Finite Group Databasebeta

← C2×#10590405 #11857525

Subgroups — C2×#10590405 #11857525

Order 1152.

1681 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic
2C2×C3×#877C211yesmaximal, characteristic, complemented
3C2×#63955C211yesmaximal, characteristic, complemented
4C2×#63633C211yesmaximal, characteristic, complemented
5C2×C3×#806C211yesmaximal, characteristic, complemented
6C2×#63581C211yesmaximal, characteristic, complemented
7C2×#63580C211yesmaximal, characteristic, complemented
8#10590405C218yesmaximal, direct product factor
9C2×#5006—31nomaximal
10C2×#4740—31nomaximal
11C22×#638C2211yescharacteristic
12C22×C3×#67C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C22×#627C411yescharacteristic, complemented
15C22×#626C411yescharacteristic, complemented
16C22×#624C411yescharacteristic, complemented
17C2×#3804—21no—
18C2×#3804—22no—
19C2×#3804—21no—
20C2×#3804—22no—
21C2×#3804—21no—
22C2×#3804—21no—
23C2×#3804C414yescomplemented
24C2×#3804C2214yes—
25C22×D3×Dic3C411yescharacteristic, complemented
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×Dic3⋊C4—21no—
31C2×C3×C4×Dic3—21no—
32C3×#877—22no—
33C3×#877C2214yescomplemented
34C2×Dic3⋊Dic3—21no—
35#63955—22no—
36#63955C2214yescomplemented
37C2×Dic32—21no—
38#63633C2214yescomplemented
39C3×#806C2214yescomplemented
40#63581C2214yescomplemented
41#63580C2214yescomplemented
42C22×#237—31no—
43C22×#235—31no—
44C2×C3×#117—31no—
45C2×#926—31no—
46C2×#877—31no—
47C2×#877D311yescharacteristic, complemented
48C2×C3×#99—31no—
49C2×#834—31no—
50#5006—38no—
51C2×#806—31no—
52C2×#806—31no—
53C2×#806—31no—
54C2×#806—31no—
55C2×#806—31no—
56C2×#806—61no—
57C2×#806D311yescharacteristic, complemented
58#4740—38no—
59C24×C32C2311yescharacteristic
60C23×C3⋊D3C2×C411yescharacteristic
61C23×C3×D3C2×C411yescharacteristic
62C22×C32×C4—21no—
63C2×#638—21no—
64C2×#638—21no—
65C2×#638—21no—
66C2×#638—21no—
67C2×#638C2×C412yes—
68C2×#638C2312yes—
69C22×C3⋊Dic3—21no—
70C22×C3⋊Dic3C2×C411yescharacteristic
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C2×C3×#67—21no—
75C2×C3×#67C2×C412yes—
76C2×C3×#67C2312yes—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3C2×C411yescharacteristic
80C22×C3×Dic3C2×C411yescharacteristic
81C22×C3×Dic3C2×C412yes—
82C22×C3×Dic3C2×C411yescharacteristic
83C22×C3×Dic3D411yescharacteristic
84C22×C3×Dic3D412yes—
85C22×C3×Dic3D411yescharacteristic
86C22×C3×Dic3D412yes—
87C22×C3×Dic3D411yescharacteristic
88C22×C3×Dic3D411yescharacteristic
89C22×C3×Dic3C2312yes—
90C2×#627—22no—
91C2×#627—21no—
92C2×#627—21no—
93C2×#627C2×C414yescomplemented
94C2×#626—22no—
95C2×#626—21no—
96C2×#626—21no—
97C2×#626C2×C414yescomplemented
98C2×#624—22no—
99C2×#624—21no—
100C2×#624—21no—
101C2×#624C2×C414yescomplemented
102#3804—24no—
103#3804—24no—
104#3804—24no—
105#3804—24no—
106#3804—24no—
107#3804—24no—
108#3804—24no—
109#3804—24no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3C2×C414yescomplemented
114C32×C22⋊C4—21no—
115C32×C22⋊C4C2312yes—
116#3757—21no—
117#3757C2312yes—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217C2312yes—
