—
226#936—32no—
227#935—34no—
228D4×Dic3—32no—
229D4×Dic3—32no—
230D4×Dic3—34no—
231D4×Dic3—34no—
232D4×Dic3—31no—
233D4×Dic3—62no—
234D4×Dic3C2×D311yescharacteristic
235#930—32no—
236#930—32no—
237#930C2×D312yescomplemented
238#929—34no—
239#929—34no—
240C4×#67—34no—
241C4×#67—32no—
242C4×#67—32no—
243C4×#67—32no—
244C4×#67—34no—
245C4×#67C2×D312yes—
246C2×(C2×D3)⋊C4—34no—
247#926—34no—
248#926—32no—
249#926—32no—
250#926—31no—
251#926—34no—
252#926—34no—
253#926—32no—
254#926—32no—
255C2×C4⋊Dic3—32no—
256C2×C4⋊Dic3—32no—
257C2×C4⋊Dic3—62no—
258C2×C4⋊Dic3C2×D312yescomplemented
259#924—32no—
260#924—32no—
261#924—32no—
262#924—32no—
263#924—32no—
264#924—62no—
265C2×C4×Dic3—34no—
266C2×C4×Dic3—34no—
267C2×C4×Dic3—32no—
268#898—34no—
269#898—34no—
270#898—34no—
271#897—32no—
272#897—32no—
273#897C2×D312yescomplemented
274#893C2×D311yescharacteristic
275#892—34no—
276#892—34no—
277#892—32no—
278#892—31no—
279#892—32no—
280#892—32no—
281#892—32no—
282D3×C4⋊C4C2×D311yescharacteristic
283#890—32no—
284#890—32no—
285#890—32no—
286#890—62no—
287#889—34no—
288#889—34no—
289#887—32no—
290#887—32no—
291#887—31no—
292#886—34no—
293#886C2×D314yescomplemented
294#885—34no—
295#885—34no—
296#883—34no—
297#883—34no—
298#67⋊C4—34no—
299#67⋊C4—34no—
300#67⋊C4—32no—
301#67⋊C4C2×D312yes—
302D3×C22⋊C4C2×D312yes—
303#879—34no—
304#879—34no—
305#879—34no—
306#878—34no—
307#878—34no—
308#878—64no—
309#877—34no—
310#877—32no—
311C4×D12—31no—
312C4×D12C2×D311yescharacteristic
313C4×D12C2×D311yescharacteristic, complemented
314#872—32no—
315C42×D3—32no—
316C42×D3C2×D311yescharacteristic
317#870—32no—
318#869—31no—
319#869—31no—
320#869—61no—
321#869C2×D311yescharacteristic, complemented
322C4×Dic6—32no—
323C4×Dic6—31no—
324C4×Dic6—31no—
325C4×Dic6—32no—
326C4×Dic6—31no—
327C4×Dic6—61no—
328C23×C32C2412yes—
329C22×C3×D3—24no—
330C22×C3×D3—24no—
331C22×C3×D3—42no—
332C22×C3×D3C2412yes—
333C22×C3×D3C2412yes—
334C22×C3×D3C2411yescharacteristic
335C32×D4#4114yescomplemented
336C2×C32×C4—24no—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2412yes—
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C3⋊Dic3—44no—
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2414yes—
344C2×C3⋊Dic3C2412yes—
345#634—22no—
346#634—42no—
347C3×#67—24no—
348C3×#67—28no—
349C2×C3×Dic3—28no—
350C2×C3×Dic3—24no—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2411yescharacteristic
355C2×C3×Dic3C2411yescharacteristic
356C2×C3×Dic3C2411yescharacteristic
357C3×D12—22no—
358C3×D12—22no—
359C3×C4×D3—24no—
360C3×C4×D3—24no—
361C3×C4×D3—22no—
362C3×C4×D3—24no—
363C3×C4×D3—24no—
364C3×C4×D3—41no—
365C3×C4×D3#4114yescomplemented
366C3×Dic6—24no—
367#625—24no—
368#625—44no—
369D3×Dic3—24no—
370D3×Dic3—42no—
371#556—91no—
372#555—91no—
373#554—91no—
374#553—92no—
375#552—92no—
376#552—92no—
377#551—94no—
378#547—31no—
379#546—92no—
380#533—91no—
381#529—92no—
382#529—94no—
383#525—92no—
384C4×#41—91no—
385C4×#41—92no—
386C2×C4×D4—31no—
387C2×#117—92no—
388C24×C3—32no—
389C23×D3C22×D312yes—
390C3×#41—68no—
391C2×C3×Q8—32no—
