Finite Group Databasebeta

← #11906199

Subgroups — #11906199

Order 1152.

2340 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic
3C3×#5543C211yesmaximal, characteristic, complemented
4#10595272C212yesmaximal, complemented
5#10595215C212yesmaximal
6#10594988C212yesmaximal, complemented
7#10594915C212yesmaximal, complemented
8D3×#924C212yesmaximal, complemented
9C2×#63857C212yesmaximal, complemented
10#10594485C212yesmaximal, complemented
11#10594344C212yesmaximal, complemented
12#10594170C214yesmaximal, complemented
13#10594133C214yesmaximal, complemented
14#10593956C211yesmaximal, characteristic, complemented
15Dic6×D12C211yesmaximal, characteristic, complemented
16#10593873C211yesmaximal, characteristic, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86948—31nomaximal
19#85766—31nomaximal
20C22×#634C2212yescomplemented
21C2×C3×D3×D4C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C2×D3×Dic6C2212yescomplemented
24C32×C4×D4C2211yescharacteristic
25D4×C3⋊Dic3C2212yes—
26#64133C2212yescomplemented
27#64097C2212yescomplemented
28#64087C2214yescomplemented
29#64078C2211yescharacteristic, complemented
30C4×#634C2211yescharacteristic, complemented
31C3×D4×Dic3C2212yes—
32C3×D4×Dic3C2211yescharacteristic
33C3×C4×#67C2212yes—
34C2×C3×C4⋊Dic3C2212yescomplemented
35C3×#924C2212yescomplemented
36C3×#893C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#890C2212yescomplemented
39C3×#67⋊C4C2212yes—
40C3×D3×C22⋊C4C2212yes—
41C3×#878C2214yescomplemented
42C3×C4×D12C2211yescharacteristic
43C3×C42×D3C2211yescharacteristic
44C3×#869C2211yescharacteristic, complemented
45C3×C4×Dic6C2211yescharacteristic, complemented
46#63982C2214yescomplemented
47#67⋊Dic3C2214yes—
48Dic3×#67C2214yes—
49D3×#217C2214yes—
50C2×Dic3⋊Dic3C2214yescomplemented
51#63964C2214yescomplemented
52#63964C2214yescomplemented
53C2×(C2×D3)⋊Dic3C2214yes—
54#63918C2212yescomplemented
55#63918C2211yescharacteristic, complemented
56C4×#627C2212yescomplemented
57#63899C2214yescomplemented
58#63898C2212yes—
59#63896C2214yescomplemented
60#63893C2214yescomplemented
61Dic3×D12C2212yes—
62D3×C4⋊Dic3C2212yescomplemented
63#63887C2214yescomplemented
64D3×Dic3⋊C4C2214yescomplemented
65#63872C2212yescomplemented
66#63869C2212yescomplemented
67#63867C2212yescomplemented
68#63866C2211yescharacteristic, complemented
69#63857C2211yescharacteristic
70#63857C2214yes—
71#63857C2212yes—
72#63857C2214yescomplemented
73#63857C2212yescomplemented
74#63857C2212yescomplemented
75#63856C2212yes—
76#63856C2211yescharacteristic
77#63855C2212yes—
78#63851C2214yes—
79#63851C2212yes—
80#63846C2214yescomplemented
81#63844C2212yescomplemented
82Dic3×Dic6C2212yescomplemented
83#63841C2212yes—
84#63840C2214yescomplemented
85C3×#554—31no—
86C2×C3×C4×D4—31no—
87#5798—32no—
88C2×#924—32no—
89C2×#924—32no—
90#5730—31no—
91#5728—31no—
92#5690—32no—
93#5689—32no—
94#5635—34no—
95#5634—34no—
96#5632—32no—
