Finite Group Databasebeta

← #11784797

Subgroups — #11784797

Order 1152.

1321 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic, complemented
4C3×#5126C211yesmaximal, characteristic, complemented
5C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6C2×#63570C211yesmaximal, characteristic, complemented
7C2×#63568C211yesmaximal, characteristic, complemented
8#70380—31nomaximal
9#69991—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C2×D3×#67—21no—
14C2×#3804—21no—
15D3×#235—22no—
16D3×#235—22no—
17D3×#235—22no—
18D3×#235—22no—
19C2×D3×D12C411yescharacteristic, complemented
20C2×C4×D32—21no—
21C2×#3799C411yescharacteristic, complemented
22C2×#3798—21no—
23C2×#3795C411yescharacteristic, complemented
24C2×D3×Dic6C411yescharacteristic, complemented
25C2×C32×M16C2211yescharacteristic, complemented
26C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C2×C3×C4×Dic3C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C2×(C2×D3)⋊Dic3—21no—
30#63652—22no—
31C3×#825—22no—
32C3×(C2×D3)⋊C8—21no—
33C3×(C2×D3)⋊C8—21no—
34#63579—21no—
35#63570—22no—
36#63568—22no—
37C2×D3×#41—31no—
38C22×#235—31no—
39C2×C3×#104—31no—
40C3×#407—31no—
41C2×#837—31no—
42C4×#217—31no—
43C2×#825—31no—
44C2×#825—31no—
45C2×#825—31no—
46C2×#825—31no—
47C2×#825—61no—
48C2×#825D311yescharacteristic, complemented
49#5126D311yescharacteristic, complemented
50C4×(C2×D3)⋊C4—31no—
51C2×#805—31no—
52C23×C3×D3D411yescharacteristic
53C22×D32—21no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—21no—
56C22×C3⋊Dic3—21no—
57#3828—21no—
58#3828—21no—
59#3828D412yes—
60#3828D412yes—
61C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×#634C2×C411yescharacteristic
64C2×C3×#67—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C3×#235—21no—
68C3×#235—21no—
69C3×#235D412yes—
70C3×#235D412yes—
71C2×C3×D12C2×C411yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3C2×C411yescharacteristic
78C2×C3×C4×D3C2×C411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×Dic6C2×C411yescharacteristic
82D3×#67—24no—
83D3×#67—24no—
84C2×#627—21no—
85C2×#626—21no—
86C2×#626—21no—
87C2×#625—21no—
88C2×#624—21no—
89#3804—24no—
90#3804—24no—
91C2×D3×Dic3—21no—
92C2×D3×Dic3—21no—
93D3×D12—22no—
94D3×D12—22no—
95C4×D32—24no—
96C4×D32—24no—
97#3799—22no—
98#3799—22no—
99#3798—24no—
100#3798—24no—
101#3795—22no—
102#3795—22no—
103D3×Dic6—22no—
104D3×Dic6—22no—
105C32×M16—21no—
106C32×M16—21no—
107C2×C32×C8—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3—21no—
110C3×C4×Dic3—21no—
111C3×C4×Dic3—21no—
112C3×#208—21no—
113C3×#208—21no—
114C2×C3×C3⋊C8—21no—
115(C2×D3)⋊Dic3—24no—
116#1789—91noSylow
117C2×C3×#41—31no—
118C23×C3×C4—31no—
119C22×#67—61no—
120D3×#41—62no—
121D3×#41—62no—
122D3×#41—62no—
123D3×#41—62no—
124C2×#239—31no—
125C2×D3×Q8—31no—
126C2×#237—31no—
127C2×#237—61no—
128C2×D3×D4—31no—
129C2×D3×D4—61no—
130C2×#235—31no—
131C2×#235—31no—
132C2×#235—31no—
133C2×#235—31no—
134C2×#235—61no—
135C2×#235—61no—
136C2×#235—62no—
137C2×#235—62no—
138C2×#235—61no—
139C2×#235—62no—
140C2×#235—62no—
141C2×#235—61no—
142C2×#235C2×D311yescharacteristic
143C22×D12—31no—
144C22×C4×D3—61no—
145C22×C4×D3—61no—
146C22×C4×D3C2×D311yescharacteristic
147C22×Dic6—31no—
148C2×C3×M16—21no—
149C2×C3×M16—31no—