392C2×C3×D4—21no—
393C2×C3×D4—34no—
394C2×C3×D4—32no—
395C2×C3×D4—31no—
396C2×C3×D4—31no—
397C2×C3×D4—64no—
398C2×C3×D4C22×D311yescharacteristic
399C2×C3×D4C22×D311yescharacteristic
400C22×C3×C4—22no—
401C22×C3×C4—31no—
402C22×C3×C4—32no—
403C22×C3×C4—34no—
404C22×C3×C4—32no—
405C22×C3×C4—31no—
406C22×C3×C4—32no—
407C22×C3×C4—32no—
408C22×C3×C4—32no—
409C22×C3×C4—31no—
410C22×C3×C4—68no—
411C22×C3×C4C22×D312yes—
412C22×C3×C4C22×D312yes—
413C2×#67—32no—
414C2×#67—32no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67C22×D314yes—
418C2×#67C22×D312yes—
419C22×Dic3—34no—
420C22×Dic3—34no—
421C22×Dic3—32no—
422C22×Dic3—32no—
423C22×Dic3—64no—
424C22×Dic3C22×D314yes—
425C22×Dic3C22×D312yes—
426#237—28no—
427#237—64no—
428D3×D4—24no—
429#235—64no—
430C2×D12C22×D311yescharacteristic
431C2×D12C22×D311yescharacteristic
432C2×C4×D3—28no—
433C2×C4×D3—32no—
434C2×C4×D3—32no—
435C2×C4×D3C22×D312yes—
436C2×C4×D3C22×D311yescharacteristic
437C2×C4×D3C22×D312yes—
438C2×C4×D3C22×D312yes—
439C2×C4×D3C22×D312yes—
440C2×C4×D3C22×D311yescharacteristic
441C2×C4×D3C22×D311yescharacteristic
442C2×Dic6—31no—
443C2×Dic6—31no—
444C2×Dic6—32no—
445C2×Dic6—32no—
446C2×Dic6—61no—
447C2×Dic6—62no—
448C2×Dic6C22×D312yes—
449C3×C4⋊C4—21no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4C22×D311yescharacteristic
457C3×C4⋊C4C22×D311yescharacteristic
458C3×C22⋊C4—22no—
459C3×C22⋊C4—32no—
460C3×C22⋊C4—32no—
461C3×C22⋊C4—32no—
462C3×C22⋊C4—32no—
463C3×C22⋊C4—34no—
464C3×C22⋊C4C22×D312yes—
465C3×C22⋊C4C22×D312yes—
466C3×C42—21no—
467C3×C42—31no—
468C3×C42—31no—
469C3×C42—31no—
470C3×C42C22×D311yescharacteristic
471C3×C42C22×D311yescharacteristic
472#217—34no—
473#217—34no—
474#217—32no—
475#217—34no—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—34no—
480#217—32no—
481#217—64no—
482#217C22×D312yes—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4C22×D312yes—
491(C2×D3)⋊C4C22×D312yes—
492(C2×D3)⋊C4C22×D312yes—
493(C2×D3)⋊C4C22×D314yes—
494C4⋊Dic3—32no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—32no—
498C4⋊Dic3—32no—
499C4⋊Dic3—32no—
500C4⋊Dic3—34no—
501C4⋊Dic3—34no—
502C4⋊Dic3—34no—
503C4⋊Dic3—34no—
504C4⋊Dic3—61no—
505C4⋊Dic3—62no—
506C4⋊Dic3—62no—
507C4⋊Dic3—64no—
508C4⋊Dic3C22×D312yes—
509C4⋊Dic3C22×D311yescharacteristic
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D311yescharacteristic
512C4⋊Dic3C22×D314yes—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—32no—
520Dic3⋊C4—34no—
521Dic3⋊C4—32no—
522Dic3⋊C4—34no—
523Dic3⋊C4—62no—
524Dic3⋊C4—64no—
525Dic3⋊C4C22×D312yes—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—34no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—34no—
532C4×Dic3—32no—
533C4×Dic3—34no—
534C4×Dic3—34no—
535C4×Dic3—34no—
536C4×Dic3—32no—
537C4×Dic3—34no—
538C4×Dic3—62no—
539C4×Dic3C22×D311yescharacteristic
540C4×Dic3C22×D311yescharacteristic
541C4×Dic3C22×D311yescharacteristic
542C22×C32—22no—
543C22×C32—22no—
544C22×C32C2×#4114yes—
545C22×C32C2511yescharacteristic
546C2×C3×D3—21no—
547C2×C3×D3—21no—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—48no—
