Finite Group Databasebeta

← #11906364

Subgroups — #11906364

Order 1152.

2265 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic, complemented
2C3×#5504C211yesmaximal, characteristic
3C3×#5500C211yesmaximal, characteristic, complemented
4#10595052C211yesmaximal, characteristic, complemented
5#10595050C211yesmaximal, characteristic, complemented
6#10594992C211yesmaximal, characteristic
7#10594959C214yesmaximal, complemented
8#10594958C211yesmaximal, characteristic
9#10594915C214yesmaximal, complemented
10#10594502C212yesmaximal, complemented
11#10594485C212yesmaximal, complemented
12#10594477C212yesmaximal, complemented
13#10594376C212yesmaximal, complemented
14D3×#888C212yesmaximal, complemented
15#10594344C212yesmaximal, complemented
16#10594322C212yesmaximal, complemented
17#10594312C212yesmaximal, complemented
18#86586—31nomaximal
19#85889—31nomaximal
20C22×#634C2212yes—
21C2×C3×#235C2211yescharacteristic
22C2×D3×Dic6C2214yes—
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×#3750C2212yes—
26C2×C4×C3⋊Dic3C2211yescharacteristic
27#64097C2212yes—
28#64097C2212yes—
29#64097C2212yes—
30#64097C2212yes—
31C3×C4×#67C2214yes—
32C3×#926C2211yescharacteristic
33C3×#926C2211yescharacteristic
34C3×#926C2211yescharacteristic
35C3×#924C2214yes—
36C3×#893C2212yes—
37C3×#892C2212yes—
38C3×D3×C4⋊C4C2212yes—
39C3×#890C2212yes—
40C3×#890C2212yes—
41C3×#888C2212yes—
42C3×#888C2212yes—
43C3×#887C2212yes—
44#63982C2212yes—
45#63982C2214yes—
46#63982C2212yes—
47#67⋊Dic3C2212yes—
48#67⋊Dic3C2214yes—
49#67⋊Dic3C2212yes—
50#63919C2211yescharacteristic
51#63919C2211yescharacteristic
52#63918C2212yes—
53#63918C2212yes—
54C4×#627C2212yes—
55C4×#627C2212yes—
56#63899C2214yes—
57#63898C2211yescharacteristic
58#63898C2211yescharacteristic
59#63896C2214yes—
60#63896C2214yes—
61Dic3×D12C2212yes—
62D3×C4⋊Dic3C2212yes—
63#63887C2214yes—
64D3×Dic3⋊C4C2214yes—
65C4×D3×Dic3C2212yes—
66#63872C2211yescharacteristic
67#63872C2211yescharacteristic
68#63869C2212yes—
69#63869C2212yes—
70#63867C2214yes—
71#63866C2214yes—
72#63857C2214yes—
73#63855C2212yes—
74#63851C2214yes—
75#63846C2214yes—
76#63844C2214yes—
77#63843C2211yescharacteristic
78#63843C2211yescharacteristic
79Dic3×Dic6C2212yes—
80#63841C2212yes—
81#63840C2214yes—
82#63840C2214yes—
83#63839C2214yes—
84#63837C2214yes—
85C3×#544—31no—
86C3×#520—31no—
87#5827—31no—
88Dic3×#41—31no—
89#5729—32no—
90#5727—32no—
91D3×C4⋊Q8—32no—
92#5722—32no—
93#5690—32no—
94#5689—32no—
95#5688—32no—
96#5685—32no—
97#5636—34no—
98#5632—34no—
99#5569—32no—
100Q8×Dic6—32no—
101#5539—34no—
102#5539—32no—
103D4×Dic6—34no—
104D4×Dic6—32no—
105#5523—31no—
106#5522—31no—
107#5519—31no—
108#5519—31no—
109#5519—32no—
110#5517—31no—
111#5517—31no—
112#5517—32no—
113#5504D311yescharacteristic
114#5500—32no—
115#5500D311yescharacteristic, complemented
116C2×#888—31no—
117C2×#888—31no—
118C2×#888—32no—
119C2×#888—61no—
120C22×C32×C4C2312yes—
121C22×C32×C4C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2312yes—
125C2×#634—44no—
126C2×#634C2314yes—