150C2×C3×M16C2×D311yescharacteristic, complemented
151C2×C3×M16C2×D311yescharacteristic, complemented
152C2×C3×C42—31no—
153C2×#217—61no—
154C2×(C2×D3)⋊C4—61no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—61no—
158C2×C4×Dic3C2×D311yescharacteristic, complemented
159C2×#208C2×D311yescharacteristic, complemented
160C3×#104—62no—
161C3×C22⋊C8—61no—
162C3×C22⋊C8—61no—
163#837—62no—
164C3⋊#95—61no—
165C3⋊#95—61no—
166#825—22no—
167#825—62no—
168#825—62no—
169#825—62no—
170#825—64no—
171#825—62no—
172(C2×D3)⋊C8—21no—
173(C2×D3)⋊C8—21no—
174#805—62no—
175C23×C32C2×D411yescharacteristic
176C22×C3⋊D3—21no—
177C22×C3×D3—21no—
178C22×C3×D3—21no—
179C22×C3×D3—21no—
180C22×C3×D3—22no—
181C22×C3×D3—41no—
182C22×C3×D3C22⋊C411yescharacteristic
183C22×C3×D3C22⋊C411yescharacteristic
184C2×D32—24no—
185C2×D32—42no—
186C2×D32—42no—
187C2×C32×C4C22×C411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193#638—22no—
194#638—22no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—41no—
198C2×C3⋊Dic3—41no—
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)C22⋊C412yescomplemented
201C4×C3⋊D3—22no—
202C4×C3⋊D3—22no—
203#634—21no—
204#634C22⋊C412yescomplemented
205C3×#67—22no—
206C3×#67—22no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—41no—
212C2×C3×Dic3—41no—
213C2×C3×Dic3C22⋊C411yescharacteristic
214C2×C3×Dic3C22⋊C411yescharacteristic
215C3×D12—21no—
216C3×D12C22⋊C412yescomplemented
217C3×C4×D3—21no—
218C3×C4×D3—21no—
219C3×C4×D3—21no—
220C3×C4×D3—21no—
221C3×C4×D3—21no—
222C3×C4×D3—21no—
223C3×C4×D3—22no—
224C3×C4×D3—22no—
225C3×C4×D3—21no—
226C3×C4×D3—21no—
227C3×Dic6—21no—
228C3×Dic6C22⋊C412yescomplemented
229#627—24no—
230#626—24no—
231#626—24no—
232#625—24no—
233#624—24no—
234D3×Dic3—24no—
235D3×Dic3—24no—
236C32×C8—41no—
237C3×C3⋊C8—41no—
238C22×#41—91no—
239C2×#104—31no—
240C2×#104—91no—
241C2×#104—91no—
242C2×#104—91no—
243#407—31no—
244C4×C22⋊C4—91no—
245C24×C3—31no—
246C23×D3—61no—
247C23×D3—61no—
248C23×D3D1211yescharacteristic
249C3×#41—32no—
250C3×#41—32no—
251C3×#41—61no—
252C3×#41—61no—
253C2×C3×Q8—31no—
254C2×C3×D4—31no—
255C2×C3×D4—61no—
256C22×C3×C4—21no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—61no—
263C22×C3×C4—61no—
264C22×C3×C4—61no—
265C22×C3×C4—61no—
266C22×C3×C4—61no—
267C22×C3×C4—61no—
268C22×C3×C4C22×D311yescharacteristic
269C22×C3×C4C22×D311yescharacteristic
270C2×#67—21no—
271C2×#67—61no—
272C2×#67—64no—
273C2×#67—64no—
274C2×#67—61no—
275C2×#67—61no—
276C2×#67—61no—
277C2×#67—61no—
278C2×#67—61no—
279C2×#67—121no—
280C22×Dic3—21no—
281C22×Dic3—61no—
282C22×Dic3—61no—
283C22×Dic3—61no—
284C22×Dic3—61no—
285C22×Dic3—121no—
286C22×Dic3D1211yescharacteristic
287#239—62no—
288#239—62no—
289D3×Q8—62no—
290D3×Q8—62no—
291#237—62no—
292#237—62no—
293#237—64no—
294#237—64no—
295D3×D4—62no—
296D3×D4—62no—
297D3×D4—64no—
298D3×D4—64no—
299#235—21no—
300#235—21no—
301#235—32no—
302#235—32no—
303#235—32no—
304#235—32no—
305#235—62no—
306#235—62no—
307#235—62no—
308#235—62no—
309#235—64no—
310#235—64no—
311#235—64no—
312#235—64no—
313#235—64no—
314#235—64no—
315#235—61no—
316#235—61no—
317#235—61no—
318#235—61no—
319#235—62no—
320#235—62no—
321#235—121no—
322#235—121no—
323#235D1212yes—