121C3×#217C2312yes—
122C3×Dic3⋊C4—24no—
123C3×C4×Dic3—24no—
124Dic3⋊Dic3—24no—
125Dic32—24no—
126C2×#410—91noSylow
127C22×C3×D4—31no—
128C23×C3×C4—31no—
129C22×#67—31no—
130C22×#67—31no—
131C22×#67—31no—
132C22×#67—61no—
133C22×#67C2×D311yescharacteristic
134C23×Dic3—31no—
135C23×Dic3C2×D311yescharacteristic
136C2×#237—34no—
137C2×#237—34no—
138C2×#237—62no—
139C2×#237—61no—
140C2×#237—61no—
141C2×#237—62no—
142C2×#237—61no—
143C2×#237—61no—
144C2×#235—34no—
145C2×#235—34no—
146C2×#235—61no—
147C2×#235—61no—
148C2×#235—62no—
149C2×#235—61no—
150C2×#235—61no—
151C2×#235—62no—
152C22×D12—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×Dic6—31no—
157C22×Dic6—31no—
158C3×#117—34no—
159C3×#117—62no—
160C2×C3×C4⋊C4—61no—
161C2×C3×C22⋊C4—21no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4C2×D311yescharacteristic
165C2×C3×C22⋊C4C2×D311yescharacteristic
166C2×C3×C42—61no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—61no—
170C2×#217C2×D311yescharacteristic
171C2×#217C2×D311yescharacteristic
172#926—34no—
173#926—62no—
174C2×C4⋊Dic3—61no—
175C2×Dic3⋊C4—21no—
176C2×Dic3⋊C4—61no—
177C2×C4×Dic3—21no—
178C2×C4×Dic3—61no—
179C2×C4×Dic3—61no—
180#877—22no—
181#877—34no—
182#877—62no—
183#877C2×D314yescomplemented
184C3×#99—34no—
185#834—34no—
186#806—34no—
187#806—34no—
188#806—34no—
189#806—34no—
190#806—34no—
191#806—64no—
192#806C2×D314yescomplemented
193C23×C32—42no—
194C23×C32C22×C411yescharacteristic
195C23×C32C22×C411yescharacteristic
196C23×C32C2×D411yescharacteristic
197C23×C32C2×D411yescharacteristic
198C23×C32C2×D411yescharacteristic
199C23×C32C2×D411yescharacteristic
200C23×C32C2411yescharacteristic
201C22×C3⋊D3—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3—42no—
204C22×C3⋊D3C22×C412yes—
205C22×C3×D3—21no—
206C22×C3×D3—21no—
207C22×C3×D3—42no—
208C22×C3×D3C22×C412yes—
209C2×C32×C4—22no—
210C2×C32×C4—42no—
211#638—22no—
212#638—22no—
213#638—22no—
214#638—22no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—42no—
219C2×C3⋊Dic3C22×C412yes—
220C3×#67—22no—
221C3×#67—22no—
222C3×#67—22no—
223C3×#67—22no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—42no—
229C2×C3×Dic3—42no—
230C2×C3×Dic3C22⋊C412yes—
231C2×C3×Dic3C22⋊C411yescharacteristic
232C2×C3×Dic3C22⋊C411yescharacteristic
233C2×C3×Dic3C22⋊C412yes—
234C2×C3×Dic3C22⋊C412yes—
235C2×C3×Dic3C22⋊C412yes—
236C2×C3×Dic3C22⋊C412yes—
237C2×C3×Dic3C22⋊C412yes—
238C2×C3×Dic3C22⋊C411yescharacteristic
239C2×C3×Dic3C22⋊C411yescharacteristic
240C2×C3×Dic3C22×C412yes—
241C2×C3×Dic3C22×C412yes—
242C2×C3×Dic3C22×C412yes—
243C2×C3×Dic3C2×D412yes—
244C2×C3×Dic3C2×D412yes—
245C2×C3×Dic3C2×D412yes—
246C2×C3×Dic3C2×D412yes—
247#627—24no—
248#627—24no—
249#626—24no—
250#626—24no—
251#624—24no—
252#624—24no—
253D3×Dic3—24no—
254D3×Dic3—24no—
255C22×#41—91no—
256C2×#117—31no—
257C2×#117—91no—
258#410—98no—
259C2×#99—31no—
260C2×#99—91no—
261C2×#99—91no—
262C2×#99—91no—
263C24×C3—21no—
264C24×C3—31no—
265C24×C3C22×D311yescharacteristic
266C24×C3C22×D311yescharacteristic
