Finite Group Databasebeta

← #11909313

Subgroups — #11909313

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#10596026C211yesmaximal, characteristic, complemented
2C3×#5557C211yesmaximal, characteristic, complemented
3C3×#5551C211yesmaximal, characteristic, complemented
4#10595306C212yesmaximal, complemented
5#10595161C212yesmaximal, complemented
6#10595067C212yesmaximal, complemented
7#10594993C212yesmaximal, complemented
8#10594992C212yesmaximal, complemented
9#10594814C212yesmaximal, complemented
10D3×#897C212yesmaximal, complemented
11#10594553C212yesmaximal, complemented
12#10594303C214yesmaximal, complemented
13#10594128C214yesmaximal, complemented
14C4×D3×D12C211yesmaximal, characteristic, complemented
15Dic6×D12C211yesmaximal, characteristic, complemented
16#10593865C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86685—31nomaximal
19#86167—31nomaximal
20C2×#3830C2212yescomplemented
21C2×C3×#235C2212yes—
22C2×D3×D12C2211yescharacteristic
23C2×C4×D32C2212yes—
24C2×D3×Dic6C2212yescomplemented
25C32×C4×D4C2211yescharacteristic, complemented
26#64139C2212yes—
27C2×C4⋊(C3⋊Dic3)C2212yescomplemented
28#64106C2212yescomplemented
29#64095C2214yescomplemented
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31#64078C2211yescharacteristic, complemented
32C3×#938C2211yescharacteristic
33C3×#938C2212yescomplemented
34C3×#936C2211yescharacteristic, complemented
35C3×C4×#67C2212yes—
36C3×#926C2212yescomplemented
37C3×#924C2212yescomplemented
38C3×#897C2211yescharacteristic
39C3×D3×C4⋊C4C2212yescomplemented
40C3×#890C2211yescharacteristic, complemented
41C3×#883C2212yes—
42C3×#883C2214yescomplemented
43C3×#879C2212yescomplemented
44C3×C4×D12C2211yescharacteristic
45C3×C42×D3C2211yescharacteristic
46C3×#869C2211yescharacteristic, complemented
47C3×C4×Dic6C2211yescharacteristic, complemented
48#63983C2214yes—
49#63982C2214yescomplemented
50#63975C2214yescomplemented
51#67⋊Dic3C2214yes—
52#67⋊Dic3C2214yescomplemented
53#67⋊Dic3C2214yescomplemented
54#63971C2214yes—
55#63953C2214yescomplemented
56D3×(C2×D3)⋊C4C2214yes—
57D3×(C2×D3)⋊C4C2212yes—
58#63918C2212yescomplemented
59C4×#626C2212yes—
60#63895C2214yescomplemented
61#63894C2211yescharacteristic
62#63893C2214yes—
63#63893C2214yescomplemented
64Dic3×D12C2212yes—
65Dic3×D12C2211yescharacteristic
66D3×C4⋊Dic3C2211yescharacteristic
67D3×C4⋊Dic3C2214yescomplemented
68#63880C2212yes—
69#63871C2212yescomplemented
70#63869C2212yescomplemented
71#63864C2212yes—
72#63857C2212yes—
73#63857C2212yescomplemented
74#63856C2212yes—
75#63850C2214yes—
76#63849C2212yescomplemented
77#63848C2214yescomplemented
78#63848C2214yescomplemented
79#63845C2214yescomplemented
80#63844C2212yescomplemented
81Dic3×Dic6C2212yescomplemented
82Dic3×Dic6C2212yescomplemented
83#63841C2212yes—
84#63841C2214yescomplemented
85C3×#547—31no—
86C3×#529—31no—
87#5829—32no—
88#5827—32no—
89#5732—31no—
90#5728—31no—
91#5707—34no—
92#5694—32no—
93#5677—32no—
94#5665—34no—
95#5658—34no—
