Finite Group Databasebeta

← #29452142

Subgroups — #29452142

Order 15104.

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×#16838238C211yesmaximal, characteristic
2C2×#16838167C211yesmaximal, characteristic, complemented
3C2×#131×D59C211yesmaximal, characteristic, complemented
4#21432546C213yesmaximal, complemented
5#21432545C211yesmaximal, characteristic, complemented
6#21432544C213yesmaximal, complemented
7#21432544C213yesmaximal, complemented
8#21432543C211yesmaximal, characteristic, complemented
9#21432543C211yesmaximal, characteristic, complemented
10#21432542C213yesmaximal, complemented
11#21432539C213yesmaximal, complemented
12#21432538C213yesmaximal, complemented
13C2×#16837367C213yesmaximal, complemented
14#408×D59C213yesmaximal, complemented
15C59×#2880C211yesmaximal, characteristic, complemented
16#16838238—28no—
17#16838238—28no—
18C2×#14273775C411yescharacteristic
19C2×#14273775C411yescharacteristic
20C2×#14273774C413yes—
21C2×#14273774C411yescharacteristic
22C2×#14273773C411yescharacteristic
23C2×#14273773C413yes—
24C2×#14273772C413yes—
25C2×#14273772C413yes—
26C22×#11745685C2213yes—
27C22×#11745685C2213yes—
28C2×#41×D59C2213yes—
29C2×#41×D59C2211yescharacteristic
30C2×#41×D59C2213yes—
31C2×#41×D59C2211yescharacteristic
32#16838167—28no—
33C2×#14273735C2213yescomplemented
34C2×#14273735C2213yescomplemented
35C2×#14273734C2211yescharacteristic, complemented
36C2×#14273734C2211yescharacteristic, complemented
37C2×#14273733C2213yescomplemented
38C2×#14273733C2213yescomplemented
39#131×D59—28no—
40C22×#11745659C2213yescomplemented
41C2×M16×D59C2213yescomplemented
42C2×M16×D59C2213yescomplemented
43C22×C8×D59C2213yescomplemented
44#16837370C2213yescomplemented
45#16837370C2213yescomplemented
46#16837369C2213yescomplemented
47#16837369C2213yescomplemented
48#16837368C2213yescomplemented
49#16837368C2213yescomplemented
50#16837367C2213yescomplemented
51#16837367C2216yescomplemented
52#16837367C2211yescharacteristic, complemented
53#16837367C2213yescomplemented
54#16837367C2213yescomplemented
55#16837367C2213yescomplemented
56#16837367C2213yescomplemented
57#16837367C2213yescomplemented
58#16837367C2213yescomplemented
59#16837367C2216yescomplemented
60#16837367C2216yescomplemented
61#16837366C2213yescomplemented
62#16837365C2213yescomplemented
63#16837365C2213yescomplemented
64#16837364C2216yescomplemented
65#16837364C2216yescomplemented
66C2×C22⋊(C59⋊C8)C2213yescomplemented
67C2×(C2×D59)⋊C8C2213yescomplemented
68C2×(C2×D59)⋊C8C2213yescomplemented
69C22⋊C8×D59C2216yescomplemented
70C22⋊C8×D59C2216yescomplemented
71C22×#41×C59C2211yescharacteristic
72C2×#131×C59C2211yescharacteristic, complemented
73C2×#131×C59C2211yescharacteristic, complemented
74C59×#408C2213yescomplemented
75C59×#408C2213yescomplemented
