Finite Group Databasebeta

← #11906366

Subgroups — #11906366

Order 1152.

2223 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595971C211yesmaximal, characteristic, complemented
2C3×#5504C211yesmaximal, characteristic
3C2×C3×#888C211yesmaximal, characteristic, complemented
4#10595051C211yesmaximal, characteristic, complemented
5#10595049C211yesmaximal, characteristic, complemented
6#10594986C211yesmaximal, characteristic
7#10594951C214yesmaximal, complemented
8Dic3×#235C211yesmaximal, characteristic
9Dic6×#67C214yesmaximal, complemented
10#10594502C212yesmaximal, complemented
11#10594460C212yesmaximal, complemented
12#10594445C212yesmaximal, complemented
13#10594376C212yesmaximal, complemented
14D3×#888C212yesmaximal, complemented
15#10594342C212yesmaximal, complemented
16#10594317C212yesmaximal, complemented
17#10594312C212yesmaximal, complemented
18#86215—31nomaximal
19#85889—31nomaximal
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6C2212yes—
22C2×D3×Dic6C2214yes—
23C2×C32×C4⋊C4C2211yescharacteristic
24#64135C2211yescharacteristic
25#64135C2211yescharacteristic
26#64133C2214yes—
27#64099C2212yes—
28#64099C2212yes—
29#64097C2212yes—
30#64097C2212yes—
31C3×C4×#67C2214yes—
32C3×#926C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×C4×Dic3C2211yescharacteristic
36C3×#893C2212yes—
37C3×#892C2212yes—
38C3×D3×C4⋊C4C2212yes—
39C3×#888C2212yes—
40C3×#888C2212yes—
41C3×#888C2212yes—
42C3×#888C2212yes—
43C3×#887C2212yes—
44Dic3×#67C2212yes—
45Dic3×#67C2214yes—
46Dic3×#67C2212yes—
47#63964C2212yes—
48#63964C2214yes—
49#63964C2212yes—
50#63919C2212yes—
51#63918C2212yes—
52#63918C2211yescharacteristic
53#63918C2211yescharacteristic
54C4×#627C2212yes—
55C4×#627C2212yes—
56#63898C2212yes—
57#63896C2214yes—
58#63893C2214yes—
59Dic3×D12C2211yescharacteristic
60Dic3×D12C2211yescharacteristic
61D3×C4⋊Dic3C2212yes—
62#63887C2214yes—
63#63887C2214yes—
64D3×Dic3⋊C4C2214yes—
65C4×D3×Dic3C2212yes—
66#63872C2212yes—
67#63869C2212yes—
68#63869C2211yescharacteristic
69#63869C2211yescharacteristic
70#63867C2214yes—
71#63866C2214yes—
72#63856C2214yes—
73#63855C2212yes—
74#63851C2214yes—
75#63845C2214yes—
76#63843C2212yes—
77Dic3×Dic6C2211yescharacteristic
78Dic3×Dic6C2211yescharacteristic
79Dic3×Dic6C2214yes—
80#63841C2212yes—
81#63840C2214yes—
82#63839C2214yes—
83#63839C2214yes—
84#63837C2214yes—
85C2×C3×C4⋊Q8—31no—
86C3×#520—31no—
87#5827—31no—
88Dic3×#41—31no—
89Q8×#67—34no—
90#5730—32no—
91#5729—32no—
92#5729—32no—
93#5728—32no—
94#5727—32no—
95D3×C4⋊Q8—32no—
96#5722—32no—
97#5721—32no—
98#5569—32no—
99Q8×Dic6—32no—
100#5539—34no—
101#5539—32no—
102D4×Dic6—34no—
103D4×Dic6—32no—
104#5519—31no—
105#5519—32no—
106#5517—31no—
107#5517—32no—
108#5511—34no—
109#5504—31no—
110#5504D311yescharacteristic
111#5500—31no—
112#5500—31no—
113#5500—31no—
114#5500—32no—
115#5500—61no—
116C2×#888—32no—
117C2×#888D311yescharacteristic, complemented
118C4×#235—31no—
119#5470—31no—
120C22×C32×C4C2312yes—
121C22×C32×C4C2311yescharacteristic