267C23×D3—31no—
268C23×D3—31no—
269C23×D3—61no—
270C23×D3C4×D311yescharacteristic
271C2×C3×D4—32no—
272C2×C3×D4—32no—
273C2×C3×D4—61no—
274C2×C3×D4—61no—
275C2×C3×D4—61no—
276C2×C3×D4—61no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—32no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—32no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—32no—
288C22×C3×C4—32no—
289C22×C3×C4—31no—
290C22×C3×C4—41no—
291C22×C3×C4—61no—
292C22×C3×C4—61no—
293C2×#67—21no—
294C2×#67—21no—
295C2×#67—21no—
296C2×#67—21no—
297C2×#67—32no—
298C2×#67—32no—
299C2×#67—32no—
300C2×#67—32no—
301C2×#67—34no—
302C2×#67—62no—
303C2×#67—62no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—62no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—121no—
316C2×#67—121no—
317C2×#67—121no—
318C2×#67—121no—
319C2×#67C4×D312yes—
320C2×#67C22×D312yes—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—34no—
326C22×Dic3—61no—
327C22×Dic3—62no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—121no—
333C22×Dic3C4×D311yescharacteristic
334C22×Dic3C4×D311yescharacteristic
335C22×Dic3C4×D311yescharacteristic
336C22×Dic3C4×D312yes—
337C22×Dic3D1212yes—
338C22×Dic3D1211yescharacteristic
339C22×Dic3D1211yescharacteristic
340C22×Dic3#6712yes—
341C22×Dic3#6711yescharacteristic
342C22×Dic3#6711yescharacteristic
343C22×Dic3C22×D312yes—
344#237—64no—
345#237—64no—
346#237—64no—
347#237—64no—
348#237—64no—
349#237—64no—
350#237—64no—
351#237—64no—
352#235—64no—
353#235—64no—
354#235—64no—
355#235—64no—
356#235—64no—
357#235—64no—
358#235—64no—
359#235—64no—
360C2×D12—34no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12—61no—
364C2×C4×D3—34no—
365C2×C4×D3—34no—
366C2×C4×D3—34no—
367C2×C4×D3—62no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—62no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—62no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×Dic6—34no—
377C2×Dic6—34no—
378C2×Dic6—62no—
379C2×Dic6—61no—
380C2×Dic6—61no—
381C2×Dic6—62no—
382C2×Dic6—61no—
383C2×Dic6—61no—
384C3×C4⋊C4—64no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—22no—
388C3×C22⋊C4—32no—
389C3×C22⋊C4—32no—
390C3×C22⋊C4—41no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4C22×D312yes—
394C3×C22⋊C4C22×D312yes—
395C3×C42—64no—
396#217—21no—
397#217—21no—
398#217—32no—
399#217—32no—
400#217—62no—
401#217—61no—
402#217—61no—
403#217—121no—
404#217C22×D312yes—
405#217C22×D312yes—
406C4⋊Dic3—64no—
407Dic3⋊C4—24no—
408Dic3⋊C4—64no—
409C4×Dic3—24no—
410C4×Dic3—64no—
411C4×Dic3—64no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C2×C22⋊C411yescharacteristic
420C22×C32C2×C22⋊C411yescharacteristic
421C22×C32C2×C22⋊C411yescharacteristic
422C22×C32C2×C22⋊C411yescharacteristic
423C22×C32C23×C411yescharacteristic
424C22×C32C22×D411yescharacteristic
425C22×C32C22×D411yescharacteristic
426C2×C3⋊D3—22no—
427C2×C3⋊D3—42no—
428C2×C3⋊D3—42no—
429C2×C3⋊D3—42no—
430C2×C3×D3—22no—
431C2×C3×D3—42no—
432C2×C3×D3—42no—
433C2×C3×D3—42no—
434C32×C4—42no—
435C3⋊Dic3—22no—
436C3⋊Dic3—42no—
437C3×Dic3—22no—
438C3×Dic3—42no—