76C59×#407C2213yescomplemented
77C2×C22⋊C8×C59C2213yescomplemented
78#14273775—28no—
79#14273775—28no—
80#14273774—28no—
81#14273774—224no—
82#14273773—28no—
83#14273773—224no—
84#14273772—224no—
85#14273772—224no—
86C2×#11745689C2×C411yescharacteristic
87C2×#11745689C2×C413yes—
88C2×#11745689C2×C413yes—
89C2×#11745689C2×C411yescharacteristic
90C2×#11745685—212no—
91C2×#11745685—212no—
92C2×#11745685—212no—
93C2×#11745685—212no—
94C2×#11745685C2×C413yes—
95C2×#11745685C2×C413yes—
96C2×#11745685C2×C413yes—
97C2×#11745685C2×C413yes—
98C2×#11745685C2×C416yes—
99C2×#11745685C2×C413yes—
100C2×#11745685C2×C413yes—
101C2×#11745685C2313yes—
102C2×#11745685C2313yes—
103C2×#11745685C2313yes—
104C2×#11745685C2311yescharacteristic
105C2×#11745685C2313yes—
106C2×#11745685C2313yes—
107C2×#11745687C2×C413yes—
108C2×#11745687C2×C416yes—
109C2×#11745687C2×C416yes—
110C2×#11745687C2×C413yes—
111C2×#11745687C2×C413yes—
112C2×#11745687C2×C413yes—
113#41×D59—24no—
114#41×D59—24no—
115#41×D59—212no—
116#41×D59—212no—
117#41×D59—212no—
118#41×D59—212no—
119#41×D59D418yes—
120#41×D59D418yes—
121C22×Dic118C2×C413yes—
122C22×Dic118C2×C413yes—
123C2×Q8×D59C2×C411yescharacteristic
124C2×Q8×D59C2×C413yes—
125C2×Q8×D59C2×C413yes—
126C2×Q8×D59C2×C411yescharacteristic
127C22×D236C2×C413yes—
128C22×D236C2×C413yes—
129C22×C22⋊D59C2×C413yes—
130C22×C22⋊D59C2×C416yes—
131C22×C22⋊D59C2×C413yes—
132C2×D4×D59C2×C416yes—
133C2×D4×D59C2×C413yes—
134C2×D4×D59C2×C416yes—
135C2×D4×D59C2×C413yes—
136C2×D4×D59C2×C413yes—
137C2×D4×D59C2×C413yes—
138C22×C4×D59C2316yes—
139C22×C4×D59C2313yes—
140C22×C4×D59C2313yes—
141#14273735—212no—
142#14273735—212no—
143#14273734—24no—
144#14273734—24no—
145#14273733—212no—
146#14273733—212no—
147C2×#11745664C2313yes—
148C2×#11745664C2313yes—
149C2×#11745659—212no—
150C2×#11745659C2313yes—
151C2×#11745659C2316yes—
152C2×#11745659C2311yescharacteristic
153C2×#11745659C2313yes—
154C2×#11745659C2313yes—
155M16×D59—212no—
156M16×D59—212no—
157C22×C59⋊C8C2313yes—
158C22×C59⋊C8C2313yes—
159C2×C8×D59—212no—
160C2×C8×D59C2311yescharacteristic
161C2×C8×D59C2313yes—
162C2×C8×D59C2313yes—
163C2×C8×D59C2313yes—
164C2×C8×D59C2316yes—
165C22⋊(C59⋊C8)C2313yes—
166C22⋊(C59⋊C8)C2316yes—
167C22⋊(C59⋊C8)C2311yescharacteristic
168C22⋊(C59⋊C8)C2313yes—
169C22⋊(C59⋊C8)C2313yes—
170(C2×D59)⋊C8C2313yes—
171(C2×D59)⋊C8C2313yes—
172(C2×D59)⋊C8C2316yes—
173(C2×D59)⋊C8C2316yes—
174(C2×D59)⋊C8C2311yescharacteristic
175(C2×D59)⋊C8C2311yescharacteristic
176(C2×D59)⋊C8C2313yes—
177(C2×D59)⋊C8C2313yes—
178(C2×D59)⋊C8C2313yes—
179(C2×D59)⋊C8C2313yes—
180C2×#41×C59—24no—
181C2×#41×C59—24no—
182C2×#41×C59C2×C411yescharacteristic
183C2×#41×C59C2×C413yes—
184C2×#41×C59C2313yes—
185C2×#41×C59C2311yescharacteristic
186C22×Q8×C59C2×C411yescharacteristic
187C22×D4×C59C2×C413yes—