122C2×#634C2314yes—
123C2×C3×#67C2312yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2312yes—
127C3×#235Q818yescomplemented
128C2×C3×D12C2311yescharacteristic
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2312yes—
131C2×C3×Dic6—44no—
132C2×C3×Dic6C2314yes—
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—
144#3757C2312yes—
145#3757C2312yes—
146C4⋊(C3⋊Dic3)C2311yescharacteristic
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4⋊(C3⋊Dic3)C2314yes—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151#3750C2314yes—
152#3750C2314yes—
153C4×C3⋊Dic3C2312yes—
154C4×C3⋊Dic3C2312yes—
155C3×#217C2312yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2314yes—
164C3×C4×Dic3C2314yes—
165C3×C4×Dic3C2312yes—
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2311yescharacteristic
170#3724C2312yes—
171#3724C2314yes—
172#3724C2312yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
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—
190C22×C3×Q8—32no—
191C2×D3×Q8—34no—
192C2×#235C2×D311yescharacteristic
193C22×Dic6—34no—
194C22×Dic6C2×D312yes—
195C3×C4⋊Q8—32no—
196C3×C4⋊Q8—32no—
197C3×C4⋊Q8—32no—
198C3×C4⋊Q8—32no—
199C3×C4×Q8—32no—
200C3×C4×D4—34no—
201C3×C4×D4—32no—
202C3×#117—31no—
203C3×#117—32no—
204C2×C3×C4⋊C4—21no—
205C2×C3×C4⋊C4—32no—
206C2×C3×C4⋊C4—31no—
207C2×C3×C4⋊C4—32no—
208C2×C3×C4⋊C4C2×D311yescharacteristic
209C2×C3×C4⋊C4C2×D311yescharacteristic
210C2×C3×C42—31no—
211#946—34no—
212#946—34no—
213#946—34no—
214Q8×Dic3—32no—
215Q8×Dic3—34no—
216Q8×Dic3—31no—
217Q8×Dic3—31no—
218#944—34no—
219#944—34no—
220#944—34no—
221D4×Dic3—32no—
222D4×Dic3—34no—
223D4×Dic3—32no—
224D4×Dic3—32no—
225D4×Dic3—31no—
226D4×Dic3—31no—
227C4×#67—32no—
228C4×#67—32no—
229C4×#67—34no—
230C4×#67C2×D314yes—
231#926—31no—
232#926—31no—
233#926—31no—
234#926—31no—
235#926—32no—
236#926—32no—
237#926—61no—
238#926—61no—
239#926C2×D311yescharacteristic
240C2×C4⋊Dic3—32no—
241C2×C4⋊Dic3C2×D311yescharacteristic
242#924—34no—
243#924—34no—
244#924—34no—
245#924—32no—
246#924—32no—
247#924—34no—
248#924—34no—
249#924—64no—
250C2×Dic3⋊C4—34no—
251C2×Dic3⋊C4C2×D312yes—
252C2×C4×Dic3—32no—
253C2×C4×Dic3C2×D311yescharacteristic
254#897—34no—
255#896—34no—
256#896—34no—
257#893—32no—
258#893C2×D312yes—
259#892—32no—
260#892C2×D312yes—
261D3×C4⋊C4—32no—
262D3×C4⋊C4—34no—
263D3×C4⋊C4C2×D312yes—
264#890—32no—
265#890—32no—
266#890—32no—
267#890—32no—
268#890—32no—
269#890—32no—
270#890—34no—
271#890—32no—
272#890—31no—
273#890—31no—
274#890—62no—
275#890—62no—
276#889—34no—
277#889—34no—
278#888—34no—
279#888—34no—
280#888—32no—
281#888—32no—
282#888—32no—
283#888—32no—
284#888—32no—
285#888—32no—
286#888—34no—
287#888—34no—
288#888—32no—
289#888—31no—
290#888—31no—
291#888—62no—
292#888—62no—
293#888C2×D312yes—
294#888C2×D312yes—
295#888C2×D312yes—
296#888C2×D312yes—
297#887—32no—
298#887—34no—
299#887C2×D312yes—
300#878—32no—
301#878—32no—
302#878—34no—
303#878—34no—
304#878—34no—
305#878—34no—
306#878—34no—
307C4×D12—31no—
