Finite Group Databasebeta

← #25960050

Subgroups — #25960050

Order 11008.

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×#14583735C211yesmaximal, characteristic
2C2×#14583664C211yesmaximal, characteristic, complemented
3C2×#131×D43C211yesmaximal, characteristic, complemented
4#19143045C213yesmaximal, complemented
5#19143044C211yesmaximal, characteristic, complemented
6#19143043C213yesmaximal, complemented
7#19143043C213yesmaximal, complemented
8#19143042C211yesmaximal, characteristic, complemented
9#19143042C211yesmaximal, characteristic, complemented
10#19143041C213yesmaximal, complemented
11#19143038C213yesmaximal, complemented
12#19143037C213yesmaximal, complemented
13C2×#14582864C213yesmaximal, complemented
14#408×D43C213yesmaximal, complemented
15C43×#2880C211yesmaximal, characteristic, complemented
16#14583735—28no—
17#14583735—28no—
18C2×#13063373C411yescharacteristic
19C2×#13063373C411yescharacteristic
20C2×#13063372C413yes—
21C2×#13063372C411yescharacteristic
22C2×#13063371C411yescharacteristic
23C2×#13063371C413yes—
24C2×#13063370C413yes—
25C2×#13063370C413yes—
26C22×#10621898C2213yes—
27C22×#10621898C2213yes—
28C2×#41×D43C2213yes—
29C2×#41×D43C2211yescharacteristic
30C2×#41×D43C2213yes—
31C2×#41×D43C2211yescharacteristic
32#14583664—28no—
33C2×#13063333C2213yescomplemented
34C2×#13063333C2213yescomplemented
35C2×#13063332C2211yescharacteristic, complemented
36C2×#13063332C2211yescharacteristic, complemented
37C2×#13063331C2213yescomplemented
38C2×#13063331C2213yescomplemented
39#131×D43—28no—
40C22×#10621872C2213yescomplemented
41C2×M16×D43C2213yescomplemented
42C2×M16×D43C2213yescomplemented
43C22×C8×D43C2213yescomplemented
44#14582867C2213yescomplemented
45#14582867C2213yescomplemented
46#14582866C2213yescomplemented
47#14582866C2213yescomplemented
48#14582865C2213yescomplemented
49#14582865C2213yescomplemented
50#14582864C2213yescomplemented
51#14582864C2216yescomplemented
52#14582864C2211yescharacteristic, complemented
53#14582864C2213yescomplemented
54#14582864C2213yescomplemented
55#14582864C2213yescomplemented
56#14582864C2213yescomplemented
57#14582864C2213yescomplemented
58#14582864C2213yescomplemented
59#14582864C2216yescomplemented
60#14582864C2216yescomplemented
61#14582863C2213yescomplemented
62#14582862C2213yescomplemented
63#14582862C2213yescomplemented
64#14582861C2216yescomplemented
65#14582861C2216yescomplemented
66C2×C22⋊(C43⋊C8)C2213yescomplemented
67C2×(C2×D43)⋊C8C2213yescomplemented
68C2×(C2×D43)⋊C8C2213yescomplemented
69C22⋊C8×D43C2216yescomplemented
70C22⋊C8×D43C2216yescomplemented
71C22×#41×C43C2211yescharacteristic
72C2×#131×C43C2211yescharacteristic, complemented
73C2×#131×C43C2211yescharacteristic, complemented
74C43×#408C2213yescomplemented
75C43×#408C2213yescomplemented
