Finite Group Databasebeta

← #31719284

Subgroups — #31719284

Order 17152.

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×#16864232C211yesmaximal, characteristic
2C2×#16864161C211yesmaximal, characteristic, complemented
3C2×#131×D67C211yesmaximal, characteristic, complemented
4#22568659C213yesmaximal, complemented
5#22568658C211yesmaximal, characteristic, complemented
6#22568657C213yesmaximal, complemented
7#22568657C213yesmaximal, complemented
8#22568656C211yesmaximal, characteristic, complemented
9#22568656C211yesmaximal, characteristic, complemented
10#22568655C213yesmaximal, complemented
11#22568652C213yesmaximal, complemented
12#22568651C213yesmaximal, complemented
13C2×#16863361C213yesmaximal, complemented
14#408×D67C213yesmaximal, complemented
15C67×#2880C211yesmaximal, characteristic, complemented
16#16864232—28no—
17#16864232—28no—
18C2×#14524091C411yescharacteristic
19C2×#14524091C411yescharacteristic
20C2×#14524090C413yes—
21C2×#14524090C411yescharacteristic
22C2×#14524089C411yescharacteristic
23C2×#14524089C413yes—
24C2×#14524088C413yes—
25C2×#14524088C413yes—
26C22×#11761628C2213yes—
27C22×#11761628C2213yes—
28C2×#41×D67C2213yes—
29C2×#41×D67C2211yescharacteristic
30C2×#41×D67C2213yes—
31C2×#41×D67C2211yescharacteristic
32#16864161—28no—
33C2×#14524051C2213yescomplemented
34C2×#14524051C2213yescomplemented
35C2×#14524050C2211yescharacteristic, complemented
36C2×#14524050C2211yescharacteristic, complemented
37C2×#14524049C2213yescomplemented
38C2×#14524049C2213yescomplemented
39#131×D67—28no—
40C22×#11761611C2213yescomplemented
41C2×M16×D67C2213yescomplemented
42C2×M16×D67C2213yescomplemented
43C22×C8×D67C2213yescomplemented
44#16863364C2213yescomplemented
45#16863364C2213yescomplemented
46#16863363C2213yescomplemented
47#16863363C2213yescomplemented
48#16863362C2213yescomplemented
49#16863362C2213yescomplemented
50#16863361C2213yescomplemented
51#16863361C2216yescomplemented
52#16863361C2211yescharacteristic, complemented
53#16863361C2213yescomplemented
54#16863361C2213yescomplemented
55#16863361C2213yescomplemented
56#16863361C2213yescomplemented
57#16863361C2213yescomplemented
58#16863361C2213yescomplemented
59#16863361C2216yescomplemented
60#16863361C2216yescomplemented
61#16863360C2213yescomplemented
62#16863359C2213yescomplemented
63#16863359C2213yescomplemented
64#16863358C2216yescomplemented
65#16863358C2216yescomplemented
66C2×C22⋊(C67⋊C8)C2213yescomplemented
67C2×(C2×D67)⋊C8C2213yescomplemented
68C2×(C2×D67)⋊C8C2213yescomplemented
69C22⋊C8×D67C2216yescomplemented
70C22⋊C8×D67C2216yescomplemented
71C22×#41×C67C2211yescharacteristic
72C2×#131×C67C2211yescharacteristic, complemented
73C2×#131×C67C2211yescharacteristic, complemented