188C23×C4×C59C2313yes—
189#131×C59—24no—
190#131×C59—24no—
191C2×M16×C59C2313yes—
192C2×M16×C59C2313yes—
193C22×C8×C59C2313yes—
194C22×C8×C59C2313yes—
195C22⋊C8×C59C2311yescharacteristic
196C22⋊C8×C59C2313yes—
197C22⋊C8×C59C2313yes—
198C22⋊C8×C59C2313yes—
199C22⋊C8×C59C2316yes—
200C24×C59C22×C413yes—
201C23×D59C22×C413yes—
202C23×D59C22×C416yes—
203C23×D59C22×C413yes—
204#41×C59—24no—
205#41×C59—212no—
206#41×C59—26no—
207#41×C59—26no—
208#41×C59C2×D414yes—
209#41×C59C2×D414yes—
210C2×Q8×C59—24no—
211C2×Q8×C59C22×C413yes—
212C2×Q8×C59C22×C411yescharacteristic
213C2×D4×C59—212no—
214C2×D4×C59C22×C416yes—
215C2×D4×C59C22×C413yes—
216C2×D4×C59C22×C413yes—
217C22×C4×C59—26no—
218C22×C4×C59—26no—
219C22×C4×C59C22×C413yes—
220C22×C4×C59C22×C413yes—
221C22×C4×C59C22×C413yes—
222C22×C4×C59C2411yescharacteristic
223C22×C4×C59C2413yes—
224C22×C4×C59C2413yes—
225C2×C22⋊D59—212no—
226C2×C22⋊D59—224no—
227C2×C22⋊D59—212no—
228C2×C22⋊D59C22×C416yes—
229C2×C22⋊D59C22×C413yes—
230C2×C22⋊D59C22×C413yes—
231C2×C22⋊D59C22×C413yes—
232C2×C22⋊D59C22×C413yes—
233C2×C22⋊D59C22×C413yes—
234C2×C22⋊D59C22×C411yescharacteristic
235C2×C22⋊D59C22×C411yescharacteristic
236C2×C22⋊D59C22×C413yes—
237C2×C22⋊D59C22×C416yes—
238C22×Dic59C22×C413yes—
239C22×Dic59C22×C416yes—
240C22×Dic59C22×C413yes—
241#11745689—24no—
242#11745689—212no—
243#11745689—212no—
244#11745689C22⋊C418yes—
245Q8×D59—24no—
246Q8×D59—212no—
247Q8×D59—212no—
248Q8×D59C22⋊C418yes—
249#11745687—212no—
250#11745687—224no—
251#11745687—224no—
252#11745687—212no—
253#11745687—212no—
254#11745687C22⋊C4124yes—
255D4×D59—224no—
256D4×D59—212no—
257D4×D59—224no—
258D4×D59—212no—
259D4×D59—212no—
260D4×D59C22⋊C4124yes—
261#11745685—26no—
262#11745685—26no—
263#11745685—224no—
264#11745685—212no—
265#11745685—212no—
266#11745685—212no—
267#11745685—212no—
268#11745685—212no—
269#11745685—26no—
270#11745685—26no—
271#11745685—26no—
272#11745685—26no—
273#11745685—22no—
274#11745685—26no—
275#11745685—26no—
276#11745685—22no—
277#11745685—212no—
278#11745685C2×D4112yes—
279#11745685C2×D4112yes—
280C2×D236—212no—
281C2×D236—212no—
282C2×D236C22×C413yes—
283C2×D236C22×C413yes—
284C2×D236C22×C413yes—
285C2×D236C22×C413yes—
286C2×D236C22×C411yescharacteristic
287C2×D236C22×C413yes—
288C2×C4×D59—26no—
289C2×C4×D59—26no—
290C2×C4×D59—212no—
291C2×C4×D59—212no—
292C2×C4×D59C22×C416yes—
293C2×C4×D59C22×C413yes—
294C2×C4×D59C22×C413yes—
295C2×C4×D59C22×C416yes—
296C2×C4×D59C22×C413yes—
297C2×C4×D59C22×C413yes—
298C2×C4×D59C2×D4112yes—
299C2×C4×D59C2×D4112yes—
300C2×C4×D59C2413yes—
301C2×C4×D59C2411yescharacteristic
302C2×C4×D59C2411yescharacteristic
303C2×C4×D59C2413yes—
304C2×Dic118—212no—
305C2×Dic118—212no—
306C2×Dic118C22×C413yes—
307C2×Dic118C22×C413yes—
308C2×Dic118C22×C413yes—
309C2×Dic118C22×C411yescharacteristic