439C3×Dic3—42no—
440C3×Dic3C2×C22⋊C412yes—
441C3×Dic3C2×C22⋊C412yes—
442C3×Dic3C2×C22⋊C412yes—
443C3×Dic3C2×C22⋊C412yes—
444C2×#41—94no—
445C2×#41—94no—
446C2×#41—181no—
447C2×#41—181no—
448C2×#41—182no—
449C2×#41—181no—
450C2×#41—181no—
451C2×#41—182no—
452C22×Q8—91no—
453C22×D4—31no—
454C22×D4—91no—
455C22×D4—91no—
456C23×C4—31no—
457C23×C4—91no—
458C23×C4—91no—
459#117—34no—
460#117—62no—
461#117—94no—
462#117—182no—
463C2×C4⋊C4—61no—
464C2×C4⋊C4—181no—
465C2×C22⋊C4—31no—
466C2×C22⋊C4—31no—
467C2×C22⋊C4—91no—
468C2×C22⋊C4D3211yescharacteristic
469C2×C42—61no—
470C2×C42—181no—
471#99—34no—
472#99—94no—
473#99—94no—
474#99—94no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—32no—
483C23×C3—42no—
484C23×C3—42no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—82no—
488C23×C3—122no—
489C23×C3C2×C4×D311yescharacteristic
490C23×C3C2×C4×D311yescharacteristic
491C23×C3C2×C4×D311yescharacteristic
492C23×C3C2×C4×D311yescharacteristic
493C23×C3C2×D1211yescharacteristic
494C23×C3C2×D1211yescharacteristic
495C23×C3D3×D411yescharacteristic
496C23×C3D3×D411yescharacteristic
497C23×C3D3×D411yescharacteristic
498C23×C3D3×D411yescharacteristic
499C23×C3C2×#6711yescharacteristic
500C23×C3C2×#6711yescharacteristic
501C23×C3C23×D311yescharacteristic
502C23×C3C23×D311yescharacteristic
503C22×D3—21no—
504C22×D3—21no—
505C22×D3—32no—
506C22×D3—32no—
507C22×D3—42no—
508C22×D3—62no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—121no—
514C22×D3—121no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3—242no—
518C22×D3C2×C4×D312yes—
519C3×D4—62no—
520C3×D4—62no—
521C3×D4—62no—
522C3×D4—62no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—32no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—32no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—42no—
543C2×C3×C4—42no—
544C2×C3×C4—42no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—62no—
548C2×C3×C4—62no—
549C2×C3×C4—82no—
550C2×C3×C4—122no—
551C2×C3×C4—122no—
552#67—22no—
553#67—22no—
554#67—22no—
555#67—22no—
556#67—62no—
557#67—62no—
558#67—62no—
559#67—62no—
560#67—62no—
561#67—62no—
562#67—62no—
563#67—62no—
564#67—64no—
565#67—64no—
566#67—122no—
567#67—122no—
568#67—122no—
569#67—122no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—32no—
575C2×Dic3—32no—
576C2×Dic3—42no—
577C2×Dic3—42no—
578C2×Dic3—62no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—64no—
584C2×Dic3—64no—
585C2×Dic3—62no—
586C2×Dic3—62no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—122no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3—242no—
593C2×Dic3(C2×D3)⋊C412yes—
594C2×Dic3(C2×D3)⋊C411yescharacteristic
595C2×Dic3(C2×D3)⋊C411yescharacteristic
596C2×Dic3(C2×D3)⋊C412yes—
597C2×Dic3(C2×D3)⋊C411yescharacteristic
598C2×Dic3(C2×D3)⋊C411yescharacteristic
599C2×Dic3(C2×D3)⋊C412yes—
600C2×Dic3(C2×D3)⋊C412yes—
601C2×Dic3(C2×D3)⋊C412yes—
602C2×Dic3(C2×D3)⋊C412yes—
603C2×Dic3C2×C4×D312yes—
604C2×Dic3C2×C4×D312yes—
605C2×Dic3C2×C4×D312yes—
606C2×Dic3C2×D1212yes—
607C2×Dic3C2×D1212yes—
608C2×Dic3C2×#6712yes—