74#408×C67C2213yescomplemented
75#408×C67C2213yescomplemented
76#407×C67C2213yescomplemented
77C2×C22⋊C8×C67C2213yescomplemented
78#14524091—28no—
79#14524091—28no—
80#14524090—224no—
81#14524090—28no—
82#14524089—28no—
83#14524089—224no—
84#14524088—224no—
85#14524088—224no—
86C2×#11761629C2×C413yes—
87C2×#11761629C2×C413yes—
88C2×#11761629C2×C411yescharacteristic
89C2×#11761629C2×C411yescharacteristic
90C2×#11761628—212no—
91C2×#11761628—212no—
92C2×#11761628—212no—
93C2×#11761628—212no—
94C2×#11761628C2×C413yes—
95C2×#11761628C2×C413yes—
96C2×#11761628C2×C413yes—
97C2×#11761628C2×C413yes—
98C2×#11761628C2×C416yes—
99C2×#11761628C2×C413yes—
100C2×#11761628C2×C413yes—
101C2×#11761628C2313yes—
102C2×#11761628C2313yes—
103C2×#11761628C2311yescharacteristic
104C2×#11761628C2313yes—
105C2×#11761628C2313yes—
106C2×#11761628C2313yes—
107C2×#11761627C2×C413yes—
108C2×#11761627C2×C416yes—
109C2×#11761627C2×C416yes—
110C2×#11761627C2×C413yes—
111C2×#11761627C2×C413yes—
112C2×#11761627C2×C413yes—
113#41×D67—212no—
114#41×D67—212no—
115#41×D67—212no—
116#41×D67—212no—
117#41×D67—24no—
118#41×D67—24no—
119#41×D67D418yes—
120#41×D67D418yes—
121C22×Dic134C2×C413yes—
122C22×Dic134C2×C413yes—
123C2×Q8×D67C2×C413yes—
124C2×Q8×D67C2×C413yes—
125C2×Q8×D67C2×C411yescharacteristic
126C2×Q8×D67C2×C411yescharacteristic
127C22×D268C2×C413yes—
128C22×D268C2×C413yes—
129C22×C22⋊D67C2×C413yes—
130C22×C22⋊D67C2×C416yes—
131C22×C22⋊D67C2×C413yes—
132C2×D4×D67C2×C416yes—
133C2×D4×D67C2×C416yes—
134C2×D4×D67C2×C413yes—
135C2×D4×D67C2×C413yes—
136C2×D4×D67C2×C413yes—
137C2×D4×D67C2×C413yes—
138C22×C4×D67C2316yes—
139C22×C4×D67C2313yes—
140C22×C4×D67C2313yes—
141#14524051—212no—
142#14524051—212no—
143#14524050—24no—
144#14524050—24no—
145#14524049—212no—
146#14524049—212no—
147C2×#11761612C2313yes—
148C2×#11761612C2313yes—
149C2×#11761611—212no—
150C2×#11761611C2316yes—
151C2×#11761611C2313yes—
152C2×#11761611C2313yes—
153C2×#11761611C2313yes—
154C2×#11761611C2311yescharacteristic
155M16×D67—212no—
156M16×D67—212no—
157C22×C67⋊C8C2313yes—
158C22×C67⋊C8C2313yes—
159C2×C8×D67—212no—
160C2×C8×D67C2313yes—
161C2×C8×D67C2313yes—
162C2×C8×D67C2316yes—
163C2×C8×D67C2311yescharacteristic
164C2×C8×D67C2313yes—
165C22⋊(C67⋊C8)C2313yes—
166C22⋊(C67⋊C8)C2316yes—
167C22⋊(C67⋊C8)C2311yescharacteristic
168C22⋊(C67⋊C8)C2313yes—
169C22⋊(C67⋊C8)C2313yes—
170(C2×D67)⋊C8C2313yes—
171(C2×D67)⋊C8C2313yes—
172(C2×D67)⋊C8C2316yes—
173(C2×D67)⋊C8C2316yes—
174(C2×D67)⋊C8C2311yescharacteristic
175(C2×D67)⋊C8C2311yescharacteristic
176(C2×D67)⋊C8C2313yes—
177(C2×D67)⋊C8C2313yes—
178(C2×D67)⋊C8C2313yes—
179(C2×D67)⋊C8C2313yes—
180C2×#41×C67—24no—
181C2×#41×C67—24no—
182C2×#41×C67C2×C411yescharacteristic
