Finite Group Databasebeta

← C2×#21459465 #30588175

Subgroups — C2×#21459465 #30588175

Order 15616.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519824C211yesmaximal, characteristic, complemented
2C23×Q8×D61C211yesmaximal, characteristic, complemented
3#21459465C2132yesmaximal, direct product factor
4C2×Q8×D244C211yesmaximal, characteristic, complemented
5C2×D4×Dic122C213yesmaximal, complemented
6C2×Q8×C22⋊D61C211yesmaximal, characteristic, complemented
7C2×#16840425C213yesmaximal, complemented
8C2×#16840420C213yesmaximal, complemented
9C2×#16840419C211yesmaximal, characteristic, complemented
10C2×#16840418C213yesmaximal, complemented
11C2×#16840335C213yesmaximal, complemented
12C2×#16840332C213yesmaximal, complemented
13C2×#16840272C213yesmaximal, complemented
14C2×#16840271C213yesmaximal, complemented
15C2×#16840238C211yesmaximal, characteristic, complemented
16C2×C61×#548C211yesmaximal, characteristic, complemented
17C2×#14519824—216no—
18C2×#14519824C22116yescomplemented
19C22×#11758222C2213yes—
20C22×#11758224C2213yes—
21C22×#11758224C2213yescomplemented
22C23×Dic122C2213yes—
23C23×Dic122C2213yescomplemented
24C22×Q8×D61—216no—
25C22×Q8×D61C2211yescharacteristic
26C22×Q8×D61C2213yes—
27C22×Q8×D61C2213yes—
28C22×Q8×D61C2211yescharacteristic
29C22×Q8×D61C22116yescomplemented
30C22×Q8×D61C2211yescharacteristic, complemented
31C23×C4×D61C2213yes—
32Q8×D244C22116yescomplemented
33D4×Dic122C22148yescomplemented
34Q8×C22⋊D61C22116yescomplemented
35#16840425C22148yescomplemented
36#16840420C22148yescomplemented
37#16840419C22116yescomplemented
38#16840418C22148yescomplemented
39#16840335C22148yescomplemented
40#16840332C22148yescomplemented
41C2×#14519777C2213yescomplemented
42C2×#14519776C2216yescomplemented
43C2×#14519775C2213yescomplemented
44C2×#14519764C2213yescomplemented
45C2×#14519763C2216yescomplemented
46#16840272C22148yescomplemented
47#16840271C22148yescomplemented
48C2×#14519762C2213yes—
49C2×#14519759C2213yes—
50C2×#14519759C2216yes—
51C2×#14519757C2213yes—
52C2×#14519757C2213yescomplemented
53C2×#14519756C2213yes—
54C2×#14519756C2213yescomplemented
55C2×#14519755C2213yes—
56C2×#14519754C2213yes—
57C2×#14519754C2216yescomplemented
58C2×#14519754C2216yescomplemented
59C2×#14519753C2213yescomplemented
60C2×#14519750C2213yes—
61C2×#14519749C2213yes—
62C2×#14519748C2213yes—
63C2×#14519747C2211yescharacteristic
64C2×#14519745C2213yes—
65#16840238C22116yescomplemented
66C2×Q8×Dic61C2211yescharacteristic, complemented
67C2×C4×Dic122C2213yescomplemented
68C2×#14519742C2213yescomplemented
69C2×C4×D244C2213yes—
70C2×D4×Dic61C2216yes—
71C2×C4×C22⋊D61C2213yes—
72C2×C4×C22⋊D61C2213yes—
73C2×#14519737C2216yes—
74C2×#14519735C2213yes—