310C2×Dic118C22×C413yes—
311C2×Dic118C22×C413yes—
312M16×C59—26no—
313M16×C59—26no—
314C2×C8×C59—26no—
315C2×C8×C59—26no—
316C2×C8×C59C2411yescharacteristic
317C2×C8×C59C2411yescharacteristic
318C2×C8×C59C2413yes—
319C2×C8×C59C2413yes—
320#11745664—26no—
321#11745664—26no—
322C2×C59⋊C8—26no—
323C2×C59⋊C8—26no—
324C2×C59⋊C8C2411yescharacteristic
325C2×C59⋊C8C2413yes—
326C2×C59⋊C8C2413yes—
327C2×C59⋊C8C2411yescharacteristic
328#11745659—26no—
329#11745659—212no—
330#11745659—22no—
331#11745659—26no—
332#11745659—26no—
333C8×D59—22no—
334C8×D59—26no—
335C8×D59—26no—
336C8×D59—26no—
337C8×D59—212no—
338C23×C59—26no—
339C23×C59—43no—
340C23×C59—43no—
341C23×C59C23×C413yes—
342C23×C59C23×C411yescharacteristic
343C23×C59C23×C413yes—
344C22×D59—26no—
345C22×D59—212no—
346C22×D59—43no—
347C22×D59—43no—
348C22×D59—46no—
349C22×D59—46no—
350C22×D59—43no—
351C22×D59—43no—
352C22×D59C2×C22⋊C4112yes—
353C22×D59C23×C411yescharacteristic
354C22×D59C23×C413yes—
355C22×D59C23×C413yes—
356C22×D59C23×C411yescharacteristic
357Q8×C59—26no—
358Q8×C59C2×C22⋊C414yes—
359D4×C59—212no—
360D4×C59—26no—
361D4×C59C2×C22⋊C4112yes—
362C2×C4×C59—26no—
363C2×C4×C59—26no—
364C2×C4×C59—26no—
365C2×C4×C59—23no—
366C2×C4×C59—23no—
367C2×C4×C59—21no—
368C2×C4×C59—21no—
369C2×C4×C59C23×C411yescharacteristic
370C2×C4×C59C23×C413yes—
371C2×C4×C59C23×C413yes—
372C2×C4×C59C22×D416yes—
373C2×C4×C59C22×D416yes—
374C2×C4×C59C2511yescharacteristic
375C22⋊D59—212no—
376C22⋊D59—26no—
377C22⋊D59—22no—
378C22⋊D59—26no—
379C22⋊D59—26no—
380C22⋊D59—22no—
381C22⋊D59—26no—
382C22⋊D59—26no—
383C22⋊D59—26no—
384C22⋊D59C2×C22⋊C4124yes—
385C2×Dic59—26no—
386C2×Dic59—212no—
387C2×Dic59C2×C22⋊C4112yes—
388C2×Dic59C23×C413yes—
389C2×Dic59C23×C411yescharacteristic
390C2×Dic59C23×C411yescharacteristic
391C2×Dic59C23×C413yes—
392D236—26no—
393D236—22no—
394D236—26no—
395D236—26no—
396D236—26no—
397D236C2×C22⋊C4112yes—
398C4×D59—212no—
399C4×D59—26no—
400C4×D59—26no—
401C4×D59—21no—
402C4×D59—21no—
403C4×D59—23no—
404C4×D59—23no—
405C4×D59—212no—
406C4×D59C2×C22⋊C4112yes—
407C4×D59C2×C22⋊C4112yes—
408C4×D59C22×D412yes—
409C4×D59C22×D416yes—
410C4×D59C22×D416yes—
411C4×D59C22×D412yes—
412Dic118—26no—
413Dic118—22no—
414Dic118—26no—
415Dic118—26no—
416Dic118—26no—
417Dic118C2×C22⋊C4112yes—
418C8×C59—21no—
419C8×C59—23no—
420C8×C59—23no—
421C8×C59—21no—
422C59⋊C8—21no—
423C59⋊C8—23no—
424C59⋊C8—23no—
425C59⋊C8—21no—
426#60065—591nomaximal, Sylow
427C22×C59—23no—
428C22×C59—23no—
429C22×C59—23no—
430C22×C59—21no—
431C22×C59—23no—
432C22×C59—23no—
433C22×C59—21no—
434C22×C59—21no—
435C22×C59—86no—
436C22×C59C22×C22⋊C416yes—
437C22×C59C24×C411yescharacteristic
438C2×D59—21no—
439C2×D59—23no—
440C2×D59—21no—
441C2×D59—23no—
442C2×D59—21no—
443C2×D59—23no—
444C2×D59—23no—
445C2×D59—21no—
