Finite Group Databasebeta

← #30543466

Subgroups — #30543466

Order 15616.

4874 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840598C211yesmaximal, characteristic
2C2×#16840527C211yesmaximal, characteristic, complemented
3C2×#131×D61C211yesmaximal, characteristic, complemented
4#21454269C213yesmaximal, complemented
5#21454268C211yesmaximal, characteristic, complemented
6#21454267C213yesmaximal, complemented
7#21454267C213yesmaximal, complemented
8#21454266C211yesmaximal, characteristic, complemented
9#21454266C211yesmaximal, characteristic, complemented
10#21454265C213yesmaximal, complemented
11#21454262C213yesmaximal, complemented
12#21454261C213yesmaximal, complemented
13C2×#16839727C213yesmaximal, complemented
14#408×D61C213yesmaximal, complemented
15C61×#2880C211yesmaximal, characteristic, complemented
16#16840598—28no—
17#16840598—28no—
18C2×#14519825C411yescharacteristic
19C2×#14519825C411yescharacteristic
20C2×#14519824C413yes—
21C2×#14519824C411yescharacteristic
22C2×#14519823C411yescharacteristic
23C2×#14519823C413yes—
24C2×#14519822C413yes—
25C2×#14519822C413yes—
26C22×#11758222C2213yes—
27C22×#11758222C2213yes—
28C2×#41×D61C2213yes—
29C2×#41×D61C2211yescharacteristic
30C2×#41×D61C2213yes—
31C2×#41×D61C2211yescharacteristic
32#16840527—28no—
33C2×#14519785C2213yescomplemented
34C2×#14519785C2213yescomplemented
35C2×#14519784C2211yescharacteristic, complemented
36C2×#14519784C2211yescharacteristic, complemented
37C2×#14519783C2213yescomplemented
38C2×#14519783C2213yescomplemented
39#131×D61—28no—
40C22×#11758189C2213yescomplemented
41C2×M16×D61C2213yescomplemented
42C2×M16×D61C2213yescomplemented
43C22×C8×D61C2213yescomplemented
44#16839730C2213yescomplemented
45#16839730C2213yescomplemented
46#16839729C2213yescomplemented
47#16839729C2213yescomplemented
48#16839728C2213yescomplemented
49#16839728C2213yescomplemented
50#16839727C2213yescomplemented
51#16839727C2216yescomplemented
52#16839727C2211yescharacteristic, complemented
53#16839727C2213yescomplemented
54#16839727C2213yescomplemented
55#16839727C2213yescomplemented
56#16839727C2213yescomplemented
57#16839727C2213yescomplemented
58#16839727C2213yescomplemented
59#16839727C2216yescomplemented
60#16839727C2216yescomplemented
61#16839726C2213yescomplemented
62#16839725C2213yescomplemented
63#16839725C2213yescomplemented
64#16839724C2216yescomplemented
65#16839724C2216yescomplemented
66C2×C22⋊#92418C2213yescomplemented
67C2×#14519689C2213yescomplemented
68C2×#14519689C2213yescomplemented
69C22⋊C8×D61C2216yescomplemented
70C22⋊C8×D61C2216yescomplemented
71C22×#41×C61C2211yescharacteristic
72C2×#131×C61C2211yescharacteristic, complemented
73C2×#131×C61C2211yescharacteristic, complemented
74C61×#408C2213yescomplemented
75C61×#408C2213yescomplemented