308C4×D12—31no—
309#872—32no—
310C42×D3—32no—
311#870—31no—
312#870—31no—
313#870—32no—
314#870—34no—
315#869—34no—
316#869—31no—
317#869—31no—
318#869—32no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—34no—
322C4×Dic6—34no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—32no—
327C23×C32C2411yescharacteristic
328C22×C3×D3C2412yes—
329C2×C32×C4—42no—
330C2×C32×C4C2×Q814yescomplemented
331C2×C32×C4C2414yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338#634—44no—
339C3×#67C2×Q818yescomplemented
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—42no—
343C2×C3×Dic3C2414yes—
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2411yescharacteristic
350C2×C3×Dic3C2411yescharacteristic
351C3×D12C2×Q814yescomplemented
352C3×C4×D3—44no—
353C3×C4×D3C2×Q818yescomplemented
354C3×Dic6—28no—
355C3×Dic6—44no—
356C3×Dic6C2×Q814yescomplemented
357#627—24no—
358#627—24no—
359#627—44no—
360D3×Dic3—24no—
361D3×Dic3—24no—
362D3×Dic3—44no—
363Q82—92no—
364#557—92no—
365#554—94no—
366#554—92no—
367D4×Q8—92no—
368D4×Q8—94no—
369#544—91no—
370#544—92no—
371#544—92no—
372#544—91no—
373#533—91no—
374#533—92no—
375C2×C4⋊Q8—31no—
376C2×C4⋊Q8—92no—
377#520—31no—
378#520—91no—
379C4×#41—91no—
380C3×#41—38no—
381C2×C3×Q8—31no—
382C2×C3×Q8—34no—
383C2×C3×Q8—34no—
384C2×C3×Q8—124no—
385C2×C3×D4—32no—
386C2×C3×D4—31no—
387C22×C3×C4—21no—
388C22×C3×C4—22no—
389C22×C3×C4—32no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—32no—
393C22×C3×C4—34no—
394C22×C3×C4C22×D312yes—
395C22×C3×C4C22×D312yes—
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C2×#67C22×D312yes—
399C22×Dic3—32no—
400C22×Dic3—32no—
401C22×Dic3—34no—
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D312yes—
405D3×Q8—128no—
406#235Dic618yescomplemented
407C2×D12C22×D311yescharacteristic
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—34no—
411C2×C4×D3C22×D314yes—
412C2×C4×D3C22×D312yes—
413C2×Dic6—32no—
414C2×Dic6—32no—
415C2×Dic6—32no—
416C2×Dic6—32no—
417C2×Dic6—34no—
418C2×Dic6—34no—
419C2×Dic6—34no—
420C2×Dic6—34no—
421C2×Dic6—44no—
422C2×Dic6—64no—
423C2×Dic6—128no—
424C2×Dic6C22×D314yes—
425C2×Dic6C22×D314yes—
426C2×Dic6C22×D311yescharacteristic
427C3×C4⋊C4—22no—
428C3×C4⋊C4—22no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—31no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—34no—
436C3×C4⋊C4C22×D312yes—
437C3×C4⋊C4C22×D312yes—
438C3×C4⋊C4C22×D312yes—
439C3×C4⋊C4C22×D312yes—
440C3×C22⋊C4—32no—
441C3×C22⋊C4—34no—
442C3×C42—31no—
443C3×C42—31no—
444C3×C42—34no—
445C3×C42—32no—
446C3×C42—31no—
447C3×C42—31no—
448#217—32no—
449#217—32no—
450#217—32no—
451#217—32no—
452#217—34no—
453#217—32no—
454#217—32no—
455#217—62no—
456#217—62no—
457#217C22×D312yes—
458(C2×D3)⋊C4—32no—
459(C2×D3)⋊C4—32no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4C22×D314yes—
462C4⋊Dic3—31no—
463C4⋊Dic3—31no—
464C4⋊Dic3—34no—
465C4⋊Dic3—31no—
466C4⋊Dic3—31no—
467C4⋊Dic3—31no—
468C4⋊Dic3—31no—
469C4⋊Dic3—31no—
470C4⋊Dic3—31no—
471C4⋊Dic3—34no—
472C4⋊Dic3—34no—