446C2×D59—23no—
447C2×D59—21no—
448C2×D59—412no—
449C2×D59—812no—
450C2×D59—86no—
451C2×D59C22×C22⋊C416yes—
452C2×D59C22×C22⋊C412yes—
453C4×C59—21no—
454C4×C59—23no—
455C4×C59C22×C22⋊C416yes—
456C4×C59C23×D411yescharacteristic
457C4×C59C23×D411yescharacteristic
458Dic59—23no—
459Dic59—21no—
460Dic59C22×C22⋊C412yes—
461Dic59C22×C22⋊C416yes—
462C2×#585—591no—
463C2×#568—591no—
464C22×#131—591no—
465#2880—593no—
466#2880—593no—
467#2880—593no—
468#2880—593no—
469#2880—591no—
470#2880—591no—
471#2880—591no—
472#2880D5911yescharacteristic, complemented
473#2879—593no—
474#2879—593no—
475C2×#408—593no—
476C2×#408—593no—
477C2×C59—26no—
478C2×C59—43no—
479C2×C59—41no—
480C2×C59C23×C22⋊C411yescharacteristic
481C2×C59#357311yescharacteristic
482C2×C59#357311yescharacteristic
483D59—22no—
484D59—26no—
485D59—43no—
486D59—41no—
487#585—1188no—
488#585—1188no—
489C2×2−1+4—591no—
490C2×2−1+4—593no—
491C2×2−1+4—591no—
492C2×2−1+4—591no—
493C2×H(5,𝔽2)—593no—
494C2×H(5,𝔽2)—591no—
495C2×H(5,𝔽2)—593no—
496C2×H(5,𝔽2)—593no—
497C22×#41—591no—
498C22×#41—593no—
499C22×#41—593no—
500C22×#41—591no—
501C22×#41—593no—
502C22×#41—593no—
503C22×#41C2×D5911yescharacteristic
504#568—1188no—
505C2×#131—591no—
506C2×#131—591no—
507C2×#131—593no—
508C2×#131—593no—
509C2×#131—593no—
510C2×#131—593no—
511C2×#131—1188no—
512C2×#131C2×D5911yescharacteristic, complemented
513C2×#131C2×D5911yescharacteristic, complemented
514C22×M16—593no—
515C22×M16—593no—
516C22×M16—593no—
517C23×C8—593no—
518#408—593no—
519#408—593no—
520#408—593no—
521#408—593no—
522#408—593no—
523#408—593no—
524#408—593no—
525#408—591no—
526#408—596no—
527#408—593no—
528#408—593no—
529#408—593no—
530#408—593no—
531#408—593no—
532#408—593no—
533#408—596no—
534#408—596no—
535#408C2×D5913yescomplemented
536#408C2×D5913yescomplemented
537#407—593no—
538#407—593no—
539#407—593no—
540#407—596no—
541#407—596no—
542#407C2×D5913yescomplemented
543C2×C22⋊C8—593no—
544C2×C22⋊C8—593no—
545C2×C22⋊C8—593no—
546C2×C22⋊C8—596no—
547C2×C22⋊C8—596no—
548C2×C22⋊C8C2×D5913yescomplemented
549C59#6006511yescharacteristic, complemented, Sylow
5502−1+4—1188no—
5512−1+4—1188no—
5522−1+4—1188no—
5532−1+4—11824no—
554H(5,𝔽2)—11824no—
555H(5,𝔽2)—11824no—
556H(5,𝔽2)—11824no—
557H(5,𝔽2)—1188no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—598no—
561C2×#41—598no—
562C2×#41—591no—
563C2×#41—593no—
564C2×#41—593no—
565C2×#41—591no—
566C2×#41—593no—
567C2×#41—596no—
568C2×#41—593no—
569C2×#41—596no—
570C2×#41—593no—
571C2×#41—593no—
572C2×#41—593no—
573C2×#41—593no—
574C2×#41—593no—
575C2×#41—593no—
576C2×#41—596no—
577C2×#41—593no—
578C2×#41—593no—
579C2×#41—593no—
580C2×#41—593no—
581C2×#41—593no—
582C2×#41—591no—
583C2×#41—593no—
584C2×#41—593no—
585C2×#41—11812no—
586C2×#41—11812no—
587C2×#41—11812no—
588C2×#41—11812no—