76C61×#407C2213yescomplemented
77C2×C22⋊C8×C61C2213yescomplemented
78#14519825—28no—
79#14519825—28no—
80#14519824—28no—
81#14519824—224no—
82#14519823—28no—
83#14519823—224no—
84#14519822—224no—
85#14519822—224no—
86C2×#11758226C2×C411yescharacteristic
87C2×#11758226C2×C413yes—
88C2×#11758226C2×C413yes—
89C2×#11758226C2×C411yescharacteristic
90C2×#11758222—212no—
91C2×#11758222—212no—
92C2×#11758222—212no—
93C2×#11758222—212no—
94C2×#11758222C2×C413yes—
95C2×#11758222C2×C413yes—
96C2×#11758222C2×C413yes—
97C2×#11758222C2×C413yes—
98C2×#11758222C2×C416yes—
99C2×#11758222C2×C413yes—
100C2×#11758222C2×C413yes—
101C2×#11758222C2313yes—
102C2×#11758222C2313yes—
103C2×#11758222C2311yescharacteristic
104C2×#11758222C2313yes—
105C2×#11758222C2313yes—
106C2×#11758222C2313yes—
107C2×#11758224C2×C413yes—
108C2×#11758224C2×C416yes—
109C2×#11758224C2×C416yes—
110C2×#11758224C2×C413yes—
111C2×#11758224C2×C413yes—
112C2×#11758224C2×C413yes—
113#41×D61—24no—
114#41×D61—24no—
115#41×D61—212no—
116#41×D61—212no—
117#41×D61—212no—
118#41×D61—212no—
119#41×D61D418yes—
120#41×D61D418yes—
121C22×Dic122C2×C413yes—
122C22×Dic122C2×C413yes—
123C2×Q8×D61C2×C411yescharacteristic
124C2×Q8×D61C2×C413yes—
125C2×Q8×D61C2×C413yes—
126C2×Q8×D61C2×C411yescharacteristic
127C22×D244C2×C413yes—
128C22×D244C2×C413yes—
129C22×C22⋊D61C2×C413yes—
130C22×C22⋊D61C2×C416yes—
131C22×C22⋊D61C2×C413yes—
132C2×D4×D61C2×C416yes—
133C2×D4×D61C2×C413yes—
134C2×D4×D61C2×C416yes—
135C2×D4×D61C2×C413yes—
136C2×D4×D61C2×C413yes—
137C2×D4×D61C2×C413yes—
138C22×C4×D61C2316yes—
139C22×C4×D61C2313yes—
140C22×C4×D61C2313yes—
141#14519785—212no—
142#14519785—212no—
143#14519784—24no—
144#14519784—24no—
145#14519783—212no—
146#14519783—212no—
147C2×#11758194C2313yes—
148C2×#11758194C2313yes—
149C2×#11758189—212no—
150C2×#11758189C2316yes—
151C2×#11758189C2313yes—
152C2×#11758189C2313yes—
153C2×#11758189C2313yes—
154C2×#11758189C2311yescharacteristic
155M16×D61—212no—
156M16×D61—212no—
157C22×#92418C2313yes—
158C22×#92418C2313yes—
159C2×C8×D61—212no—
160C2×C8×D61C2313yes—
161C2×C8×D61C2313yes—
162C2×C8×D61C2316yes—
163C2×C8×D61C2311yescharacteristic
164C2×C8×D61C2313yes—
165C22⋊#92418C2313yes—
166C22⋊#92418C2316yes—
167C22⋊#92418C2311yescharacteristic
168C22⋊#92418C2313yes—
169C22⋊#92418C2313yes—
170#14519689C2313yes—
171#14519689C2313yes—
172#14519689C2316yes—
173#14519689C2316yes—
174#14519689C2311yescharacteristic
175#14519689C2311yescharacteristic
176#14519689C2313yes—
177#14519689C2313yes—
178#14519689C2313yes—
179#14519689C2313yes—
180C2×#41×C61—24no—
181C2×#41×C61—24no—
182C2×#41×C61C2×C411yescharacteristic
183C2×#41×C61C2×C413yes—
184C2×#41×C61C2313yes—
185C2×#41×C61C2311yescharacteristic
186C22×Q8×C61C2×C411yescharacteristic
187C22×D4×C61C2×C413yes—
188C23×C4×C61C2313yes—