76C43×#407C2213yescomplemented
77C2×C22⋊C8×C43C2213yescomplemented
78#13063373—28no—
79#13063373—28no—
80#13063372—28no—
81#13063372—224no—
82#13063371—28no—
83#13063371—224no—
84#13063370—224no—
85#13063370—224no—
86C2×#10621902C2×C411yescharacteristic
87C2×#10621902C2×C413yes—
88C2×#10621902C2×C413yes—
89C2×#10621902C2×C411yescharacteristic
90C2×#10621898—212no—
91C2×#10621898—212no—
92C2×#10621898—212no—
93C2×#10621898—212no—
94C2×#10621898C2×C413yes—
95C2×#10621898C2×C413yes—
96C2×#10621898C2×C413yes—
97C2×#10621898C2×C413yes—
98C2×#10621898C2×C416yes—
99C2×#10621898C2×C413yes—
100C2×#10621898C2×C413yes—
101C2×#10621898C2313yes—
102C2×#10621898C2313yes—
103C2×#10621898C2311yescharacteristic
104C2×#10621898C2313yes—
105C2×#10621898C2313yes—
106C2×#10621898C2313yes—
107C2×#10621900C2×C413yes—
108C2×#10621900C2×C416yes—
109C2×#10621900C2×C416yes—
110C2×#10621900C2×C413yes—
111C2×#10621900C2×C413yes—
112C2×#10621900C2×C413yes—
113#41×D43—24no—
114#41×D43—24no—
115#41×D43—212no—
116#41×D43—212no—
117#41×D43—212no—
118#41×D43—212no—
119#41×D43D418yes—
120#41×D43D418yes—
121C22×Dic86C2×C413yes—
122C22×Dic86C2×C413yes—
123C2×Q8×D43C2×C411yescharacteristic
124C2×Q8×D43C2×C413yes—
125C2×Q8×D43C2×C413yes—
126C2×Q8×D43C2×C411yescharacteristic
127C22×D172C2×C413yes—
128C22×D172C2×C413yes—
129C22×C22⋊D43C2×C416yes—
130C22×C22⋊D43C2×C413yes—
131C22×C22⋊D43C2×C413yes—
132C2×D4×D43C2×C413yes—
133C2×D4×D43C2×C416yes—
134C2×D4×D43C2×C416yes—
135C2×D4×D43C2×C413yes—
136C2×D4×D43C2×C413yes—
137C2×D4×D43C2×C413yes—
138C22×C4×D43C2316yes—
139C22×C4×D43C2313yes—
140C22×C4×D43C2313yes—
141#13063333—212no—
142#13063333—212no—
143#13063332—24no—
144#13063332—24no—
145#13063331—212no—
146#13063331—212no—
147C2×#10621877C2313yes—
148C2×#10621877C2313yes—
149C2×#10621872—212no—
150C2×#10621872C2316yes—
151C2×#10621872C2313yes—
152C2×#10621872C2313yes—
153C2×#10621872C2313yes—
154C2×#10621872C2311yescharacteristic
155M16×D43—212no—
156M16×D43—212no—
157C22×C43⋊C8C2313yes—
158C22×C43⋊C8C2313yes—
159C2×C8×D43—212no—
160C2×C8×D43C2313yes—
161C2×C8×D43C2313yes—
162C2×C8×D43C2316yes—
163C2×C8×D43C2311yescharacteristic
164C2×C8×D43C2313yes—
165C22⋊(C43⋊C8)C2313yes—
166C22⋊(C43⋊C8)C2316yes—
167C22⋊(C43⋊C8)C2311yescharacteristic
168C22⋊(C43⋊C8)C2313yes—
169C22⋊(C43⋊C8)C2313yes—
170(C2×D43)⋊C8C2313yes—
171(C2×D43)⋊C8C2313yes—
172(C2×D43)⋊C8C2316yes—
173(C2×D43)⋊C8C2316yes—
174(C2×D43)⋊C8C2311yescharacteristic
175(C2×D43)⋊C8C2311yescharacteristic
176(C2×D43)⋊C8C2313yes—
177(C2×D43)⋊C8C2313yes—
178(C2×D43)⋊C8C2313yes—
179(C2×D43)⋊C8C2313yes—
180C2×#41×C43—24no—
181C2×#41×C43—24no—
182C2×#41×C43C2×C411yescharacteristic
183C2×#41×C43C2×C413yes—
184C2×#41×C43C2313yes—
185C2×#41×C43C2311yescharacteristic
186C22×Q8×C43C2×C411yescharacteristic