324#235#6712yes—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12C4×D311yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—64no—
339C2×C4×D3—64no—
340C2×C4×D3—64no—
341C2×C4×D3—64no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—121no—
349C2×C4×D3C4×D311yescharacteristic
350C2×C4×D3C4×D311yescharacteristic
351C2×C4×D3#6711yescharacteristic
352C2×C4×D3#6711yescharacteristic
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—61no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6—62no—
360C2×Dic6C4×D311yescharacteristic
361C3×M16—22no—
362C3×M16—21no—
363C3×M16—21no—
364C3×M16—21no—
365C3×M16—21no—
366C3×M16—41no—
367C3×M16—61no—
368C3×M16—61no—
369C2×C3×C8—21no—
370C2×C3×C8—21no—
371C2×C3×C8—41no—
372C2×C3×C8—61no—
373C3×C42—61no—
374C3×C42—61no—
375#217—64no—
376(C2×D3)⋊C4—64no—
377C4×Dic3—21no—
378C4×Dic3—21no—
379C4×Dic3—62no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—121no—
385#208—21no—
386#208—21no—
387C2×C3⋊C8—21no—
388C22×C32—21no—
389C22×C32—21no—
390C22×C32C2×C22⋊C411yescharacteristic
391C22×C32#12011yescharacteristic
392C22×C32#12011yescharacteristic
393C2×C3⋊D3—22no—
394C2×C3⋊D3—41no—
395C2×C3⋊D3—41no—
396C2×C3×D3—21no—
397C2×C3×D3—21no—
398C2×C3×D3—22no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—21no—
402C2×C3×D3—42no—
403C2×C3×D3—42no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3#10412yescomplemented
407D32—48no—
408C32×C4C2×C22⋊C411yescharacteristic
409C32×C4C2×C22⋊C411yescharacteristic
410C32×C4#12011yescharacteristic
411C32×C4#12011yescharacteristic
412C3⋊Dic3—22no—
413C3⋊Dic3—42no—
414C3×Dic3—21no—
415C3×Dic3—22no—
416C3×Dic3—21no—
417C3×Dic3—42no—
418C2×#41—31no—
419C2×#41—91no—
420C2×#41—91no—
421C2×#41—91no—
422C2×#41—181no—
423C2×#41—181no—
424C2×#41—182no—
425C2×#41—182no—
426C2×#41—182no—
427C2×#41—182no—
428C22×Q8—91no—
429C22×D4—91no—
430C22×D4—181no—
431C23×C4—31no—
432C23×C4—181no—
433C2×M16—31no—
434C2×M16D3211yescharacteristic, complemented
435C2×C22⋊C4—181no—
436C2×C42—31no—
437C2×C42—91no—
438#104—62no—
439#104—182no—
440#104—182no—
441#104—182no—
442C22⋊C8—61no—
443C22⋊C8—61no—
444#95—181no—
445C23×C3—21no—
446C23×C3—31no—
447C23×C3—31no—
448C23×C3—62no—
449C23×C3—61no—
450C23×C3—61no—
451C23×C3—61no—
452C23×C3—121no—
453C23×C3C2×D1211yescharacteristic
454C23×C3D3×D411yescharacteristic
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—22no—
459C22×D3—41no—
460C22×D3—64no—
461C22×D3—64no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—121no—
465C22×D3—122no—
466C22×D3—122no—
467C22×D3—122no—
468C22×D3—122no—
469C22×D3(C2×D3)⋊C411yescharacteristic
470C22×D3(C2×D3)⋊C411yescharacteristic
471C3×Q8—32no—
472C3×Q8—61no—
473C3×D4—32no—
474C3×D4—62no—
475C3×D4—62no—
476C3×D4—61no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—62no—
499C2×C3×C4—121no—
500C2×C3×C4—121no—
501C2×C3×C4C2×C4×D311yescharacteristic
502C2×C3×C4C2×C4×D311yescharacteristic
503C2×C3×C4C2×D1211yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513#67—22no—
514#67—22no—
515#67—64no—
516#67—64no—
517#67—64no—
518#67—64no—
519#67—62no—
520#67—62no—
521#67—62no—
522#67—62no—
523#67—122no—
524#67—122no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—22no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—64no—
532C2×Dic3—64no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—62no—