75C2×#14519734C2213yes—
76C22×#41×C61C2211yescharacteristic, complemented
77C23×Q8×C61C2211yescharacteristic
78C61×#548C22116yescomplemented
79C2×#124×C61C2213yescomplemented
80C2×C22⋊Q8×C61C2213yescomplemented
81C2×#121×C61C2213yes—
82C2×C4×Q8×C61C2211yescharacteristic, complemented
83C2×C4×D4×C61C2213yes—
84C24×D61C2311yescharacteristic
85#14519824—2128no—
86C2×#11758222—224no—
87C2×#11758222C23124yes—
88C2×#11758224—224no—
89C2×#11758224—224no—
90C2×#11758224C23124yes—
91C2×#11758224C23124yescomplemented
92C22×Dic122—224no—
93C22×Dic122—224no—
94C22×Dic122C2313yes—
95C22×Dic122C2316yes—
96C22×Dic122C2313yes—
97C22×Dic122C2313yes—
98C22×Dic122C23124yes—
99C22×Dic122C2313yes—
100C22×Dic122C23124yescomplemented
101C2×Q8×D61—28no—
102C2×Q8×D61—28no—
103C2×Q8×D61—2128no—
104C2×Q8×D61—224no—
105C2×Q8×D61—224no—
106C2×Q8×D61D4116yescomplemented
107C2×Q8×D61C23124yes—
108C2×Q8×D61C2318yes—
109C2×Q8×D61C23124yes—
110C2×Q8×D61C2318yes—
111C2×Q8×D61C2318yescomplemented
112C22×D244C2311yescharacteristic
113C22×D244C2311yescharacteristic
114C22×C22⋊D61C2313yes—
115C22×C22⋊D61C2311yescharacteristic
116C22×C22⋊D61C2313yes—
117C22×C22⋊D61C2313yes—
118C23×Dic61C2316yes—
119C23×Dic61C2313yes—
120C22×C4×D61—224no—
121C22×C4×D61C2313yes—
122C22×C4×D61C2313yes—
123C22×C4×D61C2313yes—
124C22×C4×D61C2313yes—
125C22×C4×D61C23124yes—
126C22×C4×D61C2313yes—
127#14519777C23124yescomplemented
128#14519776C23148yescomplemented
129#14519775C23124yescomplemented
130#14519764C23124yescomplemented
131#14519763C23148yescomplemented
132#14519762C23124yes—
133#14519759C23124yes—
134#14519759C23148yes—
135#14519757C23124yes—
136#14519757C23124yescomplemented
137#14519756C23124yes—
138#14519756C23124yescomplemented
139#14519755C23124yes—
140#14519754C23124yes—
141#14519754C23148yescomplemented
142#14519754C23148yescomplemented
143#14519753C23124yescomplemented
144#14519750C23124yes—
145#14519749C23124yes—
146#14519748C23124yes—
147#14519747C2318yes—
148#14519745C23124yes—
149Q8×Dic61C2318yescomplemented
150C4×Dic122C23124yescomplemented
151#14519742C23124yescomplemented
152C4×D244C23124yes—
153D4×Dic61C23148yes—
154C4×C22⋊D61C23124yes—
155C4×C22⋊D61C23124yes—
156#14519737C23148yes—
157#14519735C23124yes—
158#14519734C23124yes—
159C2×C4⋊Dic61C2313yes—
160C2×C4⋊Dic61C2316yes—
161C2×C4⋊Dic61C2313yes—
162C2×#11758196C2313yes—
163C2×#11758196C2313yes—
164C2×#11758196C2316yes—
165C2×#11758196C2313yes—
166C2×#11758196C2313yes—
167C2×C22⋊Dic61C2313yes—
168C2×C22⋊Dic61C2313yes—
169C2×C22⋊Dic61C2316yes—
170C2×#11758198C2311yescharacteristic
171C2×#11758198C2313yes—
172C2×#11758198C2313yes—
173C2×#11758198C2311yescharacteristic
174C2×#11758198C2313yes—
175C2×#11758198C2313yes—