187C22×D4×C43C2×C413yes—
188C23×C4×C43C2313yes—
189#131×C43—24no—
190#131×C43—24no—
191C2×M16×C43C2313yes—
192C2×M16×C43C2313yes—
193C22×C8×C43C2313yes—
194C22×C8×C43C2313yes—
195C22⋊C8×C43C2313yes—
196C22⋊C8×C43C2316yes—
197C22⋊C8×C43C2313yes—
198C22⋊C8×C43C2311yescharacteristic
199C22⋊C8×C43C2313yes—
200C24×C43C22×C413yes—
201C23×D43C22×C413yes—
202C23×D43C22×C416yes—
203C23×D43C22×C413yes—
204#41×C43—24no—
205#41×C43—212no—
206#41×C43—26no—
207#41×C43—26no—
208#41×C43C2×D414yes—
209#41×C43C2×D414yes—
210C2×Q8×C43—24no—
211C2×Q8×C43C22×C413yes—
212C2×Q8×C43C22×C411yescharacteristic
213C2×D4×C43—212no—
214C2×D4×C43C22×C413yes—
215C2×D4×C43C22×C416yes—
216C2×D4×C43C22×C413yes—
217C22×C4×C43—26no—
218C22×C4×C43—26no—
219C22×C4×C43C22×C413yes—
220C22×C4×C43C22×C413yes—
221C22×C4×C43C22×C413yes—
222C22×C4×C43C2411yescharacteristic
223C22×C4×C43C2413yes—
224C22×C4×C43C2413yes—
225C2×C22⋊D43—224no—
226C2×C22⋊D43—212no—
227C2×C22⋊D43—212no—
228C2×C22⋊D43C22×C413yes—
229C2×C22⋊D43C22×C413yes—
230C2×C22⋊D43C22×C416yes—
231C2×C22⋊D43C22×C413yes—
232C2×C22⋊D43C22×C413yes—
233C2×C22⋊D43C22×C411yescharacteristic
234C2×C22⋊D43C22×C413yes—
235C2×C22⋊D43C22×C413yes—
236C2×C22⋊D43C22×C411yescharacteristic
237C2×C22⋊D43C22×C416yes—
238C22×Dic43C22×C416yes—
239C22×Dic43C22×C413yes—
240C22×Dic43C22×C413yes—
241#10621902—24no—
242#10621902—212no—
243#10621902—212no—
244#10621902C22⋊C418yes—
245Q8×D43—24no—
246Q8×D43—212no—
247Q8×D43—212no—
248Q8×D43C22⋊C418yes—
249#10621900—212no—
250#10621900—224no—
251#10621900—224no—
252#10621900—212no—
253#10621900—212no—
254#10621900C22⋊C4124yes—
255D4×D43—212no—
256D4×D43—224no—
257D4×D43—212no—
258D4×D43—212no—
259D4×D43—224no—
260D4×D43C22⋊C4124yes—
261#10621898—26no—
262#10621898—26no—
263#10621898—224no—
264#10621898—212no—
265#10621898—212no—
266#10621898—212no—
267#10621898—212no—
268#10621898—212no—
269#10621898—26no—
270#10621898—26no—
271#10621898—26no—
272#10621898—26no—
273#10621898—22no—
274#10621898—26no—
275#10621898—26no—
276#10621898—22no—
277#10621898—212no—
278#10621898C2×D4112yes—
279#10621898C2×D4112yes—
280C2×D172—212no—
281C2×D172—212no—
282C2×D172C22×C413yes—
283C2×D172C22×C413yes—
284C2×D172C22×C413yes—
285C2×D172C22×C413yes—
286C2×D172C22×C411yescharacteristic
287C2×D172C22×C413yes—
288C2×C4×D43—26no—
289C2×C4×D43—26no—
290C2×C4×D43—212no—
291C2×C4×D43—212no—
292C2×C4×D43C22×C413yes—
293C2×C4×D43C22×C413yes—
294C2×C4×D43C22×C416yes—
295C2×C4×D43C22×C416yes—
296C2×C4×D43C22×C413yes—
297C2×C4×D43C22×C413yes—
298C2×C4×D43C2×D4112yes—
299C2×C4×D43C2×D4112yes—
300C2×C4×D43C2413yes—
301C2×C4×D43C2411yescharacteristic
302C2×C4×D43C2411yescharacteristic
303C2×C4×D43C2413yes—
304C2×Dic86—212no—
305C2×Dic86—212no—
306C2×Dic86C22×C413yes—
307C2×Dic86C22×C413yes—