127C2×#634C2314yes—
128C2×C3×#67C2312yes—
129C3×#235Q818yescomplemented
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×Dic6C2314yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2312yes—
136C2×#627C2312yes—
137C2×#627C2314yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2314yes—
141D3×Dic6—48no—
142C32×C4⋊C4C2312yes—
143C32×C4⋊C4C2312yes—
144C4⋊(C3⋊Dic3)C2312yes—
145C4⋊(C3⋊Dic3)C2312yes—
146#3750C2314yes—
147#3750C2314yes—
148C4×C3⋊Dic3C2311yescharacteristic
149C4×C3⋊Dic3C2311yescharacteristic
150C4×C3⋊Dic3C2311yescharacteristic
151C4×C3⋊Dic3C2311yescharacteristic
152C3×#217C2312yes—
153C3×#217C2312yes—
154C3×#217C2312yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×C4⋊Dic3C2311yescharacteristic
158C3×C4⋊Dic3C2314yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2311yescharacteristic
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×C4×Dic3C2314yes—
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170#3724C2312yes—
171#3724C2312yes—
172#3724C2314yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188#3503—91noSylow
189C2×C3×#41—31no—
190C2×D3×Q8—34no—
191C2×#235C2×D311yescharacteristic
192C22×Dic6—32no—
193C22×Dic6—32no—
194C22×Dic6—34no—
195C22×Dic6—62no—
196C3×C4⋊Q8—32no—
197C3×C4⋊Q8—32no—
198C3×#125—32no—
199C3×#125—32no—
200C3×C22⋊Q8—34no—
201C3×C4×Q8—32no—
202C3×C4×D4—34no—
203C3×C4×D4—32no—
204C3×#117—31no—
205C3×#117—31no—
206C3×#117—31no—
207C3×#117—32no—
208C2×C3×C4⋊C4—21no—
209C2×C3×C4⋊C4—32no—
210C2×C3×C4⋊C4C2×D311yescharacteristic
211C2×C3×C4⋊C4C2×D311yescharacteristic
212#946—34no—
213Q8×Dic3—31no—
214Q8×Dic3—31no—
215Q8×Dic3—32no—
216#944—34no—
217#944—34no—
218D4×Dic3—32no—
219D4×Dic3—34no—
220D4×Dic3—32no—
221D4×Dic3—31no—
222D4×Dic3—31no—
223D4×Dic3—32no—
224C4×#67C2×D314yes—
225#926—32no—
226#926—32no—
227#926C2×D311yescharacteristic
228#926C2×D311yescharacteristic
229#926C2×D311yescharacteristic
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—32no—
233C2×C4⋊Dic3—61no—
234#924—34no—
235#924—34no—
236#924C2×D314yes—
237C2×Dic3⋊C4—32no—
238C2×Dic3⋊C4—32no—
239C2×Dic3⋊C4—34no—
240C2×Dic3⋊C4—62no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3—32no—
244C2×C4×Dic3—61no—
245#897—34no—
246#896—34no—
247#896—34no—
248#896—34no—
249#896—34no—
250#893—31no—
251#893—31no—
252#893C2×D312yes—
253#892—32no—
254#892C2×D312yes—
255D3×C4⋊C4—34no—
256D3×C4⋊C4—32no—
257D3×C4⋊C4C2×D312yes—
258#890—31no—
259#890—31no—
260#890—34no—
261#890—31no—
262#890—31no—
263#890—32no—
264#890—32no—
265#890C2×D312yes—
266#890C2×D312yes—
267#889—34no—
268#889—34no—
269#888—34no—
270#888—32no—
271#888—32no—
272#888—32no—
273#888—32no—
274#888—32no—
275#888—32no—
276#888—32no—
277#888—32no—
278#888—31no—
279#888—31no—
280#888—31no—
281#888—31no—
282#888—34no—
283#888—34no—
284#888—34no—
285#888—34no—
286#888—32no—
287#888—32no—
288#888—62no—
289#888—62no—
290#888—62no—
291#888—62no—
292#888C2×D312yes—
293#888C2×D312yes—
294#887—31no—
295#887—31no—
296#887—34no—
297#887—34no—
298#887C2×D312yes—
299#67⋊C4—32no—