589C2×#41—11812no—
590C2×#41—11812no—
591C2×#41—11812no—
592C2×#41—11812no—
593C2×#41—1184no—
594C2×#41—1184no—
595C2×#41C4×D5911yescharacteristic
596C2×#41C4×D5913yes—
597C2×#41C22×D5913yes—
598C2×#41C22×D5911yescharacteristic
599C22×Q8—591no—
600C22×Q8—593no—
601C22×Q8—593no—
602C22×Q8—591no—
603C22×Q8—593no—
604C22×Q8—593no—
605C22×Q8C4×D5911yescharacteristic
606C22×D4—593no—
607C22×D4—593no—
608C22×D4—596no—
609C22×D4—593no—
610C22×D4—593no—
611C22×D4—596no—
612C22×D4—593no—
613C22×D4—596no—
614C22×D4—593no—
615C22×D4—593no—
616C22×D4—593no—
617C22×D4C4×D5913yes—
618C23×C4—593no—
619C23×C4—596no—
620C23×C4—593no—
621C23×C4C22×D5913yes—
622#131—24no—
623#131—24no—
624#131—11812no—
625#131—11812no—
626#131—11812no—
627#131—11812no—
628#131—1184no—
629#131—1184no—
630C2×M16—593no—
631C2×M16—593no—
632C2×M16—593no—
633C2×M16—591no—
634C2×M16—596no—
635C2×M16—593no—
636C2×M16—593no—
637C2×M16—11812no—
638C2×M16—11812no—
639C2×M16—11812no—
640C2×M16C22×D5913yes—
641C2×M16C22×D5913yes—
642C22×C8—593no—
643C22×C8—593no—
644C22×C8—591no—
645C22×C8—593no—
646C22×C8—593no—
647C22×C8—593no—
648C22×C8—596no—
649C22×C8—11812no—
650C22×C8C22×D5913yes—
651C22×C8C22×D5913yes—
652C22⋊C8—593no—
653C22⋊C8—591no—
654C22⋊C8—596no—
655C22⋊C8—593no—
656C22⋊C8—593no—
657C22⋊C8—593no—
658C22⋊C8—591no—
659C22⋊C8—593no—
660C22⋊C8—591no—
661C22⋊C8—596no—
662C22⋊C8—596no—
663C22⋊C8—593no—
664C22⋊C8—593no—
665C22⋊C8—593no—
666C22⋊C8—593no—
667C22⋊C8C22×D5913yes—
668C22⋊C8C22×D5916yes—
669C22⋊C8C22×D5911yescharacteristic
670C22⋊C8C22×D5913yes—
671C22⋊C8C22×D5913yes—
672C24—593no—
673C24—596no—
674C24—593no—
675C24C2×C4×D5913yes—
676#41—24no—
677#41—212no—
678#41—26no—
679#41—26no—
680#41—598no—
681#41—5924no—
682#41—5912no—
683#41—5912no—
684#41—1182no—
685#41—1186no—
686#41—1186no—
687#41—1182no—
688#41—1186no—
689#41—1186no—
690#41—1186no—
691#41—1186no—
692#41—11812no—
693#41—11812no—
694#41—11812no—
695#41—11812no—
696#41—11824no—
697#41—11812no—
698#41—11812no—
699#41—11824no—
700#41—11812no—
701#41—11812no—
702#41—11824no—
703#41—11812no—
704#41—11812no—
705#41—1184no—
706#41—11812no—
707#41—1186no—
708#41—1186no—
709#41D4×D5914yes—
710#41D4×D5914yes—
711C2×Q8—24no—
712C2×Q8—598no—
713C2×Q8—593no—
714C2×Q8—593no—
715C2×Q8—593no—
716C2×Q8—591no—
717C2×Q8—593no—
718C2×Q8—593no—
719C2×Q8—11812no—
720C2×Q8—11812no—
721C2×Q8—11812no—
722C2×Q8—11812no—
723C2×Q8—1184no—
724C2×Q8C2×C4×D5913yes—
725C2×Q8C2×C4×D5911yescharacteristic
726C2×D4—212no—
727C2×D4—596no—
728C2×D4—5924no—
729C2×D4—593no—
730C2×D4—593no—
731C2×D4—591no—
732C2×D4—593no—
733C2×D4—593no—
734C2×D4—593no—
735C2×D4—591no—
736C2×D4—593no—
737C2×D4—596no—
738C2×D4—593no—
739C2×D4—593no—
740C2×D4—593no—
741C2×D4—591no—
742C2×D4—593no—
743C2×D4—593no—
744C2×D4—11812no—
745C2×D4—11812no—