189#131×C61—24no—
190#131×C61—24no—
191C2×M16×C61C2313yes—
192C2×M16×C61C2313yes—
193C22×C8×C61C2313yes—
194C22×C8×C61C2313yes—
195C22⋊C8×C61C2313yes—
196C22⋊C8×C61C2316yes—
197C22⋊C8×C61C2313yes—
198C22⋊C8×C61C2311yescharacteristic
199C22⋊C8×C61C2313yes—
200C24×C61C22×C413yes—
201C23×D61C22×C413yes—
202C23×D61C22×C416yes—
203C23×D61C22×C413yes—
204#41×C61—24no—
205#41×C61—212no—
206#41×C61—26no—
207#41×C61—26no—
208#41×C61C2×D414yes—
209#41×C61C2×D414yes—
210C2×Q8×C61—24no—
211C2×Q8×C61C22×C413yes—
212C2×Q8×C61C22×C411yescharacteristic
213C2×D4×C61—212no—
214C2×D4×C61C22×C416yes—
215C2×D4×C61C22×C413yes—
216C2×D4×C61C22×C413yes—
217C22×C4×C61—26no—
218C22×C4×C61—26no—
219C22×C4×C61C22×C413yes—
220C22×C4×C61C22×C413yes—
221C22×C4×C61C22×C413yes—
222C22×C4×C61C2413yes—
223C22×C4×C61C2411yescharacteristic
224C22×C4×C61C2413yes—
225C2×C22⋊D61—212no—
226C2×C22⋊D61—224no—
227C2×C22⋊D61—212no—
228C2×C22⋊D61C22×C416yes—
229C2×C22⋊D61C22×C413yes—
230C2×C22⋊D61C22×C413yes—
231C2×C22⋊D61C22×C413yes—
232C2×C22⋊D61C22×C413yes—
233C2×C22⋊D61C22×C413yes—
234C2×C22⋊D61C22×C411yescharacteristic
235C2×C22⋊D61C22×C411yescharacteristic
236C2×C22⋊D61C22×C413yes—
237C2×C22⋊D61C22×C416yes—
238C22×Dic61C22×C413yes—
239C22×Dic61C22×C416yes—
240C22×Dic61C22×C413yes—
241#11758226—24no—
242#11758226—212no—
243#11758226—212no—
244#11758226C22⋊C418yes—
245Q8×D61—24no—
246Q8×D61—212no—
247Q8×D61—212no—
248Q8×D61C22⋊C418yes—
249#11758224—212no—
250#11758224—224no—
251#11758224—224no—
252#11758224—212no—
253#11758224—212no—
254#11758224C22⋊C4124yes—
255D4×D61—224no—
256D4×D61—212no—
257D4×D61—224no—
258D4×D61—212no—
259D4×D61—212no—
260D4×D61C22⋊C4124yes—
261#11758222—26no—
262#11758222—26no—
263#11758222—224no—
264#11758222—212no—
265#11758222—212no—
266#11758222—212no—
267#11758222—212no—
268#11758222—212no—
269#11758222—26no—
270#11758222—26no—
271#11758222—26no—
272#11758222—26no—
273#11758222—22no—
274#11758222—26no—
275#11758222—26no—
276#11758222—22no—
277#11758222—212no—
278#11758222C2×D4112yes—
279#11758222C2×D4112yes—
280C2×D244—212no—
281C2×D244—212no—
282C2×D244C22×C413yes—
283C2×D244C22×C413yes—
284C2×D244C22×C413yes—
285C2×D244C22×C413yes—
286C2×D244C22×C411yescharacteristic
287C2×D244C22×C413yes—
288C2×C4×D61—26no—
289C2×C4×D61—26no—
290C2×C4×D61—212no—
291C2×C4×D61—212no—
292C2×C4×D61C22×C416yes—
293C2×C4×D61C22×C413yes—
294C2×C4×D61C22×C413yes—
295C2×C4×D61C22×C416yes—
296C2×C4×D61C22×C413yes—
297C2×C4×D61C22×C413yes—
298C2×C4×D61C2×D4112yes—
299C2×C4×D61C2×D4112yes—
300C2×C4×D61C2413yes—
301C2×C4×D61C2411yescharacteristic
302C2×C4×D61C2411yescharacteristic
303C2×C4×D61C2413yes—
304C2×Dic122—212no—
305C2×Dic122—212no—
306C2×Dic122C22×C413yes—
307C2×Dic122C22×C413yes—
308C2×Dic122C22×C413yes—
309C2×Dic122C22×C411yescharacteristic
310C2×Dic122C22×C413yes—
