Finite Group Databasebeta

← C2×#11796827 #72227380

Subgroups — C2×#11796827 #72227380

Order 2304.

2728 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10594684C211yesmaximal, characteristic
2C2×#10590625C211yesmaximal, characteristic, complemented
3C2×C3⋊D3×#106C211yesmaximal, characteristic, complemented
4C2×#10589124C212yesmaximal, complemented
5#11796827C218yesmaximal, direct product factor
6C2×C3×#4488C212yesmaximal, complemented
7C2×D3×#360—32nomaximal
8C2×#64306—21no—
9C22×C8×C3⋊D3C2211yescharacteristic
10C2×C4⋊C4×C3⋊D3—21no—
11C2×C3×#904C2212yes—
12C2×#63822—21no—
13C2×#63810C412yescomplemented
14C2×#63809—21no—
15C2×#63802C411yescharacteristic, complemented
16#10594684—22no—
17#10594684—22no—
18#10594684C414yescomplemented
19#10594684C2214yes—
20C2×#63797C411yescharacteristic, complemented
21C2×#63796—21no—
22C2×C32×#106C2211yescharacteristic, complemented
23C2×#63644C2211yescharacteristic, complemented
24C2×#63635—21no—
25C3⋊D3×#106—22no—
26C3⋊D3×#106C2214yescomplemented
27C2×C3×#812C2212yescomplemented
28C2×#63544—21no—
29#10590625—22no—
30#10590625C2214yescomplemented
31C2×#63542—21no—
32C3×#4488C2218yescomplemented
33#10589124C2218yescomplemented
34C2×D3×#135—32no—
35C2×D3×M32—32no—
36C2×D3×#106—32no—
37C2×D3×#106—61no—
38C2×C3×#360—32no—
39C2×#4566—32no—
40C2×#4518—32no—
41C2×#4488D312yescomplemented
42D3×#360—316no—
43C22×C4×C3⋊D3—41no—
44C22×C4×C3⋊D3D411yescharacteristic
45C2×C3×#235—22no—
46C2×#3811—41no—
47C2×#3805—41no—
48#64306—24no—
49#64306—24no—
50#64306—42no—
51#64306—42no—
52C2×#3802—21no—
53C2×C4×D32—41no—
54C2×#3798—41no—
55C2×#3797—21no—
56C2×#3796—22no—
57C22×C32×C8C2311yescharacteristic
58C2×C32×C4⋊C4—21no—
59C2×C4⋊(C3⋊Dic3)—21no—
60C2×#3750—41no—
61C22×C3⋊(C3⋊C8)D411yescharacteristic
62C2×C8×C3⋊D3C2×C411yescharacteristic
63C2×C8×C3⋊D3C2×C412yes—
64C2×C8×C3⋊D3C2×C411yescharacteristic
65C2×C8×C3⋊D3D412yes—
66C2×C8×C3⋊D3D411yescharacteristic
67C2×C8×C3⋊D3D412yes—
68C2×C8×C3⋊D3D411yescharacteristic
69C2×C8×C3⋊D3C2312yes—
70C4⋊C4×C3⋊D3—24no—
71C4⋊C4×C3⋊D3—42no—
72C2×C3×Dic12C2×C412yescomplemented
73C3×#904—22no—
74C3×#904—22no—
75C3×#904C2×C414yescomplemented
76C3×#904C2314yes—
77C2×C3×D24C2×C412yescomplemented
78C2×C3×#204—22no—
79C2×#3718—21no—
80C2×#3715—22no—
81#63822—24no—
82#63822—24no—
83C2×#3713—21no—
84#63810—24no—
85#63810C2×C418yescomplemented
86#63809—24no—
87#63809—24no—
88#63802—22no—
89#63802C2×C414yescomplemented
90#63797—22no—
91#63797C2×C414yescomplemented
92#63796—24no—
93#63796—24no—
94C32×#106—21no—