96#5658—34no—
97#5643—32no—
98#5635—32no—
99D3×C22⋊Q8—32no—
100#5606—32no—
101#5606—32no—
102#5598—32no—
103#5584—31no—
104Q8×D12—31no—
105#5557D311yescharacteristic, complemented
106#5555—31no—
107#5555—31no—
108#5555—61no—
109#5551D311yescharacteristic, complemented
110#5550—32no—
111C4×D3×D4—31no—
112#5543—32no—
113D4×Dic6—31no—
114#5534—32no—
115#5523—32no—
116#5513—32no—
117C2×#897—32no—
118C2×C4×D12—31no—
119#5470—31no—
120C22×D32C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#638C2314yes—
124C22×C3⋊Dic3C2314yes—
125#3830—44no—
126C2×C4⋊(C3⋊D3)C2311yescharacteristic
127C2×C4×C3⋊D3C2312yes—
128C2×#634C2312yes—
129C2×C3×#67C2312yes—
130C2×C3×#67C2314yes—
131C3×#235—28no—
132C2×C3×D12C2311yescharacteristic
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2314yes—
135C2×C3×C4×D3C2312yes—
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139C2×C3×Dic6C2312yes—
140C2×#627C2314yes—
141C2×#626C2312yes—
142C2×#624C2312yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2312yes—
146D3×D12—24no—
147C4×D32—44no—
148D3×Dic6—44no—
149C32×C4⋊C4C2311yescharacteristic
150C32×C22⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152#3752C2312yes—
153#3752C2314yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2312yes—
156C4⋊(C3⋊Dic3)C2311yescharacteristic
157C4⋊(C3⋊Dic3)C2314yes—
158C3×#217C2312yes—
159C3×#217C2312yes—
160C3×#217C2312yes—
161C3×#217C2314yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2311yescharacteristic
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2314yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2311yescharacteristic
175C3×C4×Dic3C2311yescharacteristic
176C3×C4×Dic3C2312yes—
177#3724C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2314yes—
182#3722C2314yes—
183#3722C2312yes—
184#3722C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2312yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2314yes—
189Dic32C2314yes—
190#3520—91noSylow
191C2×C3×#41—32no—
192C2×D3×Q8—32no—
193C2×#237—32no—
194C2×#237—32no—
195C2×#237—62no—
196C2×D3×D4—31no—
197C2×#235C2×D312yes—
198C22×D12—31no—
199C22×C4×D3—32no—
200C22×C4×D3—32no—
201C22×Dic6—32no—
202C3×C4⋊Q8—31no—
203C3×#126—32no—
204C3×#125—31no—
205C3×#124—31no—
206C3×#123—32no—
207C3×#123—34no—
208C3×C22⋊Q8—32no—
209C3×C22⋊Q8—31no—
210C3×#121—31no—
211C3×#121—32no—
212C3×C4×Q8—31no—
213C3×C4×D4—21no—
214C3×C4×D4—32no—
215C3×C4×D4—31no—
216C3×C4×D4C2×D311yescharacteristic, complemented
217C3×C4×D4C2×D311yescharacteristic, complemented
218C3×#117—32no—
219C2×C3×C4⋊C4—32no—
220C2×C3×C42—31no—
221#947—32no—
222#946—32no—
223#946—32no—
224Q8×Dic3—32no—
225Q8×Dic3—32no—
226#939—34no—
227#938C2×D311yescharacteristic
228#938C2×D312yescomplemented
229#937—34no—
230#937—34no—
231#936C2×D311yescharacteristic, complemented
232D4×Dic3—34no—
233D4×Dic3—34no—
234D4×Dic3—34no—
235D4×Dic3—32no—
236D4×Dic3—31no—
237#930—32no—
238#930—32no—
239#930—62no—
240#929—34no—
241C4×#67—32no—
242C4×#67C2×D312yes—
243C2×(C2×D3)⋊C4—32no—