311C2×Dic122C22×C413yes—
312M16×C61—26no—
313M16×C61—26no—
314C2×C8×C61—26no—
315C2×C8×C61—26no—
316C2×C8×C61C2411yescharacteristic
317C2×C8×C61C2411yescharacteristic
318C2×C8×C61C2413yes—
319C2×C8×C61C2413yes—
320#11758194—26no—
321#11758194—26no—
322C2×#92418—26no—
323C2×#92418—26no—
324C2×#92418C2411yescharacteristic
325C2×#92418C2413yes—
326C2×#92418C2413yes—
327C2×#92418C2411yescharacteristic
328#11758189—26no—
329#11758189—212no—
330#11758189—22no—
331#11758189—26no—
332#11758189—26no—
333C8×D61—22no—
334C8×D61—26no—
335C8×D61—26no—
336C8×D61—26no—
337C8×D61—212no—
338C23×C61—26no—
339C23×C61—43no—
340C23×C61—43no—
341C23×C61C23×C413yes—
342C23×C61C23×C411yescharacteristic
343C23×C61C23×C413yes—
344C22×D61—26no—
345C22×D61—212no—
346C22×D61—43no—
347C22×D61—43no—
348C22×D61—46no—
349C22×D61—46no—
350C22×D61—43no—
351C22×D61—43no—
352C22×D61C2×C22⋊C4112yes—
353C22×D61C23×C411yescharacteristic
354C22×D61C23×C413yes—
355C22×D61C23×C413yes—
356C22×D61C23×C411yescharacteristic
357Q8×C61—26no—
358Q8×C61C2×C22⋊C414yes—
359D4×C61—212no—
360D4×C61—26no—
361D4×C61C2×C22⋊C4112yes—
362C2×C4×C61—26no—
363C2×C4×C61—26no—
364C2×C4×C61—26no—
365C2×C4×C61—23no—
366C2×C4×C61—23no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61C23×C411yescharacteristic
370C2×C4×C61C23×C413yes—
371C2×C4×C61C23×C413yes—
372C2×C4×C61C22×D416yes—
373C2×C4×C61C22×D416yes—
374C2×C4×C61C2511yescharacteristic
375C22⋊D61—212no—
376C22⋊D61—26no—
377C22⋊D61—22no—
378C22⋊D61—26no—
379C22⋊D61—26no—
380C22⋊D61—22no—
381C22⋊D61—26no—
382C22⋊D61—26no—
383C22⋊D61—26no—
384C22⋊D61C2×C22⋊C4124yes—
385C2×Dic61—26no—
386C2×Dic61—212no—
387C2×Dic61C2×C22⋊C4112yes—
388C2×Dic61C23×C413yes—
389C2×Dic61C23×C411yescharacteristic
390C2×Dic61C23×C411yescharacteristic
391C2×Dic61C23×C413yes—
392D244—26no—
393D244—22no—
394D244—26no—
395D244—26no—
396D244—26no—
397D244C2×C22⋊C4112yes—
398C4×D61—212no—
399C4×D61—26no—
400C4×D61—26no—
401C4×D61—21no—
402C4×D61—21no—
403C4×D61—23no—
404C4×D61—23no—
405C4×D61—212no—
406C4×D61C2×C22⋊C4112yes—
407C4×D61C2×C22⋊C4112yes—
408C4×D61C22×D412yes—
409C4×D61C22×D416yes—
410C4×D61C22×D416yes—
411C4×D61C22×D412yes—
412Dic122—26no—
413Dic122—22no—
414Dic122—26no—
415Dic122—26no—
416Dic122—26no—
417Dic122C2×C22⋊C4112yes—
418C8×C61—21no—
419C8×C61—23no—
420C8×C61—23no—
421C8×C61—21no—
422#92418—21no—
423#92418—23no—
424#92418—23no—
425#92418—21no—
426#60065—611nomaximal, Sylow
427C22×C61—23no—
428C22×C61—23no—
429C22×C61—23no—
430C22×C61—21no—
431C22×C61—23no—
432C22×C61—23no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—86no—
436C22×C61C22×C22⋊C416yes—
437C22×C61C24×C411yescharacteristic
438C2×D61—21no—
439C2×D61—23no—
440C2×D61—21no—
441C2×D61—23no—
442C2×D61—21no—
443C2×D61—23no—
444C2×D61—23no—
445C2×D61—21no—
446C2×D61—23no—