746C2×D4—11812no—
747C2×D4—11812no—
748C2×D4—11824no—
749C2×D4—11812no—
750C2×D4—11824no—
751C2×D4—11824no—
752C2×D4—11812no—
753C2×D4—11812no—
754C2×D4C2×C4×D5916yes—
755C2×D4C2×C4×D5913yes—
756C2×D4C2×C4×D5913yes—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—593no—
760C22×C4—593no—
761C22×C4—593no—
762C22×C4—5912no—
763C22×C4—5912no—
764C22×C4—591no—
765C22×C4—593no—
766C22×C4—596no—
767C22×C4—593no—
768C22×C4—596no—
769C22×C4—596no—
770C22×C4—593no—
771C22×C4—593no—
772C22×C4—593no—
773C22×C4—591no—
774C22×C4—11812no—
775C22×C4—11812no—
776C22×C4—1186no—
777C22×C4—1186no—
778C22×C4C2×C4×D5913yes—
779C22×C4C2×C4×D5913yes—
780C22×C4C2×C4×D5913yes—
781C22×C4C23×D5913yes—
782C22×C4C23×D5911yescharacteristic
783C22×C4C23×D5913yes—
784M16—26no—
785M16—26no—
786M16—1182no—
787M16—1186no—
788M16—1186no—
789M16—11812no—
790M16—1186no—
791M16—1186no—
792M16—1186no—
793C2×C8—26no—
794C2×C8—26no—
795C2×C8—591no—
796C2×C8—593no—
797C2×C8—591no—
798C2×C8—593no—
799C2×C8—1182no—
800C2×C8—1186no—
801C2×C8—1186no—
802C2×C8—1186no—
803C2×C8—11812no—
804C2×C8—1186no—
805C2×C8—1186no—
806C2×C8C23×D5911yescharacteristic
807C2×C8C23×D5913yes—
808C2×C8C23×D5913yes—
809C2×C8C23×D5911yescharacteristic
810C23—26no—
811C23—43no—
812C23—43no—
813C23—591no—
814C23—593no—
815C23—5912no—
816C23—593no—
817C23—591no—
818C23—11812no—
819C23—1186no—
820C23—2363no—
821C23—2363no—
822C23—2366no—
823C23—2366no—
824C23—2363no—
825C23—2363no—
826C23C22×C4×D5913yes—
827C23C22×C4×D5911yescharacteristic
828C23C22×C4×D5913yes—
829Q8—26no—
830Q8—5912no—
831Q8—1182no—
832Q8—1186no—
833Q8—1186no—
834Q8—1186no—
835Q8—1186no—
836Q8C22⋊C4×D5914yes—
837D4—212no—
838D4—26no—
839D4—5924no—
840D4—5912no—
841D4—1182no—
842D4—1186no—
843D4—1186no—
844D4—1186no—
845D4—1182no—
846D4—1186no—
847D4—1186no—
848D4—1186no—
849D4—1182no—
850D4—1186no—
851D4—1186no—
852D4—1186no—
853D4—11812no—
854D4—1186no—
855D4C22⋊C4×D59112yes—
856C2×C4—26no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—23no—
860C2×C4—23no—
861C2×C4—26no—
862C2×C4—26no—
863C2×C4—591no—
864C2×C4—593no—
865C2×C4—5912no—
866C2×C4—592no—
867C2×C4—596no—
868C2×C4—596no—
869C2×C4—592no—
870C2×C4—5912no—
871C2×C4—5912no—
872C2×C4—593no—
873C2×C4—591no—
874C2×C4—11812no—
875C2×C4—11812no—
876C2×C4—11812no—
877C2×C4—1186no—
878C2×C4—1183no—
879C2×C4—1183no—
880C2×C4—1181no—
881C2×C4—1181no—
882C2×C4—1186no—
883C2×C4—1186no—
884C2×C4C22×C4×D5913yes—
885C2×C4C22×C4×D5911yescharacteristic
886C2×C4C22×C4×D5913yes—
887C2×C4C2×D4×D5916yes—
888C2×C4C2×D4×D5916yes—
889C2×C4C24×D5911yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—1181no—
895C8—1183no—
896C8—1183no—
897C8—1181no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—592no—
908C22—596no—
909C22—1183no—
910C22—1181no—
911C22—1183no—
912C22—1181no—