300#67⋊C4—34no—
301#67⋊C4—32no—
302#878—34no—
303#878—32no—
304#878—34no—
305#878—32no—
306#878—32no—
307#878—32no—
308#878—34no—
309#878—34no—
310#878—34no—
311#878—34no—
312C4×D12—32no—
313#872—32no—
314C42×D3—32no—
315#870—32no—
316#870—32no—
317#870—34no—
318#869—34no—
319#869—32no—
320#869—32no—
321C4×Dic6—32no—
322C4×Dic6—34no—
323C4×Dic6—34no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—32no—
327C4×Dic6—32no—
328C23×C32C2411yescharacteristic
329C22×C3×D3C2412yes—
330C2×C32×C4—42no—
331C2×C32×C4C2×Q814yescomplemented
332C2×C32×C4C2414yes—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C3⋊Dic3—22no—
336C2×C3⋊Dic3—22no—
337C2×C3⋊Dic3—42no—
338C2×C3⋊Dic3C2414yes—
339C2×C3⋊Dic3C2411yescharacteristic
340C2×C3⋊Dic3C2411yescharacteristic
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2411yescharacteristic
343#634—28no—
344#634—44no—
345C3×#67C2×Q818yescomplemented
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C3×D12C2×Q814yescomplemented
354C3×C4×D3—44no—
355C3×C4×D3C2×Q818yescomplemented
356C3×Dic6—44no—
357C3×Dic6C2×Q814yescomplemented
358#627—24no—
359#627—24no—
360#627—44no—
361D3×Dic3—24no—
362D3×Dic3—24no—
363D3×Dic3—44no—
364Q82—92no—
365#557—92no—
366#554—94no—
367#554—92no—
368D4×Q8—94no—
369D4×Q8—92no—
370#544—31no—
371#544—92no—
372#544—91no—
373#544—92no—
374#533—91no—
375#533—92no—
376C2×C4⋊Q8—92no—
377C2×C4⋊Q8—91no—
378#520—31no—
379#520—91no—
380C4×#41—91no—
381C3×#41—38no—
382C2×C3×Q8—31no—
383C2×C3×Q8—34no—
384C2×C3×D4—32no—
385C2×C3×D4—31no—
386C22×C3×C4—21no—
387C22×C3×C4—22no—
388C22×C3×C4—32no—
389C22×C3×C4—34no—
390C22×C3×C4C22×D312yes—
391C22×C3×C4C22×D312yes—
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C2×#67C22×D312yes—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—32no—
400C22×Dic3—32no—
401C22×Dic3—32no—
402C22×Dic3—32no—
403C22×Dic3—34no—
404C22×Dic3—61no—
405C22×Dic3—61no—
406C22×Dic3—62no—
407D3×Q8—128no—
408#235Dic618yescomplemented
409C2×D12C22×D311yescharacteristic
410C2×C4×D3—32no—
411C2×C4×D3—32no—
412C2×C4×D3—34no—
413C2×C4×D3C22×D314yes—
414C2×C4×D3C22×D312yes—
415C2×Dic6—34no—
416C2×Dic6—34no—
417C2×Dic6—32no—
418C2×Dic6—32no—
419C2×Dic6—32no—
420C2×Dic6—32no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—64no—
426C2×Dic6—64no—
427C2×Dic6—128no—
428C2×Dic6—124no—
429C2×Dic6—124no—
430C2×Dic6—128no—
431C2×Dic6C22×D314yes—
432C2×Dic6C22×D311yescharacteristic
433C3×C4⋊C4—22no—
434C3×C4⋊C4—22no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—34no—
437C3×C4⋊C4—34no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—34no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—34no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4C22×D312yes—
446C3×C4⋊C4C22×D312yes—
447C3×C4⋊C4C22×D312yes—
448C3×C4⋊C4C22×D312yes—
449C3×C22⋊C4—32no—
450C3×C22⋊C4—32no—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—34no—
453C3×C42—32no—
454C3×C42—34no—
455C3×C42—32no—
456C3×C42—32no—
457#217—32no—
458#217—32no—
459#217—34no—
460#217C22×D312yes—
461#217C22×D312yes—
