Finite Group Databasebeta

← #27079731

Subgroups — #27079731

Order 12032.

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×#15689959C211yesmaximal, characteristic
2C2×#15689888C211yesmaximal, characteristic, complemented
3C2×#131×D47C211yesmaximal, characteristic, complemented
4#20251838C213yesmaximal, complemented
5#20251837C211yesmaximal, characteristic, complemented
6#20251836C213yesmaximal, complemented
7#20251836C213yesmaximal, complemented
8#20251835C211yesmaximal, characteristic, complemented
9#20251835C211yesmaximal, characteristic, complemented
10#20251834C213yesmaximal, complemented
11#20251831C213yesmaximal, complemented
12#20251830C213yesmaximal, complemented
13C2×#15689088C213yesmaximal, complemented
14#408×D47C213yesmaximal, complemented
15C47×#2880C211yesmaximal, characteristic, complemented
16#15689959—28no—
17#15689959—28no—
18C2×#13094072C411yescharacteristic
19C2×#13094072C411yescharacteristic
20C2×#13094071C413yes—
21C2×#13094071C411yescharacteristic
22C2×#13094070C411yescharacteristic
23C2×#13094070C413yes—
24C2×#13094069C413yes—
25C2×#13094069C413yes—
26C22×#10625350C2213yes—
27C22×#10625350C2213yes—
28C2×#41×D47C2213yes—
29C2×#41×D47C2211yescharacteristic
30C2×#41×D47C2213yes—
31C2×#41×D47C2211yescharacteristic
32#15689888—28no—
33C2×#13094032C2213yescomplemented
34C2×#13094032C2213yescomplemented
35C2×#13094031C2211yescharacteristic, complemented
36C2×#13094031C2211yescharacteristic, complemented
37C2×#13094030C2213yescomplemented
38C2×#13094030C2213yescomplemented
39#131×D47—28no—
40C22×#10625324C2213yescomplemented
41C2×M16×D47C2213yescomplemented
42C2×M16×D47C2213yescomplemented
43C22×C8×D47C2213yescomplemented
44#15689091C2213yescomplemented
45#15689091C2213yescomplemented
46#15689090C2213yescomplemented
47#15689090C2213yescomplemented
48#15689089C2213yescomplemented
49#15689089C2213yescomplemented
50#15689088C2213yescomplemented
51#15689088C2216yescomplemented
52#15689088C2211yescharacteristic, complemented
53#15689088C2213yescomplemented
54#15689088C2213yescomplemented
55#15689088C2213yescomplemented
56#15689088C2213yescomplemented
57#15689088C2213yescomplemented
58#15689088C2213yescomplemented
59#15689088C2216yescomplemented
60#15689088C2216yescomplemented
61#15689087C2213yescomplemented
62#15689086C2213yescomplemented
63#15689086C2213yescomplemented
64#15689085C2216yescomplemented
65#15689085C2216yescomplemented
66C2×C22⋊(C47⋊C8)C2213yescomplemented
67C2×(C2×D47)⋊C8C2213yescomplemented
68C2×(C2×D47)⋊C8C2213yescomplemented
69C22⋊C8×D47C2216yescomplemented
70C22⋊C8×D47C2216yescomplemented
71C22×#41×C47C2211yescharacteristic
72C2×#131×C47C2211yescharacteristic, complemented
73C2×#131×C47C2211yescharacteristic, complemented
74C47×#408C2213yescomplemented