244C2×(C2×D3)⋊C4—34no—
245#926—32no—
246#926—34no—
247#926C2×D312yescomplemented
248C2×C4⋊Dic3—32no—
249C2×C4⋊Dic3—32no—
250C2×C4⋊Dic3—34no—
251C2×C4⋊Dic3—31no—
252C2×C4⋊Dic3—62no—
253#924—32no—
254#924—32no—
255#924—32no—
256#924C2×D312yescomplemented
257#898—34no—
258#898—34no—
259#898—34no—
260#898—34no—
261#897—32no—
262#897—32no—
263#897—32no—
264#897—32no—
265#897—32no—
266#897—34no—
267#897—34no—
268#897—34no—
269#897—62no—
270#897C2×D311yescharacteristic
271#896—34no—
272#894—34no—
273#893—31no—
274#892—32no—
275#892—34no—
276#892—32no—
277#892—32no—
278D3×C4⋊C4—31no—
279D3×C4⋊C4—34no—
280D3×C4⋊C4C2×D312yescomplemented
281#890—34no—
282#890—32no—
283#890C2×D311yescharacteristic, complemented
284#889—34no—
285#888—32no—
286#887—32no—
287#886—34no—
288#886—34no—
289#886—64no—
290#885—34no—
291#885—34no—
292#884—34no—
293#883—34no—
294#883—34no—
295#883C2×D312yes—
296#883C2×D314yescomplemented
297#67⋊C4—34no—
298#67⋊C4—34no—
299#67⋊C4—34no—
300#67⋊C4—32no—
301D3×C22⋊C4—32no—
302D3×C22⋊C4—34no—
303#879C2×D312yescomplemented
304#878—34no—
305#878—34no—
306#878—34no—
307#878—34no—
308#875—32no—
309C4×D12—31no—
310C4×D12—32no—
311C4×D12—32no—
312C4×D12—31no—
313C4×D12—31no—
314C4×D12—32no—
315C4×D12—31no—
316C4×D12—61no—
317C4×D12C2×D311yescharacteristic
318C42×D3C2×D311yescharacteristic
319#870—32no—
320#869—31no—
321#869—31no—
322#869—32no—
323#869—61no—
324#869C2×D311yescharacteristic, complemented
325C4×Dic6—32no—
326C4×Dic6—32no—
327C4×Dic6—32no—
328C4×Dic6C2×D311yescharacteristic, complemented
329C23×C32C2412yes—
330C22×C3⋊D3C2412yes—
331C22×C3×D3C2412yes—
332C22×C3×D3C2411yescharacteristic
333C2×D32—24no—
334C2×D32—24no—
335C2×D32—42no—
336C32×D4—22no—
337C2×C32×C4—24no—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2412yes—
340C2×C32×C4C2411yescharacteristic
341C2×C32×C4C2411yescharacteristic
342#638—44no—
343C2×C3⋊Dic3—44no—
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2414yes—
346C4⋊(C3⋊D3)—22no—
347C4×C3⋊D3—24no—
348#634—24no—
349C3×#67—28no—
350C3×#67—24no—
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2411yescharacteristic
357C2×C3×Dic3C2411yescharacteristic
358C3×D12#4114yescomplemented
359C3×C4×D3—28no—
360C3×C4×D3—22no—
361C3×C4×D3—22no—
362C3×C4×D3—24no—
363C3×C4×D3—22no—
364C3×Dic6—24no—
365C3×Dic6—22no—
366#627—44no—
367#626—24no—
368#624—42no—
369D3×Dic3—44no—
370D3×Dic3—42no—
371D3×Dic3—42no—
372#556—91no—
373#554—92no—
374#552—92no—
375#551—94no—
376D4×Q8—91no—
377#548—92no—
378#547—31no—
379#547—91no—
380#546—92no—
381#542—92no—
382#539—94no—
383#533—91no—
384#529—31no—
385#525—92no—
386C2×C22⋊Q8—92no—
387#520—92no—
388C2×C4×D4—91no—
389C23×D3—32no—
390C23×D3—32no—
391C3×#41—68no—
392C2×C3×Q8—32no—
393C2×C3×Q8—31no—
394C2×C3×D4—21no—
395C2×C3×D4—32no—
396C2×C3×D4—34no—
397C2×C3×D4—31no—
398C2×C3×D4C22×D311yescharacteristic
399C2×C3×D4C22×D311yescharacteristic
400C22×C3×C4—22no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—32no—