95C32×#106C2312yescomplemented
96#63644—21no—
97#63644C2312yescomplemented
98#63635—24no—
99C3×#812—22no—
100C3×#812C2314yescomplemented
101C2×C3×C3⋊C16—22no—
102#63544—24no—
103#63542—24no—
104C22×#360—91noSylow
105C2×D3×#41—62no—
106C2×C3×#135—32no—
107C2×#950—62no—
108D3×#135—38no—
109D3×#135—38no—
110D3×#135—64no—
111D3×#135—64no—
112C2×#919—32no—
113C2×D3×Q16—32no—
114C2×#916—62no—
115C2×D3×SD16—62no—
116C2×#912—32no—
117C2×D3×D8—32no—
118C2×#904C2×D312yes—
119C22×D3×C8—32no—
120C22×D3×C8—61no—
121C2×D3×C4⋊C4—62no—
122C2×D3×C4⋊C4—62no—
123C2×C3×M32—32no—
124C2×C3×#106—21no—
125C2×C3×#106C2×D312yescomplemented
126C2×#817—32no—
127C2×#817—61no—
128C2×#812C2×D312yescomplemented
129C2×#808—62no—
130C2×#808—62no—
131D3×M32—38no—
132D3×M32—64no—
133C2×#798—62no—
134C2×D3×C16—62no—
135D3×#106—38no—
136D3×#106—64no—
137D3×#106—64no—
138D3×#106—64no—
139C3×#360—38no—
140#4566—38no—
141#4518—38no—
142#4488C2×D318yescomplemented
143C23×C3⋊D3D811yescharacteristic
144C22×D32—41no—
145C22×C32×C4—41no—
146C22×C32×C4C2×D411yescharacteristic
147C22×C3⋊Dic3—41no—
148C22×C3⋊Dic3D811yescharacteristic
149C2×C4×C3⋊D3—44no—
150C2×C4×C3⋊D3—84no—
151C2×C4×C3⋊D3C22⋊C411yescharacteristic
152C2×C4×C3⋊D3C22⋊C411yescharacteristic
153C2×C4×C3⋊D3C22⋊C412yes—
154C2×C4×C3⋊D3D812yes—
155C2×C4×C3⋊D3SD1611yescharacteristic
156C2×C4×C3⋊D3SD1611yescharacteristic
157C2×C4×C3⋊D3SD1612yes—
158C2×C4×C3⋊D3C2×D412yes—
159C2×C3×#67—42no—
160C3×#235—24no—
161C3×#235—24no—
162C3×#235—42no—
163C3×#235—42no—
164C2×C3×D12—22no—
165C2×C3×C4×D3—42no—
166C2×C3×Dic6—22no—
167#3811—44no—
168#3811—44no—
169C2×#627—41no—
170C2×#626—42no—
171C2×#625—41no—
172C2×#624—41no—
173#3805—44no—
174#3805—44no—
175C2×D3×Dic3—42no—
176#3802—24no—
177#3802—42no—
178C4×D32—44no—
179C4×D32—44no—
180#3798—44no—
181#3798—44no—
182#3797—24no—
183#3797—42no—
184#3796—28no—
185#3796—44no—
186C2×C32×C8C22×C411yescharacteristic
187C2×C32×C8C22×C411yescharacteristic
188C2×C32×C8C2×D411yescharacteristic
189C2×C32×C8C2×D411yescharacteristic
190C2×C32×C8C2×D411yescharacteristic
191C2×C32×C8C2411yescharacteristic
192C32×C4⋊C4—22no—
193C32×C4⋊C4—41no—
194C4⋊(C3⋊Dic3)—22no—
195C4⋊(C3⋊Dic3)—41no—
196#3750—44no—
197C2×C3⋊(C3⋊C8)C22⋊C411yescharacteristic
198C2×C3⋊(C3⋊C8)C22⋊C412yes—
199C2×C3⋊(C3⋊C8)C22⋊C411yescharacteristic
200C2×C3⋊(C3⋊C8)C2×D412yes—
201C8×C3⋊D3C22⋊C412yes—
202C8×C3⋊D3C22⋊C412yes—
203C8×C3⋊D3C22⋊C412yes—
204C8×C3⋊D3C22⋊C412yes—
205C8×C3⋊D3C22×C412yes—
206C8×C3⋊D3C22×C412yes—
207C8×C3⋊D3C2×D412yes—
208C8×C3⋊D3C2×D412yes—
209C3×Dic12—22no—