308C2×Dic86C22×C413yes—
309C2×Dic86C22×C411yescharacteristic
310C2×Dic86C22×C413yes—
311C2×Dic86C22×C413yes—
312M16×C43—26no—
313M16×C43—26no—
314C2×C8×C43—26no—
315C2×C8×C43—26no—
316C2×C8×C43C2411yescharacteristic
317C2×C8×C43C2411yescharacteristic
318C2×C8×C43C2413yes—
319C2×C8×C43C2413yes—
320#10621877—26no—
321#10621877—26no—
322C2×C43⋊C8—26no—
323C2×C43⋊C8—26no—
324C2×C43⋊C8C2411yescharacteristic
325C2×C43⋊C8C2413yes—
326C2×C43⋊C8C2413yes—
327C2×C43⋊C8C2411yescharacteristic
328#10621872—26no—
329#10621872—212no—
330#10621872—22no—
331#10621872—26no—
332#10621872—26no—
333C8×D43—22no—
334C8×D43—26no—
335C8×D43—26no—
336C8×D43—26no—
337C8×D43—212no—
338C23×C43—26no—
339C23×C43—43no—
340C23×C43—43no—
341C23×C43C23×C413yes—
342C23×C43C23×C411yescharacteristic
343C23×C43C23×C413yes—
344C22×D43—26no—
345C22×D43—212no—
346C22×D43—43no—
347C22×D43—43no—
348C22×D43—46no—
349C22×D43—46no—
350C22×D43—43no—
351C22×D43—43no—
352C22×D43C2×C22⋊C4112yes—
353C22×D43C23×C411yescharacteristic
354C22×D43C23×C413yes—
355C22×D43C23×C413yes—
356C22×D43C23×C411yescharacteristic
357Q8×C43—26no—
358Q8×C43C2×C22⋊C414yes—
359D4×C43—212no—
360D4×C43—26no—
361D4×C43C2×C22⋊C4112yes—
362C2×C4×C43—26no—
363C2×C4×C43—26no—
364C2×C4×C43—26no—
365C2×C4×C43—23no—
366C2×C4×C43—23no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43C23×C411yescharacteristic
370C2×C4×C43C23×C413yes—
371C2×C4×C43C23×C413yes—
372C2×C4×C43C22×D416yes—
373C2×C4×C43C22×D416yes—
374C2×C4×C43C2511yescharacteristic
375C22⋊D43—212no—
376C22⋊D43—26no—
377C22⋊D43—22no—
378C22⋊D43—26no—
379C22⋊D43—26no—
380C22⋊D43—22no—
381C22⋊D43—26no—
382C22⋊D43—26no—
383C22⋊D43—26no—
384C22⋊D43C2×C22⋊C4124yes—
385C2×Dic43—26no—
386C2×Dic43—212no—
387C2×Dic43C2×C22⋊C4112yes—
388C2×Dic43C23×C413yes—
389C2×Dic43C23×C411yescharacteristic
390C2×Dic43C23×C411yescharacteristic
391C2×Dic43C23×C413yes—
392D172—26no—
393D172—22no—
394D172—26no—
395D172—26no—
396D172—26no—
397D172C2×C22⋊C4112yes—
398C4×D43—212no—
399C4×D43—26no—
400C4×D43—26no—
401C4×D43—21no—
402C4×D43—21no—
403C4×D43—23no—
404C4×D43—23no—
405C4×D43—212no—
406C4×D43C2×C22⋊C4112yes—
407C4×D43C2×C22⋊C4112yes—
408C4×D43C22×D412yes—
409C4×D43C22×D416yes—
410C4×D43C22×D416yes—
411C4×D43C22×D412yes—
412Dic86—26no—
413Dic86—22no—
414Dic86—26no—
415Dic86—26no—
416Dic86—26no—
417Dic86C2×C22⋊C4112yes—
418C8×C43—21no—
419C8×C43—23no—
420C8×C43—23no—
421C8×C43—21no—
422C43⋊C8—21no—
423C43⋊C8—23no—
424C43⋊C8—23no—
425C43⋊C8—21no—
426#60065—431nomaximal, Sylow
427C22×C43—23no—
428C22×C43—23no—
429C22×C43—23no—
430C22×C43—21no—
431C22×C43—23no—
432C22×C43—23no—
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—86no—
436C22×C43C22×C22⋊C416yes—
437C22×C43C24×C411yescharacteristic
438C2×D43—21no—
439C2×D43—23no—
440C2×D43—21no—
441C2×D43—23no—