75C47×#408C2213yescomplemented
76C47×#407C2213yescomplemented
77C2×C22⋊C8×C47C2213yescomplemented
78#13094072—28no—
79#13094072—28no—
80#13094071—28no—
81#13094071—224no—
82#13094070—28no—
83#13094070—224no—
84#13094069—224no—
85#13094069—224no—
86C2×#10625354C2×C411yescharacteristic
87C2×#10625354C2×C413yes—
88C2×#10625354C2×C413yes—
89C2×#10625354C2×C411yescharacteristic
90C2×#10625350—212no—
91C2×#10625350—212no—
92C2×#10625350—212no—
93C2×#10625350—212no—
94C2×#10625350C2×C413yes—
95C2×#10625350C2×C413yes—
96C2×#10625350C2×C413yes—
97C2×#10625350C2×C413yes—
98C2×#10625350C2×C416yes—
99C2×#10625350C2×C413yes—
100C2×#10625350C2×C413yes—
101C2×#10625350C2313yes—
102C2×#10625350C2313yes—
103C2×#10625350C2311yescharacteristic
104C2×#10625350C2313yes—
105C2×#10625350C2313yes—
106C2×#10625350C2313yes—
107C2×#10625352C2×C413yes—
108C2×#10625352C2×C416yes—
109C2×#10625352C2×C416yes—
110C2×#10625352C2×C413yes—
111C2×#10625352C2×C413yes—
112C2×#10625352C2×C413yes—
113#41×D47—24no—
114#41×D47—24no—
115#41×D47—212no—
116#41×D47—212no—
117#41×D47—212no—
118#41×D47—212no—
119#41×D47D418yes—
120#41×D47D418yes—
121C22×Dic94C2×C413yes—
122C22×Dic94C2×C413yes—
123C2×Q8×D47C2×C411yescharacteristic
124C2×Q8×D47C2×C413yes—
125C2×Q8×D47C2×C413yes—
126C2×Q8×D47C2×C411yescharacteristic
127C22×D188C2×C413yes—
128C22×D188C2×C413yes—
129C22×C22⋊D47C2×C413yes—
130C22×C22⋊D47C2×C416yes—
131C22×C22⋊D47C2×C413yes—
132C2×D4×D47C2×C416yes—
133C2×D4×D47C2×C413yes—
134C2×D4×D47C2×C416yes—
135C2×D4×D47C2×C413yes—
136C2×D4×D47C2×C413yes—
137C2×D4×D47C2×C413yes—
138C22×C4×D47C2316yes—
139C22×C4×D47C2313yes—
140C22×C4×D47C2313yes—
141#13094032—212no—
142#13094032—212no—
143#13094031—24no—
144#13094031—24no—
145#13094030—212no—
146#13094030—212no—
147C2×#10625329C2313yes—
148C2×#10625329C2313yes—
149C2×#10625324—212no—
150C2×#10625324C2316yes—
151C2×#10625324C2313yes—
152C2×#10625324C2313yes—
153C2×#10625324C2313yes—
154C2×#10625324C2311yescharacteristic
155M16×D47—212no—
156M16×D47—212no—
157C22×C47⋊C8C2313yes—
158C22×C47⋊C8C2313yes—
159C2×C8×D47—212no—
160C2×C8×D47C2313yes—
161C2×C8×D47C2313yes—
162C2×C8×D47C2316yes—
163C2×C8×D47C2311yescharacteristic
164C2×C8×D47C2313yes—
165C22⋊(C47⋊C8)C2313yes—
166C22⋊(C47⋊C8)C2316yes—
167C22⋊(C47⋊C8)C2311yescharacteristic
168C22⋊(C47⋊C8)C2313yes—
169C22⋊(C47⋊C8)C2313yes—
170(C2×D47)⋊C8C2313yes—
171(C2×D47)⋊C8C2313yes—
172(C2×D47)⋊C8C2316yes—
173(C2×D47)⋊C8C2316yes—
174(C2×D47)⋊C8C2311yescharacteristic
175(C2×D47)⋊C8C2311yescharacteristic
176(C2×D47)⋊C8C2313yes—
177(C2×D47)⋊C8C2313yes—
178(C2×D47)⋊C8C2313yes—
179(C2×D47)⋊C8C2313yes—
180C2×#41×C47—24no—
181C2×#41×C47—24no—
182C2×#41×C47C2×C411yescharacteristic
183C2×#41×C47C2×C413yes—
184C2×#41×C47C2313yes—
185C2×#41×C47C2311yescharacteristic