609C2×Dic3C2×#6712yes—
610D12—64no—
611D12—64no—
612C4×D3—64no—
613C4×D3—64no—
614C4×D3—64no—
615C4×D3—64no—
616C4×D3—64no—
617C4×D3—64no—
618Dic6—64no—
619Dic6—64no—
620Dic6—64no—
621Dic6—64no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32#41012yescomplemented
629C2×C32C22×C22⋊C411yescharacteristic
630C3⋊D3—42no—
631C3×D3—42no—
632C24—31no—
633C24—91no—
634C24C2×D3211yescharacteristic
635#41—184no—
636#41—184no—
637#41—184no—
638#41—184no—
639#41—184no—
640#41—184no—
641#41—184no—
642#41—184no—
643C2×Q8—94no—
644C2×Q8—182no—
645C2×Q8—181no—
646C2×Q8—181no—
647C2×D4—32no—
648C2×D4—32no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—94no—
654C2×D4—92no—
655C2×D4—92no—
656C2×D4—182no—
657C2×D4—181no—
658C2×D4—181no—
659C2×D4—181no—
660C2×D4—181no—
661C2×D4—181no—
662C2×D4—181no—
663C22×C4—21no—
664C22×C4—32no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—32no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—32no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—32no—
674C22×C4—31no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—94no—
678C22×C4—94no—
679C22×C4—91no—
680C22×C4—182no—
681C22×C4—181no—
682C22×C4—181no—
683C22×C4—182no—
684C22×C4—181no—
685C22×C4—181no—
686C22×C4—181no—
687C4⋊C4—64no—
688C4⋊C4—184no—
689C22⋊C4—21no—
690C22⋊C4—32no—
691C22⋊C4—32no—
692C22⋊C4—61no—
693C22⋊C4—61no—
694C22⋊C4—92no—
695C22⋊C4—181no—
696C22⋊C4C2×D3212yes—
697C42—64no—
698C42—184no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—62no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—81no—
727C22×C3—81no—
728C22×C3—122no—
729C22×C3—122no—
730C22×C3—122no—
731C22×C3D3×C22⋊C411yescharacteristic
732C22×C3D3×C22⋊C411yescharacteristic
733C22×C3D3×C22⋊C411yescharacteristic
734C22×C3D3×C22⋊C411yescharacteristic
735C22×C3C2×(C2×D3)⋊C411yescharacteristic
736C22×C3C2×(C2×D3)⋊C411yescharacteristic
737C22×C3C2×(C2×D3)⋊C411yescharacteristic
738C22×C3C2×(C2×D3)⋊C411yescharacteristic
739C22×C3C22×C4×D311yescharacteristic
740C22×C3C22×C4×D311yescharacteristic
741C22×C3C22×D1211yescharacteristic
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C2×D3×D411yescharacteristic
744C22×C3C22×#6711yescharacteristic
745C2×D3—22no—
746C2×D3—42no—
747C2×D3—42no—
748C2×D3—42no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—122no—
758C2×D3—242no—
759C2×D3—242no—
760C2×D3—242no—
761C3×C4—32no—
762C3×C4—32no—
763C3×C4—32no—
764C3×C4—32no—
765C3×C4—42no—
766C3×C4—42no—
767C3×C4—62no—
768C3×C4—82no—
769C3×C4—122no—
770C3×C4—122no—
771Dic3—22no—
772Dic3—42no—
773Dic3—42no—
774Dic3—62no—
775Dic3—62no—
776Dic3—122no—
777Dic3—122no—
778Dic3—122no—
779Dic3—242no—
780Dic3C2×(C2×D3)⋊C412yes—
781Dic3C2×(C2×D3)⋊C412yes—
782Dic3C2×(C2×D3)⋊C412yes—
783Dic3C2×(C2×D3)⋊C412yes—
784C32C2×#41011yescharacteristic, complemented, Sylow
785C23—32no—
786C23—42no—
787C23—61no—
788C23—61no—
789C23—92no—
790C23—122no—
791C23—181no—
792C23—181no—
793C23—362no—
794C23C4×D3211yescharacteristic
795C23C4×D3211yescharacteristic
796C23D3×D1211yescharacteristic
797C23D3×D1211yescharacteristic