473C4⋊Dic3—32no—
474C4⋊Dic3—32no—
475C4⋊Dic3—32no—
476C4⋊Dic3—32no—
477C4⋊Dic3—32no—
478C4⋊Dic3—34no—
479C4⋊Dic3—32no—
480C4⋊Dic3—34no—
481C4⋊Dic3—61no—
482C4⋊Dic3—61no—
483C4⋊Dic3—64no—
484C4⋊Dic3—61no—
485C4⋊Dic3—61no—
486C4⋊Dic3C22×D311yescharacteristic
487C4⋊Dic3C22×D312yes—
488C4⋊Dic3C22×D311yescharacteristic
489C4⋊Dic3C22×D312yes—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
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—32no—
503Dic3⋊C4—32no—
504Dic3⋊C4—32no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—64no—
510Dic3⋊C4—64no—
511Dic3⋊C4C22×D314yes—
512Dic3⋊C4C22×D314yes—
513Dic3⋊C4C22×D314yes—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—32no—
519C4×Dic3—32no—
520C4×Dic3—34no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—34no—
524C4×Dic3—62no—
525C4×Dic3—62no—
526C4×Dic3C22×D312yes—
527C4×Dic3C22×D311yescharacteristic
528C4×Dic3C22×D311yescharacteristic
529C4×Dic3C22×D314yes—
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D311yescharacteristic
532C22×C32—21no—
533C22×C32—21no—
534C22×C32C22×Q812yes—
535C22×C32C2511yescharacteristic
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3C22×Q814yes—
539C32×C4—24no—
540C32×C4C22×Q812yes—
541C32×C4C22×Q812yes—
542C3⋊Dic3—22no—
543C3⋊Dic3—22no—
544C3⋊Dic3—22no—
545C3⋊Dic3—22no—
546C3×Dic3—24no—
547C3×Dic3—22no—
548C3×Dic3—21no—
549C3×Dic3—22no—
550C3×Dic3—21no—
551C3×Dic3C22×Q814yes—
552C3×Dic3H(5,𝔽2)12yes—
553C3×Dic32−1+412yes—
554C2×#41—31no—
555C22×Q8—32no—
556C22×Q8—94no—
557C4⋊Q8—32no—
558C4⋊Q8—32no—
559C4⋊Q8—32no—
560C4⋊Q8—32no—
561C4⋊Q8—91no—
562C4⋊Q8—91no—
563C4⋊Q8—92no—
564C4⋊Q8—94no—
565C4⋊Q8—92no—
566C4⋊Q8—94no—
567C4⋊Q8—94no—
568C4⋊Q8—94no—
569C4⋊Q8—92no—
570C4⋊Q8—92no—
571#125—91no—
572#125—91no—
573#125—94no—
574#125—92no—
575#125—92no—
576#125—94no—
577#125—92no—
578#125—92no—
579C22⋊Q8—94no—
580C22⋊Q8—94no—
581C22⋊Q8—92no—
582C22⋊Q8—92no—
583C22⋊Q8—94no—
584C22⋊Q8—94no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C4×Q8—32no—
590C4×Q8—92no—
591C4×Q8—92no—
592C4×Q8—94no—
593C4×Q8—91no—
594C4×Q8—91no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×D4—34no—
598C4×D4—32no—
599C4×D4—91no—
600C4×D4—91no—
601C4×D4—92no—
602C4×D4—92no—
603C4×D4—92no—
604C4×D4—94no—
605#117—31no—
606#117—32no—
607#117—92no—
608#117—92no—
609#117—91no—
610#117—91no—
611C2×C4⋊C4—31no—
612C2×C4⋊C4—32no—
613C2×C4⋊C4—32no—
614C2×C4⋊C4—92no—
615C2×C4⋊C4—94no—
616C2×C4⋊C4D3211yescharacteristic
617C2×C42—31no—
618C2×C42—92no—
619C23×C3—21no—
620C23×C3—32no—
621C23×C3C23×D311yescharacteristic
622C23×C3C23×D311yescharacteristic
623C22×D3C23×D312yes—
624C3×Q8—34no—
625C3×Q8—68no—
626C3×Q8—124no—
627C3×D4—38no—
628C3×D4—34no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—24no—
632C2×C3×C4—24no—
633C2×C3×C4—32no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—38no—
637C2×C3×C4—34no—
638C2×C3×C4—31no—
639C2×C3×C4—31no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—42no—
643C2×C3×C4—42no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—82no—