447C2×D61—21no—
448C2×D61—412no—
449C2×D61—812no—
450C2×D61—86no—
451C2×D61C22×C22⋊C416yes—
452C2×D61C22×C22⋊C412yes—
453C4×C61—21no—
454C4×C61—23no—
455C4×C61C22×C22⋊C416yes—
456C4×C61C23×D411yescharacteristic
457C4×C61C23×D411yescharacteristic
458Dic61—23no—
459Dic61—21no—
460Dic61C22×C22⋊C412yes—
461Dic61C22×C22⋊C416yes—
462C2×#585—611no—
463C2×#568—611no—
464C22×#131—611no—
465#2880—613no—
466#2880—613no—
467#2880—613no—
468#2880—613no—
469#2880—611no—
470#2880—611no—
471#2880—611no—
472#2880D6111yescharacteristic, complemented
473#2879—613no—
474#2879—613no—
475C2×#408—613no—
476C2×#408—613no—
477C2×C61—26no—
478C2×C61—43no—
479C2×C61—41no—
480C2×C61C23×C22⋊C411yescharacteristic
481C2×C61#357311yescharacteristic
482C2×C61#357311yescharacteristic
483D61—22no—
484D61—26no—
485D61—43no—
486D61—41no—
487#585—1228no—
488#585—1228no—
489C2×2−1+4—611no—
490C2×2−1+4—613no—
491C2×2−1+4—611no—
492C2×2−1+4—611no—
493C2×H(5,𝔽2)—613no—
494C2×H(5,𝔽2)—611no—
495C2×H(5,𝔽2)—613no—
496C2×H(5,𝔽2)—613no—
497C22×#41—611no—
498C22×#41—613no—
499C22×#41—613no—
500C22×#41—611no—
501C22×#41—613no—
502C22×#41—613no—
503C22×#41C2×D6111yescharacteristic
504#568—1228no—
505C2×#131—611no—
506C2×#131—611no—
507C2×#131—613no—
508C2×#131—613no—
509C2×#131—613no—
510C2×#131—613no—
511C2×#131—1228no—
512C2×#131C2×D6111yescharacteristic, complemented
513C2×#131C2×D6111yescharacteristic, complemented
514C22×M16—613no—
515C22×M16—613no—
516C22×M16—613no—
517C23×C8—613no—
518#408—613no—
519#408—613no—
520#408—613no—
521#408—613no—
522#408—613no—
523#408—613no—
524#408—613no—
525#408—611no—
526#408—616no—
527#408—613no—
528#408—613no—
529#408—613no—
530#408—613no—
531#408—613no—
532#408—613no—
533#408—616no—
534#408—616no—
535#408C2×D6113yescomplemented
536#408C2×D6113yescomplemented
537#407—613no—
538#407—613no—
539#407—613no—
540#407—616no—
541#407—616no—
542#407C2×D6113yescomplemented
543C2×C22⋊C8—613no—
544C2×C22⋊C8—613no—
545C2×C22⋊C8—613no—
546C2×C22⋊C8—616no—
547C2×C22⋊C8—616no—
548C2×C22⋊C8C2×D6113yescomplemented
549C61#6006511yescharacteristic, complemented, Sylow
5502−1+4—1228no—
5512−1+4—1228no—
5522−1+4—1228no—
5532−1+4—12224no—
554H(5,𝔽2)—12224no—
555H(5,𝔽2)—12224no—
556H(5,𝔽2)—12224no—
557H(5,𝔽2)—1228no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—618no—
561C2×#41—618no—
562C2×#41—611no—
563C2×#41—613no—
564C2×#41—613no—
565C2×#41—611no—
566C2×#41—613no—
567C2×#41—616no—
568C2×#41—613no—
569C2×#41—616no—
570C2×#41—613no—
571C2×#41—613no—
572C2×#41—613no—
573C2×#41—613no—
574C2×#41—613no—
575C2×#41—613no—
576C2×#41—616no—
577C2×#41—613no—
578C2×#41—613no—
579C2×#41—613no—
580C2×#41—613no—
581C2×#41—613no—
582C2×#41—611no—
583C2×#41—613no—
584C2×#41—613no—
585C2×#41—12212no—
586C2×#41—12212no—
587C2×#41—12212no—
588C2×#41—12212no—