555C2×C3×D3C2×#4112yes—
556C32×C4—22no—
557C32×C4—21no—
558C32×C4C2×#4112yes—
559C32×C4C2×#4112yes—
560C3⋊Dic3—22no—
561C3⋊Dic3—22no—
562C3⋊Dic3—24no—
563C3×Dic3—24no—
564C3×Dic3—22no—
565C3×Dic3—22no—
566C3×Dic3—21no—
567C3×Dic3—21no—
568C3×Dic3C2×#4112yes—
569C2×#41—32no—
570C2×#41—91no—
571C22×D4—31no—
572C23×C4—32no—
573C4⋊Q8—31no—
574C4⋊Q8—91no—
575#126—94no—
576#126—94no—
577#126—94no—
578#125—92no—
579#125—94no—
580#125—92no—
581#124—94no—
582#124—92no—
583#123—34no—
584#123—94no—
585#123—94no—
586#123—94no—
587C22⋊Q8—32no—
588C22⋊Q8—92no—
589C22⋊Q8—92no—
590C22⋊Q8—92no—
591C22⋊Q8—92no—
592C22⋊Q8—94no—
593#121—32no—
594#121—92no—
595#121—92no—
596#121—94no—
597#120—94no—
598C4×Q8—91no—
599C4×Q8—92no—
600C4×Q8—92no—
601C4×Q8—92no—
602C4×Q8—91no—
603C4×D4—31no—
604C4×D4—32no—
605C4×D4—31no—
606C4×D4—32no—
607C4×D4—31no—
608C4×D4—31no—
609C4×D4—91no—
610C4×D4—92no—
611C4×D4—94no—
612C4×D4—94no—
613C4×D4—92no—
614C4×D4—94no—
615C4×D4—92no—
616C4×D4D3211yescharacteristic
617#117—92no—
618#117—94no—
619#117—91no—
620#117—92no—
621#117—94no—
622#117—94no—
623#117—92no—
624#117—92no—
625#117—92no—
626C2×C4⋊C4—32no—
627C2×C4⋊C4—31no—
628C2×C4⋊C4—92no—
629C2×C22⋊C4—32no—
630C2×C22⋊C4—94no—
631C2×C42—31no—
632C2×C42—92no—
633C2×C42—94no—
634C23×C3—22no—
635C23×C3—31no—
636C23×C3—32no—
637C23×C3—32no—
638C23×C3—64no—
639C23×C3—64no—
640C23×C3—122no—
641C23×C3C23×D312yes—
642C23×C3C23×D312yes—
643C22×D3—24no—
644C22×D3—24no—
645C22×D3—42no—
646C22×D3C23×D312yes—
647C22×D3C23×D312yes—
648C22×D3C23×D311yescharacteristic
649C3×Q8—64no—
650C3×D4—24no—
651C3×D4—68no—
652C3×D4—64no—
653C3×D4—62no—
654C3×D4—62no—
655C3×D4#23514yescomplemented
656C3×D4#23714yescomplemented
657C2×C3×C4—24no—
658C2×C3×C4—24no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—22no—
662C2×C3×C4—21no—
663C2×C3×C4—31no—
664C2×C3×C4—34no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—31no—
668C2×C3×C4—34no—
669C2×C3×C4—31no—
670C2×C3×C4—44no—
671C2×C3×C4—64no—
672C2×C3×C4—64no—
673C2×C3×C4—64no—
674C2×C3×C4—68no—
675C2×C3×C4—64no—
676C2×C3×C4—62no—
677C2×C3×C4—64no—
678C2×C3×C4—121no—
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D312yes—
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D311yescharacteristic
687#67—24no—
688#67—28no—
689#67—64no—
690#67—64no—
691#67—124no—
692#67—124no—
693C2×Dic3—28no—
694C2×Dic3—24no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—34no—
700C2×Dic3—34no—
701C2×Dic3—62no—
702C2×Dic3—62no—
703C2×Dic3—64no—
704C2×Dic3—64no—
705C2×Dic3—122no—
706C2×Dic3—124no—
707C2×Dic3—124no—
708C2×Dic3—244no—
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D312yes—
711C2×Dic3C23×D311yescharacteristic
712C2×Dic3C23×D314yes—
713C2×Dic3C23×D311yescharacteristic
714C2×Dic3C23×D311yescharacteristic
715D12—22no—
716D12—22no—
717C4×D3—24no—
718C4×D3—22no—
719C4×D3—24no—
720C4×D3—24no—
721C4×D3—24no—
722C4×D3—41no—
723C4×D3—64no—
724C4×D3—122no—
725C4×D3#23714yescomplemented
726Dic6—24no—
727Dic6—62no—
728Dic6—62no—
729Dic6—122no—