186C22×Q8×C47C2×C411yescharacteristic
187C22×D4×C47C2×C413yes—
188C23×C4×C47C2313yes—
189#131×C47—24no—
190#131×C47—24no—
191C2×M16×C47C2313yes—
192C2×M16×C47C2313yes—
193C22×C8×C47C2313yes—
194C22×C8×C47C2313yes—
195C22⋊C8×C47C2313yes—
196C22⋊C8×C47C2316yes—
197C22⋊C8×C47C2313yes—
198C22⋊C8×C47C2311yescharacteristic
199C22⋊C8×C47C2313yes—
200C24×C47C22×C413yes—
201C23×D47C22×C413yes—
202C23×D47C22×C416yes—
203C23×D47C22×C413yes—
204#41×C47—24no—
205#41×C47—212no—
206#41×C47—26no—
207#41×C47—26no—
208#41×C47C2×D414yes—
209#41×C47C2×D414yes—
210C2×Q8×C47—24no—
211C2×Q8×C47C22×C413yes—
212C2×Q8×C47C22×C411yescharacteristic
213C2×D4×C47—212no—
214C2×D4×C47C22×C416yes—
215C2×D4×C47C22×C413yes—
216C2×D4×C47C22×C413yes—
217C22×C4×C47—26no—
218C22×C4×C47—26no—
219C22×C4×C47C22×C413yes—
220C22×C4×C47C22×C413yes—
221C22×C4×C47C22×C413yes—
222C22×C4×C47C2411yescharacteristic
223C22×C4×C47C2413yes—
224C22×C4×C47C2413yes—
225C2×C22⋊D47—212no—
226C2×C22⋊D47—224no—
227C2×C22⋊D47—212no—
228C2×C22⋊D47C22×C416yes—
229C2×C22⋊D47C22×C413yes—
230C2×C22⋊D47C22×C413yes—
231C2×C22⋊D47C22×C413yes—
232C2×C22⋊D47C22×C413yes—
233C2×C22⋊D47C22×C413yes—
234C2×C22⋊D47C22×C411yescharacteristic
235C2×C22⋊D47C22×C411yescharacteristic
236C2×C22⋊D47C22×C413yes—
237C2×C22⋊D47C22×C416yes—
238C22×Dic47C22×C413yes—
239C22×Dic47C22×C416yes—
240C22×Dic47C22×C413yes—
241#10625354—24no—
242#10625354—212no—
243#10625354—212no—
244#10625354C22⋊C418yes—
245Q8×D47—24no—
246Q8×D47—212no—
247Q8×D47—212no—
248Q8×D47C22⋊C418yes—
249#10625352—212no—
250#10625352—224no—
251#10625352—224no—
252#10625352—212no—
253#10625352—212no—
254#10625352C22⋊C4124yes—
255D4×D47—224no—
256D4×D47—212no—
257D4×D47—224no—
258D4×D47—212no—
259D4×D47—212no—
260D4×D47C22⋊C4124yes—
261#10625350—26no—
262#10625350—26no—
263#10625350—224no—
264#10625350—212no—
265#10625350—212no—
266#10625350—212no—
267#10625350—212no—
268#10625350—212no—
269#10625350—26no—
270#10625350—26no—
271#10625350—26no—
272#10625350—26no—
273#10625350—22no—
274#10625350—26no—
275#10625350—26no—
276#10625350—22no—
277#10625350—212no—
278#10625350C2×D4112yes—
279#10625350C2×D4112yes—
280C2×D188—212no—
281C2×D188—212no—
282C2×D188C22×C413yes—
283C2×D188C22×C413yes—
284C2×D188C22×C413yes—
285C2×D188C22×C413yes—
286C2×D188C22×C411yescharacteristic
287C2×D188C22×C413yes—
288C2×C4×D47—26no—
289C2×C4×D47—26no—
290C2×C4×D47—212no—
291C2×C4×D47—212no—
292C2×C4×D47C22×C416yes—
293C2×C4×D47C22×C413yes—
294C2×C4×D47C22×C413yes—
295C2×C4×D47C22×C416yes—
296C2×C4×D47C22×C413yes—
297C2×C4×D47C22×C413yes—
298C2×C4×D47C2×D4112yes—
299C2×C4×D47C2×D4112yes—
300C2×C4×D47C2413yes—
301C2×C4×D47C2411yescharacteristic
302C2×C4×D47C2411yescharacteristic
303C2×C4×D47C2413yes—
304C2×Dic94—212no—
305C2×Dic94—212no—
306C2×Dic94C22×C413yes—