97D3×C22⋊Q8—32no—
98#5578—31no—
99Q8×D12—31no—
100#5545—32no—
101C4×D3×D4D311yescharacteristic
102#5543—32no—
103#5543—32no—
104#5543—31no—
105#5543D311yescharacteristic, complemented
106#5539—32no—
107#5539—32no—
108#5539—34no—
109D4×Dic6—31no—
110D4×Dic6—31no—
111D4×Dic6—32no—
112D4×Dic6—31no—
113D4×Dic6—61no—
114#5511—32no—
115C2×#897—32no—
116#5500—32no—
117#5483—34no—
118#5470—31no—
119#5470—31no—
120C23×C3×D3C2312yes—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C22×C3⋊Dic3C2314yes—
124C2×#634—44no—
125C2×#634C2312yes—
126C2×#634C2311yescharacteristic
127C2×#634C2314yes—
128C2×C3×#67C2312yes—
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2312yes—
131C3×D3×D4Q818yescomplemented
132C2×C3×D12C2311yescharacteristic
133C2×C3×C4×D3—44no—
134C2×C3×C4×D3C2312yes—
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2312yes—
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×Dic6C2311yescharacteristic
141C2×C3×Dic6C2312yes—
142C2×#627C2314yes—
143C2×#627C2312yes—
144C2×D3×Dic3C2314yes—
145C2×D3×Dic3C2314yes—
146D3×Dic6—44no—
147C32×C4⋊C4C2311yescharacteristic
148C32×C22⋊C4C2312yes—
149C32×C42C2311yescharacteristic
150#3757C2314yes—
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152C4⋊(C3⋊Dic3)C2312yes—
153C4⋊(C3⋊Dic3)C2312yes—
154#3750C2312yes—
155#3750C2314yes—
156C4×C3⋊Dic3C2312yes—
157C3×#217C2314yes—
158C3×#217C2312yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×C4⋊Dic3C2314yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173#3724C2314yes—
174#3724C2312yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2314yes—
189#3501—91noSylow
190C22×C3×D4—31no—
191C23×C3×C4—32no—
192C2×D3×Q8—32no—
193C2×D3×D4C2×D311yescharacteristic
194C22×C4×D3C2×D312yes—
195C22×Dic6—32no—
196C22×Dic6—32no—
197C22×Dic6—32no—
198C22×Dic6—62no—
199C3×C4⋊Q8—31no—
200C3×#125—32no—
201C3×C22⋊Q8—32no—
202C3×C22⋊Q8—34no—
203C3×C4×Q8—31no—
204C3×C4×D4—21no—
205C3×C4×D4—31no—
206C3×C4×D4—32no—
207C3×C4×D4—32no—
208C3×C4×D4—31no—
209C3×C4×D4—32no—
210C3×C4×D4—31no—
211C3×C4×D4C2×D311yescharacteristic
212C3×C4×D4C2×D311yescharacteristic
213C2×C3×C4⋊C4—32no—
214C2×C3×C4⋊C4—31no—
215C2×C3×C22⋊C4—32no—
216C2×C3×C42—31no—
217C2×#217—34no—
218C2×#217—34no—
219#946—32no—
220#946—31no—
221#946—34no—
222Q8×Dic3—32no—
223#944—31no—
224D4×Dic3—32no—
225D4×Dic3—32no—
226D4×Dic3—34no—
227D4×Dic3—34no—
228D4×Dic3—32no—
229D4×Dic3—32no—
230D4×Dic3—62no—
231D4×Dic3C2×D312yes—
232D4×Dic3C2×D311yescharacteristic
233C4×#67—34no—
234C4×#67C2×D312yes—
235C2×(C2×D3)⋊C4—34no—
236#926—32no—
237#926—32no—
238C2×C4⋊Dic3—34no—
239C2×C4⋊Dic3—32no—
240C2×C4⋊Dic3C2×D312yescomplemented
241#924—32no—
242#924—32no—
243#924—32no—
244#924—31no—
245#924—34no—
246#924—34no—
247#924—32no—
248#924—31no—
249#924—34no—
250#924—32no—
251#924—32no—
252#924—34no—
253#924—32no—
254#924—34no—
255#924—62no—
256#924C2×D312yescomplemented
257C2×Dic3⋊C4—34no—
258C2×Dic3⋊C4—34no—
259#897—32no—