536C2×Dic3—62no—
537C2×Dic3—121no—
538C2×Dic3—122no—
539C2×Dic3—122no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—122no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3(C2×D3)⋊C411yescharacteristic
546C2×Dic3(C2×D3)⋊C411yescharacteristic
547D12—21no—
548D12—32no—
549D12—32no—
550D12—62no—
551D12—64no—
552D12—64no—
553D12—61no—
554D12—61no—
555D12—121no—
556D12(C2×D3)⋊C412yescomplemented
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—22no—
562C4×D3—21no—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—22no—
567C4×D3—64no—
568C4×D3—64no—
569C4×D3—64no—
570C4×D3—64no—
571C4×D3—62no—
572C4×D3—62no—
573C4×D3—62no—
574C4×D3—62no—
575C4×D3—122no—
576C4×D3—122no—
577Dic6—21no—
578Dic6—32no—
579Dic6—32no—
580Dic6—62no—
581Dic6—64no—
582Dic6—64no—
583Dic6—61no—
584Dic6—61no—
585Dic6—121no—
586Dic6(C2×D3)⋊C412yescomplemented
587C3×C8—42no—
588C3×C8—41no—
589C3×C8—41no—
590C3×C8—121no—
591C3⋊C8—41no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32#37911yescharacteristic
595C2×C32C2×#10411yescharacteristic
596C2×C32#42111yescharacteristic
597C3⋊D3—42no—
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—41no—
601C24—31no—
602C24—181no—
603#41—32no—
604#41—32no—
605#41—61no—
606#41—61no—
607#41—92no—
608#41—92no—
609#41—184no—
610#41—184no—
611#41—182no—
612#41—182no—
613#41—184no—
614#41—184no—
615#41—182no—
616#41—182no—
617#41—181no—
618#41—181no—
619C2×Q8—31no—
620C2×Q8—91no—
621C2×Q8—181no—
622C2×Q8—182no—
623C2×Q8—182no—
624C2×D4—31no—
625C2×D4—61no—
626C2×D4—91no—
627C2×D4—181no—
628C2×D4—182no—
629C2×D4—182no—
630C2×D4—181no—
631C2×D4—184no—
632C2×D4—184no—
633C2×D4—181no—
634C2×D4—181no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—184no—
649C22×C4—184no—
650C22×C4—181no—
651C22×C4—181no—
652C22×C4—181no—
653C22×C4C2×D3211yescharacteristic
654M16—21no—
655M16—21no—
656M16—61no—
657M16—61no—
658C2×C8—21no—
659C2×C8—61no—
660C22⋊C4—184no—
661C42—61no—
662C42—61no—
663C42—181no—
664C42—181no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—32no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—62no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—122no—
682C22×C3—122no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3D3×C22⋊C411yescharacteristic
686C22×C3#88211yescharacteristic
687C22×C3#88211yescharacteristic
688C22×C3#88211yescharacteristic
689C22×C3C2×(C2×D3)⋊C411yescharacteristic
690C22×C3#93711yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—22no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—62no—
702C2×D3—62no—
703C2×D3—122no—
704C2×D3—128no—
705C2×D3—128no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3#82512yescomplemented
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—61no—
718C3×C4—62no—
719C3×C4—61no—
720C3×C4—122no—
721C3×C4D3×C22⋊C411yescharacteristic
722C3×C4D3×C22⋊C411yescharacteristic
723C3×C4D3×C22⋊C411yescharacteristic
724C3×C4#88211yescharacteristic
725C3×C4C2×(C2×D3)⋊C411yescharacteristic
726C3×C4#93711yescharacteristic
727C3×C4#93711yescharacteristic
728C3×C4#93711yescharacteristic
729Dic3—22no—
730Dic3—21no—
731Dic3—21no—
732Dic3—42no—
733Dic3—62no—
734Dic3—62no—
735Dic3—122no—
736Dic3—122no—
737Dic3—122no—
738Dic3—124no—