730Dic6—122no—
731Dic6—122no—
732Dic6—242no—
733C2×C32—24no—
734C2×C32C22×#4111yescharacteristic
735C2×C32C22×#4111yescharacteristic
736C2×C32#58511yescharacteristic
737C3×D3—22no—
738C3×D3—42no—
739C3×D3—42no—
740C24—32no—
741#41—68no—
742#41—184no—
743C2×Q8—32no—
744C2×Q8—91no—
745C2×Q8—92no—
746C2×D4—32no—
747C2×D4—34no—
748C2×D4—31no—
749C2×D4—31no—
750C2×D4—64no—
751C2×D4—92no—
752C2×D4—94no—
753C2×D4C2×D3211yescharacteristic
754C22×C4—31no—
755C22×C4—32no—
756C22×C4—34no—
757C22×C4—31no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—32no—
762C22×C4—31no—
763C22×C4—68no—
764C22×C4—92no—
765C22×C4—92no—
766C22×C4—94no—
767C22×C4C2×D3212yes—
768C4⋊C4—31no—
769C4⋊C4—31no—
770C4⋊C4—32no—
771C4⋊C4—34no—
772C4⋊C4—32no—
773C4⋊C4—32no—
774C4⋊C4—94no—
775C4⋊C4—94no—
776C4⋊C4—92no—
777C4⋊C4—94no—
778C4⋊C4—91no—
779C4⋊C4—92no—
780C4⋊C4—94no—
781C4⋊C4—92no—
782C4⋊C4—92no—
783C4⋊C4—94no—
784C4⋊C4C2×D3211yescharacteristic
785C22⋊C4—32no—
786C22⋊C4—32no—
787C22⋊C4—32no—
788C22⋊C4—32no—
789C22⋊C4—34no—
790C22⋊C4—92no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—92no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4—94no—
798C22⋊C4C2×D3212yes—
799C42—31no—
800C42—31no—
801C42—31no—
802C42—92no—
803C42—94no—
804C42—94no—
805C42—92no—
806C42—94no—
807C42—92no—
808C42C2×D3211yescharacteristic
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—24no—
814C22×C3—21no—
815C22×C3—32no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—128no—
827C22×C3C2×#23514yes—
828C22×C3C2×#23714yes—
829C22×C3C24×D311yescharacteristic
830C22×C3C24×D311yescharacteristic
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—48no—
840C2×D3C2×#23712yes—
841C3×C4—22no—
842C3×C4—22no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—32no—
848C3×C4—41no—
849C3×C4—42no—
850C3×C4—62no—
851C3×C4—64no—
852C3×C4—61no—
853C3×C4—62no—
854C3×C4—61no—
855C3×C4C2×#23512yes—
856C3×C4C2×#23712yes—
857C3×C4C2×#23712yes—
858C3×C4D3×#4112yes—
859Dic3—21no—
860Dic3—24no—
861Dic3—22no—
862Dic3—22no—
863Dic3—21no—
864Dic3—62no—
865Dic3—62no—
866Dic3—64no—
867Dic3—62no—
868Dic3—64no—
869Dic3—62no—
870Dic3—122no—
871Dic3—124no—
872Dic3—122no—
873Dic3C2×#23712yes—
874C32#347511yescharacteristic, complemented, Sylow
875C23—31no—
876C23—32no—
877C23—32no—
878C23—64no—
879C23—64no—
880C23—122no—
881C23C22×D3212yes—
882Q8—64no—
883Q8—182no—
884Q8—362no—
885D4—64no—
886D4—68no—
887D4—62no—
888D4—62no—
889D4—184no—
890D4—364no—
891D4#379514yescomplemented
892C2×C4—24no—
893C2×C4—31no—
894C2×C4—34no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—32no—
898C2×C4—32no—
899C2×C4—34no—
900C2×C4—64no—
901C2×C4—64no—
902C2×C4—64no—
903C2×C4—68no—
904C2×C4—62no—
905C2×C4—64no—
906C2×C4—64no—
907C2×C4—92no—
908C2×C4—92no—
909C2×C4—94no—
910C2×C4—121no—
911C2×C4—184no—
912C2×C4—362no—
913C2×C4—364no—
914C2×C4C22×D3211yescharacteristic
915C2×C4C22×D3212yes—
916C2×C4C22×D3211yescharacteristic
917C2×C4C22×D3211yescharacteristic
918C2×C3—24no—
919C2×C3—24no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—44no—