260#897—34no—
261#897—34no—
262#897—32no—
263#897—31no—
264#897—32no—
265#897—34no—
266#896—32no—
267#896—34no—
268#896—34no—
269#896—34no—
270#893—32no—
271#893C2×D311yescharacteristic
272#892—32no—
273D3×C4⋊C4—34no—
274D3×C4⋊C4—32no—
275D3×C4⋊C4C2×D311yescharacteristic
276#890—32no—
277#890—34no—
278#890—32no—
279#890—32no—
280#890C2×D312yescomplemented
281#889—34no—
282#889—32no—
283#888—32no—
284#888—32no—
285#888—34no—
286#888—34no—
287#888—32no—
288#888—31no—
289#888—62no—
290#887—32no—
291#67⋊C4—34no—
292#67⋊C4C2×D312yes—
293D3×C22⋊C4—34no—
294D3×C22⋊C4C2×D312yes—
295#878—34no—
296#878—34no—
297#878—34no—
298#878—34no—
299#878—34no—
300#878—34no—
301#878—34no—
302#878—34no—
303#878—34no—
304#878—34no—
305#878—64no—
306#878C2×D314yescomplemented
307C4×D12—32no—
308C4×D12C2×D311yescharacteristic
309#872—32no—
310C42×D3C2×D311yescharacteristic
311#870—32no—
312#870—32no—
313#869—31no—
314#869—31no—
315#869—31no—
316#869—32no—
317#869—31no—
318#869—61no—
319#869C2×D311yescharacteristic, complemented
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic, complemented
328C23×C32C2412yes—
329C22×C3×D3—42no—
330C22×C3×D3—42no—
331C22×C3×D3C2×Q818yescomplemented
332C22×C3×D3C2411yescharacteristic
333C22×C3×D3C2412yes—
334C32×D4C2×Q814yescomplemented
335C2×C32×C4—24no—
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3—44no—
341C2×C3⋊Dic3C2414yes—
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2412yes—
344#634—22no—
345#634—24no—
346#634—44no—
347C3×#67C2×Q818yescomplemented
348C2×C3×Dic3—42no—
349C2×C3×Dic3—44no—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2411yescharacteristic
356C2×C3×Dic3C2411yescharacteristic
357C3×D12C2×Q814yescomplemented
358C3×C4×D3—24no—
359C3×C4×D3—22no—
360C3×C4×D3—42no—
361C3×C4×D3—42no—
362C3×C4×D3—41no—
363C3×C4×D3C2×Q814yescomplemented
364C3×Dic6—22no—
365C3×Dic6—42no—
366#627—44no—
367#627—42no—
368D3×Dic3—44no—
369D3×Dic3—44no—
370#554—31no—
371#554—92no—
372#554—92no—
373#554—94no—
374#554—92no—
375#554—91no—
376D4×Q8—91no—
377D4×Q8—92no—
378D4×Q8—91no—
379#544—92no—
380#543—94no—
381#533—91no—
382#533—91no—
383C2×C22⋊Q8—92no—
384C2×C22⋊Q8—92no—
385#518—92no—
386C2×C4×D4—31no—
387C24×C3—32no—
388C23×D3C22×D312yes—
389C2×C3×Q8—31no—
390C2×C3×Q8—32no—
391C2×C3×D4—21no—
392C2×C3×D4—32no—
393C2×C3×D4—38no—
394C2×C3×D4—31no—
395C2×C3×D4C22×D311yescharacteristic
396C2×C3×D4C22×D311yescharacteristic
397C22×C3×C4—22no—
398C22×C3×C4—31no—
399C22×C3×C4—32no—
400C22×C3×C4—34no—
401C22×C3×C4—31no—
402C22×C3×C4—32no—
403C22×C3×C4—32no—
404C22×C3×C4—31no—
405C22×C3×C4—32no—
406C22×C3×C4—124no—
407C22×C3×C4C22×D312yes—
408C22×C3×C4C22×D312yes—
409C2×#67C22×D312yes—
410C22×Dic3—34no—
411C22×Dic3—34no—
412C22×Dic3—34no—
413C22×Dic3—34no—
414C22×Dic3—64no—
415C22×Dic3C22×D312yes—
416C22×Dic3C22×D314yes—
417D3×Q8—124no—
418D3×D4Dic618yescomplemented
419C2×D12C22×D311yescharacteristic
420C2×C4×D3—34no—
421C2×C4×D3—34no—