404C22×C3×C4—34no—
405C22×C3×C4—31no—
406C22×C3×C4C22×D312yes—
407C22×C3×C4C22×D312yes—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—32no—
411C2×#67—64no—
412C2×#67C22×D312yes—
413C2×#67C22×D314yes—
414C22×Dic3—34no—
415C22×Dic3—34no—
416C22×Dic3—32no—
417C22×Dic3—34no—
418C22×Dic3—32no—
419C22×Dic3—64no—
420D3×Q8—124no—
421#237—124no—
422#237—124no—
423#237—128no—
424D3×D4—64no—
425#235—28no—
426C2×D12—32no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—61no—
430C2×D12—64no—
431C2×D12C22×D311yescharacteristic
432C2×C4×D3—32no—
433C2×C4×D3—32no—
434C2×C4×D3—32no—
435C2×C4×D3—34no—
436C2×C4×D3—32no—
437C2×C4×D3—32no—
438C2×C4×D3—32no—
439C2×C4×D3—62no—
440C2×C4×D3—124no—
441C2×C4×D3—124no—
442C2×C4×D3C22×D311yescharacteristic
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D311yescharacteristic
445C2×C4×D3C22×D312yes—
446C2×C4×D3C22×D314yes—
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—34no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—32no—
462C3×C4⋊C4—31no—
463C3×C4⋊C4—32no—
464C3×C4⋊C4—32no—
465C3×C4⋊C4C22×D311yescharacteristic
466C3×C4⋊C4C22×D311yescharacteristic
467C3×C22⋊C4—22no—
468C3×C22⋊C4—32no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—32no—
471C3×C22⋊C4—32no—
472C3×C22⋊C4—32no—
473C3×C22⋊C4—32no—
474C3×C22⋊C4C22×D312yes—
475C3×C22⋊C4C22×D312yes—
476C3×C42—21no—
477C3×C42—31no—
478C3×C42—31no—
479C3×C42—32no—
480C3×C42—31no—
481C3×C42C22×D311yescharacteristic
482C3×C42C22×D311yescharacteristic
483#217—34no—
484#217—34no—
485#217—32no—
486#217C22×D312yes—
487#217C22×D314yes—
488#217C22×D312yes—
489#217C22×D312yes—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—32no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—32no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—62no—
504(C2×D3)⋊C4—64no—
505(C2×D3)⋊C4C22×D312yes—
506(C2×D3)⋊C4C22×D312yes—
507C4⋊Dic3—31no—
508C4⋊Dic3—32no—
509C4⋊Dic3—32no—
510C4⋊Dic3—32no—
511C4⋊Dic3—32no—
512C4⋊Dic3—31no—
513C4⋊Dic3—34no—
514C4⋊Dic3—34no—
515C4⋊Dic3—34no—
516C4⋊Dic3—32no—
517C4⋊Dic3—34no—
518C4⋊Dic3—34no—
519C4⋊Dic3—62no—
520C4⋊Dic3—62no—
521C4⋊Dic3—61no—
522C4⋊Dic3—64no—
523C4⋊Dic3C22×D312yes—
524C4⋊Dic3C22×D311yescharacteristic
525C4⋊Dic3C22×D311yescharacteristic
526C4⋊Dic3C22×D312yes—
527C4⋊Dic3C22×D312yes—
528C4⋊Dic3C22×D312yes—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—32no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4C22×D312yes—
536Dic3⋊C4C22×D314yes—
537Dic3⋊C4C22×D312yes—
538C4×Dic3—34no—
539C4×Dic3—34no—
540C4×Dic3—34no—
541C4×Dic3—34no—
542C4×Dic3C22×D312yes—
543C4×Dic3C22×D311yescharacteristic
544C4×Dic3C22×D311yescharacteristic
545C4×Dic3C22×D311yescharacteristic
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×D3C2×#4114yes—
558C2×C3×D32−1+412yes—
559D32—48no—
560C32×C4—22no—
561C32×C4—21no—
562C32×C4C2×#4112yes—
563C32×C4H(5,𝔽2)12yes—
564C3⋊Dic3—22no—
565C3⋊Dic3—24no—
566C3×Dic3—21no—
567C3×Dic3—24no—
568C3×Dic3—21no—
569C3×Dic3—22no—
570C3×Dic3—22no—
571C3×Dic3—21no—