798C23D3×#6711yescharacteristic
799C23D3×#6711yescharacteristic
800C23C22×D3211yescharacteristic
801Q8—184no—
802Q8—184no—
803D4—62no—
804D4—62no—
805D4—62no—
806D4—62no—
807D4—184no—
808D4—184no—
809D4—182no—
810D4—182no—
811D4—182no—
812D4—182no—
813C2×C4—22no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—32no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—31no—
827C2×C4—31no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—32no—
831C2×C4—42no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—92no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4—184no—
840C2×C4—184no—
841C2×C4—184no—
842C2×C4—184no—
843C2×C4—181no—
844C2×C4—181no—
845C2×C4—182no—
846C2×C4—362no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—22no—
860C2×C3—21no—
861C2×C3—41no—
862C2×C3—41no—
863C2×C3—41no—
864C2×C3—41no—
865C2×C3—41no—
866C2×C3—41no—
867C2×C3—122no—
868C2×C3#474012yescomplemented
869C2×C3#500612yescomplemented
870C2×C3C2×D3×C22⋊C411yescharacteristic
871C2×C3C22×(C2×D3)⋊C411yescharacteristic
872D3—42no—
873D3—122no—
874D3—122no—
875D3—242no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—62no—
884C22—122no—
885C22—122no—
886C22—122no—
887C22—182no—
888C22—362no—
889C22—362no—
890C22—362no—
891C22D3×(C2×D3)⋊C411yescharacteristic
892C22D3×(C2×D3)⋊C411yescharacteristic
893C22D3×(C2×D3)⋊C411yescharacteristic
894C22D3×(C2×D3)⋊C411yescharacteristic
895C22C2×C4×D3211yescharacteristic
896C22C2×D3×D1211yescharacteristic
897C22C2×D3×#6711yescharacteristic
898C4—32no—
899C4—32no—
900C4—32no—
901C4—32no—
902C4—42no—
903C4—62no—
904C4—122no—
905C4—122no—
906C4—182no—
907C4—362no—
908C3—21no—
909C3C2×#474011yescharacteristic, complemented
910C3C2×#500611yescharacteristic, complemented
911C2—21no—
912C2—21no—
913C2—21no—
914C2—21no—
915C2—21no—
916C2—21no—
917C2—122no—
918C2—362no—
919C2#1059040512yesdirect product factor
920C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3804C2
cosocleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#410
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#877C2semidirect
3. C2×#63955C2semidirect
4. C2×#63633C2semidirect
5. C2×C3×#806C2semidirect
6. C2×#63581C2semidirect
7. C2×#63580C2semidirect
8. #10590405C2direct (N × H)
14. C22×#627C4semidirect
15. C22×#626C4semidirect
16. C22×#624C4semidirect
23. C2×#3804C4semidirect
25. C22×D3×Dic3C4semidirect
33. C3×#877C22semidirect
36. #63955C22semidirect
38. #63633C22semidirect
39. C3×#806C22semidirect
40. #63581C22semidirect
41. #63580C22semidirect
47. C2×#877D3semidirect
57. C2×#806D3semidirect
93. C2×#627C2×C4semidirect
97. C2×#626C2×C4semidirect
101. C2×#624C2×C4semidirect
113. C2×D3×Dic3C2×C4semidirect
183. #877C2×D3semidirect
192. #806C2×D3semidirect
628. C2×C32#410semidirect
784. C32C2×#410semidirect
868. C2×C3#4740semidirect
869. C2×C3#5006semidirect
909. C3C2×#4740semidirect
910. C3C2×#5006semidirect
919. C2#10590405direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C2×C3×#8772
C2×#639552
C2×#636332
C2×C3×#8062
C2×#635812
C2×#635802
#105904052
C2×#50063
C2×#47403