176C2×C4×Dic61C2313yes—
177C2×C4×Dic61C2316yes—
178C2×#41×C61—28no—
179C2×#41×C61C2318yescomplemented
180C22×Q8×C61—28no—
181C22×Q8×C61C2318yes—
182C22×Q8×C61C2313yes—
183C22×Q8×C61C2311yescharacteristic
184C22×D4×C61C2313yes—
185C22×D4×C61C2313yes—
186C23×C4×C61C2313yes—
187C23×C4×C61C2313yes—
188#124×C61C23124yescomplemented
189C22⋊Q8×C61C23124yescomplemented
190#121×C61C23124yes—
191C4×Q8×C61C2318yescomplemented
192C4×D4×C61C23124yes—
193C2×C4⋊C4×C61C2313yes—
194C2×C4⋊C4×C61C2313yes—
195C2×C22⋊C4×C61C2316yes—
196C2×C22⋊C4×C61C2311yescharacteristic
197C2×C22⋊C4×C61C2313yes—
198C2×C42×C61C2313yes—
199C24×C61C2413yes—
200C24×C61C2411yescharacteristic
201C23×D61—24no—
202C23×D61—24no—
203C23×D61—24no—
204C23×D61C2414yes—
205C23×D61C2411yescharacteristic
206C23×D61C2411yescharacteristic
207C23×D61C2411yescharacteristic
208#41×C61—232no—
209C2×Q8×C61—232no—
210C2×Q8×C61—212no—
211C2×Q8×C61C2×D418yes—
212C2×Q8×C61C24112yes—
213C2×Q8×C61C2414yes—
214C2×D4×C61—212no—
215C2×D4×C61—212no—
216C2×D4×C61C24112yes—
217C2×D4×C61C24112yes—
218C22×C4×C61—212no—
219C22×C4×C61—212no—
220C22×C4×C61C2413yes—
221C22×C4×C61C24112yes—
222C22×C4×C61C2411yescharacteristic
223C22×C4×C61C2411yescharacteristic
224C22×C4×C61C24112yes—
225C22×C4×C61C2413yes—
226C22×C4×C61C2413yes—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—212no—
229C2×C22⋊D61—212no—
230C2×C22⋊D61—212no—
231C2×C22⋊D61C24112yes—
232C2×C22⋊D61C24112yes—
233C2×C22⋊D61C24112yes—
234C2×C22⋊D61C2414yes—
235C22×Dic61—212no—
236C22×Dic61—224no—
237C22×Dic61C2413yes—
238C22×Dic61C24112yes—
239C22×Dic61C2413yes—
240C22×Dic61C24124yes—
241C22×Dic61C2411yescharacteristic
242C22×Dic61C2413yes—
243C22×Dic61C2413yes—
244Q8×D61—232no—
245Q8×D61—232no—
246Q8×D61—296no—
247Q8×D61—296no—
248Q8×D61C2×D4164yescomplemented
249#11758224—296no—
250#11758224—296no—
251#11758222—296no—
252C2×D244—24no—
253C2×D244—24no—
254C2×D244C2414yes—
255C2×D244C2414yes—
256C2×C4×D61—212no—
257C2×C4×D61—212no—
258C2×C4×D61—212no—
259C2×C4×D61—212no—
260C2×C4×D61—296no—
261C2×C4×D61C2×D4124yes—
262C2×C4×D61C24112yes—
263C2×C4×D61C24112yes—
264C2×C4×D61C24112yes—
265C2×C4×D61C24112yes—
266C2×C4×D61C24112yes—
267C2×Dic122—212no—
268C2×Dic122—212no—
269C2×Dic122—224no—
270C2×Dic122—212no—
271C2×Dic122—296no—
272C2×Dic122—296no—
273C2×Dic122C2×D4124yes—
274C2×Dic122C24124yes—
275C2×Dic122C24112yes—
276C2×Dic122C24112yes—
277C2×Dic122C24112yes—
278C2×Dic122C24112yes—
279C4⋊C4×C61C24112yes—
280C4⋊C4×C61C24112yes—
281C22⋊C4×C61C2414yes—
282C22⋊C4×C61C24112yes—
283C22⋊C4×C61C24124yes—
284C42×C61C24112yes—
285C22⋊Dic61C24112yes—
286C22⋊Dic61C24112yes—
287C22⋊Dic61C24124yes—
288#11758198C2414yes—
289#11758198C24112yes—