647C2×C3×C4—124no—
648C2×C3×C4—122no—
649C2×C3×C4C2×Dic614yescomplemented
650C2×C3×C4D3×Q814yescomplemented
651C2×C3×C4C23×D314yes—
652C2×C3×C4C23×D314yes—
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657#67C2×Dic618yescomplemented
658C2×Dic3—22no—
659C2×Dic3—22no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—32no—
667C2×Dic3—32no—
668C2×Dic3—42no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—62no—
672C2×Dic3—62no—
673C2×Dic3—64no—
674C2×Dic3—64no—
675C2×Dic3—124no—
676C2×Dic3C23×D314yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D311yescharacteristic
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D311yescharacteristic
683C2×Dic3C23×D311yescharacteristic
684D12C2×Dic614yescomplemented
685C4×D3—44no—
686C4×D3—64no—
687C4×D3—64no—
688C4×D3—124no—
689C4×D3C2×Dic618yescomplemented
690Dic6—28no—
691Dic6—44no—
692Dic6—64no—
693Dic6—64no—
694Dic6—64no—
695Dic6—64no—
696Dic6—124no—
697Dic6—124no—
698Dic6—124no—
699Dic6—124no—
700Dic6—244no—
701Dic6C2×Dic614yescomplemented
702C2×C32—22no—
703C2×C32C23×Q811yescharacteristic
704C2×C32C2×H(5,𝔽2)11yescharacteristic
705C2×C32C2×2−1+411yescharacteristic
706C3×D3—24no—
707#41—38no—
708C2×Q8—31no—
709C2×Q8—34no—
710C2×Q8—34no—
711C2×Q8—92no—
712C2×Q8—92no—
713C2×Q8—94no—
714C2×Q8—94no—
715C2×Q8—124no—
716C2×Q8—368no—
717C2×D4—32no—
718C2×D4—31no—
719C22×C4—32no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—32no—
723C22×C4—34no—
724C22×C4—92no—
725C22×C4—92no—
726C22×C4—94no—
727C22×C4C2×D3212yes—
728C22×C4C2×D3211yescharacteristic
729C4⋊C4—31no—
730C4⋊C4—32no—
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—32no—
734C4⋊C4—34no—
735C4⋊C4—31no—
736C4⋊C4—92no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—92no—
740C4⋊C4—92no—
741C4⋊C4—92no—
742C4⋊C4—92no—
743C4⋊C4—94no—
744C4⋊C4—92no—
745C4⋊C4—92no—
746C4⋊C4—92no—
747C4⋊C4—94no—
748C4⋊C4—91no—
749C4⋊C4—94no—
750C4⋊C4—91no—
751C4⋊C4—91no—
752C4⋊C4—91no—
753C4⋊C4—94no—
754C4⋊C4—94no—
755C4⋊C4C2×D3212yes—
756C4⋊C4C2×D3212yes—
757C22⋊C4—32no—
758C22⋊C4—34no—
759C22⋊C4—92no—
760C22⋊C4—92no—
761C22⋊C4—94no—
762C22⋊C4—92no—
763C22⋊C4—92no—
764C42—31no—
765C42—31no—
766C42—31no—
767C42—31no—
768C42—34no—
769C42—32no—
770C42—92no—
771C42—92no—
772C42—94no—
773C42—92no—
774C42—92no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—22no—
780C22×C3—21no—
781C22×C3—34no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3C22×Dic612yes—
787C22×C3C2×D3×Q812yes—
788C22×C3C24×D311yescharacteristic
789C22×C3C24×D311yescharacteristic
790C2×D3—22no—
791C2×D3—22no—
792C2×D3C22×Dic614yes—
793C3×C4—24no—
794C3×C4—24no—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—34no—
798C3×C4—32no—
799C3×C4—32no—
800C3×C4—44no—
801C3×C4—62no—
802C3×C4—62no—
803C3×C4—64no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4C22×Dic612yes—
807C3×C4C22×Dic612yes—
808C3×C4C2×D3×Q812yes—
809C3×C4C2×D3×Q812yes—
810Dic3—24no—
811Dic3—21no—
812Dic3—21no—
813Dic3—22no—
814Dic3—22no—
815Dic3—62no—