183C2×#41×C67C2×C413yes—
184C2×#41×C67C2313yes—
185C2×#41×C67C2311yescharacteristic
186C22×Q8×C67C2×C411yescharacteristic
187C22×D4×C67C2×C413yes—
188C23×C4×C67C2313yes—
189#131×C67—24no—
190#131×C67—24no—
191C2×M16×C67C2313yes—
192C2×M16×C67C2313yes—
193C22×C8×C67C2313yes—
194C22×C8×C67C2313yes—
195C22⋊C8×C67C2313yes—
196C22⋊C8×C67C2316yes—
197C22⋊C8×C67C2313yes—
198C22⋊C8×C67C2311yescharacteristic
199C22⋊C8×C67C2313yes—
200C23×D67C22×C413yes—
201C23×D67C22×C416yes—
202C23×D67C22×C413yes—
203#11761629—24no—
204#11761629—212no—
205#11761629—212no—
206#11761629C22⋊C418yes—
207#11761628—26no—
208#11761628—26no—
209#11761628—224no—
210#11761628—212no—
211#11761628—212no—
212#11761628—212no—
213#11761628—212no—
214#11761628—212no—
215#11761628—26no—
216#11761628—26no—
217#11761628—26no—
218#11761628—26no—
219#11761628—22no—
220#11761628—26no—
221#11761628—26no—
222#11761628—22no—
223#11761628—212no—
224#11761628C2×D4112yes—
225#11761628C2×D4112yes—
226#11761627—212no—
227#11761627—224no—
228#11761627—224no—
229#11761627—212no—
230#11761627—212no—
231#11761627C22⋊C4124yes—
232C2×Dic134—212no—
233C2×Dic134—212no—
234C2×Dic134C22×C413yes—
235C2×Dic134C22×C413yes—
236C2×Dic134C22×C413yes—
237C2×Dic134C22×C411yescharacteristic
238C2×Dic134C22×C413yes—
239C2×Dic134C22×C413yes—
240Q8×D67—24no—
241Q8×D67—212no—
242Q8×D67—212no—
243Q8×D67C22⋊C418yes—
244C2×D268—212no—
245C2×D268—212no—
246C2×D268C22×C413yes—
247C2×D268C22×C413yes—
248C2×D268C22×C413yes—
249C2×D268C22×C413yes—
250C2×D268C22×C411yescharacteristic
251C2×D268C22×C413yes—
252C2×C22⋊D67—212no—
253C2×C22⋊D67—224no—
254C2×C22⋊D67—212no—
255C2×C22⋊D67C22×C416yes—
256C2×C22⋊D67C22×C413yes—
257C2×C22⋊D67C22×C413yes—
258C2×C22⋊D67C22×C413yes—
259C2×C22⋊D67C22×C413yes—
260C2×C22⋊D67C22×C413yes—
261C2×C22⋊D67C22×C411yescharacteristic
262C2×C22⋊D67C22×C411yescharacteristic
263C2×C22⋊D67C22×C413yes—
264C2×C22⋊D67C22×C416yes—
265D4×D67—224no—
266D4×D67—212no—
267D4×D67—224no—
268D4×D67—212no—
269D4×D67—212no—
270D4×D67C22⋊C4124yes—
271C22×Dic67C22×C413yes—
272C22×Dic67C22×C416yes—
273C22×Dic67C22×C413yes—
274C2×C4×D67—26no—
275C2×C4×D67—26no—
276C2×C4×D67—212no—
277C2×C4×D67—212no—
278C2×C4×D67C22×C416yes—
279C2×C4×D67C22×C413yes—
280C2×C4×D67C22×C413yes—
281C2×C4×D67C22×C416yes—
282C2×C4×D67C22×C413yes—
283C2×C4×D67C22×C413yes—
284C2×C4×D67C2×D4112yes—
285C2×C4×D67C2×D4112yes—
286C2×C4×D67C2413yes—
287C2×C4×D67C2411yescharacteristic
288C2×C4×D67C2411yescharacteristic
289C2×C4×D67C2413yes—
290#11761612—26no—
291#11761612—26no—
292#11761611—26no—
293#11761611—212no—
294#11761611—22no—
295#11761611—26no—
296#11761611—26no—
297C2×C67⋊C8—26no—
298C2×C67⋊C8—26no—
299C2×C67⋊C8C2411yescharacteristic
300C2×C67⋊C8C2413yes—