462#217C22×D312yes—
463(C2×D3)⋊C4—32no—
464(C2×D3)⋊C4—32no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4C22×D314yes—
467C4⋊Dic3—32no—
468C4⋊Dic3—32no—
469C4⋊Dic3—32no—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—34no—
473C4⋊Dic3—32no—
474C4⋊Dic3—32no—
475C4⋊Dic3—32no—
476C4⋊Dic3—32no—
477C4⋊Dic3—34no—
478C4⋊Dic3—34no—
479C4⋊Dic3—32no—
480C4⋊Dic3—62no—
481C4⋊Dic3—62no—
482C4⋊Dic3C22×D314yes—
483C4⋊Dic3C22×D311yescharacteristic
484C4⋊Dic3C22×D311yescharacteristic
485C4⋊Dic3C22×D311yescharacteristic
486C4⋊Dic3C22×D311yescharacteristic
487C4⋊Dic3C22×D311yescharacteristic
488C4⋊Dic3C22×D311yescharacteristic
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—32no—
494Dic3⋊C4—32no—
495Dic3⋊C4—34no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—32no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—32no—
507Dic3⋊C4—32no—
508Dic3⋊C4—64no—
509Dic3⋊C4—64no—
510Dic3⋊C4C22×D314yes—
511Dic3⋊C4C22×D314yes—
512Dic3⋊C4C22×D314yes—
513C4×Dic3—31no—
514C4×Dic3—31no—
515C4×Dic3—31no—
516C4×Dic3—31no—
517C4×Dic3—31no—
518C4×Dic3—31no—
519C4×Dic3—31no—
520C4×Dic3—31no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—34no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—61no—
528C4×Dic3—61no—
529C4×Dic3—61no—
530C4×Dic3—61no—
531C4×Dic3C22×D312yes—
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D314yes—
534C4×Dic3C22×D312yes—
535C22×C32—21no—
536C22×C32—21no—
537C22×C32C22×Q812yes—
538C22×C32C2511yescharacteristic
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3C22×Q814yes—
542C32×C4—24no—
543C32×C4C22×Q812yes—
544C32×C4C22×Q812yes—
545C3⋊Dic3—21no—
546C3⋊Dic3—21no—
547C3⋊Dic3—24no—
548C3⋊Dic3H(5,𝔽2)12yes—
549C3⋊Dic32−1+412yes—
550C3×Dic3—22no—
551C3×Dic3—22no—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3C22×Q814yes—
557C2×#41—31no—
558C22×Q8—94no—
559C22×Q8—92no—
560C4⋊Q8—32no—
561C4⋊Q8—32no—
562C4⋊Q8—92no—
563C4⋊Q8—92no—
564C4⋊Q8—94no—
565C4⋊Q8—91no—
566C4⋊Q8—94no—
567C4⋊Q8—91no—
568C4⋊Q8—94no—
569C4⋊Q8—94no—
570C4⋊Q8—92no—
571C4⋊Q8—92no—
572C4⋊Q8—92no—
573C4⋊Q8—92no—
574#125—32no—
575#125—32no—
576#125—92no—
577#125—94no—
578#125—92no—
579#125—91no—
580#125—91no—
581#125—94no—
582C22⋊Q8—34no—
583C22⋊Q8—92no—
584C22⋊Q8—92no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C4×Q8—32no—
593C4×Q8—92no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—94no—
597C4×Q8—92no—
598C4×Q8—91no—
599C4×Q8—91no—
600C4×D4—34no—
601C4×D4—32no—
602C4×D4—92no—
603C4×D4—92no—
604C4×D4—92no—
605C4×D4—94no—
606C4×D4—91no—
607C4×D4—91no—
608#117—31no—
609#117—31no—
610#117—31no—
611#117—32no—
612#117—92no—
613#117—92no—
614C2×C4⋊C4—32no—
615C2×C4⋊C4—92no—
616C2×C4⋊C4—94no—
617C2×C4⋊C4—91no—
618C2×C4⋊C4—92no—
619C2×C4⋊C4D3211yescharacteristic
620C2×C42—92no—
621C2×C42—91no—
622C23×C3—21no—
623C23×C3—32no—
624C23×C3C23×D311yescharacteristic
625C23×C3C23×D311yescharacteristic
626C22×D3C23×D312yes—
627C3×Q8—34no—
628C3×Q8—124no—
629C3×D4—38no—
630C3×D4—34no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—24no—
634C2×C3×C4—24no—
