Finite Group Databasebeta

← #11863892

Subgroups — #11863892

Order 1152.

1602 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic, complemented
2C2×C3×#919C211yesmaximal, characteristic, complemented
3#10595424C211yesmaximal, characteristic, complemented
4C2×#63947C211yesmaximal, characteristic, complemented
5#10592885C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591652C211yesmaximal, characteristic, complemented
9#10591592C211yesmaximal, characteristic, complemented
10#10591586C211yesmaximal, characteristic, complemented
11#10591556C211yesmaximal, characteristic, complemented
12#10590962C211yesmaximal, characteristic, complemented
13#10590954C211yesmaximal, characteristic, complemented
14#10590945C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
16#83911—31nomaximal
17#80226—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×#239C2211yescharacteristic, complemented
22#64319—24no—
23#64319—24no—
24C2×#3802—21no—
25C2×#3802C2211yescharacteristic
26C2×C4×D32—21no—
27C2×C4×D32C2211yescharacteristic
28C2×#3795—21no—
29C2×#3795—21no—
30C2×#3795C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic
34C2×#3756C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#215C2211yescharacteristic, complemented
39C3×#919—24no—
40C2×C3×D24C2211yescharacteristic, complemented
41C2×C3×D3×C8C2211yescharacteristic, complemented
42#63947—24no—
43#63922—21no—
44#63916C2211yescharacteristic
45#63908C2211yescharacteristic, complemented
46#63904—21no—
47#63884—21no—
48#63879—21no—
49#63841C2211yescharacteristic, complemented
50C2×#3716C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63647C2211yescharacteristic
55#63643C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×C3×#135—31no—
68#5828—31no—
69C2×#950—31no—
70C2×#919D311yescharacteristic, complemented
71C2×#916—31no—
72#5627—31no—
73C3×#452—31no—
74#5238—31no—
75#5233—31no—
76#5187D311yescharacteristic, complemented
77#5186—31no—
78#5186—31no—
79#5186—61no—
80#5173—31no—
81#5172—31no—
82#5170—31no—
83#5169—31no—
84#5169—31no—
85#5158—31no—
86#5156—31no—
87#5113—31no—
88C2×(C2×D3)⋊C8—31no—
89#5047—31no—
90#4806—31no—
91#4804—31no—
92#4773—31no—
93#4772—31no—
94#4734—31no—
95D3×C22⋊C8—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100Q8×C3⋊D3—22no—
101Q8×C3⋊D3—22no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634—21no—
105C2×#634C2311yescharacteristic
106C3×#239—22no—
107C3×#239—22no—
108C3×#239—22no—
109C3×#239—22no—
110C3×#239—22no—
111C3×#239D414yescomplemented
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×#626—21no—
124C2×#625—21no—
125C2×#625—21no—
126C2×#625—21no—
127C2×#625—21no—
128C2×#624D411yescharacteristic
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3D411yescharacteristic
132C2×D3×Dic3D411yescharacteristic
133#3802—28no—
134#3802—22no—
135#3802—22no—
136C4×D32—28no—
137C4×D32—22no—
138C4×D32—22no—
139#3795—28no—
140#3795—28no—
141#3795—22no—
142#3795—22no—
143#3795—22no—
144#3795D414yescomplemented
145C32×Q16—22no—
146C2×C32×C8C2311yescharacteristic
147#3756—22no—
148#3752—21no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3750—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C3×#215—22no—
153C3×#215—22no—
154C3×#215—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×Dic3⋊C4—21no—
158C2×C3×C3⋊C8C2311yescharacteristic
159C2×C3×C3⋊C8C2311yescharacteristic
160C3×D24—22no—
161C3×D3×C8—22no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165Dic32—21no—
166#3716—22no—
167#3713—22no—
168D3×C3⋊C8—22no—
169#3002—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C2×C3×#41—31no—
173D3×#41—64no—
174D3×#41—64no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239C2×D311yescharacteristic
178C2×#239C2×D311yescharacteristic