210C3×Dic12C22×C414yescomplemented
211C3×D24—22no—
212C3×D24C22×C414yescomplemented
213C3×#204—24no—
214C3×#204—24no—
215#3718—24no—
216#3715—28no—
217#3713—24no—
218C3×C3⋊C16—24no—
219C22×#135—91no—
220C22×M32—91no—
221C22×#106—91no—
222C2×#360—32no—
223C2×#360—92no—
224C2×#360—98no—
225C2×C3×#41—62no—
226D3×#41—68no—
227D3×#41—68no—
228D3×#41—124no—
229D3×#41—124no—
230C2×#239—62no—
231C2×D3×Q8—62no—
232C2×#237—62no—
233C2×#237—122no—
234C2×D3×D4—62no—
235C2×D3×D4—122no—
236C2×#235—22no—
237C2×#235—122no—
238C22×C4×D3—32no—
239C22×C4×D3—61no—
240C22×C4×D3—122no—
241C22×C4×D3—122no—
242C22×C4×D3—122no—
243C3×#135—34no—
244C3×#135—34no—
245C3×#135—62no—
246C3×#135—62no—
247C2×C3×Q16—32no—
248C2×C3×SD16—62no—
249C2×C3×D8—32no—
250C22×C3×C8—21no—
251C22×C3×C8C22×D312yes—
252C2×C3×C4⋊C4—22no—
253C2×C3×C4⋊C4—22no—
254#950—68no—
255#950—68no—
256C2×#216—62no—
257C2×#215—62no—
258C2×#214—62no—
259C2×#213—62no—
260C2×C4⋊Dic3—62no—
261C2×C4⋊Dic3—62no—
262C2×Dic3⋊C4—122no—
263C2×Dic3⋊C4—122no—
264C22×C3⋊C8—32no—
265C22×C3⋊C8—61no—
266#919—38no—
267#919—64no—
268D3×Q16—38no—
269D3×Q16—64no—
270#916—68no—
271#916—68no—
272D3×SD16—68no—
273D3×SD16—68no—
274#912—38no—
275#912—64no—
276D3×D8—38no—
277D3×D8—64no—
278C2×Dic12C4×D312yescomplemented
279#904—22no—
280#904—22no—
281#904C4×D314yescomplemented
282#904C22×D314yes—
283C2×D24C4×D312yescomplemented
284C2×#204—22no—
285C2×D3×C8—32no—
286C2×D3×C8—32no—
287C2×D3×C8—34no—
288C2×D3×C8—32no—
289C2×D3×C8—32no—
290C2×D3×C8—34no—
291C2×D3×C8—34no—
292C2×D3×C8—34no—
293C2×D3×C8—61no—
294C2×D3×C8—62no—
295C2×D3×C8—61no—
296C2×D3×C8—61no—
297C2×D3×C8—62no—
298C2×D3×C8—61no—
299C2×D3×C8—62no—
300C2×D3×C8—62no—
301D3×C4⋊C4—68no—
302D3×C4⋊C4—68no—
303D3×C4⋊C4—124no—
304D3×C4⋊C4—124no—
305C3×M32—34no—
306C3×M32—62no—
307C2×C3×C16—62no—
308C3×#106—22no—
309C3×#106—22no—
310C3×#106—22no—
311C3×#106C22×D314yescomplemented
312#817—34no—
313#817—62no—
314#817—62no—
315#817—62no—
316#812—22no—
317#812C22×D314yescomplemented
318C2×C3⋊C16—22no—
319#808—68no—
320#808—68no—
321#798—68no—
322D3×C16—68no—
323C23×C32C2×D811yescharacteristic
324C22×C3⋊D3—24no—
325C22×C3⋊D3#10211yescharacteristic
326C22×C3⋊D3#10212yes—
327C22×C3⋊D3#10211yescharacteristic
328C22×C3⋊D3C2×D812yes—
329C22×C3×D3—42no—
330C2×D32—44no—
331C2×D32—84no—
332C2×C32×C4—42no—
333C2×C32×C4—82no—
334C2×C32×C4C2×C22⋊C411yescharacteristic
335C2×C32×C4C2×C22⋊C411yescharacteristic
336C2×C32×C4C2×D811yescharacteristic
337C2×C32×C4C2×SD1611yescharacteristic
338C2×C32×C4C2×SD1611yescharacteristic