422C2×C4×D3—44no—
423C2×C4×D3C22×D311yescharacteristic
424C2×C4×D3C22×D312yes—
425C2×C4×D3C22×D311yescharacteristic
426C2×C4×D3C22×D312yes—
427C2×C4×D3C22×D312yes—
428C2×C4×D3C22×D311yescharacteristic
429C2×Dic6—31no—
430C2×Dic6—32no—
431C2×Dic6—31no—
432C2×Dic6—32no—
433C2×Dic6—34no—
434C2×Dic6—34no—
435C2×Dic6—32no—
436C2×Dic6—32no—
437C2×Dic6—34no—
438C2×Dic6—34no—
439C2×Dic6—61no—
440C2×Dic6—62no—
441C2×Dic6—64no—
442C2×Dic6—124no—
443C2×Dic6—124no—
444C2×Dic6—124no—
445C2×Dic6—128no—
446C2×Dic6C22×D311yescharacteristic
447C2×Dic6C22×D312yes—
448C3×C4⋊C4—21no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—31no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—34no—
456C3×C4⋊C4—32no—
457C3×C4⋊C4C22×D311yescharacteristic
458C3×C4⋊C4C22×D311yescharacteristic
459C3×C22⋊C4—22no—
460C3×C22⋊C4—32no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—32no—
463C3×C22⋊C4—32no—
464C3×C22⋊C4C22×D312yes—
465C3×C22⋊C4C22×D312yes—
466C3×C42—21no—
467C3×C42—31no—
468C3×C42—31no—
469C3×C42—31no—
470C3×C42—32no—
471C3×C42C22×D311yescharacteristic
472C3×C42C22×D311yescharacteristic
473#217—34no—
474#217—34no—
475#217—34no—
476#217—34no—
477#217—32no—
478#217—34no—
479#217—32no—
480#217—64no—
481#217C22×D312yes—
482#217C22×D314yes—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4C22×D312yes—
489(C2×D3)⋊C4C22×D312yes—
490C4⋊Dic3—32no—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—32no—
494C4⋊Dic3—32no—
495C4⋊Dic3—32no—
496C4⋊Dic3—32no—
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⋊Dic3C22×D312yes—
508C4⋊Dic3C22×D311yescharacteristic
509C4⋊Dic3C22×D311yescharacteristic
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D314yes—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—32no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—62no—
529Dic3⋊C4—64no—
530Dic3⋊C4C22×D312yes—
531Dic3⋊C4C22×D314yes—
532Dic3⋊C4C22×D312yes—
533C4×Dic3—32no—
534C4×Dic3—32no—
535C4×Dic3—34no—
536C4×Dic3—34no—
537C4×Dic3—62no—
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D312yes—
540C4×Dic3C22×D311yescharacteristic
541C4×Dic3C22×D311yescharacteristic
542C22×C32—22no—
543C22×C32—22no—
544C22×C32C22×Q814yes—
545C22×C32C2511yescharacteristic
546C2×C3×D3—22no—
547C2×C3×D3—21no—
548C2×C3×D3—22no—
549C2×C3×D3—21no—
550C2×C3×D3—48no—
551C2×C3×D3C22×Q812yes—
552C2×C3×D3C22×Q814yes—
553C32×C4—22no—
554C32×C4—21no—
555C32×C4C22×Q812yes—
556C32×C4H(5,𝔽2)12yes—
557C3⋊Dic3—22no—
558C3⋊Dic3—24no—
559C3⋊Dic3—22no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3—24no—
564C3×Dic3—21no—
565C3×Dic3—22no—
566C3×Dic3C22×Q812yes—
567C22×Q8—92no—
568C22×Q8—92no—
569C22×D4—31no—
570C23×C4—32no—
571C4⋊Q8—31no—
572C4⋊Q8—91no—
573C4⋊Q8—92no—
574C4⋊Q8—91no—
575C4⋊Q8—94no—
576C4⋊Q8—92no—
577C4⋊Q8—91no—
578#125—32no—
579#125—92no—
580#125—92no—
581#125—94no—
582#125—92no—
583C22⋊Q8—32no—
584C22⋊Q8—34no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—91no—