635C2×C3×C4—32no—
636C2×C3×C4—38no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—42no—
644C2×C3×C4—42no—
645C2×C3×C4—44no—
646C2×C3×C4—124no—
647C2×C3×C4C2×Dic614yescomplemented
648C2×C3×C4D3×Q814yescomplemented
649C2×C3×C4C23×D314yes—
650C2×C3×C4C23×D314yes—
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655#67C2×Dic618yescomplemented
656C2×Dic3—31no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—31no—
660C2×Dic3—31no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—34no—
665C2×Dic3—34no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—64no—
671C2×Dic3—64no—
672C2×Dic3—64no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—64no—
678C2×Dic3—64no—
679C2×Dic3—124no—
680C2×Dic3—122no—
681C2×Dic3—122no—
682C2×Dic3—124no—
683C2×Dic3C23×D312yes—
684C2×Dic3C23×D312yes—
685C2×Dic3C23×D312yes—
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D312yes—
690D12C2×Dic614yescomplemented
691C4×D3—44no—
692C4×D3—64no—
693C4×D3—64no—
694C4×D3—124no—
695C4×D3C2×Dic618yescomplemented
696Dic6—44no—
697Dic6—64no—
698Dic6—64no—
699Dic6—64no—
700Dic6—64no—
701Dic6—68no—
702Dic6—68no—
703Dic6—128no—
704Dic6—124no—
705Dic6—124no—
706Dic6—124no—
707Dic6—124no—
708Dic6—128no—
709Dic6C2×Dic614yescomplemented
710C2×C32—22no—
711C2×C32C23×Q811yescharacteristic
712C2×C32C2×H(5,𝔽2)11yescharacteristic
713C2×C32C2×2−1+411yescharacteristic
714C3×D3—24no—
715#41—38no—
716C2×Q8—31no—
717C2×Q8—34no—
718C2×Q8—92no—
719C2×Q8—92no—
720C2×Q8—94no—
721C2×Q8—94no—
722C2×Q8—94no—
723C2×Q8—364no—
724C2×Q8—368no—
725C2×D4—32no—
726C2×D4—31no—
727C22×C4—32no—
728C22×C4—34no—
729C22×C4—92no—
730C22×C4—92no—
731C22×C4—94no—
732C22×C4—91no—
733C22×C4—91no—
734C22×C4—92no—
735C22×C4C2×D3212yes—
736C22×C4C2×D3211yescharacteristic
737C4⋊C4—31no—
738C4⋊C4—34no—
739C4⋊C4—31no—
740C4⋊C4—34no—
741C4⋊C4—31no—
742C4⋊C4—31no—
743C4⋊C4—31no—
744C4⋊C4—31no—
745C4⋊C4—34no—
746C4⋊C4—34no—
747C4⋊C4—92no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—92no—
751C4⋊C4—92no—
752C4⋊C4—92no—
753C4⋊C4—94no—
754C4⋊C4—92no—
755C4⋊C4—92no—
756C4⋊C4—94no—
757C4⋊C4—92no—
758C4⋊C4—92no—
759C4⋊C4—92no—
760C4⋊C4—94no—
761C4⋊C4—92no—
762C4⋊C4—94no—
763C4⋊C4C2×D3212yes—
764C4⋊C4C2×D3212yes—
765C22⋊C4—32no—
766C22⋊C4—32no—
767C22⋊C4—32no—
768C22⋊C4—34no—
769C22⋊C4—94no—
770C22⋊C4—92no—
771C22⋊C4—92no—
772C42—32no—
773C42—34no—
774C42—32no—
775C42—32no—
776C42—92no—
777C42—92no—
778C42—94no—
779C42—91no—
780C42—91no—
781C42—91no—
782C42—91no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—22no—
790C22×C3—21no—
791C22×C3—34no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3C22×Dic612yes—
795C22×C3C2×D3×Q812yes—
796C22×C3C24×D311yescharacteristic
797C22×C3C24×D311yescharacteristic
798C2×D3—22no—
799C2×D3—22no—
800C2×D3C22×Dic614yes—
801C3×C4—24no—
802C3×C4—24no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—34no—
806C3×C4—44no—
807C3×C4—62no—
808C3×C4—62no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4C22×Dic612yes—
814C3×C4C22×Dic612yes—
815C3×C4C2×D3×Q812yes—