339C2×C32×C4C22×D411yescharacteristic
340C2×C3⋊Dic3—42no—
341C2×C3⋊Dic3—82no—
342C2×C3⋊Dic3#10211yescharacteristic
343C2×C3⋊Dic3#10212yes—
344C2×C3⋊Dic3#10211yescharacteristic
345C2×C3⋊Dic3C2×D812yes—
346C4×C3⋊D3—88no—
347C4×C3⋊D3#10212yes—
348C4×C3⋊D3#10212yes—
349C4×C3⋊D3#10212yes—
350C4×C3⋊D3#10212yes—
351C4×C3⋊D3C2×C22⋊C412yes—
352C4×C3⋊D3C2×C22⋊C412yes—
353C4×C3⋊D3C2×SD1612yes—
354C4×C3⋊D3C2×SD1612yes—
355C3×#67—44no—
356C3×#67—44no—
357C2×C3×Dic3—42no—
358C3×D12—24no—
359C3×D12—42no—
360C3×C4×D3—44no—
361C3×C4×D3—44no—
362C3×Dic6—24no—
363C3×Dic6—42no—
364#627—44no—
365#626—48no—
366#625—44no—
367#624—44no—
368D3×Dic3—48no—
369C32×C8C2×C22⋊C411yescharacteristic
370C32×C8C2×C22⋊C411yescharacteristic
371C32×C8C23×C411yescharacteristic
372C32×C8C22×D411yescharacteristic
373C3⋊(C3⋊C8)C2×C22⋊C412yes—
374C3⋊(C3⋊C8)C2×C22⋊C412yes—
375C22×#41—181no—
376C2×#135—32no—
377C2×#135—92no—
378C2×#135—94no—
379C2×#135—94no—
380C2×#135—181no—
381C2×#135—182no—
382C2×#135—182no—
383C2×#135—181no—
384C22×Q16—91no—
385C22×SD16—181no—
386C22×D8—91no—
387C23×C8—91no—
388C22×C4⋊C4—181no—
389C2×M32—32no—
390C2×M32—94no—
391C2×M32—181no—
392C2×M32—182no—
393C22×C16—181no—
394C2×#106—91no—
395C2×#106—94no—
396C2×#106—182no—
397C2×#106—181no—
398C2×#106D3211yescharacteristic, complemented
399#360—38no—
400#360—98no—
401C23×D3—32no—
402C23×D3—61no—
403C23×D3—122no—
404C3×#41—64no—
405C3×#41—64no—
406C3×#41—122no—
407C3×#41—122no—
408C2×C3×Q8—62no—
409C2×C3×D4—62no—
410C2×C3×D4—122no—
411C22×C3×C4—21no—
412C22×C3×C4—42no—
413C22×C3×C4—42no—
414C22×C3×C4—122no—
415C22×C3×C4D3×D412yes—
416C2×#67—42no—
417C2×#67—122no—
418C2×#67—122no—
419C22×Dic3—32no—
420C22×Dic3—61no—
421C22×Dic3—122no—
422C22×Dic3—122no—
423C22×Dic3—122no—
424#239—68no—
425#239—124no—
426D3×Q8—68no—
427D3×Q8—124no—
428#237—68no—
429#237—124no—
430#237—128no—
431#237—128no—
432D3×D4—68no—
433D3×D4—124no—
434D3×D4—128no—
435D3×D4—128no—
436#235—24no—
437#235—24no—
438#235—42no—
439#235—42no—
440#235—128no—
441#235—128no—
442C2×D12—22no—
443C2×D12—122no—
444C2×C4×D3—32no—
445C2×C4×D3—32no—
446C2×C4×D3—34no—
447C2×C4×D3—34no—
448C2×C4×D3—32no—
449C2×C4×D3—32no—
450C2×C4×D3—34no—
451C2×C4×D3—34no—
452C2×C4×D3—42no—
453C2×C4×D3—62no—
454C2×C4×D3—62no—
455C2×C4×D3—61no—
456C2×C4×D3—61no—
457C2×C4×D3—62no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—62no—
461C2×C4×D3—128no—
462C2×C4×D3—128no—
463C2×C4×D3—122no—
464C2×C4×D3—122no—
465C2×C4×D3—128no—
466C2×C4×D3—128no—
467C2×C4×D3—248no—
468C2×C4×D3—248no—