589C2×#41—12212no—
590C2×#41—12212no—
591C2×#41—12212no—
592C2×#41—12212no—
593C2×#41—1224no—
594C2×#41—1224no—
595C2×#41C4×D6111yescharacteristic
596C2×#41C4×D6113yes—
597C2×#41C22×D6113yes—
598C2×#41C22×D6111yescharacteristic
599C22×Q8—611no—
600C22×Q8—613no—
601C22×Q8—613no—
602C22×Q8—611no—
603C22×Q8—613no—
604C22×Q8—613no—
605C22×Q8C4×D6111yescharacteristic
606C22×D4—613no—
607C22×D4—613no—
608C22×D4—616no—
609C22×D4—613no—
610C22×D4—613no—
611C22×D4—616no—
612C22×D4—613no—
613C22×D4—616no—
614C22×D4—613no—
615C22×D4—613no—
616C22×D4—613no—
617C22×D4C4×D6113yes—
618C23×C4—613no—
619C23×C4—616no—
620C23×C4—613no—
621C23×C4C22×D6113yes—
622#131—24no—
623#131—24no—
624#131—12212no—
625#131—12212no—
626#131—12212no—
627#131—12212no—
628#131—1224no—
629#131—1224no—
630C2×M16—613no—
631C2×M16—613no—
632C2×M16—613no—
633C2×M16—611no—
634C2×M16—616no—
635C2×M16—613no—
636C2×M16—613no—
637C2×M16—12212no—
638C2×M16—12212no—
639C2×M16—12212no—
640C2×M16C22×D6113yes—
641C2×M16C22×D6113yes—
642C22×C8—613no—
643C22×C8—613no—
644C22×C8—611no—
645C22×C8—613no—
646C22×C8—613no—
647C22×C8—613no—
648C22×C8—616no—
649C22×C8—12212no—
650C22×C8C22×D6113yes—
651C22×C8C22×D6113yes—
652C22⋊C8—613no—
653C22⋊C8—611no—
654C22⋊C8—616no—
655C22⋊C8—613no—
656C22⋊C8—613no—
657C22⋊C8—613no—
658C22⋊C8—611no—
659C22⋊C8—613no—
660C22⋊C8—611no—
661C22⋊C8—616no—
662C22⋊C8—616no—
663C22⋊C8—613no—
664C22⋊C8—613no—
665C22⋊C8—613no—
666C22⋊C8—613no—
667C22⋊C8C22×D6113yes—
668C22⋊C8C22×D6116yes—
669C22⋊C8C22×D6111yescharacteristic
670C22⋊C8C22×D6113yes—
671C22⋊C8C22×D6113yes—
672C24—613no—
673C24—616no—
674C24—613no—
675C24C2×C4×D6113yes—
676#41—24no—
677#41—212no—
678#41—26no—
679#41—26no—
680#41—618no—
681#41—6124no—
682#41—6112no—
683#41—6112no—
684#41—1222no—
685#41—1226no—
686#41—1226no—
687#41—1222no—
688#41—1226no—
689#41—1226no—
690#41—1226no—
691#41—1226no—
692#41—12212no—
693#41—12212no—
694#41—12212no—
695#41—12212no—
696#41—12224no—
697#41—12212no—
698#41—12212no—
699#41—12224no—
700#41—12212no—
701#41—12212no—
702#41—12224no—
703#41—12212no—
704#41—12212no—
705#41—1224no—
706#41—12212no—
707#41—1226no—
708#41—1226no—
709#41D4×D6114yes—
710#41D4×D6114yes—
711C2×Q8—24no—
712C2×Q8—618no—
713C2×Q8—613no—
714C2×Q8—613no—
715C2×Q8—613no—
716C2×Q8—611no—
717C2×Q8—613no—
718C2×Q8—613no—
719C2×Q8—12212no—
720C2×Q8—12212no—
721C2×Q8—12212no—
722C2×Q8—12212no—
723C2×Q8—1224no—
724C2×Q8C2×C4×D6113yes—
725C2×Q8C2×C4×D6111yescharacteristic
726C2×D4—212no—
727C2×D4—616no—
728C2×D4—6124no—
729C2×D4—613no—
730C2×D4—613no—
731C2×D4—611no—
732C2×D4—613no—
733C2×D4—613no—
734C2×D4—613no—
735C2×D4—611no—
736C2×D4—613no—
737C2×D4—616no—
738C2×D4—613no—
739C2×D4—613no—
740C2×D4—613no—
741C2×D4—611no—
742C2×D4—613no—
743C2×D4—613no—
744C2×D4—12212no—
745C2×D4—12212no—