290#11758198C24112yes—
291#11758198C2414yes—
292#11758198C24112yes—
293#11758198C24112yes—
294C4⋊Dic61C24112yes—
295C4⋊Dic61C24124yes—
296C4⋊Dic61C24112yes—
297#11758196C24112yes—
298#11758196C24112yes—
299#11758196C24124yes—
300#11758196C24112yes—
301#11758196C24112yes—
302C4×Dic61C24112yes—
303C4×Dic61C24124yes—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—26no—
307C23×C61—26no—
308C23×C61—26no—
309C23×C612−1+414yescomplemented
310C23×C61C2516yes—
311C23×C61C2512yes—
312C23×C61C2511yescharacteristic
313C22×D61—232no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—28no—
319C22×D61—28no—
320C22×D61—28no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61C22×D414yes—
325C22×D612−1+414yescomplemented
326C22×D61C2512yes—
327C22×D61C2512yes—
328C22×D61C2512yes—
329Q8×C61—224no—
330Q8×C61C22×D4116yes—
331D4×C61—224no—
332D4×C61—224no—
333C2×C4×C61—22no—
334C2×C4×C61—26no—
335C2×C4×C61—22no—
336C2×C4×C61—26no—
337C2×C4×C61—224no—
338C2×C4×C61—224no—
339C2×C4×C61C22×D4112yes—
340C2×C4×C61C2516yes—
341C2×C4×C61C2512yes—
342C2×C4×C61C2516yes—
343C2×C4×C61C2512yes—
344C2×C4×C61C2516yes—
345C22⋊D61—28no—
346C22⋊D61—224no—
347C22⋊D61—224no—
348C22⋊D61—224no—
349C2×Dic61—26no—
350C2×Dic61—26no—
351C2×Dic61—26no—
352C2×Dic61—22no—
353C2×Dic61—224no—
354C2×Dic61—248no—
355C2×Dic61C22×D4112yes—
356C2×Dic61C2512yes—
357C2×Dic61C2516yes—
358C2×Dic61C2516yes—
359C2×Dic61C2516yes—
360C2×Dic61C2516yes—
361D244—28no—
362D244—28no—
363C4×D61—224no—
364C4×D61—224no—
365C4×D61—224no—
366C4×D61—224no—
367C4×D61C22×D4148yes—
368Dic122—224no—
369Dic122—224no—
370Dic122—224no—
371Dic122—248no—
372Dic122C22×D4148yes—
373C2×#3486—611nomaximal, Sylow
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—28no—
377C22×C61—26no—
378C22×C61—26no—
379C22×C61—26no—
380C22×C61—412no—
381C22×C61C23×D412yes—
382C22×C61C2×2−1+412yes—
383C22×C61C2×2−1+412yes—
384C22×C61C2×2−1+414yescomplemented
385C22×C61C2611yescharacteristic
386C2×D61—232no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—28no—
392C2×D61—28no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—22no—
396C2×D61—44no—
397C2×D61C23×D414yes—
398C2×D61C2×2−1+414yescomplemented
399C4×C61—22no—
400C4×C61—26no—
401C4×C61—22no—
402C4×C61—26no—
403C4×C61C23×D4112yes—
404Dic61—26no—
405Dic61—26no—
406Dic61—26no—
407Dic61—22no—
408Dic61C23×D4112yes—
409C22×2−1+4—611no—
410C24×Q8—611no—
411#3486—6132no—
412C2×D4×Q8—611no—
413C2×D4×Q8—613no—
414C2×D4×Q8—611no—
415C2×D4×Q8—613no—
416C2×#548—611no—
417C2×#548—613no—
418C2×#548—613no—
419C2×#548D6111yescharacteristic, complemented
420C2×#536—613no—
421C2×#536—613no—
422C2×#525—613no—
423C2×#525—613no—
424C2×#519—611no—
425C2×C61—24no—
426C2×C61—46no—