307C2×Dic94C22×C413yes—
308C2×Dic94C22×C413yes—
309C2×Dic94C22×C411yescharacteristic
310C2×Dic94C22×C413yes—
311C2×Dic94C22×C413yes—
312M16×C47—26no—
313M16×C47—26no—
314C2×C8×C47—26no—
315C2×C8×C47—26no—
316C2×C8×C47C2411yescharacteristic
317C2×C8×C47C2411yescharacteristic
318C2×C8×C47C2413yes—
319C2×C8×C47C2413yes—
320#10625329—26no—
321#10625329—26no—
322C2×C47⋊C8—26no—
323C2×C47⋊C8—26no—
324C2×C47⋊C8C2411yescharacteristic
325C2×C47⋊C8C2413yes—
326C2×C47⋊C8C2413yes—
327C2×C47⋊C8C2411yescharacteristic
328#10625324—26no—
329#10625324—212no—
330#10625324—22no—
331#10625324—26no—
332#10625324—26no—
333C8×D47—22no—
334C8×D47—26no—
335C8×D47—26no—
336C8×D47—26no—
337C8×D47—212no—
338C23×C47—26no—
339C23×C47—43no—
340C23×C47—43no—
341C23×C47C23×C413yes—
342C23×C47C23×C411yescharacteristic
343C23×C47C23×C413yes—
344C22×D47—26no—
345C22×D47—212no—
346C22×D47—43no—
347C22×D47—43no—
348C22×D47—46no—
349C22×D47—46no—
350C22×D47—43no—
351C22×D47—43no—
352C22×D47C2×C22⋊C4112yes—
353C22×D47C23×C411yescharacteristic
354C22×D47C23×C413yes—
355C22×D47C23×C413yes—
356C22×D47C23×C411yescharacteristic
357Q8×C47—26no—
358Q8×C47C2×C22⋊C414yes—
359D4×C47—212no—
360D4×C47—26no—
361D4×C47C2×C22⋊C4112yes—
362C2×C4×C47—26no—
363C2×C4×C47—26no—
364C2×C4×C47—26no—
365C2×C4×C47—23no—
366C2×C4×C47—23no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47C23×C411yescharacteristic
370C2×C4×C47C23×C413yes—
371C2×C4×C47C23×C413yes—
372C2×C4×C47C22×D416yes—
373C2×C4×C47C22×D416yes—
374C2×C4×C47C2511yescharacteristic
375C22⋊D47—212no—
376C22⋊D47—26no—
377C22⋊D47—22no—
378C22⋊D47—26no—
379C22⋊D47—26no—
380C22⋊D47—22no—
381C22⋊D47—26no—
382C22⋊D47—26no—
383C22⋊D47—26no—
384C22⋊D47C2×C22⋊C4124yes—
385C2×Dic47—26no—
386C2×Dic47—212no—
387C2×Dic47C2×C22⋊C4112yes—
388C2×Dic47C23×C413yes—
389C2×Dic47C23×C411yescharacteristic
390C2×Dic47C23×C411yescharacteristic
391C2×Dic47C23×C413yes—
392D188—26no—
393D188—22no—
394D188—26no—
395D188—26no—
396D188—26no—
397D188C2×C22⋊C4112yes—
398C4×D47—212no—
399C4×D47—26no—
400C4×D47—26no—
401C4×D47—21no—
402C4×D47—21no—
403C4×D47—23no—
404C4×D47—23no—
405C4×D47—212no—
406C4×D47C2×C22⋊C4112yes—
407C4×D47C2×C22⋊C4112yes—
408C4×D47C22×D412yes—
409C4×D47C22×D416yes—
410C4×D47C22×D416yes—
411C4×D47C22×D412yes—
412Dic94—26no—
413Dic94—22no—
414Dic94—26no—
415Dic94—26no—
416Dic94—26no—
417Dic94C2×C22⋊C4112yes—
418C8×C47—21no—
419C8×C47—23no—
420C8×C47—23no—
421C8×C47—21no—
422C47⋊C8—21no—
423C47⋊C8—23no—
424C47⋊C8—23no—
425C47⋊C8—21no—
426#60065—471nomaximal, Sylow
427C22×C47—23no—
428C22×C47—23no—
429C22×C47—23no—
430C22×C47—21no—
431C22×C47—23no—
432C22×C47—23no—
433C22×C47—21no—
434C22×C47—21no—
435C22×C47—86no—
436C22×C47C22×C22⋊C416yes—
437C22×C47C24×C411yescharacteristic
438C2×D47—21no—
439C2×D47—23no—
440C2×D47—21no—