179C2×#239C2×D311yescharacteristic, complemented
180C2×D3×Q8—31no—
181C2×D3×Q8—31no—
182C2×D3×Q8—61no—
183C2×#237—31no—
184C2×#237—31no—
185C2×#237—61no—
186C2×#237—61no—
187C2×D3×D4—31no—
188C2×D3×D4—31no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3—61no—
199C3×#135—64no—
200C2×C3×Q16—21no—
201C2×C3×Q16C2×D311yescharacteristic, complemented
202C2×C3×Q16C2×D311yescharacteristic, complemented
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×D8—31no—
207C22×C3×C8—31no—
208C3×C22⋊Q8—31no—
209#950—64no—
210#946—31no—
211#946—31no—
212#946—61no—
213#946C2×D311yescharacteristic, complemented
214C2×#216—31no—
215C2×#216—31no—
216C2×#216—61no—
217C2×#215C2×D311yescharacteristic, complemented
218C2×#215C2×D311yescharacteristic, complemented
219C2×#215C2×D311yescharacteristic, complemented
220#938—31no—
221#938—31no—
222#937—61no—
223#935—61no—
224C2×#214—31no—
225C2×#213—31no—
226C2×#213—31no—
227#930—31no—
228C4×#67—61no—
229C4×#67—61no—
230#926—31no—
231C22×C3⋊C8—31no—
232#919—24no—
233#916—64no—
234C2×D24C2×D311yescharacteristic, complemented
235C2×#204—31no—
236C2×D3×C8—31no—
237C2×D3×C8C2×D311yescharacteristic, complemented
238#895—31no—
239#894—61no—
240#893—61no—
241#892—31no—
242#882—61no—
243#67⋊C4—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—61no—
250#835C2×D311yescharacteristic, complemented
251#832—31no—
252#832—31no—
253#832—31no—
254#830—31no—
255#821—31no—
256#821—31no—
257#821C2×D311yescharacteristic, complemented
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—61no—
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265#816—31no—
266#816—31no—
267#816—31no—
268#816—61no—
269#810—31no—
270#809—31no—
271C22×C3⋊D3C2×D411yescharacteristic
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—24no—
278C2×D32—22no—
279C2×D32—22no—
280C2×D32—41no—
281C2×D32—42no—
282C2×D32—42no—
283C32×Q8—21no—
284C32×Q8—21no—
285C32×Q8—21no—
286C32×Q8C2×D412yes—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4C2411yescharacteristic
290C2×C3⋊Dic3—21no—
291C2×C3⋊Dic3—21no—
292C2×C3⋊Dic3C2×D411yescharacteristic
293C4×C3⋊D3—24no—
294C4×C3⋊D3—21no—
295C4×C3⋊D3—21no—
296#634—24no—
297#634—21no—
298#634C2×D412yes—
299C2×C3×Dic3—21no—
300C2×C3×Dic3C2×D411yescharacteristic
301C2×C3×Dic3C2×D411yescharacteristic
302C3×D12—24no—
303C3×D12—24no—
304C3×D12—21no—
305C3×D12—21no—
306C3×D12—21no—
307C3×D12—21no—
308C3×D12—42no—
309C3×D12C2×D412yes—
310C3×D12C2×D412yes—
311C3×C4×D3—24no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—24no—
315C3×C4×D3—42no—
316C3×C4×D3C2×D412yes—
317C3×C4×D3C2×D412yes—
318#626—42no—
319#625—24no—
320#625—24no—
321#625—24no—
322#625—42no—
323#624—22no—
324D3×Dic3—24no—
325D3×Dic3—22no—
326D3×Dic3—22no—
327D3×Dic3—24no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#135—31no—
334C2×#135—91no—
335#525—91no—
336#452—31no—
337#452—91no—
338#451—91no—
339#450—91no—
340#449—91no—
341#449—91no—
342#448—91no—
343#447—91no—
344#416—91no—
345#416—91no—
346C2×C22⋊C8—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C3×#41—34no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C3×#41—62no—
356C3×#41—62no—
357C2×C3×Q8—21no—
358C2×C3×Q8—21no—
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×Q8C22×D311yescharacteristic
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C2×C3×D4—61no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C22×C3×C4—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387#239—22no—
388#239—22no—
389#239—22no—
390#239—22no—
391#239—22no—
392#239#6714yescomplemented
393D3×Q8—62no—
394D3×Q8—62no—
395D3×Q8—62no—
396D3×Q8—62no—
397D3×Q8—122no—
398D3×Q8—122no—
399#237—34no—
400#237—62no—
401#237—62no—
402#237—68no—
403#237—68no—
404#237—62no—
405D3×D4—62no—
406D3×D4—62no—
407D3×D4—68no—
408D3×D4—68no—
409D3×D4—62no—