427C2×C61#348614yescomplemented
428C2×C61C24×D411yescharacteristic
429C2×C61C22×2−1+411yescharacteristic
430C2×C61C22×2−1+411yescharacteristic
431D61—24no—
432D61—24no—
433D61—42no—
434C2×2−1+4—6116no—
435C2×2−1+4—12216no—
436C22×#41—613no—
437C22×#41—613no—
438C22×#41—613no—
439C22×#41C2×D6111yescharacteristic, complemented
440C23×Q8—611no—
441C23×Q8—613no—
442C23×Q8—613no—
443C23×Q8—611no—
444C23×Q8—6116no—
445C23×Q8—611no—
446C23×Q8—613no—
447C23×Q8—613no—
448C23×Q8—12216no—
449C23×Q8C2×D6111yescharacteristic
450C24×C4—613no—
451D4×Q8—6116no—
452D4×Q8—6148no—
453D4×Q8—6116no—
454D4×Q8—6148no—
455#548—6116no—
456#548—6148no—
457#548—6148no—
458#548C2×D61116yescomplemented
459#536—6148no—
460#536—6148no—
461C2×C4⋊Q8—613no—
462C2×C4⋊Q8—616no—
463C2×C4⋊Q8—613no—
464C2×#124—613no—
465C2×#124—616no—
466C2×#124C2×D6113yescomplemented
467#525—6148no—
468#525—6148no—
469C2×#123—613no—
470C2×#123—616no—
471C2×#123—613no—
472C2×C22⋊Q8—613no—
473C2×C22⋊Q8—613no—
474C2×C22⋊Q8—613no—
475C2×C22⋊Q8—613no—
476C2×C22⋊Q8—613no—
477C2×C22⋊Q8—613no—
478C2×C22⋊Q8—613no—
479C2×C22⋊Q8—616no—
480C2×C22⋊Q8—616no—
481C2×C22⋊Q8C2×D6113yescomplemented
482C2×#121—613no—
483C2×#121—613no—
484C2×#121—613no—
485C2×#121C2×D6113yes—
486C2×#120—613no—
487C2×#120—611no—
488#519—6116no—
489C2×C4×Q8—611no—
490C2×C4×Q8—613no—
491C2×C4×Q8—613no—
492C2×C4×Q8C2×D6111yescharacteristic, complemented
493C2×C4×D4—616no—
494C2×C4×D4—613no—
495C2×C4×D4—613no—
496C2×C4×D4—616no—
497C2×C4×D4—613no—
498C2×C4×D4C2×D6113yes—
499C2×#117—613no—
500C2×#117—613no—
501C61C2×#348611yescharacteristic, complemented, Sylow
502C25—611no—
5032−1+4—122128no—
504C2×#41—28no—
505C2×#41—6124no—
506C2×#41—6124no—
507C2×#41—6124no—
508C2×#41—12224no—
509C2×#41—12224no—
510C2×#41—12224no—
511C2×#41C22×D6118yescomplemented
512C22×Q8—28no—
513C22×Q8—6116no—
514C22×Q8—618no—
515C22×Q8—6124no—
516C22×Q8—6124no—
517C22×Q8—618no—
518C22×Q8—618no—
519C22×Q8—613no—
520C22×Q8—616no—
521C22×Q8—613no—
522C22×Q8—613no—
523C22×Q8—613no—
524C22×Q8—6124no—
525C22×Q8—6124no—
526C22×Q8—12224no—
527C22×Q8—12224no—
528C22×Q8—12224no—
529C22×Q8—122128no—
530C22×Q8—12224no—
531C22×Q8—1228no—
532C22×Q8—1228no—
533C22×Q8C22×D6113yes—
534C22×Q8C22×D6118yes—
535C22×Q8C22×D6111yescharacteristic
536C22×D4—613no—
537C22×D4—611no—
538C22×D4—613no—
539C22×D4—613no—
540C22×D4—611no—
541C22×D4—611no—
542C22×D4C22×D6113yes—
543C22×D4C22×D6113yes—
544C23×C4—613no—
545C23×C4—613no—
546C23×C4—616no—
547C23×C4—613no—
548C23×C4—613no—
549C23×C4—613no—
550C23×C4—613no—
551C23×C4—6124no—
552C23×C4—12224no—
553C23×C4C22×D6113yes—
554C23×C4C22×D6113yes—
555C4⋊Q8—6124no—
556C4⋊Q8—6148no—
557C4⋊Q8—6124no—
558#124—6124no—
559#124—6148no—