301C2×C67⋊C8C2413yes—
302C2×C67⋊C8C2411yescharacteristic
303C8×D67—22no—
304C8×D67—26no—
305C8×D67—26no—
306C8×D67—26no—
307C8×D67—212no—
308C24×C67C22×C413yes—
309#41×C67—24no—
310#41×C67—212no—
311#41×C67—26no—
312#41×C67—26no—
313#41×C67C2×D414yes—
314#41×C67C2×D414yes—
315C2×Q8×C67—24no—
316C2×Q8×C67C22×C413yes—
317C2×Q8×C67C22×C411yescharacteristic
318C2×D4×C67—212no—
319C2×D4×C67C22×C416yes—
320C2×D4×C67C22×C413yes—
321C2×D4×C67C22×C413yes—
322C22×C4×C67—26no—
323C22×C4×C67—26no—
324C22×C4×C67C22×C413yes—
325C22×C4×C67C22×C413yes—
326C22×C4×C67C22×C413yes—
327C22×C4×C67C2411yescharacteristic
328C22×C4×C67C2413yes—
329C22×C4×C67C2413yes—
330M16×C67—26no—
331M16×C67—26no—
332C2×C8×C67—26no—
333C2×C8×C67—26no—
334C2×C8×C67C2411yescharacteristic
335C2×C8×C67C2411yescharacteristic
336C2×C8×C67C2413yes—
337C2×C8×C67C2413yes—
338C23×C67—26no—
339C23×C67—43no—
340C23×C67—43no—
341C23×C67C23×C411yescharacteristic
342C23×C67C23×C413yes—
343C23×C67C23×C413yes—
344C22×D67—26no—
345C22×D67—212no—
346C22×D67—43no—
347C22×D67—43no—
348C22×D67—46no—
349C22×D67—46no—
350C22×D67—43no—
351C22×D67—43no—
352C22×D67C2×C22⋊C4112yes—
353C22×D67C23×C411yescharacteristic
354C22×D67C23×C413yes—
355C22×D67C23×C413yes—
356C22×D67C23×C411yescharacteristic
357Q8×C67—26no—
358Q8×C67C2×C22⋊C414yes—
359D4×C67—212no—
360D4×C67—26no—
361D4×C67C2×C22⋊C4112yes—
362C2×C4×C67—26no—
363C2×C4×C67—26no—
364C2×C4×C67—26no—
365C2×C4×C67—21no—
366C2×C4×C67—21no—
367C2×C4×C67—23no—
368C2×C4×C67—23no—
369C2×C4×C67C23×C411yescharacteristic
370C2×C4×C67C23×C413yes—
371C2×C4×C67C23×C413yes—
372C2×C4×C67C22×D416yes—
373C2×C4×C67C22×D416yes—
374C2×C4×C67C2511yescharacteristic
375C22⋊D67—212no—
376C22⋊D67—26no—
377C22⋊D67—26no—
378C22⋊D67—26no—
379C22⋊D67—22no—
380C22⋊D67—26no—
381C22⋊D67—26no—
382C22⋊D67—22no—
383C22⋊D67—26no—
384C22⋊D67C2×C22⋊C4124yes—
385C2×Dic67—26no—
386C2×Dic67—212no—
387C2×Dic67C2×C22⋊C4112yes—
388C2×Dic67C23×C413yes—
389C2×Dic67C23×C411yescharacteristic
390C2×Dic67C23×C411yescharacteristic
391C2×Dic67C23×C413yes—
392D268—26no—
393D268—26no—
394D268—26no—
395D268—22no—
396D268—26no—
397D268C2×C22⋊C4112yes—
398C4×D67—212no—
399C4×D67—26no—
400C4×D67—26no—
401C4×D67—21no—
402C4×D67—21no—
403C4×D67—23no—
404C4×D67—23no—
405C4×D67—212no—
406C4×D67C2×C22⋊C4112yes—
407C4×D67C2×C22⋊C4112yes—
408C4×D67C22×D412yes—
409C4×D67C22×D416yes—
410C4×D67C22×D416yes—
411C4×D67C22×D412yes—
412Dic134—26no—
413Dic134—26no—
414Dic134—26no—
415Dic134—22no—
416Dic134—26no—
417Dic134C2×C22⋊C4112yes—
418C8×C67—21no—
419C8×C67—21no—
420C8×C67—23no—
421C8×C67—23no—
422C67⋊C8—21no—
423C67⋊C8—23no—
424C67⋊C8—23no—
425C67⋊C8—21no—
426C22×C67—23no—
427C22×C67—23no—
428C22×C67—23no—
429C22×C67—21no—