572C3×Dic3—22no—
573C2×#41—32no—
574C2×#41—92no—
575C22×Q8—92no—
576C22×D4—91no—
577C23×C4—92no—
578C4⋊Q8—31no—
579C4⋊Q8—92no—
580C4⋊Q8—91no—
581#126—32no—
582#126—94no—
583#126—94no—
584#125—31no—
585#125—92no—
586#125—94no—
587#124—31no—
588#124—92no—
589#124—94no—
590#123—32no—
591#123—34no—
592#123—94no—
593#123—94no—
594#123—94no—
595C22⋊Q8—32no—
596C22⋊Q8—31no—
597C22⋊Q8—94no—
598C22⋊Q8—94no—
599C22⋊Q8—94no—
600C22⋊Q8—94no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604C22⋊Q8—92no—
605C22⋊Q8—92no—
606#121—31no—
607#121—32no—
608#121—94no—
609#121—92no—
610#120—94no—
611C4×Q8—31no—
612C4×Q8—92no—
613C4×Q8—92no—
614C4×Q8—92no—
615C4×D4—32no—
616C4×D4—31no—
617C4×D4—92no—
618C4×D4—91no—
619C4×D4—92no—
620C4×D4—91no—
621C4×D4—92no—
622C4×D4—94no—
623C4×D4—94no—
624C4×D4—94no—
625C4×D4—91no—
626C4×D4D3211yescharacteristic, complemented
627#117—32no—
628#117—92no—
629#117—94no—
630#117—92no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4—91no—
633C2×C4⋊C4—94no—
634C2×C4⋊C4—92no—
635C2×C22⋊C4—92no—
636C2×C22⋊C4—94no—
637C2×C42—31no—
638C23×C3—22no—
639C23×C3—31no—
640C23×C3—32no—
641C23×C3C23×D312yes—
642C23×C3C23×D312yes—
643C22×D3—32no—
644C22×D3—32no—
645C22×D3—62no—
646C22×D3—64no—
647C22×D3—64no—
648C22×D3—64no—
649C22×D3—64no—
650C22×D3—122no—
651C22×D3—122no—
652C22×D3C23×D312yes—
653C22×D3C23×D311yescharacteristic
654C3×Q8—64no—
655C3×Q8—62no—
656C3×D4—24no—
657C3×D4—22no—
658C3×D4—22no—
659C3×D4—34no—
660C3×D4—64no—
661C3×D4—68no—
662C2×C3×C4—24no—
663C2×C3×C4—24no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—22no—
668C2×C3×C4—31no—
669C2×C3×C4—34no—
670C2×C3×C4—32no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—32no—
674C2×C3×C4—32no—
675C2×C3×C4—44no—
676C2×C3×C4—62no—
677C2×C3×C4—68no—
678C2×C3×C4—62no—
679C2×C3×C4—64no—
680C2×C3×C4—62no—
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D312yes—
683C2×C3×C4C23×D312yes—
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D311yescharacteristic
687C2×C3×C4C23×D311yescharacteristic
688C2×C3×C4C23×D311yescharacteristic
689#67—28no—
690#67—24no—
691#67—64no—
692#67—124no—
693#67—124no—
694#67—128no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—34no—
698C2×Dic3—34no—
699C2×Dic3—64no—
700C2×Dic3—62no—
701C2×Dic3—124no—
702C2×Dic3—122no—
703C2×Dic3—122no—
704C2×Dic3—124no—
705C2×Dic3—124no—
706C2×Dic3—128no—
707C2×Dic3C23×D311yescharacteristic
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D314yes—
710C2×Dic3C23×D311yescharacteristic
711C2×Dic3C23×D311yescharacteristic
712C2×Dic3C23×D312yes—
713C2×Dic3C23×D312yes—
714D12—64no—
715D12—62no—
716D12—62no—
717D12—122no—
718D12#23714yescomplemented
719C4×D3—28no—
720C4×D3—22no—
721C4×D3—22no—
722C4×D3—22no—
723C4×D3—24no—
724C4×D3—64no—
725C4×D3—64no—
726C4×D3—124no—
727C4×D3—122no—
728C4×D3—122no—
729C4×D3—122no—
730C4×D3—122no—
731C4×D3—124no—
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—92no—
747#41—68no—
748#41—364no—
749C2×Q8—31no—