441C2×D47—23no—
442C2×D47—21no—
443C2×D47—23no—
444C2×D47—23no—
445C2×D47—21no—
446C2×D47—23no—
447C2×D47—21no—
448C2×D47—412no—
449C2×D47—812no—
450C2×D47—86no—
451C2×D47C22×C22⋊C416yes—
452C2×D47C22×C22⋊C412yes—
453C4×C47—21no—
454C4×C47—23no—
455C4×C47C22×C22⋊C416yes—
456C4×C47C23×D411yescharacteristic
457C4×C47C23×D411yescharacteristic
458Dic47—23no—
459Dic47—21no—
460Dic47C22×C22⋊C412yes—
461Dic47C22×C22⋊C416yes—
462C2×#585—471no—
463C2×#568—471no—
464C22×#131—471no—
465#2880—473no—
466#2880—473no—
467#2880—473no—
468#2880—473no—
469#2880—471no—
470#2880—471no—
471#2880—471no—
472#2880D4711yescharacteristic, complemented
473#2879—473no—
474#2879—473no—
475C2×#408—473no—
476C2×#408—473no—
477C2×C47—26no—
478C2×C47—43no—
479C2×C47—41no—
480C2×C47C23×C22⋊C411yescharacteristic
481C2×C47#357311yescharacteristic
482C2×C47#357311yescharacteristic
483D47—22no—
484D47—26no—
485D47—43no—
486D47—41no—
487#585—948no—
488#585—948no—
489C2×2−1+4—471no—
490C2×2−1+4—473no—
491C2×2−1+4—471no—
492C2×2−1+4—471no—
493C2×H(5,𝔽2)—473no—
494C2×H(5,𝔽2)—471no—
495C2×H(5,𝔽2)—473no—
496C2×H(5,𝔽2)—473no—
497C22×#41—471no—
498C22×#41—473no—
499C22×#41—473no—
500C22×#41—471no—
501C22×#41—473no—
502C22×#41—473no—
503C22×#41C2×D4711yescharacteristic
504#568—948no—
505C2×#131—471no—
506C2×#131—471no—
507C2×#131—473no—
508C2×#131—473no—
509C2×#131—473no—
510C2×#131—473no—
511C2×#131—948no—
512C2×#131C2×D4711yescharacteristic, complemented
513C2×#131C2×D4711yescharacteristic, complemented
514C22×M16—473no—
515C22×M16—473no—
516C22×M16—473no—
517C23×C8—473no—
518#408—473no—
519#408—473no—
520#408—473no—
521#408—473no—
522#408—473no—
523#408—473no—
524#408—473no—
525#408—471no—
526#408—476no—
527#408—473no—
528#408—473no—
529#408—473no—
530#408—473no—
531#408—473no—
532#408—473no—
533#408—476no—
534#408—476no—
535#408C2×D4713yescomplemented
536#408C2×D4713yescomplemented
537#407—473no—
538#407—473no—
539#407—473no—
540#407—476no—
541#407—476no—
542#407C2×D4713yescomplemented
543C2×C22⋊C8—473no—
544C2×C22⋊C8—473no—
545C2×C22⋊C8—473no—
546C2×C22⋊C8—476no—
547C2×C22⋊C8—476no—
548C2×C22⋊C8C2×D4713yescomplemented
549C47#6006511yescharacteristic, complemented, Sylow
5502−1+4—948no—
5512−1+4—948no—
5522−1+4—948no—
5532−1+4—9424no—
554H(5,𝔽2)—9424no—
555H(5,𝔽2)—9424no—
556H(5,𝔽2)—9424no—
557H(5,𝔽2)—948no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—478no—
561C2×#41—478no—
562C2×#41—471no—
563C2×#41—473no—
564C2×#41—473no—
565C2×#41—471no—
566C2×#41—473no—
567C2×#41—476no—
568C2×#41—473no—
569C2×#41—476no—
570C2×#41—473no—
571C2×#41—473no—
572C2×#41—473no—
573C2×#41—473no—
574C2×#41—473no—
575C2×#41—473no—
576C2×#41—476no—
577C2×#41—473no—
578C2×#41—473no—
579C2×#41—473no—
580C2×#41—473no—
581C2×#41—473no—
582C2×#41—471no—