410D3×D4—62no—
411#235—34no—
412#235—62no—
413#235—62no—
414#235—68no—
415#235—68no—
416#235—62no—
417C2×D12—21no—
418C2×D12—21no—
419C2×D12—21no—
420C2×D12—61no—
421C2×D12C22×D311yescharacteristic
422C2×D12C22×D311yescharacteristic
423C2×D12C22×D311yescharacteristic
424C2×C4×D3—21no—
425C2×C4×D3—21no—
426C2×C4×D3—21no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—61no—
434C2×C4×D3—62no—
435C2×C4×D3—62no—
436C2×C4×D3—68no—
437C2×C4×D3—68no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—62no—
443C2×C4×D3—62no—
444C2×C4×D3—121no—
445C2×C4×D3C22×D311yescharacteristic
446C2×C4×D3C22×D311yescharacteristic
447C2×Dic6—31no—
448C2×Dic6—31no—
449C2×Dic6—61no—
450C2×Dic6—61no—
451C2×Dic6—61no—
452C2×Dic6—121no—
453C3×Q16—22no—
454C3×Q16—22no—
455C3×Q16—42no—
456C3×SD16—62no—
457C3×SD16—62no—
458C3×SD16—62no—
459C3×D8—62no—
460C2×C3×C8—21no—
461C2×C3×C8—31no—
462C2×C3×C8—31no—
463C2×C3×C8—62no—
464C2×C3×C8C22×D311yescharacteristic
465C2×C3×C8C22×D311yescharacteristic
466C3×C4⋊C4—31no—
467C3×C4⋊C4—61no—
468C3×C22⋊C4—61no—
469#217—61no—
470#217—61no—
471#217—61no—
472#216—62no—
473#216—62no—
474#216—122no—
475#215—22no—
476#215—22no—
477#215—22no—
478#214—62no—
479#213—62no—
480#213—62no—
481(C2×D3)⋊C4—21no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—61no—
491C4⋊Dic3C22×D311yescharacteristic
492Dic3⋊C4—21no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—121no—
496C4×Dic3—61no—
497C4×Dic3—61no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8—62no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504D24—22no—
505#204—62no—
506D3×C8—22no—
507D3×C8—62no—
508C22×C32C22×D411yescharacteristic
509C2×C3⋊D3—21no—
510C2×C3⋊D3—21no—
511C2×C3⋊D3#13512yescomplemented
512C2×C3×D3—21no—
513C2×C3×D3—21no—
514C2×C3×D3—21no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—21no—
518C2×C3×D3—21no—
519C2×C3×D3—41no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527D32—44no—
528D32—48no—
529C32×C4—22no—
530C32×C4—41no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3⋊Dic3—21no—
534C3⋊Dic3—22no—
535C3⋊Dic3—41no—
536C3×Dic3—21no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—31no—
541C2×#41—31no—
542C2×#41—91no—
543C2×#41—91no—
544C2×#41—181no—
545C2×#41—181no—
546C2×#41—184no—
547C2×#41—184no—
548C22×Q8—91no—
549C22×D4—91no—
550C22×D4—181no—
551C23×C4—91no—
552C23×C4—181no—
553#135—64no—
554#135—184no—
555C2×Q16—91no—
556C2×Q16D3211yescharacteristic, complemented
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16—31no—
560C2×SD16—91no—
561C2×D8—31no—
562C2×D8—91no—
563C22×C8—31no—
564C22×C8—91no—
565#123—181no—
566C22⋊Q8—31no—
567C22⋊Q8—91no—
568#121—91no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—91no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103—91no—
578#102—31no—
579#102—91no—
580#102—91no—
581#102—91no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—31no—
595C22×D3—31no—
596C22×D3—61no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—64no—
601C22×D3—64no—
602C22×D3—62no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3D3×D411yescharacteristic
610C22×D3D3×D411yescharacteristic
611C3×Q8—21no—
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—21no—
616C3×Q8—21no—
617C3×Q8—22no—
618C3×Q8—41no—
619C3×Q8—41no—
620C3×Q8—41no—
621C3×Q8D3×D412yes—
622C3×Q8C2×#6712yes—
623C3×D4—32no—
624C3×D4—32no—
625C3×D4—64no—
626C3×D4—64no—
627C3×D4—61no—
628C3×D4—61no—
629C3×D4—61no—
630C3×D4—61no—
631C3×D4—122no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—31no—
638C2×C3×C4—32no—
639C2×C3×C4—32no—
640C2×C3×C4—31no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—64no—
644C2×C3×C4—64no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—122no—
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651#67—64no—