442C2×D43—21no—
443C2×D43—23no—
444C2×D43—23no—
445C2×D43—21no—
446C2×D43—23no—
447C2×D43—21no—
448C2×D43—412no—
449C2×D43—812no—
450C2×D43—86no—
451C2×D43C22×C22⋊C416yes—
452C2×D43C22×C22⋊C412yes—
453C4×C43—21no—
454C4×C43—23no—
455C4×C43C22×C22⋊C416yes—
456C4×C43C23×D411yescharacteristic
457C4×C43C23×D411yescharacteristic
458Dic43—23no—
459Dic43—21no—
460Dic43C22×C22⋊C412yes—
461Dic43C22×C22⋊C416yes—
462C2×#585—431no—
463C2×#568—431no—
464C22×#131—431no—
465#2880—433no—
466#2880—433no—
467#2880—433no—
468#2880—433no—
469#2880—431no—
470#2880—431no—
471#2880—431no—
472#2880D4311yescharacteristic, complemented
473#2879—433no—
474#2879—433no—
475C2×#408—433no—
476C2×#408—433no—
477C2×C43—26no—
478C2×C43—43no—
479C2×C43—41no—
480C2×C43C23×C22⋊C411yescharacteristic
481C2×C43#357311yescharacteristic
482C2×C43#357311yescharacteristic
483D43—22no—
484D43—26no—
485D43—43no—
486D43—41no—
487#585—868no—
488#585—868no—
489C2×2−1+4—431no—
490C2×2−1+4—433no—
491C2×2−1+4—431no—
492C2×2−1+4—431no—
493C2×H(5,𝔽2)—433no—
494C2×H(5,𝔽2)—431no—
495C2×H(5,𝔽2)—433no—
496C2×H(5,𝔽2)—433no—
497C22×#41—431no—
498C22×#41—433no—
499C22×#41—433no—
500C22×#41—431no—
501C22×#41—433no—
502C22×#41—433no—
503C22×#41C2×D4311yescharacteristic
504#568—868no—
505C2×#131—431no—
506C2×#131—431no—
507C2×#131—433no—
508C2×#131—433no—
509C2×#131—433no—
510C2×#131—433no—
511C2×#131—868no—
512C2×#131C2×D4311yescharacteristic, complemented
513C2×#131C2×D4311yescharacteristic, complemented
514C22×M16—433no—
515C22×M16—433no—
516C22×M16—433no—
517C23×C8—433no—
518#408—433no—
519#408—433no—
520#408—433no—
521#408—433no—
522#408—433no—
523#408—433no—
524#408—433no—
525#408—431no—
526#408—436no—
527#408—433no—
528#408—433no—
529#408—433no—
530#408—433no—
531#408—433no—
532#408—433no—
533#408—436no—
534#408—436no—
535#408C2×D4313yescomplemented
536#408C2×D4313yescomplemented
537#407—433no—
538#407—433no—
539#407—433no—
540#407—436no—
541#407—436no—
542#407C2×D4313yescomplemented
543C2×C22⋊C8—433no—
544C2×C22⋊C8—433no—
545C2×C22⋊C8—433no—
546C2×C22⋊C8—436no—
547C2×C22⋊C8—436no—
548C2×C22⋊C8C2×D4313yescomplemented
549C43#6006511yescharacteristic, complemented, Sylow
5502−1+4—868no—
5512−1+4—868no—
5522−1+4—868no—
5532−1+4—8624no—
554H(5,𝔽2)—8624no—
555H(5,𝔽2)—8624no—
556H(5,𝔽2)—8624no—
557H(5,𝔽2)—868no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—438no—
561C2×#41—438no—
562C2×#41—431no—
563C2×#41—433no—
564C2×#41—433no—
565C2×#41—431no—
566C2×#41—433no—
567C2×#41—436no—
568C2×#41—433no—
569C2×#41—436no—
570C2×#41—433no—
571C2×#41—433no—
572C2×#41—433no—
573C2×#41—433no—
574C2×#41—433no—
575C2×#41—433no—
576C2×#41—436no—
577C2×#41—433no—
578C2×#41—433no—
579C2×#41—433no—
580C2×#41—433no—
581C2×#41—433no—
582C2×#41—431no—
583C2×#41—433no—
584C2×#41—433no—