583C2×#41—473no—
584C2×#41—473no—
585C2×#41—9412no—
586C2×#41—9412no—
587C2×#41—9412no—
588C2×#41—9412no—
589C2×#41—9412no—
590C2×#41—9412no—
591C2×#41—9412no—
592C2×#41—9412no—
593C2×#41—944no—
594C2×#41—944no—
595C2×#41C4×D4711yescharacteristic
596C2×#41C4×D4713yes—
597C2×#41C22×D4713yes—
598C2×#41C22×D4711yescharacteristic
599C22×Q8—471no—
600C22×Q8—473no—
601C22×Q8—473no—
602C22×Q8—471no—
603C22×Q8—473no—
604C22×Q8—473no—
605C22×Q8C4×D4711yescharacteristic
606C22×D4—473no—
607C22×D4—473no—
608C22×D4—476no—
609C22×D4—473no—
610C22×D4—473no—
611C22×D4—476no—
612C22×D4—473no—
613C22×D4—476no—
614C22×D4—473no—
615C22×D4—473no—
616C22×D4—473no—
617C22×D4C4×D4713yes—
618C23×C4—473no—
619C23×C4—476no—
620C23×C4—473no—
621C23×C4C22×D4713yes—
622#131—24no—
623#131—24no—
624#131—9412no—
625#131—9412no—
626#131—9412no—
627#131—9412no—
628#131—944no—
629#131—944no—
630C2×M16—473no—
631C2×M16—473no—
632C2×M16—473no—
633C2×M16—471no—
634C2×M16—476no—
635C2×M16—473no—
636C2×M16—473no—
637C2×M16—9412no—
638C2×M16—9412no—
639C2×M16—9412no—
640C2×M16C22×D4713yes—
641C2×M16C22×D4713yes—
642C22×C8—473no—
643C22×C8—473no—
644C22×C8—471no—
645C22×C8—473no—
646C22×C8—473no—
647C22×C8—473no—
648C22×C8—476no—
649C22×C8—9412no—
650C22×C8C22×D4713yes—
651C22×C8C22×D4713yes—
652C22⋊C8—473no—
653C22⋊C8—471no—
654C22⋊C8—476no—
655C22⋊C8—473no—
656C22⋊C8—473no—
657C22⋊C8—473no—
658C22⋊C8—471no—
659C22⋊C8—473no—
660C22⋊C8—471no—
661C22⋊C8—476no—
662C22⋊C8—476no—
663C22⋊C8—473no—
664C22⋊C8—473no—
665C22⋊C8—473no—
666C22⋊C8—473no—
667C22⋊C8C22×D4713yes—
668C22⋊C8C22×D4716yes—
669C22⋊C8C22×D4711yescharacteristic
670C22⋊C8C22×D4713yes—
671C22⋊C8C22×D4713yes—
672C24—473no—
673C24—476no—
674C24—473no—
675C24C2×C4×D4713yes—
676#41—24no—
677#41—212no—
678#41—26no—
679#41—26no—
680#41—478no—
681#41—4724no—
682#41—4712no—
683#41—4712no—
684#41—942no—
685#41—946no—
686#41—946no—
687#41—942no—
688#41—946no—
689#41—946no—
690#41—946no—
691#41—946no—
692#41—9412no—
693#41—9412no—
694#41—9412no—
695#41—9412no—
696#41—9424no—
697#41—9412no—
698#41—9412no—
699#41—9424no—
700#41—9412no—
701#41—9412no—
702#41—9424no—
703#41—9412no—
704#41—9412no—
705#41—944no—
706#41—9412no—
707#41—946no—
708#41—946no—
709#41D4×D4714yes—
710#41D4×D4714yes—
711C2×Q8—24no—
712C2×Q8—478no—
713C2×Q8—473no—
714C2×Q8—473no—
715C2×Q8—473no—
716C2×Q8—471no—
717C2×Q8—473no—
718C2×Q8—473no—
719C2×Q8—9412no—
720C2×Q8—9412no—
721C2×Q8—9412no—
722C2×Q8—9412no—
723C2×Q8—944no—
724C2×Q8C2×C4×D4713yes—
725C2×Q8C2×C4×D4711yescharacteristic
726C2×D4—212no—
727C2×D4—476no—
728C2×D4—4724no—
729C2×D4—473no—
730C2×D4—473no—
731C2×D4—471no—
732C2×D4—473no—
733C2×D4—473no—
734C2×D4—473no—
735C2×D4—471no—
736C2×D4—473no—
737C2×D4—476no—
738C2×D4—473no—
739C2×D4—473no—
740C2×D4—473no—