469C2×Dic6—22no—
470C2×Dic6—122no—
471C3×Q16—34no—
472C3×Q16—62no—
473C3×SD16—64no—
474C3×SD16—64no—
475C3×D8—34no—
476C3×D8—62no—
477C2×C3×C8—21no—
478C2×C3×C8—21no—
479C2×C3×C8—21no—
480C2×C3×C8—21no—
481C2×C3×C8—21no—
482C2×C3×C8—21no—
483C2×C3×C8C2×C4×D312yes—
484C2×C3×C8C2×C4×D312yes—
485C2×C3×C8D3×D412yes—
486C2×C3×C8D3×D412yes—
487C2×C3×C8D3×D412yes—
488C2×C3×C8C23×D312yes—
489C3×C4⋊C4—24no—
490C3×C4⋊C4—24no—
491C3×C4⋊C4—42no—
492C3×C4⋊C4—42no—
493#216—68no—
494#215—68no—
495#214—68no—
496#213—68no—
497C4⋊Dic3—64no—
498C4⋊Dic3—64no—
499C4⋊Dic3—122no—
500C4⋊Dic3—122no—
501Dic3⋊C4—128no—
502Dic3⋊C4—128no—
503C2×C3⋊C8—32no—
504C2×C3⋊C8—32no—
505C2×C3⋊C8—34no—
506C2×C3⋊C8—34no—
507C2×C3⋊C8—62no—
508C2×C3⋊C8—61no—
509C2×C3⋊C8—61no—
510C2×C3⋊C8—62no—
511Dic12—22no—
512Dic12C2×C4×D314yescomplemented
513D24—22no—
514D24C2×C4×D314yescomplemented
515#204—24no—
516#204—24no—
517D3×C8—34no—
518D3×C8—34no—
519D3×C8—34no—
520D3×C8—34no—
521D3×C8—34no—
522D3×C8—34no—
523D3×C8—34no—
524D3×C8—34no—
525D3×C8—62no—
526D3×C8—62no—
527D3×C8—62no—
528D3×C8—62no—
529D3×C8—62no—
530D3×C8—62no—
531D3×C8—62no—
532D3×C8—62no—
533C3×C16—64no—
534C3⋊C16—24no—
535C22×C32—22no—
536C22×C32C2×#10211yescharacteristic
537C22×C32C2×#10211yescharacteristic
538C22×C32C22×D811yescharacteristic
539C2×C3⋊D3—22no—
540C2×C3⋊D3—24no—
541C2×C3⋊D3—24no—
542C2×C3⋊D3#36014yescomplemented
543C2×C3⋊D3C2×#10212yes—
544C2×C3⋊D3C2×#10212yes—
545C2×C3×D3—44no—
546C2×C3×D3—84no—
547D32—88no—
548C32×C4—82no—
549C32×C4C2×#10211yescharacteristic
550C32×C4C2×#10211yescharacteristic
551C32×C4C22×C22⋊C411yescharacteristic
552C32×C4C22×SD1611yescharacteristic
553C3⋊Dic3—82no—
554C3⋊Dic3C2×#10212yes—
555C3⋊Dic3C2×#10212yes—
556C3×Dic3—44no—
557C2×#41—62no—
558C2×#41—182no—
559C2×#41—184no—
560C2×#41—184no—
561C2×#41—361no—
562C2×#41—361no—
563C2×#41—362no—
564C2×#41—362no—
565C22×Q8—181no—
566C22×D4—181no—
567C22×D4—361no—
568C23×C4—91no—
569C23×C4—361no—
570C23×C4—361no—
571#135—34no—
572#135—34no—
573#135—62no—
574#135—62no—
575#135—98no—
576#135—184no—
577#135—184no—
578#135—184no—
579#135—184no—
580#135—184no—
581C2×Q16—32no—
582C2×Q16—94no—
583C2×Q16—182no—
584C2×Q16—181no—
585C2×SD16—62no—
586C2×SD16—184no—
587C2×SD16—184no—
588C2×SD16—182no—
589C2×D8—32no—
590C2×D8—94no—
591C2×D8—182no—
592C2×D8—181no—
593C22×C8—91no—
594C22×C8—92no—
595C22×C8—91no—
596C22×C8—91no—
597C22×C8—92no—
598C22×C8—91no—
599C22×C8—91no—
600C22×C8—92no—
601C22×C8—92no—
602C22×C8C2×D3211yescharacteristic
603C2×C4⋊C4—21no—
604C2×C4⋊C4—184no—