593C22⋊Q8—92no—
594C22⋊Q8—94no—
595C22⋊Q8—94no—
596C22⋊Q8—92no—
597C22⋊Q8—92no—
598C22⋊Q8—94no—
599C22⋊Q8—92no—
600C22⋊Q8—91no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—94no—
604C4×Q8—31no—
605C4×Q8—92no—
606C4×Q8—92no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×D4—31no—
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—31no—
613C4×D4—32no—
614C4×D4—31no—
615C4×D4—92no—
616C4×D4—94no—
617C4×D4—92no—
618C4×D4—94no—
619C4×D4—92no—
620C4×D4D3211yescharacteristic
621#117—92no—
622#117—92no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—31no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C4⋊C4—94no—
628C2×C22⋊C4—32no—
629C2×C22⋊C4—94no—
630C2×C22⋊C4—94no—
631C2×C42—31no—
632C23×C3—22no—
633C23×C3—31no—
634C23×C3—32no—
635C23×C3—38no—
636C23×C3—122no—
637C23×C3—122no—
638C23×C3C23×D312yes—
639C23×C3C23×D312yes—
640C22×D3—42no—
641C22×D3—42no—
642C22×D3C2×Dic618yescomplemented
643C22×D3C23×D311yescharacteristic
644C22×D3C23×D312yes—
645C3×Q8—62no—
646C3×Q8—122no—
647C3×D4—24no—
648C3×D4—38no—
649C3×D4—34no—
650C3×D4C2×Dic614yescomplemented
651C3×D4D3×Q814yescomplemented
652C2×C3×C4—24no—
653C2×C3×C4—24no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—22no—
658C2×C3×C4—31no—
659C2×C3×C4—34no—
660C2×C3×C4—34no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—44no—
667C2×C3×C4—64no—
668C2×C3×C4—62no—
669C2×C3×C4—121no—
670C2×C3×C4—122no—
671C2×C3×C4—122no—
672C2×C3×C4—124no—
673C2×C3×C4—122no—
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D312yes—
677C2×C3×C4C23×D312yes—
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682#67C2×Dic618yescomplemented
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—34no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—34no—
689C2×Dic3—42no—
690C2×Dic3—44no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—64no—
694C2×Dic3—124no—
695C2×Dic3—124no—
696C2×Dic3—124no—
697C2×Dic3—124no—
698C2×Dic3—128no—
699C2×Dic3C23×D314yes—
700C2×Dic3C23×D311yescharacteristic
701C2×Dic3C23×D311yescharacteristic
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D311yescharacteristic
706D12C2×Dic614yescomplemented
707C4×D3—22no—
708C4×D3—24no—
709C4×D3—42no—
710C4×D3—42no—
711C4×D3—41no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3C2×Dic614yescomplemented
715Dic6—22no—
716Dic6—42no—
717Dic6—64no—
718Dic6—62no—
719Dic6—64no—
720Dic6—62no—
721Dic6—64no—
722Dic6—124no—
723Dic6—122no—
724Dic6—122no—
725Dic6—124no—
726Dic6—124no—
727Dic6—124no—
728Dic6—124no—
729Dic6—128no—
730C2×C32—24no—
731C2×C32C23×Q811yescharacteristic
732C2×C32C2×H(5,𝔽2)11yescharacteristic
733C2×C32#58511yescharacteristic
734C3×D3—22no—
735C3×D3—24no—
736C24—32no—
737C2×Q8—31no—
738C2×Q8—32no—
739C2×Q8—92no—
740C2×Q8—94no—
741C2×Q8—91no—
742C2×Q8—92no—
743C2×Q8—94no—
744C2×Q8—364no—
745C2×Q8—364no—
746C2×D4—32no—
747C2×D4—38no—
748C2×D4—31no—
749C2×D4C2×D3211yescharacteristic
750C22×C4—31no—