924C2×C3—62no—
925C2×C3—122no—
926C2×C3—122no—
927C2×C3C22×#23511yescharacteristic
928C2×C3C22×#23711yescharacteristic
929C2×C3C22×#23711yescharacteristic
930C2×C3C2×D3×#4111yescharacteristic
931C2×C3#596411yescharacteristic
932C2×C3#596811yescharacteristic
933D3—22no—
934D3—42no—
935D3—42no—
936C22—22no—
937C22—22no—
938C22—32no—
939C22—61no—
940C22—61no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—62no—
947C22—128no—
948C22C2×#379514yes—
949C22C23×D3211yescharacteristic
950C4—22no—
951C4—21no—
952C4—32no—
953C4—62no—
954C4—61no—
955C4—64no—
956C4—62no—
957C4—61no—
958C4—182no—
959C4—182no—
960C4—184no—
961C4C2×#379512yes—
962C4D3×#23712yes—
963C3—21no—
964C3#8576411yescharacteristic, complemented
965C3#8667511yescharacteristic, complemented
966C2—24no—
967C2—62no—
968C2—122no—
969C2—122no—
970C2C22×#379511yescharacteristic
971C2C2×D3×#23711yescharacteristic
972C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596014C2semidirect
2. C3×#5555C2semidirect
3. C3×C4×D3×D4C2semidirect
4. #10595244C2semidirect
5. Dic3×#237C2semidirect
6. #10594995C2semidirect
7. #10594892C2semidirect
8. #10594849C2semidirect
9. C2×#63841C2semidirect
10. #10594551C2semidirect
11. #10594444C2semidirect
12. #10594211C2semidirect
13. #10594131C2semidirect
14. #10593988C2semidirect
15. C4×#3795C2semidirect
16. #10593863C2semidirect
17. #10593859C2semidirect
26. C2×C4⋊(C3⋊Dic3)C22semidirect
27. #64133C22semidirect
28. #64099C22semidirect
29. #64087C22semidirect
30. #64078C22semidirect
31. C4×#634C22semidirect
33. C3×#930C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C3×#897C22semidirect
39. C3×#886C22semidirect
43. C3×C4×D12C22semidirect
45. C3×#869C22semidirect
48. #67⋊Dic3C22semidirect
49. Dic3×#67C22semidirect
52. #63955C22semidirect
53. C2×Dic32C22semidirect
54. #63913C22semidirect
56. #63908C22semidirect
59. Dic3×D12C22semidirect
60. #63891C22semidirect
62. #63879C22semidirect
63. #63877C22semidirect
64. C4×D3×Dic3C22semidirect
65. #63869C22semidirect
67. #63861C22semidirect
68. #63858C22semidirect
69. #63858C22semidirect
71. #63857C22semidirect
73. #63847C22semidirect
74. #63844C22semidirect
75. #63844C22semidirect
76. #63843C22semidirect
77. Dic3×Dic6C22semidirect
81. #63841C22semidirect
82. #63841C22semidirect
83. #63841C22semidirect
84. #63841C22semidirect
104. #5555D3semidirect
105. C4×D3×D4D3semidirect
237. #930C2×D3semidirect
258. C2×C4⋊Dic3C2×D3semidirect
273. #897C2×D3semidirect
293. #886C2×D3semidirect
313. C4×D12C2×D3semidirect
321. #869C2×D3semidirect
335. C32×D4#41semidirect
365. C3×C4×D3#41semidirect
655. C3×D4#235semidirect
656. C3×D4#237semidirect
725. C4×D3#237semidirect
874. C32#3475semidirect
891. D4#3795semidirect
964. C3#85764semidirect
965. C3#86675semidirect

Maximal subgroups

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

subgroupindex
#105960142
C3×#55552
C3×C4×D3×D42
#105952442
Dic3×#2372
#105949952
#105948922
#105948492
C2×#638412
#105945512
#105944442
#105942112
#105941312
#105939882
C4×#37952
#105938632
#105938592
#866753
#857643