741C2×D4—471no—
742C2×D4—473no—
743C2×D4—473no—
744C2×D4—9412no—
745C2×D4—9412no—
746C2×D4—9412no—
747C2×D4—9412no—
748C2×D4—9424no—
749C2×D4—9412no—
750C2×D4—9424no—
751C2×D4—9424no—
752C2×D4—9412no—
753C2×D4—9412no—
754C2×D4C2×C4×D4716yes—
755C2×D4C2×C4×D4713yes—
756C2×D4C2×C4×D4713yes—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—473no—
760C22×C4—473no—
761C22×C4—473no—
762C22×C4—4712no—
763C22×C4—4712no—
764C22×C4—471no—
765C22×C4—473no—
766C22×C4—476no—
767C22×C4—473no—
768C22×C4—476no—
769C22×C4—476no—
770C22×C4—473no—
771C22×C4—473no—
772C22×C4—473no—
773C22×C4—471no—
774C22×C4—9412no—
775C22×C4—9412no—
776C22×C4—946no—
777C22×C4—946no—
778C22×C4C2×C4×D4713yes—
779C22×C4C2×C4×D4713yes—
780C22×C4C2×C4×D4713yes—
781C22×C4C23×D4713yes—
782C22×C4C23×D4711yescharacteristic
783C22×C4C23×D4713yes—
784M16—26no—
785M16—26no—
786M16—942no—
787M16—946no—
788M16—946no—
789M16—9412no—
790M16—946no—
791M16—946no—
792M16—946no—
793C2×C8—26no—
794C2×C8—26no—
795C2×C8—471no—
796C2×C8—473no—
797C2×C8—473no—
798C2×C8—471no—
799C2×C8—942no—
800C2×C8—946no—
801C2×C8—946no—
802C2×C8—946no—
803C2×C8—9412no—
804C2×C8—946no—
805C2×C8—946no—
806C2×C8C23×D4711yescharacteristic
807C2×C8C23×D4713yes—
808C2×C8C23×D4713yes—
809C2×C8C23×D4711yescharacteristic
810C23—26no—
811C23—43no—
812C23—43no—
813C23—471no—
814C23—473no—
815C23—4712no—
816C23—473no—
817C23—471no—
818C23—9412no—
819C23—946no—
820C23—1883no—
821C23—1883no—
822C23—1886no—
823C23—1886no—
824C23—1883no—
825C23—1883no—
826C23C22×C4×D4713yes—
827C23C22×C4×D4711yescharacteristic
828C23C22×C4×D4713yes—
829Q8—26no—
830Q8—4712no—
831Q8—942no—
832Q8—946no—
833Q8—946no—
834Q8—946no—
835Q8—946no—
836Q8C22⋊C4×D4714yes—
837D4—212no—
838D4—26no—
839D4—4724no—
840D4—4712no—
841D4—942no—
842D4—946no—
843D4—946no—
844D4—946no—
845D4—942no—
846D4—946no—
847D4—946no—
848D4—946no—
849D4—942no—
850D4—946no—
851D4—946no—
852D4—946no—
853D4—9412no—
854D4—946no—
855D4C22⋊C4×D47112yes—
856C2×C4—26no—
857C2×C4—26no—
858C2×C4—26no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—23no—
862C2×C4—23no—
863C2×C4—4712no—
864C2×C4—471no—
865C2×C4—473no—
866C2×C4—4712no—
867C2×C4—4712no—
868C2×C4—472no—
869C2×C4—476no—
870C2×C4—476no—
871C2×C4—472no—
872C2×C4—473no—
873C2×C4—471no—
874C2×C4—9412no—
875C2×C4—9412no—
876C2×C4—9412no—
877C2×C4—946no—
878C2×C4—946no—
879C2×C4—946no—
880C2×C4—943no—
881C2×C4—943no—
882C2×C4—941no—
883C2×C4—941no—
884C2×C4C22×C4×D4713yes—
885C2×C4C22×C4×D4711yescharacteristic
886C2×C4C22×C4×D4713yes—
887C2×C4C2×D4×D4716yes—
888C2×C4C2×D4×D4716yes—
889C2×C4C24×D4711yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—941no—
895C8—943no—
896C8—943no—
897C8—941no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—472no—
908C22—476no—
909C22—943no—
910C22—941no—