605C2×C4⋊C4—181no—
606C2×C4⋊C4—362no—
607C2×C4⋊C4—361no—
608M32—34no—
609M32—62no—
610M32—184no—
611C2×C16—62no—
612C2×C16—184no—
613#106—21no—
614#106—92no—
615#106—184no—
616#106—181no—
617#106C2×D3212yescomplemented
618C23×C3—21no—
619C23×C3—122no—
620C23×C3D3×D812yes—
621C22×D3—32no—
622C22×D3—34no—
623C22×D3—32no—
624C22×D3—34no—
625C22×D3—42no—
626C22×D3—61no—
627C22×D3—62no—
628C22×D3—61no—
629C22×D3—62no—
630C22×D3—68no—
631C22×D3—68no—
632C22×D3—128no—
633C22×D3—248no—
634C3×Q8—64no—
635C3×Q8—122no—
636C3×D4—64no—
637C3×D4—124no—
638C3×D4—124no—
639C3×D4—122no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—44no—
647C2×C3×C4—44no—
648C2×C3×C4—84no—
649C2×C3×C4—84no—
650C2×C3×C4—122no—
651C2×C3×C4—124no—
652C2×C3×C4—124no—
653C2×C3×C4D3×C22⋊C412yes—
654C2×C3×C4D3×C22⋊C412yes—
655C2×C3×C4D3×D812yes—
656C2×C3×C4D3×SD1612yes—
657C2×C3×C4D3×SD1612yes—
658C2×C3×C4C2×D3×D412yes—
659#67—44no—
660#67—44no—
661#67—128no—
662#67—128no—
663C2×Dic3—34no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—34no—
667C2×Dic3—42no—
668C2×Dic3—62no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—62no—
672C2×Dic3—128no—
673C2×Dic3—124no—
674C2×Dic3—124no—
675C2×Dic3—244no—
676C2×Dic3—244no—
677D12—24no—
678D12—42no—
679D12—128no—
680C4×D3—34no—
681C4×D3—34no—
682C4×D3—34no—
683C4×D3—34no—
684C4×D3—34no—
685C4×D3—34no—
686C4×D3—34no—
687C4×D3—34no—
688C4×D3—44no—
689C4×D3—44no—
690C4×D3—62no—
691C4×D3—62no—
692C4×D3—62no—
693C4×D3—62no—
694C4×D3—62no—
695C4×D3—62no—
696C4×D3—62no—
697C4×D3—62no—
698C4×D3—128no—
699C4×D3—128no—
700C4×D3—2416no—
701C4×D3—2416no—
702Dic6—24no—
703Dic6—42no—
704Dic6—128no—
705C3×C8—21no—
706C3×C8—21no—
707C3×C8—21no—
708C3×C8—21no—
709C3×C8D3×C22⋊C412yes—
710C3×C8D3×C22⋊C412yes—
711C3×C8C22×C4×D312yes—
712C3×C8C2×D3×D412yes—
713C3⋊C8—34no—
714C3⋊C8—34no—
715C3⋊C8—62no—
716C3⋊C8—62no—
717C2×C32—21no—
718C2×C32—21no—
719C2×C32C2×#36012yescomplemented
720C2×C32C22×#10211yescharacteristic
721C3⋊D3—22no—
722C3⋊D3C2×#36014yescomplemented
723C3×D3—84no—
724C24—91no—
725C24—361no—
726#41—64no—
727#41—64no—
728#41—122no—
729#41—122no—
730#41—188no—
731#41—364no—
732#41—364no—
733#41—364no—
734#41—364no—
735#41—364no—
736C2×Q8—62no—
737C2×Q8—184no—
738C2×Q8—361no—
739C2×Q8—362no—
740C2×D4—62no—
741C2×D4—122no—
742C2×D4—184no—
743C2×D4—362no—
744C2×D4—361no—
745C2×D4—362no—
746C2×D4—364no—
747C2×D4—364no—
748C22×C4—41no—
749C22×C4—91no—
750C22×C4—92no—
751C22×C4—91no—
752C22×C4—92no—
753C22×C4—91no—
754C22×C4—92no—
755C22×C4—91no—
756C22×C4—92no—