746C2×D4—12212no—
747C2×D4—12212no—
748C2×D4—12224no—
749C2×D4—12212no—
750C2×D4—12224no—
751C2×D4—12224no—
752C2×D4—12212no—
753C2×D4—12212no—
754C2×D4C2×C4×D6116yes—
755C2×D4C2×C4×D6113yes—
756C2×D4C2×C4×D6113yes—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—613no—
760C22×C4—613no—
761C22×C4—613no—
762C22×C4—6112no—
763C22×C4—6112no—
764C22×C4—611no—
765C22×C4—613no—
766C22×C4—616no—
767C22×C4—613no—
768C22×C4—616no—
769C22×C4—616no—
770C22×C4—613no—
771C22×C4—613no—
772C22×C4—613no—
773C22×C4—611no—
774C22×C4—12212no—
775C22×C4—12212no—
776C22×C4—1226no—
777C22×C4—1226no—
778C22×C4C2×C4×D6113yes—
779C22×C4C2×C4×D6113yes—
780C22×C4C2×C4×D6113yes—
781C22×C4C23×D6113yes—
782C22×C4C23×D6111yescharacteristic
783C22×C4C23×D6113yes—
784M16—26no—
785M16—26no—
786M16—1222no—
787M16—1226no—
788M16—1226no—
789M16—12212no—
790M16—1226no—
791M16—1226no—
792M16—1226no—
793C2×C8—26no—
794C2×C8—26no—
795C2×C8—611no—
796C2×C8—613no—
797C2×C8—611no—
798C2×C8—613no—
799C2×C8—1222no—
800C2×C8—1226no—
801C2×C8—1226no—
802C2×C8—1226no—
803C2×C8—12212no—
804C2×C8—1226no—
805C2×C8—1226no—
806C2×C8C23×D6111yescharacteristic
807C2×C8C23×D6113yes—
808C2×C8C23×D6113yes—
809C2×C8C23×D6111yescharacteristic
810C23—26no—
811C23—43no—
812C23—43no—
813C23—611no—
814C23—613no—
815C23—6112no—
816C23—613no—
817C23—611no—
818C23—12212no—
819C23—1226no—
820C23—2443no—
821C23—2443no—
822C23—2446no—
823C23—2446no—
824C23—2443no—
825C23—2443no—
826C23C22×C4×D6113yes—
827C23C22×C4×D6111yescharacteristic
828C23C22×C4×D6113yes—
829Q8—26no—
830Q8—6112no—
831Q8—1222no—
832Q8—1226no—
833Q8—1226no—
834Q8—1226no—
835Q8—1226no—
836Q8C22⋊C4×D6114yes—
837D4—212no—
838D4—26no—
839D4—6124no—
840D4—6112no—
841D4—1222no—
842D4—1226no—
843D4—1226no—
844D4—1226no—
845D4—1222no—
846D4—1226no—
847D4—1226no—
848D4—1226no—
849D4—1222no—
850D4—1226no—
851D4—1226no—
852D4—1226no—
853D4—12212no—
854D4—1226no—
855D4C22⋊C4×D61112yes—
856C2×C4—26no—
857C2×C4—26no—
858C2×C4—26no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—23no—
862C2×C4—23no—
863C2×C4—6112no—
864C2×C4—611no—
865C2×C4—613no—
866C2×C4—6112no—
867C2×C4—6112no—
868C2×C4—612no—
869C2×C4—616no—
870C2×C4—616no—
871C2×C4—612no—
872C2×C4—613no—
873C2×C4—611no—
874C2×C4—12212no—
875C2×C4—12212no—
876C2×C4—12212no—
877C2×C4—1226no—
878C2×C4—1226no—
879C2×C4—1226no—
880C2×C4—1223no—
881C2×C4—1223no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4C22×C4×D6113yes—
885C2×C4C22×C4×D6111yescharacteristic
886C2×C4C22×C4×D6113yes—
887C2×C4C2×D4×D6116yes—
888C2×C4C2×D4×D6116yes—
889C2×C4C24×D6111yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—1221no—
895C8—1223no—
896C8—1223no—
897C8—1221no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—612no—
908C22—616no—
909C22—1223no—
910C22—1221no—
911C22—1223no—
912C22—1221no—