739C32#178911yescharacteristic, complemented, Sylow
740C23—31no—
741C23—31no—
742C23—62no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—121no—
747C23—184no—
748C23—181no—
749C23—362no—
750C23—362no—
751C23D3×D1211yescharacteristic
752Q8—32no—
753Q8—61no—
754Q8—92no—
755Q8—184no—
756Q8—181no—
757D4—32no—
758D4—62no—
759D4—62no—
760D4—61no—
761D4—92no—
762D4—184no—
763D4—184no—
764D4—184no—
765D4—182no—
766D4—182no—
767D4—181no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—62no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—184no—
787C2×C4—184no—
788C2×C4—184no—
789C2×C4—181no—
790C2×C4—182no—
791C2×C4—182no—
792C2×C4—182no—
793C2×C4—361no—
794C2×C4—361no—
795C2×C4C4×D3211yescharacteristic
796C2×C4D3×D1211yescharacteristic
797C2×C4#380211yescharacteristic
798C2×C4D3×#6711yescharacteristic
799C2×C4D3×#6711yescharacteristic
800C2×C4#381111yescharacteristic
801C8—41no—
802C8—121no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—41no—
811C2×C3—41no—
812C2×C3—62no—
813C2×C3—122no—
814C2×C3—121no—
815C2×C3D3×#10411yescharacteristic
816C2×C3#482111yescharacteristic
817C2×C3#495511yescharacteristic
818C2×C3#495511yescharacteristic
819C2×C3C2×#82511yescharacteristic
820C2×C3#513911yescharacteristic
821D3—22no—
822D3—41no—
823D3—42no—
824D3—122no—
825D3—122no—
826D3—242no—
827C22—21no—
828C22—21no—
829C22—32no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—62no—
836C22—122no—
837C22—122no—
838C22—121no—
839C22—121no—
840C22—182no—
841C22—368no—
842C22—361no—
843C22—361no—
844C22D3×(C2×D3)⋊C411yescharacteristic
845C22#6392211yescharacteristic
846C22#6392311yescharacteristic
847C4—61no—
848C4—61no—
849C4—62no—
850C4—122no—
851C4—182no—
852C4—362no—
853C4D3×(C2×D3)⋊C411yescharacteristic
854C4#6392111yescharacteristic
855C4#6392211yescharacteristic
856C4#6398311yescharacteristic
857C3—21no—
858C3#6999111yescharacteristic, complemented
859C3#7038011yescharacteristic, complemented
860C2—21no—
861C2—21no—
862C2—62no—
863C2—121no—
864C2—122no—
865C2—362no—
866C2D3×#82511yescharacteristic
867C2#1059100511yescharacteristic
868C2#1059139911yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×D3×#235C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1789
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63652C2semidirect
3. C2×C3×#825C2semidirect
4. C3×#5126C2semidirect
5. C4×(C2×D3)⋊Dic3C2semidirect
6. C2×#63570C2semidirect
7. C2×#63568C2semidirect
19. C2×D3×D12C4semidirect
21. C2×#3799C4semidirect
23. C2×#3795C4semidirect
24. C2×D3×Dic6C4semidirect
25. C2×C32×M16C22semidirect
26. C2×C4×C3⋊Dic3C22semidirect
27. C2×C3×C4×Dic3C22semidirect
28. C2×C3×#208C22semidirect
48. C2×#825D3semidirect
49. #5126D3semidirect
150. C2×C3×M16C2×D3semidirect
151. C2×C3×M16C2×D3semidirect
158. C2×C4×Dic3C2×D3semidirect
159. C2×#208C2×D3semidirect
200. C4⋊(C3⋊D3)C22⋊C4semidirect
204. #634C22⋊C4semidirect
216. C3×D12C22⋊C4semidirect
228. C3×Dic6C22⋊C4semidirect
406. C2×C3×D3#104semidirect
434. C2×M16D32semidirect
556. D12(C2×D3)⋊C4semidirect
586. Dic6(C2×D3)⋊C4semidirect
712. C2×D3#825semidirect
739. C32#1789semidirect
858. C3#69991semidirect
859. C3#70380semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×#636522
C2×C3×#8252
C3×#51262
C4×(C2×D3)⋊Dic32
C2×#635702
C2×#635682
#703803
#699913