560#124C22×D61124yescomplemented
561#123—6124no—
562#123—6148no—
563#123—6124no—
564C22⋊Q8—6124no—
565C22⋊Q8—6124no—
566C22⋊Q8—6124no—
567C22⋊Q8—6124no—
568C22⋊Q8—6124no—
569C22⋊Q8—6124no—
570C22⋊Q8—6124no—
571C22⋊Q8—6148no—
572C22⋊Q8—6148no—
573C22⋊Q8C22×D61124yescomplemented
574#121—6124no—
575#121—6124no—
576#121—6124no—
577#121C22×D61124yes—
578#120—6124no—
579#120—618no—
580C4×Q8—618no—
581C4×Q8—6124no—
582C4×Q8—6124no—
583C4×Q8C22×D6118yescomplemented
584C4×D4—6148no—
585C4×D4—6124no—
586C4×D4—6124no—
587C4×D4—6148no—
588C4×D4—6124no—
589C4×D4C22×D61124yes—
590#117—6124no—
591#117—6124no—
592C2×C4⋊C4—613no—
593C2×C4⋊C4—613no—
594C2×C4⋊C4—613no—
595C2×C4⋊C4—613no—
596C2×C4⋊C4—613no—
597C2×C4⋊C4—616no—
598C2×C4⋊C4—616no—
599C2×C4⋊C4—613no—
600C2×C4⋊C4C22×D6113yes—
601C2×C4⋊C4C22×D6113yes—
602C2×C22⋊C4—613no—
603C2×C22⋊C4—616no—
604C2×C22⋊C4—613no—
605C2×C22⋊C4—613no—
606C2×C22⋊C4—611no—
607C2×C22⋊C4—611no—
608C2×C22⋊C4—613no—
609C2×C22⋊C4—613no—
610C2×C22⋊C4—613no—
611C2×C22⋊C4C22×D6116yes—
612C2×C22⋊C4C22×D6111yescharacteristic
613C2×C22⋊C4C22×D6113yes—
614C2×C42—616no—
615C2×C42—613no—
616C2×C42C22×D6113yes—
617C24—611no—
618C24—611no—
619C24—614no—
620C24—611no—
621C24—1224no—
622C24—1224no—
623C24—1224no—
624C24C23×D6113yes—
625C24C23×D6111yescharacteristic
626#41—232no—
627#41—12296no—
628#41—12296no—
629#41—12296no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—6164no—
633C2×Q8—6124no—
634C2×Q8—6112no—
635C2×Q8—6124no—
636C2×Q8—6112no—
637C2×Q8—6112no—
638C2×Q8—6112no—
639C2×Q8—12224no—
640C2×Q8—12212no—
641C2×Q8—12296no—
642C2×Q8—12296no—
643C2×Q8—12296no—
644C2×Q8—12296no—
645C2×Q8—12232no—
646C2×Q8—12232no—
647C2×Q8—12212no—
648C2×Q8—12212no—
649C2×Q8D4×D6118yes—
650C2×Q8C23×D61112yes—
651C2×Q8C23×D6114yes—
652C2×D4—212no—
653C2×D4—212no—
654C2×D4—6112no—
655C2×D4—614no—
656C2×D4—6112no—
657C2×D4—6112no—
658C2×D4—614no—
659C2×D4—614no—
660C2×D4—1224no—
661C2×D4—1224no—
662C2×D4—12212no—
663C2×D4—12212no—
664C2×D4—12212no—
665C2×D4—1224no—
666C2×D4C23×D61112yes—
667C2×D4C23×D61112yes—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—613no—
671C22×C4—6124no—
672C22×C4—6112no—
673C22×C4—6112no—
674C22×C4—6124no—
675C22×C4—613no—
676C22×C4—611no—
677C22×C4—613no—
678C22×C4—613no—
679C22×C4—6112no—
680C22×C4—6112no—
681C22×C4—6112no—
682C22×C4—6112no—
683C22×C4—12212no—
684C22×C4—12296no—
685C22×C4—12212no—
686C22×C4—12212no—
687C22×C4—12224no—
688C22×C4—12212no—
689C22×C4—12212no—
690C22×C4C23×D61112yes—
691C22×C4C23×D61112yes—
692C22×C4C23×D6113yes—
693C22×C4C23×D6111yescharacteristic
694C22×C4C23×D6113yes—
695C22×C4C23×D6111yescharacteristic
696C22×C4C23×D6113yes—
697C4⋊C4—6112no—
698C4⋊C4—6112no—
699C4⋊C4—6112no—