652#67—64no—
653#67—64no—
654#67—64no—
655#67—64no—
656#67—64no—
657#67—122no—
658#67—122no—
659#67—122no—
660C2×Dic3—21no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—61no—
664C2×Dic3—62no—
665C2×Dic3—64no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—64no—
669C2×Dic3—62no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—121no—
673C2×Dic3—121no—
674C2×Dic3D3×D411yescharacteristic
675C2×Dic3D3×D411yescharacteristic
676D12—24no—
677D12—24no—
678D12—21no—
679D12—21no—
680D12—21no—
681D12—21no—
682D12—42no—
683D12—122no—
684D12D3×D412yes—
685D12C2×#6712yes—
686C4×D3—24no—
687C4×D3—21no—
688C4×D3—21no—
689C4×D3—24no—
690C4×D3—42no—
691C4×D3—62no—
692C4×D3—64no—
693C4×D3—64no—
694C4×D3—62no—
695C4×D3—64no—
696C4×D3—64no—
697C4×D3—62no—
698C4×D3—61no—
699C4×D3—61no—
700C4×D3—61no—
701C4×D3—61no—
702C4×D3—62no—
703C4×D3—121no—
704C4×D3—121no—
705C4×D3—124no—
706C4×D3D3×D412yes—
707C4×D3C2×#6712yes—
708Dic6—32no—
709Dic6—32no—
710Dic6—62no—
711Dic6—64no—
712Dic6—64no—
713Dic6—61no—
714Dic6—61no—
715Dic6—121no—
716Dic6—124no—
717C3×C8—21no—
718C3×C8—21no—
719C3×C8—41no—
720C3×C8—61no—
721C3×C8—61no—
722C3⋊C8—21no—
723C3⋊C8—21no—
724C3⋊C8—61no—
725C3⋊C8—61no—
726C3⋊C8—121no—
727C2×C32C2×#12011yescharacteristic
728C2×C32C2×#13511yescharacteristic
729C2×C32#57511yescharacteristic
730C3⋊D3—22no—
731C3×D3—22no—
732C3×D3—41no—
733C3×D3—42no—
734C3×D3—42no—
735C3×D3—81no—
736C24—91no—
737C24—181no—
738#41—34no—
739#41—62no—
740#41—62no—
741#41—62no—
742#41—62no—
743#41—62no—
744#41—94no—
745#41—182no—
746#41—182no—
747#41—182no—
748#41—188no—
749#41—188no—
750C2×Q8—91no—
751C2×Q8—181no—
752C2×Q8—182no—
753C2×Q8—182no—
754C2×Q8C2×D3211yescharacteristic
755C2×Q8C2×D3211yescharacteristic
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—31no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4—61no—
762C2×D4—181no—
763C2×D4—181no—
764C2×D4—182no—
765C2×D4—182no—
766C2×D4—188no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—181no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—181no—
780C22×C4—182no—
781C22×C4—182no—
782C22×C4—181no—
783C22×C4—181no—
784C22×C4—188no—
785Q16—22no—
786Q16—182no—
787SD16—62no—
788SD16—62no—
789SD16—62no—
790SD16—182no—
791D8—62no—
792D8—182no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—62no—
796C2×C8—91no—
797C2×C8—182no—
798C2×C8C2×D3211yescharacteristic
799C4⋊C4—31no—
800C4⋊C4—61no—
801C4⋊C4—91no—
802C4⋊C4—181no—
803C22⋊C4—61no—
804C22⋊C4—181no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C42—181no—
809C22×C3—21no—
810C22×C3—32no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—62no—
816C22×C3—61no—
817C22×C3—62no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3C2×D3×D411yescharacteristic
826C22×C3C2×D3×D411yescharacteristic
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—21no—
830C2×D3—21no—
831C2×D3—22no—
832C2×D3—21no—
833C2×D3—22no—
834C2×D3—32no—
835C2×D3—32no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—62no—
844C2×D3—61no—
845C2×D3—61no—
846C2×D3—61no—
847C2×D3—61no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—124no—
851C2×D3—124no—
852C2×D3—128no—
853C2×D3—128no—
854C2×D3#93712yes—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—32no—
860C3×C4—42no—
861C3×C4—41no—
862C3×C4—41no—
863C3×C4—61no—
864C3×C4—81no—
865C3×C4—121no—
866C3×C4C2×D3×D411yescharacteristic
867C3×C4C2×D3×D411yescharacteristic
868C3×C4C2×D3×D411yescharacteristic
869C3×C4C22×#6711yescharacteristic
870Dic3—21no—
871Dic3—41no—
872Dic3—62no—
873Dic3—61no—
874Dic3—62no—
875Dic3—61no—
876Dic3—122no—
877Dic3—121no—
878Dic3—121no—
879Dic3—121no—
880Dic3—241no—
881Dic3#93712yes—
882C32#300211yescharacteristic, complemented, Sylow
883C23—31no—
884C23—31no—
885C23—61no—
886C23—61no—