751C22×C4—34no—
752C22×C4—32no—
753C22×C4—31no—
754C22×C4—32no—
755C22×C4—31no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—94no—
759C22×C4—94no—
760C22×C4—94no—
761C22×C4—124no—
762C22×C4C2×D3212yes—
763C4⋊C4—31no—
764C4⋊C4—32no—
765C4⋊C4—32no—
766C4⋊C4—31no—
767C4⋊C4—34no—
768C4⋊C4—34no—
769C4⋊C4—32no—
770C4⋊C4—32no—
771C4⋊C4—92no—
772C4⋊C4—92no—
773C4⋊C4—94no—
774C4⋊C4—94no—
775C4⋊C4—94no—
776C4⋊C4—94no—
777C4⋊C4—92no—
778C4⋊C4—92no—
779C4⋊C4—94no—
780C4⋊C4—92no—
781C4⋊C4—91no—
782C4⋊C4—94no—
783C4⋊C4—92no—
784C4⋊C4—92no—
785C4⋊C4—92no—
786C4⋊C4C2×D3211yescharacteristic
787C22⋊C4—32no—
788C22⋊C4—34no—
789C22⋊C4—32no—
790C22⋊C4—32no—
791C22⋊C4—92no—
792C22⋊C4—92no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4C2×D3212yes—
798C42—31no—
799C42—31no—
800C42—31no—
801C42—32no—
802C42—94no—
803C42—92no—
804C42C2×D3211yescharacteristic
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—24no—
810C22×C3—21no—
811C22×C3—32no—
812C22×C3—34no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—62no—
816C22×C3—61no—
817C22×C3—62no—
818C22×C3—61no—
819C22×C3—128no—
820C22×C3C22×Dic614yes—
821C22×C3C2×D3×Q814yes—
822C22×C3C24×D311yescharacteristic
823C22×C3C24×D311yescharacteristic
824C2×D3—21no—
825C2×D3—22no—
826C2×D3—21no—
827C2×D3—22no—
828C2×D3—48no—
829C2×D3C22×Dic612yes—
830C2×D3C22×Dic614yes—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—21no—
834C3×C4—21no—
835C3×C4—22no—
836C3×C4—22no—
837C3×C4—32no—
838C3×C4—42no—
839C3×C4—41no—
840C3×C4—62no—
841C3×C4—62no—
842C3×C4—61no—
843C3×C4—62no—
844C3×C4—64no—
845C3×C4—61no—
846C3×C4C22×Dic612yes—
847C3×C4#100412yes—
848C3×C4C2×D3×Q812yes—
849C3×C4#100912yes—
850Dic3—22no—
851Dic3—21no—
852Dic3—22no—
853Dic3—21no—
854Dic3—24no—
855Dic3—22no—
856Dic3—64no—
857Dic3—64no—
858Dic3—62no—
859Dic3—62no—
860Dic3—64no—
861Dic3—62no—
862Dic3—62no—
863Dic3—124no—
864Dic3—122no—
865Dic3C22×Dic612yes—
866C32#350111yescharacteristic, complemented, Sylow
867C23—32no—
868C23—31no—
869C23—38no—
870C23—122no—
871C23—122no—
872C23C22×D3212yes—
873Q8—62no—
874Q8—122no—
875Q8—182no—
876Q8—184no—
877Q8—364no—
878Q8—364no—
879Q8—362no—
880D4—38no—
881D4—34no—
882D4D3×Dic614yescomplemented
883C2×C4—24no—
884C2×C4—31no—
885C2×C4—34no—
886C2×C4—31no—
887C2×C4—31no—
888C2×C4—32no—
889C2×C4—32no—
890C2×C4—34no—
891C2×C4—32no—
892C2×C4—62no—
893C2×C4—64no—
894C2×C4—92no—
895C2×C4—92no—
896C2×C4—94no—
897C2×C4—122no—
898C2×C4—122no—
899C2×C4—121no—
900C2×C4—122no—
901C2×C4—124no—
902C2×C4—364no—
903C2×C4—364no—
904C2×C4—364no—
905C2×C4C22×D3211yescharacteristic
906C2×C4C22×D3212yes—
907C2×C4C22×D3211yescharacteristic
908C2×C4C22×D3211yescharacteristic
909C2×C3—24no—
910C2×C3—24no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—44no—
915C2×C3—62no—
916C2×C3—64no—
917C2×C3C23×Dic611yescharacteristic
918C2×C3C2×#100411yescharacteristic
919C2×C3C22×D3×Q811yescharacteristic
920C2×C3C2×#100911yescharacteristic