700C4⋊C4—6124no—
701C4⋊C4—6112no—
702C4⋊C4—6112no—
703C4⋊C4—6124no—
704C4⋊C4—6112no—
705C4⋊C4C23×D61112yes—
706C4⋊C4C23×D61112yes—
707C22⋊C4—6112no—
708C22⋊C4—6124no—
709C22⋊C4—6112no—
710C22⋊C4—6112no—
711C22⋊C4—614no—
712C22⋊C4—614no—
713C22⋊C4—6112no—
714C22⋊C4—6112no—
715C22⋊C4—6112no—
716C22⋊C4C23×D61124yes—
717C22⋊C4C23×D6114yes—
718C22⋊C4C23×D61112yes—
719C42—6124no—
720C42—6112no—
721C42C23×D61112yes—
722C23—22no—
723C23—22no—
724C23—26no—
725C23—26no—
726C23—26no—
727C23—614no—
728C23—614no—
729C23—612no—
730C23—612no—
731C23—612no—
732C23—1228no—
733C23—1228no—
734C23—12232no—
735C23—1222no—
736C23—1222no—
737C23—1222no—
738C23—1222no—
739C23—1228no—
740C23—1222no—
741C23—1222no—
742C23—1222no—
743C23#1451982414yescomplemented
744C23C24×D6116yes—
745C23C24×D6112yes—
746C23C24×D6111yescharacteristic
747Q8—224no—
748Q8—6148no—
749Q8—12248no—
750Q8—12224no—
751Q8—12224no—
752Q8—12224no—
753Q8C2×D4×D61116yes—
754D4—224no—
755D4—224no—
756D4—1228no—
757D4—1228no—
758D4—12224no—
759D4—12224no—
760D4—12224no—
761D4—1228no—
762C2×C4—22no—
763C2×C4—26no—
764C2×C4—22no—
765C2×C4—26no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—6112no—
769C2×C4—616no—
770C2×C4—6148no—
771C2×C4—616no—
772C2×C4—612no—
773C2×C4—616no—
774C2×C4—616no—
775C2×C4—12224no—
776C2×C4—12224no—
777C2×C4—12224no—
778C2×C4—12248no—
779C2×C4—1226no—
780C2×C4—1226no—
781C2×C4—1226no—
782C2×C4—1222no—
783C2×C4—12224no—
784C2×C4—12224no—
785C2×C4C2×D4×D61112yes—
786C2×C4C24×D6116yes—
787C2×C4C24×D6112yes—
788C2×C4C24×D6116yes—
789C2×C4C24×D6112yes—
790C2×C4C24×D6116yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—26no—
795C22—26no—
796C22—26no—
797C22—412no—
798C22—614no—
799C22—614no—
800C22—12232no—
801C22—1228no—
802C22—1228no—
803C22—1222no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—1222no—
808C22—1222no—
809C22—1222no—
810C22—2444no—
811C22C22×D4×D6112yes—
812C222−1+4×D6112yes—
813C22C2×#1451982412yes—
814C22C2×#1451982414yescomplemented
815C22C25×D6111yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—6112no—
821C4—1226no—
822C4—1226no—
823C4—1226no—
824C4—1222no—
825C4C22×D4×D61112yes—
826C2—24no—
827C2—46no—
828C2—1224no—
829C2—1224no—
830C2—2442no—
831C2#2145946514yesdirect product factor
832C2C23×D4×D6111yescharacteristic
833C2C2×2−1+4×D6111yescharacteristic
834C2C22×#1451982411yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#548C2
socleC23×C61C25
hypercenterC2×#548D61
hypocenterC61C2×#3486
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14519824C2semidirect
2. C23×Q8×D61C2semidirect
3. #21459465C2direct (N × H)
4. C2×Q8×D244C2semidirect
5. C2×D4×Dic122C2semidirect
6. C2×Q8×C22⋊D61C2semidirect
7. C2×#16840425C2semidirect