585C2×#41—8612no—
586C2×#41—8612no—
587C2×#41—8612no—
588C2×#41—8612no—
589C2×#41—8612no—
590C2×#41—8612no—
591C2×#41—8612no—
592C2×#41—8612no—
593C2×#41—864no—
594C2×#41—864no—
595C2×#41C4×D4311yescharacteristic
596C2×#41C4×D4313yes—
597C2×#41C22×D4313yes—
598C2×#41C22×D4311yescharacteristic
599C22×Q8—431no—
600C22×Q8—433no—
601C22×Q8—433no—
602C22×Q8—431no—
603C22×Q8—433no—
604C22×Q8—433no—
605C22×Q8C4×D4311yescharacteristic
606C22×D4—433no—
607C22×D4—433no—
608C22×D4—436no—
609C22×D4—433no—
610C22×D4—433no—
611C22×D4—436no—
612C22×D4—433no—
613C22×D4—436no—
614C22×D4—433no—
615C22×D4—433no—
616C22×D4—433no—
617C22×D4C4×D4313yes—
618C23×C4—433no—
619C23×C4—436no—
620C23×C4—433no—
621C23×C4C22×D4313yes—
622#131—24no—
623#131—24no—
624#131—8612no—
625#131—8612no—
626#131—8612no—
627#131—8612no—
628#131—864no—
629#131—864no—
630C2×M16—433no—
631C2×M16—433no—
632C2×M16—433no—
633C2×M16—431no—
634C2×M16—436no—
635C2×M16—433no—
636C2×M16—433no—
637C2×M16—8612no—
638C2×M16—8612no—
639C2×M16—8612no—
640C2×M16C22×D4313yes—
641C2×M16C22×D4313yes—
642C22×C8—433no—
643C22×C8—433no—
644C22×C8—431no—
645C22×C8—433no—
646C22×C8—433no—
647C22×C8—433no—
648C22×C8—436no—
649C22×C8—8612no—
650C22×C8C22×D4313yes—
651C22×C8C22×D4313yes—
652C22⋊C8—433no—
653C22⋊C8—431no—
654C22⋊C8—436no—
655C22⋊C8—433no—
656C22⋊C8—433no—
657C22⋊C8—433no—
658C22⋊C8—431no—
659C22⋊C8—433no—
660C22⋊C8—431no—
661C22⋊C8—436no—
662C22⋊C8—436no—
663C22⋊C8—433no—
664C22⋊C8—433no—
665C22⋊C8—433no—
666C22⋊C8—433no—
667C22⋊C8C22×D4313yes—
668C22⋊C8C22×D4316yes—
669C22⋊C8C22×D4311yescharacteristic
670C22⋊C8C22×D4313yes—
671C22⋊C8C22×D4313yes—
672C24—433no—
673C24—436no—
674C24—433no—
675C24C2×C4×D4313yes—
676#41—24no—
677#41—212no—
678#41—26no—
679#41—26no—
680#41—438no—
681#41—4324no—
682#41—4312no—
683#41—4312no—
684#41—862no—
685#41—866no—
686#41—866no—
687#41—862no—
688#41—866no—
689#41—866no—
690#41—866no—
691#41—866no—
692#41—8612no—
693#41—8612no—
694#41—8612no—
695#41—8612no—
696#41—8624no—
697#41—8612no—
698#41—8612no—
699#41—8624no—
700#41—8612no—
701#41—8612no—
702#41—8624no—
703#41—8612no—
704#41—8612no—
705#41—864no—
706#41—8612no—
707#41—866no—
708#41—866no—
709#41D4×D4314yes—
710#41D4×D4314yes—
711C2×Q8—24no—
712C2×Q8—438no—
713C2×Q8—433no—
714C2×Q8—433no—
715C2×Q8—433no—
716C2×Q8—431no—
717C2×Q8—433no—
718C2×Q8—433no—
719C2×Q8—8612no—
720C2×Q8—8612no—
721C2×Q8—8612no—
722C2×Q8—8612no—
723C2×Q8—864no—
724C2×Q8C2×C4×D4313yes—
725C2×Q8C2×C4×D4311yescharacteristic
726C2×D4—212no—
727C2×D4—436no—
728C2×D4—4324no—
729C2×D4—433no—
730C2×D4—433no—
731C2×D4—431no—
732C2×D4—433no—
733C2×D4—433no—
734C2×D4—433no—
735C2×D4—431no—
736C2×D4—433no—
737C2×D4—436no—
738C2×D4—433no—
739C2×D4—433no—
740C2×D4—433no—
741C2×D4—431no—
742C2×D4—433no—