887C23—61no—
888C23—91no—
889C23—182no—
890C23—182no—
891C23—184no—
892C23—361no—
893C23—362no—
894C23—362no—
895Q8—21no—
896Q8—21no—
897Q8—21no—
898Q8—92no—
899Q8—184no—
900Q8—181no—
901Q8D3×#6712yes—
902D4—32no—
903D4—32no—
904D4—64no—
905D4—64no—
906D4—61no—
907D4—61no—
908D4—61no—
909D4—61no—
910D4—122no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4—362no—
915D4—362no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—31no—
919C2×C4—32no—
920C2×C4—32no—
921C2×C4—31no—
922C2×C4—64no—
923C2×C4—64no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—91no—
928C2×C4—122no—
929C2×C4—184no—
930C2×C4—182no—
931C2×C4—182no—
932C2×C4—184no—
933C2×C4—182no—
934C2×C4—184no—
935C2×C4—181no—
936C2×C4—181no—
937C2×C4—181no—
938C2×C4—181no—
939C2×C4C22×D3211yescharacteristic
940C8—21no—
941C8—61no—
942C8—61no—
943C8—181no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—62no—
948C2×C3—122no—
949C2×C3—121no—
950C2×C3—122no—
951C2×C3—241no—
952C2×C3D3×#12011yescharacteristic
953C2×C3D3×#13511yescharacteristic
954C2×C3D3×#13511yescharacteristic
955C2×C3#576811yescharacteristic
956C2×C3#577711yescharacteristic
957C2×C3C2×#93711yescharacteristic
958D3—22no—
959D3—41no—
960D3—42no—
961D3—42no—
962D3—62no—
963D3—62no—
964D3—81no—
965D3—122no—
966C22—32no—
967C22—61no—
968C22—61no—
969C22—61no—
970C22—61no—
971C22—62no—
972C22—62no—
973C22—61no—
974C22—92no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—121no—
982C22—181no—
983C22—181no—
984C22—364no—
985C22—368no—
986C22D32×D411yescharacteristic
987C4—22no—
988C4—32no—
989C4—41no—
990C4—61no—
991C4—121no—
992C4—181no—
993C4—182no—
994C4—361no—
995C4D32×D411yescharacteristic
996C4C2×D3×#6711yescharacteristic
997C3—21no—
998C3#8022611yescharacteristic, complemented
999C3#8391111yescharacteristic, complemented
1000C2—62no—
1001C2—121no—
1002C2—122no—
1003C2—122no—
1004C2—182no—
1005C2—241no—
1006C2#1059476311yescharacteristic
1007C2#1059476411yescharacteristic
1008C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32#3002
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#64319C2semidirect
2. C2×C3×#919C2semidirect
3. #10595424C2semidirect
4. C2×#63947C2semidirect
5. #10592885C2semidirect
6. C3×#5187C2semidirect
7. #10591655C2semidirect
8. #10591652C2semidirect
9. #10591592C2semidirect
10. #10591586C2semidirect
11. #10591556C2semidirect
12. #10590962C2semidirect
13. #10590954C2semidirect
14. #10590945C2semidirect
15. D3×(C2×D3)⋊C8C2semidirect
21. C2×C3×#239C22semidirect
32. C2×C32×Q16C22semidirect
34. C2×#3756C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#215C22semidirect
40. C2×C3×D24C22semidirect
41. C2×C3×D3×C8C22semidirect
45. #63908C22semidirect
49. #63841C22semidirect
50. C2×#3716C22semidirect
51. C2×#3713C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63662C22semidirect
55. #63643C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63567C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
70. C2×#919D3semidirect
76. #5187D3semidirect
111. C3×#239D4semidirect
144. #3795D4semidirect
179. C2×#239C2×D3semidirect
201. C2×C3×Q16C2×D3semidirect
202. C2×C3×Q16C2×D3semidirect
213. #946C2×D3semidirect
217. C2×#215C2×D3semidirect
218. C2×#215C2×D3semidirect
219. C2×#215C2×D3semidirect
234. C2×D24C2×D3semidirect
237. C2×D3×C8C2×D3semidirect
250. #835C2×D3semidirect
257. #821C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
392. #239#67semidirect
511. C2×C3⋊D3#135semidirect
556. C2×Q16D32semidirect
882. C32#3002semidirect
998. C3#80226semidirect
999. C3#83911semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×C3×#9192
#105954242
C2×#639472
#105928852
C3×#51872
#105916552
#105916522
#105915922
#105915862
#105915562
#105909622
#105909542
#105909452
D3×(C2×D3)⋊C82
#839113
#802263