913C22—1183no—
914C22—1181no—
915C22—1181no—
916C22—1183no—
917C22—1181no—
918C22—1183no—
919C22—4726no—
920C22—47212no—
921C22—23612no—
922C22C2×C22⋊C4×D5916yes—
923C22C23×C4×D5911yescharacteristic
924C4—21no—
925C4—23no—
926C4—592no—
927C4—596no—
928C4—1183no—
929C4—1181no—
930C4C2×C22⋊C4×D5916yes—
931C4C22×D4×D5911yescharacteristic
932C4C22×D4×D5911yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—1186no—
937C2—1182no—
938C2—2361no—
939C2—2363no—
940C2C22×C22⋊C4×D5911yescharacteristic
941C2#2143880711yescharacteristic
942C2#2143880911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D59
commutator, socleC22×C59C24×C4
FittingC59×#2880C2
prime radicalC2×#16838238C2
cosocleC2×C4×C59C25
hypercenter#2880D59
hypocenterC59#60065
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#16838167C2semidirect
3. C2×#131×D59C2semidirect
4. #21432546C2semidirect
5. #21432545C2semidirect
6. #21432544C2semidirect
7. #21432544C2semidirect
8. #21432543C2semidirect
9. #21432543C2semidirect
10. #21432542C2semidirect
11. #21432539C2semidirect
12. #21432538C2semidirect
13. C2×#16837367C2semidirect
14. #408×D59C2semidirect
15. C59×#2880C2semidirect
33. C2×#14273735C22semidirect
34. C2×#14273735C22semidirect
35. C2×#14273734C22semidirect
36. C2×#14273734C22semidirect
37. C2×#14273733C22semidirect
38. C2×#14273733C22semidirect
40. C22×#11745659C22semidirect
41. C2×M16×D59C22semidirect
42. C2×M16×D59C22semidirect
43. C22×C8×D59C22semidirect
44. #16837370C22semidirect
45. #16837370C22semidirect
46. #16837369C22semidirect
47. #16837369C22semidirect
48. #16837368C22semidirect
49. #16837368C22semidirect
50. #16837367C22semidirect
51. #16837367C22semidirect
52. #16837367C22semidirect
53. #16837367C22semidirect
54. #16837367C22semidirect
55. #16837367C22semidirect
56. #16837367C22semidirect
57. #16837367C22semidirect
58. #16837367C22semidirect
59. #16837367C22semidirect
60. #16837367C22semidirect
61. #16837366C22semidirect
62. #16837365C22semidirect
63. #16837365C22semidirect
64. #16837364C22semidirect
65. #16837364C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
69. C22⋊C8×D59C22semidirect
70. C22⋊C8×D59C22semidirect
72. C2×#131×C59C22semidirect
73. C2×#131×C59C22semidirect
74. C59×#408C22semidirect
75. C59×#408C22semidirect
76. C59×#407C22semidirect
77. C2×C22⋊C8×C59C22semidirect
472. #2880D59semidirect
512. C2×#131C2×D59semidirect
513. C2×#131C2×D59semidirect
535. #408C2×D59semidirect
536. #408C2×D59semidirect
542. #407C2×D59semidirect
548. C2×C22⋊C8C2×D59semidirect
549. C59#60065semidirect

Maximal subgroups

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

subgroupindex
C2×#168382382
C2×#168381672
C2×#131×D592
#214325462
#214325452
#214325442
#214325432
#214325422
#214325392
#214325382
C2×#168373672
#408×D592
C59×#28802
#6006559