743C2×D4—433no—
744C2×D4—8612no—
745C2×D4—8612no—
746C2×D4—8612no—
747C2×D4—8612no—
748C2×D4—8624no—
749C2×D4—8612no—
750C2×D4—8624no—
751C2×D4—8624no—
752C2×D4—8612no—
753C2×D4—8612no—
754C2×D4C2×C4×D4316yes—
755C2×D4C2×C4×D4313yes—
756C2×D4C2×C4×D4313yes—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—433no—
760C22×C4—433no—
761C22×C4—433no—
762C22×C4—4312no—
763C22×C4—4312no—
764C22×C4—431no—
765C22×C4—433no—
766C22×C4—436no—
767C22×C4—433no—
768C22×C4—436no—
769C22×C4—436no—
770C22×C4—433no—
771C22×C4—433no—
772C22×C4—433no—
773C22×C4—431no—
774C22×C4—8612no—
775C22×C4—8612no—
776C22×C4—866no—
777C22×C4—866no—
778C22×C4C2×C4×D4313yes—
779C22×C4C2×C4×D4313yes—
780C22×C4C2×C4×D4313yes—
781C22×C4C23×D4313yes—
782C22×C4C23×D4311yescharacteristic
783C22×C4C23×D4313yes—
784M16—26no—
785M16—26no—
786M16—862no—
787M16—866no—
788M16—866no—
789M16—866no—
790M16—8612no—
791M16—866no—
792M16—866no—
793C2×C8—26no—
794C2×C8—26no—
795C2×C8—431no—
796C2×C8—431no—
797C2×C8—433no—
798C2×C8—433no—
799C2×C8—862no—
800C2×C8—866no—
801C2×C8—866no—
802C2×C8—866no—
803C2×C8—8612no—
804C2×C8—866no—
805C2×C8—866no—
806C2×C8C23×D4311yescharacteristic
807C2×C8C23×D4313yes—
808C2×C8C23×D4313yes—
809C2×C8C23×D4311yescharacteristic
810C23—26no—
811C23—43no—
812C23—43no—
813C23—431no—
814C23—433no—
815C23—4312no—
816C23—433no—
817C23—431no—
818C23—8612no—
819C23—866no—
820C23—1723no—
821C23—1723no—
822C23—1726no—
823C23—1726no—
824C23—1723no—
825C23—1723no—
826C23C22×C4×D4313yes—
827C23C22×C4×D4311yescharacteristic
828C23C22×C4×D4313yes—
829Q8—26no—
830Q8—4312no—
831Q8—862no—
832Q8—866no—
833Q8—866no—
834Q8—866no—
835Q8—866no—
836Q8C22⋊C4×D4314yes—
837D4—212no—
838D4—26no—
839D4—4324no—
840D4—4312no—
841D4—862no—
842D4—866no—
843D4—866no—
844D4—866no—
845D4—862no—
846D4—866no—
847D4—866no—
848D4—866no—
849D4—862no—
850D4—866no—
851D4—866no—
852D4—866no—
853D4—8612no—
854D4—866no—
855D4C22⋊C4×D43112yes—
856C2×C4—26no—
857C2×C4—26no—
858C2×C4—26no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—23no—
862C2×C4—23no—
863C2×C4—4312no—
864C2×C4—431no—
865C2×C4—433no—
866C2×C4—4312no—
867C2×C4—4312no—
868C2×C4—432no—
869C2×C4—436no—
870C2×C4—436no—
871C2×C4—432no—
872C2×C4—433no—
873C2×C4—431no—
874C2×C4—8612no—
875C2×C4—8612no—
876C2×C4—8612no—
877C2×C4—866no—
878C2×C4—866no—
879C2×C4—866no—
880C2×C4—863no—
881C2×C4—863no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4C22×C4×D4313yes—
885C2×C4C22×C4×D4311yescharacteristic
886C2×C4C22×C4×D4313yes—
887C2×C4C2×D4×D4316yes—
888C2×C4C2×D4×D4316yes—
889C2×C4C24×D4311yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—861no—
895C8—863no—
896C8—863no—
897C8—861no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—432no—
908C22—436no—
909C22—863no—
910C22—861no—
911C22—863no—