816C3×C4C2×D3×Q812yes—
817Dic3—22no—
818Dic3—22no—
819Dic3—22no—
820Dic3—22no—
821Dic3—22no—
822Dic3—22no—
823Dic3—32no—
824Dic3—32no—
825Dic3—32no—
826Dic3—32no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—62no—
831Dic3—64no—
832Dic3—64no—
833Dic3—61no—
834Dic3—61no—
835Dic3—61no—
836Dic3—61no—
837Dic3—124no—
838Dic3C22×Dic614yes—
839C32#350311yescharacteristic, complemented, Sylow
840C23—32no—
841C23C22×D3211yescharacteristic
842Q8—34no—
843Q8—124no—
844Q8—188no—
845Q8—184no—
846Q8—184no—
847Q8—364no—
848Q8—364no—
849D4—38no—
850D4—34no—
851C2×C4—32no—
852C2×C4—38no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—42no—
860C2×C4—91no—
861C2×C4—91no—
862C2×C4—91no—
863C2×C4—91no—
864C2×C4—94no—
865C2×C4—124no—
866C2×C4—184no—
867C2×C4—184no—
868C2×C4—182no—
869C2×C4—182no—
870C2×C4—364no—
871C2×C4—362no—
872C2×C4D3×Dic614yescomplemented
873C2×C4C22×D3214yes—
874C2×C4C22×D3211yescharacteristic
875C2×C4C22×D3211yescharacteristic
876C2×C3—24no—
877C2×C3—22no—
878C2×C3—22no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—64no—
883C2×C3C23×Dic611yescharacteristic
884C2×C3C22×D3×Q811yescharacteristic
885C2×C3D3×H(5,𝔽2)11yescharacteristic
886C2×C3D3×H(5,𝔽2)11yescharacteristic
887C2×C3D3×2−1+411yescharacteristic
888C2×C3D3×2−1+411yescharacteristic
889D3—24no—
890C22—21no—
891C22—21no—
892C22—34no—
893C22—62no—
894C22—62no—
895C22C2×D3×Dic612yes—
896C22C23×D3211yescharacteristic
897C4—24no—
898C4—34no—
899C4—62no—
900C4—62no—
901C4—62no—
902C4—62no—
903C4—62no—
904C4—62no—
905C4—92no—
906C4—92no—
907C4—181no—
908C4—184no—
909C4—181no—
910C4C2×D3×Dic612yes—
911C4C2×D3×Dic612yes—
912C3—21no—
913C3#8588911yescharacteristic, complemented
914C3#8658611yescharacteristic, complemented
915C2—22no—
916C2—64no—
917C2C22×D3×Dic611yescharacteristic
918C2#1059667511yescharacteristic
919C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
prime radicalC2×C3×#235C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64097C2semidirect
3. C3×#5500C2semidirect
4. #10595052C2semidirect
5. #10595050C2semidirect
7. #10594959C2semidirect
9. #10594915C2semidirect
10. #10594502C2semidirect
11. #10594485C2semidirect
12. #10594477C2semidirect
13. #10594376C2semidirect
14. D3×#888C2semidirect
15. #10594344C2semidirect
16. #10594322C2semidirect
17. #10594312C2semidirect
115. #5500D3semidirect
129. C3×#235Q8semidirect
331. C2×C32×C4C2×Q8semidirect
345. C3×#67C2×Q8semidirect
353. C3×D12C2×Q8semidirect
355. C3×C4×D3C2×Q8semidirect
357. C3×Dic6C2×Q8semidirect
408. #235Dic6semidirect
647. C2×C3×C4C2×Dic6semidirect
648. C2×C3×C4D3×Q8semidirect
655. #67C2×Dic6semidirect
690. D12C2×Dic6semidirect
695. C4×D3C2×Dic6semidirect
709. Dic6C2×Dic6semidirect
839. C32#3503semidirect
872. C2×C4D3×Dic6semidirect
913. C3#85889semidirect
914. C3#86586semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
C3×#55042
C3×#55002
#105950522
#105950502
#105949922
#105949592
#105949582
#105949152
#105945022
#105944852
#105944772
#105943762
D3×#8882
#105943442
#105943222
#105943122
#865863
#858893