750C2×Q8—32no—
751C2×Q8—94no—
752C2×Q8—92no—
753C2×Q8—364no—
754C2×D4—32no—
755C2×D4—34no—
756C2×D4—31no—
757C2×D4—92no—
758C2×D4—94no—
759C2×D4—91no—
760C2×D4—184no—
761C2×D4C2×D3211yescharacteristic
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—34no—
766C22×C4—32no—
767C22×C4—92no—
768C22×C4—94no—
769C22×C4—92no—
770C22×C4—92no—
771C22×C4—94no—
772C22×C4—92no—
773C22×C4—364no—
774C22×C4C2×D3212yes—
775C4⋊C4—32no—
776C4⋊C4—34no—
777C4⋊C4—32no—
778C4⋊C4—31no—
779C4⋊C4—32no—
780C4⋊C4—31no—
781C4⋊C4—32no—
782C4⋊C4—32no—
783C4⋊C4—32no—
784C4⋊C4—92no—
785C4⋊C4—94no—
786C4⋊C4—94no—
787C4⋊C4—94no—
788C4⋊C4—94no—
789C4⋊C4—91no—
790C4⋊C4—94no—
791C4⋊C4—92no—
792C4⋊C4—92no—
793C4⋊C4C2×D3211yescharacteristic
794C22⋊C4—32no—
795C22⋊C4—32no—
796C22⋊C4—32no—
797C22⋊C4—34no—
798C22⋊C4—32no—
799C22⋊C4—32no—
800C22⋊C4—92no—
801C22⋊C4—94no—
802C22⋊C4—94no—
803C22⋊C4—92no—
804C22⋊C4—94no—
805C22⋊C4—94no—
806C22⋊C4—92no—
807C22⋊C4—94no—
808C22⋊C4C2×D3212yes—
809C42—31no—
810C42—31no—
811C42—31no—
812C42—32no—
813C42—94no—
814C42—94no—
815C42C2×D3211yescharacteristic
816C22×C3—24no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—21no—
824C22×C3—34no—
825C22×C3—32no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—61no—
829C22×C3—62no—
830C22×C3—61no—
831C22×C3—62no—
832C22×C3C24×D311yescharacteristic
833C22×C3C24×D311yescharacteristic
834C2×D3—21no—
835C2×D3—22no—
836C2×D3—21no—
837C2×D3—22no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—128no—
848C2×D3—128no—
849C2×D3C2×#23714yes—
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—61no—
860C3×C4—64no—
861C3×C4—62no—
862C3×C4—62no—
863C3×C4—61no—
864C3×C4—61no—
865C3×C4—62no—
866C3×C4C2×#23712yes—
867C3×C4D3×#4112yes—
868C3×C4#100912yes—
869C3×C4#100912yes—
870Dic3—24no—
871Dic3—21no—
872Dic3—22no—
873Dic3—22no—
874Dic3—21no—
875Dic3—21no—
876Dic3—22no—
877Dic3—64no—
878Dic3—64no—
879Dic3—62no—
880Dic3—62no—
881Dic3—124no—
882Dic3—122no—
883C32#352011yescharacteristic, complemented, Sylow
884C23—31no—
885C23—32no—
886C23—92no—
887C23—184no—
888C23—184no—
889C23—362no—
890C23C22×D3212yes—
891Q8—62no—
892Q8—64no—
893Q8—184no—
894Q8—364no—
895D4—22no—
896D4—34no—
897D4—68no—
898D4—64no—
899D4—184no—
900D4—182no—
901D4—364no—
902C2×C4—24no—
903C2×C4—31no—
904C2×C4—31no—
905C2×C4—31no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—34no—
909C2×C4—32no—
910C2×C4—68no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—64no—
914C2×C4—62no—
915C2×C4—92no—
916C2×C4—94no—
917C2×C4—184no—
918C2×C4—362no—
919C2×C4—362no—
920C2×C4—362no—
921C2×C4—364no—
922C2×C4—364no—
923C2×C4C22×D3211yescharacteristic
924C2×C4C22×D3212yes—
925C2×C4C22×D3211yescharacteristic
926C2×C4C22×D3211yescharacteristic
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—44no—
931C2×C3—42no—
932C2×C3—42no—
933C2×C3—64no—
934C2×C3—62no—
935C2×C3C22×#23711yescharacteristic
936C2×C3C2×D3×#4111yescharacteristic
937C2×C3C2×#100911yescharacteristic
938C2×C3C2×#100911yescharacteristic