912C22—861no—
913C22—863no—
914C22—861no—
915C22—861no—
916C22—863no—
917C22—861no—
918C22—863no—
919C22—3446no—
920C22—34412no—
921C22—17212no—
922C22C2×C22⋊C4×D4316yes—
923C22C23×C4×D4311yescharacteristic
924C4—21no—
925C4—23no—
926C4—432no—
927C4—436no—
928C4—863no—
929C4—861no—
930C4C2×C22⋊C4×D4316yes—
931C4C22×D4×D4311yescharacteristic
932C4C22×D4×D4311yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—866no—
937C2—862no—
938C2—1721no—
939C2—1723no—
940C2C22×C22⋊C4×D4311yescharacteristic
941C2#1914930611yescharacteristic
942C2#1914930811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2880C2
prime radicalC2×#14583735C2
cosocleC2×C4×C43C25
hypercenter#2880D43
hypocenterC43#60065
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#14583664C2semidirect
3. C2×#131×D43C2semidirect
4. #19143045C2semidirect
5. #19143044C2semidirect
6. #19143043C2semidirect
7. #19143043C2semidirect
8. #19143042C2semidirect
9. #19143042C2semidirect
10. #19143041C2semidirect
11. #19143038C2semidirect
12. #19143037C2semidirect
13. C2×#14582864C2semidirect
14. #408×D43C2semidirect
15. C43×#2880C2semidirect
33. C2×#13063333C22semidirect
34. C2×#13063333C22semidirect
35. C2×#13063332C22semidirect
36. C2×#13063332C22semidirect
37. C2×#13063331C22semidirect
38. C2×#13063331C22semidirect
40. C22×#10621872C22semidirect
41. C2×M16×D43C22semidirect
42. C2×M16×D43C22semidirect
43. C22×C8×D43C22semidirect
44. #14582867C22semidirect
45. #14582867C22semidirect
46. #14582866C22semidirect
47. #14582866C22semidirect
48. #14582865C22semidirect
49. #14582865C22semidirect
50. #14582864C22semidirect
51. #14582864C22semidirect
52. #14582864C22semidirect
53. #14582864C22semidirect
54. #14582864C22semidirect
55. #14582864C22semidirect
56. #14582864C22semidirect
57. #14582864C22semidirect
58. #14582864C22semidirect
59. #14582864C22semidirect
60. #14582864C22semidirect
61. #14582863C22semidirect
62. #14582862C22semidirect
63. #14582862C22semidirect
64. #14582861C22semidirect
65. #14582861C22semidirect
66. C2×C22⋊(C43⋊C8)C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
69. C22⋊C8×D43C22semidirect
70. C22⋊C8×D43C22semidirect
72. C2×#131×C43C22semidirect
73. C2×#131×C43C22semidirect
74. C43×#408C22semidirect
75. C43×#408C22semidirect
76. C43×#407C22semidirect
77. C2×C22⋊C8×C43C22semidirect
472. #2880D43semidirect
512. C2×#131C2×D43semidirect
513. C2×#131C2×D43semidirect
535. #408C2×D43semidirect
536. #408C2×D43semidirect
542. #407C2×D43semidirect
548. C2×C22⋊C8C2×D43semidirect
549. C43#60065semidirect

Maximal subgroups

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

subgroupindex
C2×#145837352
C2×#145836642
C2×#131×D432
#191430452
#191430442
#191430432
#191430422
#191430412
#191430382
#191430372
C2×#145828642
#408×D432
C43×#28802
#6006543