921C2×C3#596411yescharacteristic
922C2×C3#596611yescharacteristic
923D3—22no—
924D3—24no—
925C22—22no—
926C22—22no—
927C22—32no—
928C22—34no—
929C22—61no—
930C22—62no—
931C22—61no—
932C22—62no—
933C22—128no—
934C22C2×D3×Dic614yes—
935C22C23×D3211yescharacteristic
936C4—22no—
937C4—21no—
938C4—32no—
939C4—61no—
940C4—62no—
941C4—62no—
942C4—62no—
943C4—64no—
944C4—61no—
945C4—182no—
946C4—184no—
947C4—182no—
948C4C2×D3×Dic612yes—
949C4#6431412yes—
950C3—21no—
951C3#8576611yescharacteristic, complemented
952C3#8694811yescharacteristic, complemented
953C2—24no—
954C2—62no—
955C2—64no—
956C2C22×D3×Dic611yescharacteristic
957C2C2×#6431411yescharacteristic
958C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×#634C2semidirect
3. C3×#5543C2semidirect
4. #10595272C2semidirect
6. #10594988C2semidirect
7. #10594915C2semidirect
8. D3×#924C2semidirect
9. C2×#63857C2semidirect
10. #10594485C2semidirect
11. #10594344C2semidirect
12. #10594170C2semidirect
13. #10594133C2semidirect
14. #10593956C2semidirect
15. Dic6×D12C2semidirect
16. #10593873C2semidirect
17. #10593859C2semidirect
20. C22×#634C22semidirect
23. C2×D3×Dic6C22semidirect
26. #64133C22semidirect
27. #64097C22semidirect
28. #64087C22semidirect
29. #64078C22semidirect
30. C4×#634C22semidirect
34. C2×C3×C4⋊Dic3C22semidirect
35. C3×#924C22semidirect
38. C3×#890C22semidirect
41. C3×#878C22semidirect
44. C3×#869C22semidirect
45. C3×C4×Dic6C22semidirect
46. #63982C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. #63964C22semidirect
52. #63964C22semidirect
54. #63918C22semidirect
55. #63918C22semidirect
56. C4×#627C22semidirect
57. #63899C22semidirect
59. #63896C22semidirect
60. #63893C22semidirect
62. D3×C4⋊Dic3C22semidirect
63. #63887C22semidirect
64. D3×Dic3⋊C4C22semidirect
65. #63872C22semidirect
66. #63869C22semidirect
67. #63867C22semidirect
68. #63866C22semidirect
72. #63857C22semidirect
73. #63857C22semidirect
74. #63857C22semidirect
80. #63846C22semidirect
81. #63844C22semidirect
82. Dic3×Dic6C22semidirect
84. #63840C22semidirect
105. #5543D3semidirect
131. C3×D3×D4Q8semidirect
240. C2×C4⋊Dic3C2×D3semidirect
256. #924C2×D3semidirect
280. #890C2×D3semidirect
306. #878C2×D3semidirect
319. #869C2×D3semidirect
327. C4×Dic6C2×D3semidirect
331. C22×C3×D3C2×Q8semidirect
334. C32×D4C2×Q8semidirect
347. C3×#67C2×Q8semidirect
357. C3×D12C2×Q8semidirect
363. C3×C4×D3C2×Q8semidirect
418. D3×D4Dic6semidirect
642. C22×D3C2×Dic6semidirect
650. C3×D4C2×Dic6semidirect
651. C3×D4D3×Q8semidirect
682. #67C2×Dic6semidirect
706. D12C2×Dic6semidirect
714. C4×D3C2×Dic6semidirect
866. C32#3501semidirect
882. D4D3×Dic6semidirect
951. C3#85766semidirect
952. C3#86948semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×C4×D3×D42
C3×#55432
#105952722
#105952152
#105949882
#105949152
D3×#9242
C2×#638572
#105944852
#105943442
#105941702
#105941332
#105939562
Dic6×D122
#105938732
#105938592
#869483
#857663