8. C2×#16840420C2semidirect
9. C2×#16840419C2semidirect
10. C2×#16840418C2semidirect
11. C2×#16840335C2semidirect
12. C2×#16840332C2semidirect
13. C2×#16840272C2semidirect
14. C2×#16840271C2semidirect
15. C2×#16840238C2semidirect
16. C2×C61×#548C2semidirect
18. C2×#14519824C22semidirect
21. C22×#11758224C22semidirect
23. C23×Dic122C22semidirect
29. C22×Q8×D61C22semidirect
30. C22×Q8×D61C22semidirect
32. Q8×D244C22semidirect
33. D4×Dic122C22semidirect
34. Q8×C22⋊D61C22semidirect
35. #16840425C22semidirect
36. #16840420C22semidirect
37. #16840419C22semidirect
38. #16840418C22semidirect
39. #16840335C22semidirect
40. #16840332C22semidirect
41. C2×#14519777C22semidirect
42. C2×#14519776C22semidirect
43. C2×#14519775C22semidirect
44. C2×#14519764C22semidirect
45. C2×#14519763C22semidirect
46. #16840272C22semidirect
47. #16840271C22semidirect
52. C2×#14519757C22semidirect
54. C2×#14519756C22semidirect
57. C2×#14519754C22semidirect
58. C2×#14519754C22semidirect
59. C2×#14519753C22semidirect
65. #16840238C22semidirect
66. C2×Q8×Dic61C22semidirect
67. C2×C4×Dic122C22semidirect
68. C2×#14519742C22semidirect
76. C22×#41×C61C22semidirect
78. C61×#548C22semidirect
79. C2×#124×C61C22semidirect
80. C2×C22⋊Q8×C61C22semidirect
82. C2×C4×Q8×C61C22semidirect
91. C2×#11758224C23semidirect
100. C22×Dic122C23semidirect
106. C2×Q8×D61D4semidirect
111. C2×Q8×D61C23semidirect
127. #14519777C23semidirect
128. #14519776C23semidirect
129. #14519775C23semidirect
130. #14519764C23semidirect
131. #14519763C23semidirect
136. #14519757C23semidirect
138. #14519756C23semidirect
141. #14519754C23semidirect
142. #14519754C23semidirect
143. #14519753C23semidirect
149. Q8×Dic61C23semidirect
150. C4×Dic122C23semidirect
151. #14519742C23semidirect
179. C2×#41×C61C23semidirect
188. #124×C61C23semidirect
189. C22⋊Q8×C61C23semidirect
191. C4×Q8×C61C23semidirect
248. Q8×D61C2×D4semidirect
309. C23×C612−1+4semidirect
325. C22×D612−1+4semidirect
384. C22×C61C2×2−1+4semidirect
398. C2×D61C2×2−1+4semidirect
419. C2×#548D61semidirect
427. C2×C61#3486semidirect
439. C22×#41C2×D61semidirect
458. #548C2×D61semidirect
466. C2×#124C2×D61semidirect
481. C2×C22⋊Q8C2×D61semidirect
492. C2×C4×Q8C2×D61semidirect
501. C61C2×#3486semidirect
511. C2×#41C22×D61semidirect
560. #124C22×D61semidirect
573. C22⋊Q8C22×D61semidirect
583. C4×Q8C22×D61semidirect
743. C23#14519824semidirect
814. C22C2×#14519824semidirect
831. C2#21459465direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198242
C23×Q8×D612
#214594652
C2×Q8×D2442
C2×D4×Dic1222
C2×Q8×C22⋊D612
C2×#168404252
C2×#168404202
C2×#168404192
C2×#168404182
C2×#168403352
C2×#168403322
C2×#168402722
C2×#168402712
C2×#168402382
C2×C61×#5482
C2×#348661