913C22—1223no—
914C22—1221no—
915C22—1221no—
916C22—1223no—
917C22—1221no—
918C22—1223no—
919C22—4886no—
920C22—48812no—
921C22—24412no—
922C22C2×C22⋊C4×D6116yes—
923C22C23×C4×D6111yescharacteristic
924C4—21no—
925C4—23no—
926C4—612no—
927C4—616no—
928C4—1223no—
929C4—1221no—
930C4C2×C22⋊C4×D6116yes—
931C4C22×D4×D6111yescharacteristic
932C4C22×D4×D6111yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—1226no—
937C2—1222no—
938C2—2441no—
939C2—2443no—
940C2C22×C22⋊C4×D6111yescharacteristic
941C2#2146053011yescharacteristic
942C2#2146053211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
FittingC61×#2880C2
prime radicalC2×#16840598C2
cosocleC2×C4×C61C25
hypercenter#2880D61
hypocenterC61#60065
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#16840527C2semidirect
3. C2×#131×D61C2semidirect
4. #21454269C2semidirect
5. #21454268C2semidirect
6. #21454267C2semidirect
7. #21454267C2semidirect
8. #21454266C2semidirect
9. #21454266C2semidirect
10. #21454265C2semidirect
11. #21454262C2semidirect
12. #21454261C2semidirect
13. C2×#16839727C2semidirect
14. #408×D61C2semidirect
15. C61×#2880C2semidirect
33. C2×#14519785C22semidirect
34. C2×#14519785C22semidirect
35. C2×#14519784C22semidirect
36. C2×#14519784C22semidirect
37. C2×#14519783C22semidirect
38. C2×#14519783C22semidirect
40. C22×#11758189C22semidirect
41. C2×M16×D61C22semidirect
42. C2×M16×D61C22semidirect
43. C22×C8×D61C22semidirect
44. #16839730C22semidirect
45. #16839730C22semidirect
46. #16839729C22semidirect
47. #16839729C22semidirect
48. #16839728C22semidirect
49. #16839728C22semidirect
50. #16839727C22semidirect
51. #16839727C22semidirect
52. #16839727C22semidirect
53. #16839727C22semidirect
54. #16839727C22semidirect
55. #16839727C22semidirect
56. #16839727C22semidirect
57. #16839727C22semidirect
58. #16839727C22semidirect
59. #16839727C22semidirect
60. #16839727C22semidirect
61. #16839726C22semidirect
62. #16839725C22semidirect
63. #16839725C22semidirect
64. #16839724C22semidirect
65. #16839724C22semidirect
66. C2×C22⋊#92418C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
69. C22⋊C8×D61C22semidirect
70. C22⋊C8×D61C22semidirect
72. C2×#131×C61C22semidirect
73. C2×#131×C61C22semidirect
74. C61×#408C22semidirect
75. C61×#408C22semidirect
76. C61×#407C22semidirect
77. C2×C22⋊C8×C61C22semidirect
472. #2880D61semidirect
512. C2×#131C2×D61semidirect
513. C2×#131C2×D61semidirect
535. #408C2×D61semidirect
536. #408C2×D61semidirect
542. #407C2×D61semidirect
548. C2×C22⋊C8C2×D61semidirect
549. C61#60065semidirect

Maximal subgroups

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

subgroupindex
C2×#168405982
C2×#168405272
C2×#131×D612
#214542692
#214542682
#214542672
#214542662
#214542652
#214542622
#214542612
C2×#168397272
#408×D612
C61×#28802
#6006561