430C22×C67—23no—
431C22×C67—23no—
432C22×C67—21no—
433C22×C67—21no—
434C22×C67—86no—
435C22×C67C22×C22⋊C416yes—
436C22×C67C24×C411yescharacteristic
437C2×D67—21no—
438C2×D67—23no—
439C2×D67—21no—
440C2×D67—23no—
441C2×D67—21no—
442C2×D67—23no—
443C2×D67—23no—
444C2×D67—21no—
445C2×D67—23no—
446C2×D67—21no—
447C2×D67—412no—
448C2×D67—812no—
449C2×D67—86no—
450C2×D67C22×C22⋊C416yes—
451C2×D67C22×C22⋊C412yes—
452C4×C67—21no—
453C4×C67—23no—
454C4×C67C22×C22⋊C416yes—
455C4×C67C23×D411yescharacteristic
456C4×C67C23×D411yescharacteristic
457Dic67—23no—
458Dic67—21no—
459Dic67C22×C22⋊C412yes—
460Dic67C22×C22⋊C416yes—
461#60065—671nomaximal, Sylow
462C2×C67—26no—
463C2×C67—43no—
464C2×C67—41no—
465C2×C67C23×C22⋊C411yescharacteristic
466C2×C67#357311yescharacteristic
467C2×C67#357311yescharacteristic
468D67—22no—
469D67—26no—
470D67—43no—
471D67—41no—
472C2×#585—671no—
473C2×#568—671no—
474C22×#131—671no—
475#2880—673no—
476#2880—673no—
477#2880—673no—
478#2880—673no—
479#2880—671no—
480#2880—671no—
481#2880—671no—
482#2880D6711yescharacteristic, complemented
483#2879—673no—
484#2879—673no—
485C2×#408—673no—
486C2×#408—673no—
487C67#6006511yescharacteristic, complemented, Sylow
488#585—1348no—
489#585—1348no—
490C2×2−1+4—671no—
491C2×2−1+4—673no—
492C2×2−1+4—671no—
493C2×2−1+4—671no—
494C2×H(5,𝔽2)—673no—
495C2×H(5,𝔽2)—671no—
496C2×H(5,𝔽2)—673no—
497C2×H(5,𝔽2)—673no—
498C22×#41—671no—
499C22×#41—673no—
500C22×#41—673no—
501C22×#41—671no—
502C22×#41—673no—
503C22×#41—673no—
504C22×#41C2×D6711yescharacteristic
505#568—1348no—
506C2×#131—671no—
507C2×#131—671no—
508C2×#131—673no—
509C2×#131—673no—
510C2×#131—673no—
511C2×#131—673no—
512C2×#131—1348no—
513C2×#131C2×D6711yescharacteristic, complemented
514C2×#131C2×D6711yescharacteristic, complemented
515C22×M16—673no—
516C22×M16—673no—
517C22×M16—673no—
518C23×C8—673no—
519#408—673no—
520#408—673no—
521#408—673no—
522#408—673no—
523#408—673no—
524#408—673no—
525#408—673no—
526#408—671no—
527#408—676no—
528#408—673no—
529#408—673no—
530#408—673no—
531#408—673no—
532#408—673no—
533#408—673no—
534#408—676no—
535#408—676no—
536#408C2×D6713yescomplemented
537#408C2×D6713yescomplemented
538#407—673no—
539#407—673no—
540#407—673no—
541#407—676no—
542#407—676no—
543#407C2×D6713yescomplemented
544C2×C22⋊C8—673no—
545C2×C22⋊C8—673no—
546C2×C22⋊C8—673no—
547C2×C22⋊C8—676no—
548C2×C22⋊C8—676no—
549C2×C22⋊C8C2×D6713yescomplemented
5502−1+4—1348no—
5512−1+4—1348no—
5522−1+4—1348no—
5532−1+4—13424no—
554H(5,𝔽2)—13424no—
555H(5,𝔽2)—13424no—
556H(5,𝔽2)—13424no—
557H(5,𝔽2)—1348no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—678no—
561C2×#41—678no—
562C2×#41—671no—
563C2×#41—673no—
564C2×#41—673no—
565C2×#41—671no—