757C22×C4—91no—
758C22×C4—122no—
759C22×C4—364no—
760C22×C4—364no—
761C22×C4—364no—
762C22×C4—362no—
763C22×C4—361no—
764C22×C4—361no—
765C22×C4—724no—
766C22×C4#381111yescharacteristic
767Q16—34no—
768Q16—62no—
769Q16—184no—
770SD16—64no—
771SD16—64no—
772SD16—188no—
773D8—34no—
774D8—62no—
775D8—184no—
776C2×C8—92no—
777C2×C8—91no—
778C2×C8—91no—
779C2×C8—92no—
780C2×C8—92no—
781C2×C8—92no—
782C2×C8—92no—
783C2×C8—92no—
784C2×C8—92no—
785C2×C8—92no—
786C2×C8—92no—
787C2×C8—92no—
788C2×C8C4×D3211yescharacteristic
789C2×C8C4×D3211yescharacteristic
790C2×C8#380211yescharacteristic
791C2×C8#380211yescharacteristic
792C2×C8#381111yescharacteristic
793C2×C8C22×D3211yescharacteristic
794C4⋊C4—22no—
795C4⋊C4—41no—
796C4⋊C4—182no—
797C4⋊C4—364no—
798C4⋊C4—361no—
799C16—64no—
800C22×C3—24no—
801C22×C3—24no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—124no—
806C22×C3—244no—
807C22×C3D3×#10212yes—
808C22×C3D3×#10212yes—
809C22×C3C2×D3×D812yes—
810C2×D3—38no—
811C2×D3—34no—
812C2×D3—34no—
813C2×D3—44no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—64no—
817C2×D3—68no—
818C2×D3—68no—
819C2×D3—68no—
820C2×D3—68no—
821C2×D3—64no—
822C2×D3—64no—
823C2×D3—84no—
824C2×D3—2416no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—84no—
830C3×C4—84no—
831C3×C4—124no—
832C3×C4D3×#10212yes—
833C3×C4D3×#10212yes—
834C3×C4C2×D3×C22⋊C412yes—
835C3×C4C2×D3×SD1612yes—
836Dic3—34no—
837Dic3—34no—
838Dic3—44no—
839Dic3—62no—
840Dic3—62no—
841Dic3—244no—
842Dic3—244no—
843C32C22×#36011yescharacteristic, complemented, Sylow
844C23—91no—
845C23—92no—
846C23—92no—
847C23—91no—
848C23—122no—
849C23—184no—
850C23—364no—
851C23—724no—
852C23#6392611yescharacteristic
853Q8—64no—
854Q8—122no—
855Q8—364no—
856D4—64no—
857D4—124no—
858D4—124no—
859D4—122no—
860D4—364no—
861D4—368no—
862C2×C4—42no—
863C2×C4—82no—
864C2×C4—92no—
865C2×C4—92no—
866C2×C4—91no—
867C2×C4—91no—
868C2×C4—92no—
869C2×C4—92no—
870C2×C4—92no—
871C2×C4—92no—
872C2×C4—92no—
873C2×C4—92no—
874C2×C4—92no—
875C2×C4—92no—
876C2×C4—122no—
877C2×C4—124no—
878C2×C4—124no—
879C2×C4—368no—
880C2×C4—364no—
881C2×C4—362no—
882C2×C4—728no—
883C2×C4—722no—
884C2×C4#6392111yescharacteristic
885C2×C4#6392111yescharacteristic
886C2×C4#6392611yescharacteristic
887C2×C4#6394011yescharacteristic
888C2×C4#6394011yescharacteristic
889C2×C4C2×#381111yescharacteristic
890C8—92no—
891C8—92no—
892C8#6392111yescharacteristic
893C8#6392111yescharacteristic
894C8C2×C4×D3211yescharacteristic
895C8C2×#380211yescharacteristic
896C2×C3—22no—