816Dic3—62no—
817Dic3—62no—
818Dic3—62no—
819Dic3—62no—
820Dic3—62no—
821Dic3—62no—
822Dic3—62no—
823Dic3—122no—
824Dic3—122no—
825Dic3—122no—
826Dic3—122no—
827Dic3C22×Dic614yes—
828Dic3#100412yes—
829Dic3#100712yes—
830C32#350311yescharacteristic, complemented, Sylow
831C23—32no—
832C23C22×D3211yescharacteristic
833Q8—34no—
834Q8—68no—
835Q8—124no—
836Q8—184no—
837Q8—184no—
838Q8—364no—
839Q8—364no—
840D4—38no—
841D4—34no—
842C2×C4—32no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—38no—
846C2×C4—32no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—32no—
850C2×C4—34no—
851C2×C4—42no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—92no—
855C2×C4—92no—
856C2×C4—92no—
857C2×C4—92no—
858C2×C4—124no—
859C2×C4—122no—
860C2×C4—184no—
861C2×C4—184no—
862C2×C4—364no—
863C2×C4D3×Dic614yescomplemented
864C2×C4C22×D3214yes—
865C2×C4C22×D3211yescharacteristic
866C2×C4C22×D3211yescharacteristic
867C2×C3—22no—
868C2×C3—22no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—42no—
873C2×C3—64no—
874C2×C3C23×Dic611yescharacteristic
875C2×C3C2×#100411yescharacteristic
876C2×C3C22×D3×Q811yescharacteristic
877C2×C3C2×#100711yescharacteristic
878C2×C3D3×H(5,𝔽2)11yescharacteristic
879C2×C3D3×2−1+411yescharacteristic
880D3—24no—
881C22—21no—
882C22—21no—
883C22—34no—
884C22—62no—
885C22—62no—
886C22C2×D3×Dic612yes—
887C22C23×D3211yescharacteristic
888C4—24no—
889C4—34no—
890C4—32no—
891C4—32no—
892C4—61no—
893C4—62no—
894C4—64no—
895C4—61no—
896C4—62no—
897C4—182no—
898C4—182no—
899C4—182no—
900C4—182no—
901C4C2×D3×Dic612yes—
902C4C2×D3×Dic612yes—
903C3—21no—
904C3#8588911yescharacteristic, complemented
905C3#8621511yescharacteristic, complemented
906C2—22no—
907C2—64no—
908C2C22×D3×Dic611yescharacteristic
909C2D3×#100411yescharacteristic
910C2D3×#100711yescharacteristic
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. #10595971C2semidirect
3. C2×C3×#888C2semidirect
4. #10595051C2semidirect
5. #10595049C2semidirect
7. #10594951C2semidirect
9. Dic6×#67C2semidirect
10. #10594502C2semidirect
11. #10594460C2semidirect
12. #10594445C2semidirect
13. #10594376C2semidirect
14. D3×#888C2semidirect
15. #10594342C2semidirect
16. #10594317C2semidirect
17. #10594312C2semidirect
117. C2×#888D3semidirect
127. C3×#235Q8semidirect
330. C2×C32×C4C2×Q8semidirect
339. C3×#67C2×Q8semidirect
351. C3×D12C2×Q8semidirect
353. C3×C4×D3C2×Q8semidirect
356. C3×Dic6C2×Q8semidirect
406. #235Dic6semidirect
649. C2×C3×C4C2×Dic6semidirect
650. C2×C3×C4D3×Q8semidirect
657. #67C2×Dic6semidirect
684. D12C2×Dic6semidirect
689. C4×D3C2×Dic6semidirect
701. Dic6C2×Dic6semidirect
830. C32#3503semidirect
863. C2×C4D3×Dic6semidirect
904. C3#85889semidirect
905. C3#86215semidirect

Maximal subgroups

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

subgroupindex
#105959712
C3×#55042
C2×C3×#8882
#105950512
#105950492
#105949862
#105949512
Dic3×#2352
Dic6×#672
#105945022
#105944602
#105944452
#105943762
D3×#8882
#105943422
#105943172
#105943122
#862153
#858893