939C2×C3C2×#101011yescharacteristic
940C2×C3D3×2−1+411yescharacteristic
941D3—22no—
942D3—24no—
943D3—122no—
944D3—122no—
945D3—242no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—34no—
950C22—32no—
951C22—62no—
952C22—61no—
953C22—61no—
954C22—62no—
955C22—182no—
956C22—182no—
957C22—182no—
958C22—368no—
959C22C23×D3211yescharacteristic
960C4—22no—
961C4—21no—
962C4—61no—
963C4—62no—
964C4—62no—
965C4—64no—
966C4—61no—
967C4—61no—
968C4—62no—
969C4—182no—
970C4—184no—
971C4#6430812yes—
972C4D3×#23712yes—
973C3—21no—
974C3#8616711yescharacteristic, complemented
975C3#8668511yescharacteristic, complemented
976C2—42no—
977C2—62no—
978C2—64no—
979C2—362no—
980C2C2×#6430811yescharacteristic
981C2C2×D3×#23711yescharacteristic
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. #10596026C2semidirect
2. C3×#5557C2semidirect
3. C3×#5551C2semidirect
4. #10595306C2semidirect
5. #10595161C2semidirect
6. #10595067C2semidirect
7. #10594993C2semidirect
8. #10594992C2semidirect
9. #10594814C2semidirect
10. D3×#897C2semidirect
11. #10594553C2semidirect
12. #10594303C2semidirect
13. #10594128C2semidirect
14. C4×D3×D12C2semidirect
15. Dic6×D12C2semidirect
16. #10593865C2semidirect
17. #10593859C2semidirect
20. C2×#3830C22semidirect
24. C2×D3×Dic6C22semidirect
25. C32×C4×D4C22semidirect
27. C2×C4⋊(C3⋊Dic3)C22semidirect
28. #64106C22semidirect
29. #64095C22semidirect
31. #64078C22semidirect
33. C3×#938C22semidirect
34. C3×#936C22semidirect
36. C3×#926C22semidirect
37. C3×#924C22semidirect
39. C3×D3×C4⋊C4C22semidirect
40. C3×#890C22semidirect
42. C3×#883C22semidirect
43. C3×#879C22semidirect
46. C3×#869C22semidirect
47. C3×C4×Dic6C22semidirect
49. #63982C22semidirect
50. #63975C22semidirect
52. #67⋊Dic3C22semidirect
53. #67⋊Dic3C22semidirect
55. #63953C22semidirect
58. #63918C22semidirect
60. #63895C22semidirect
63. #63893C22semidirect
67. D3×C4⋊Dic3C22semidirect
69. #63871C22semidirect
70. #63869C22semidirect
73. #63857C22semidirect
76. #63849C22semidirect
77. #63848C22semidirect
78. #63848C22semidirect
79. #63845C22semidirect
80. #63844C22semidirect
81. Dic3×Dic6C22semidirect
82. Dic3×Dic6C22semidirect
84. #63841C22semidirect
105. #5557D3semidirect
109. #5551D3semidirect
216. C3×C4×D4C2×D3semidirect
217. C3×C4×D4C2×D3semidirect
228. #938C2×D3semidirect
231. #936C2×D3semidirect
247. #926C2×D3semidirect
256. #924C2×D3semidirect
280. D3×C4⋊C4C2×D3semidirect
283. #890C2×D3semidirect
296. #883C2×D3semidirect
303. #879C2×D3semidirect
324. #869C2×D3semidirect
328. C4×Dic6C2×D3semidirect
358. C3×D12#41semidirect
626. C4×D4D32semidirect
718. D12#237semidirect
883. C32#3520semidirect
974. C3#86167semidirect
975. C3#86685semidirect

Maximal subgroups

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

subgroupindex
#105960262
C3×#55572
C3×#55512
#105953062
#105951612
#105950672
#105949932
#105949922
#105948142
D3×#8972
#105945532
#105943032
#105941282
C4×D3×D122
Dic6×D122
#105938652
#105938592
#866853
#861673