911C22—943no—
912C22—941no—
913C22—943no—
914C22—941no—
915C22—941no—
916C22—943no—
917C22—941no—
918C22—943no—
919C22—3766no—
920C22—37612no—
921C22—18812no—
922C22C2×C22⋊C4×D4716yes—
923C22C23×C4×D4711yescharacteristic
924C4—21no—
925C4—23no—
926C4—472no—
927C4—476no—
928C4—943no—
929C4—941no—
930C4C2×C22⋊C4×D4716yes—
931C4C22×D4×D4711yescharacteristic
932C4C22×D4×D4711yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—946no—
937C2—942no—
938C2—1881no—
939C2—1883no—
940C2C22×C22⋊C4×D4711yescharacteristic
941C2#2025809911yescharacteristic
942C2#2025810111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2880C2
prime radicalC2×#15689959C2
cosocleC2×C4×C47C25
hypercenter#2880D47
hypocenterC47#60065
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#15689888C2semidirect
3. C2×#131×D47C2semidirect
4. #20251838C2semidirect
5. #20251837C2semidirect
6. #20251836C2semidirect
7. #20251836C2semidirect
8. #20251835C2semidirect
9. #20251835C2semidirect
10. #20251834C2semidirect
11. #20251831C2semidirect
12. #20251830C2semidirect
13. C2×#15689088C2semidirect
14. #408×D47C2semidirect
15. C47×#2880C2semidirect
33. C2×#13094032C22semidirect
34. C2×#13094032C22semidirect
35. C2×#13094031C22semidirect
36. C2×#13094031C22semidirect
37. C2×#13094030C22semidirect
38. C2×#13094030C22semidirect
40. C22×#10625324C22semidirect
41. C2×M16×D47C22semidirect
42. C2×M16×D47C22semidirect
43. C22×C8×D47C22semidirect
44. #15689091C22semidirect
45. #15689091C22semidirect
46. #15689090C22semidirect
47. #15689090C22semidirect
48. #15689089C22semidirect
49. #15689089C22semidirect
50. #15689088C22semidirect
51. #15689088C22semidirect
52. #15689088C22semidirect
53. #15689088C22semidirect
54. #15689088C22semidirect
55. #15689088C22semidirect
56. #15689088C22semidirect
57. #15689088C22semidirect
58. #15689088C22semidirect
59. #15689088C22semidirect
60. #15689088C22semidirect
61. #15689087C22semidirect
62. #15689086C22semidirect
63. #15689086C22semidirect
64. #15689085C22semidirect
65. #15689085C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
69. C22⋊C8×D47C22semidirect
70. C22⋊C8×D47C22semidirect
72. C2×#131×C47C22semidirect
73. C2×#131×C47C22semidirect
74. C47×#408C22semidirect
75. C47×#408C22semidirect
76. C47×#407C22semidirect
77. C2×C22⋊C8×C47C22semidirect
472. #2880D47semidirect
512. C2×#131C2×D47semidirect
513. C2×#131C2×D47semidirect
535. #408C2×D47semidirect
536. #408C2×D47semidirect
542. #407C2×D47semidirect
548. C2×C22⋊C8C2×D47semidirect
549. C47#60065semidirect

Maximal subgroups

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

subgroupindex
C2×#156899592
C2×#156898882
C2×#131×D472
#202518382
#202518372
#202518362
#202518352
#202518342
#202518312
#202518302
C2×#156890882
#408×D472
C47×#28802
#6006547