897C2×C3—22no—
898C2×C3—22no—
899C2×C3—22no—
900C2×C3—21no—
901C2×C3—22no—
902C2×C3—244no—
903C2×C3D3×#36014yescomplemented
904C2×C3C2×D3×#10212yes—
905D3—38no—
906D3—64no—
907D3—64no—
908D3—64no—
909D3—84no—
910C22—22no—
911C22—92no—
912C22—94no—
913C22—92no—
914C22—124no—
915C22—184no—
916C22—184no—
917C22—182no—
918C22—244no—
919C22—728no—
920C22#1059059311yescharacteristic
921C22#1059059311yescharacteristic
922C22C2×#6392611yescharacteristic
923C4—82no—
924C4—92no—
925C4—92no—
926C4—124no—
927C4—722no—
928C4#1059059311yescharacteristic
929C4#1059059311yescharacteristic
930C4C2×#6392111yescharacteristic
931C4C2×#6394011yescharacteristic
932C3—21no—
933C3C2×D3×#36012yescomplemented
934C2—21no—
935C2—21no—
936C2—94no—
937C2—182no—
938C2—244no—
939C2#1179682712yesdirect product factor
940C2C2×#1059059311yescharacteristic
subgroupG/H
centerC22#10590593
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#106C22
socleC22×C32C2×#102
prime radicalC2×#10594684C2
cosocleC2×C32×C8C24
hypercenterC2×#106D32
hypocenterC32C22×#360
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#10590625C2semidirect
3. C2×C3⋊D3×#106C2semidirect
4. C2×#10589124C2semidirect
5. #11796827C2direct (N × H)
6. C2×C3×#4488C2semidirect
13. C2×#63810C4semidirect
15. C2×#63802C4semidirect
18. #10594684C4semidirect
20. C2×#63797C4semidirect
22. C2×C32×#106C22semidirect
23. C2×#63644C22semidirect
26. C3⋊D3×#106C22semidirect
27. C2×C3×#812C22semidirect
30. #10590625C22semidirect
32. C3×#4488C22semidirect
33. #10589124C22semidirect
41. C2×#4488D3semidirect
72. C2×C3×Dic12C2×C4semidirect
75. C3×#904C2×C4semidirect
77. C2×C3×D24C2×C4semidirect
85. #63810C2×C4semidirect
89. #63802C2×C4semidirect
91. #63797C2×C4semidirect
95. C32×#106C23semidirect
97. #63644C23semidirect
100. C3×#812C23semidirect
125. C2×C3×#106C2×D3semidirect
128. C2×#812C2×D3semidirect
142. #4488C2×D3semidirect
210. C3×Dic12C22×C4semidirect
212. C3×D24C22×C4semidirect
278. C2×Dic12C4×D3semidirect
281. #904C4×D3semidirect
283. C2×D24C4×D3semidirect
311. C3×#106C22×D3semidirect
317. #812C22×D3semidirect
398. C2×#106D32semidirect
512. Dic12C2×C4×D3semidirect
514. D24C2×C4×D3semidirect
542. C2×C3⋊D3#360semidirect
617. #106C2×D32semidirect
719. C2×C32C2×#360semidirect
722. C3⋊D3C2×#360semidirect
843. C32C22×#360semidirect
903. C2×C3D3×#360semidirect
933. C3C2×D3×#360semidirect
939. C2#11796827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#105946842
C2×#105906252
C2×C3⋊D3×#1062
C2×#105891242
#117968272
C2×C3×#44882
C2×D3×#3603