566C2×#41—673no—
567C2×#41—676no—
568C2×#41—673no—
569C2×#41—676no—
570C2×#41—673no—
571C2×#41—673no—
572C2×#41—673no—
573C2×#41—673no—
574C2×#41—673no—
575C2×#41—673no—
576C2×#41—676no—
577C2×#41—673no—
578C2×#41—673no—
579C2×#41—673no—
580C2×#41—673no—
581C2×#41—673no—
582C2×#41—671no—
583C2×#41—673no—
584C2×#41—673no—
585C2×#41—13412no—
586C2×#41—13412no—
587C2×#41—13412no—
588C2×#41—13412no—
589C2×#41—13412no—
590C2×#41—13412no—
591C2×#41—13412no—
592C2×#41—13412no—
593C2×#41—1344no—
594C2×#41—1344no—
595C2×#41C4×D6711yescharacteristic
596C2×#41C4×D6713yes—
597C2×#41C22×D6713yes—
598C2×#41C22×D6711yescharacteristic
599C22×Q8—671no—
600C22×Q8—673no—
601C22×Q8—673no—
602C22×Q8—671no—
603C22×Q8—673no—
604C22×Q8—673no—
605C22×Q8C4×D6711yescharacteristic
606C22×D4—673no—
607C22×D4—673no—
608C22×D4—676no—
609C22×D4—673no—
610C22×D4—673no—
611C22×D4—676no—
612C22×D4—673no—
613C22×D4—676no—
614C22×D4—673no—
615C22×D4—673no—
616C22×D4—673no—
617C22×D4C4×D6713yes—
618C23×C4—673no—
619C23×C4—676no—
620C23×C4—673no—
621C23×C4C22×D6713yes—
622#131—24no—
623#131—24no—
624#131—13412no—
625#131—13412no—
626#131—13412no—
627#131—13412no—
628#131—1344no—
629#131—1344no—
630C2×M16—673no—
631C2×M16—673no—
632C2×M16—673no—
633C2×M16—671no—
634C2×M16—676no—
635C2×M16—673no—
636C2×M16—673no—
637C2×M16—13412no—
638C2×M16—13412no—
639C2×M16—13412no—
640C2×M16C22×D6713yes—
641C2×M16C22×D6713yes—
642C22×C8—673no—
643C22×C8—673no—
644C22×C8—671no—
645C22×C8—673no—
646C22×C8—673no—
647C22×C8—673no—
648C22×C8—676no—
649C22×C8—13412no—
650C22×C8C22×D6713yes—
651C22×C8C22×D6713yes—
652C22⋊C8—673no—
653C22⋊C8—671no—
654C22⋊C8—676no—
655C22⋊C8—673no—
656C22⋊C8—673no—
657C22⋊C8—673no—
658C22⋊C8—671no—
659C22⋊C8—673no—
660C22⋊C8—671no—
661C22⋊C8—676no—
662C22⋊C8—676no—
663C22⋊C8—673no—
664C22⋊C8—673no—
665C22⋊C8—673no—
666C22⋊C8—673no—
667C22⋊C8C22×D6713yes—
668C22⋊C8C22×D6716yes—
669C22⋊C8C22×D6711yescharacteristic
670C22⋊C8C22×D6713yes—
671C22⋊C8C22×D6713yes—
672C24—673no—
673C24—676no—
674C24—673no—
675C24C2×C4×D6713yes—
676#41—24no—
677#41—212no—
678#41—26no—
679#41—26no—
680#41—678no—
681#41—6724no—
682#41—6712no—
683#41—6712no—
684#41—1342no—
685#41—1346no—
686#41—1346no—
687#41—1342no—
688#41—1346no—
689#41—1346no—
690#41—1346no—
691#41—1346no—
692#41—13412no—
693#41—13412no—
694#41—13412no—
695#41—13412no—
696#41—13424no—
697#41—13412no—
698#41—13412no—
699#41—13424no—
700#41—13412no—
701#41—13412no—
702#41—13424no—
703#41—13412no—
704#41—13412no—
705#41—1344no—
706#41—13412no—
707#41—1346no—
708#41—1346no—
709#41D4×D6714yes—
710#41D4×D6714yes—
711C2×Q8—24no—
712C2×Q8—678no—
713C2×Q8—673no—
714C2×Q8—673no—
715C2×Q8—673no—
716C2×Q8—671no—
717C2×Q8—673no—
718C2×Q8—673no—
719C2×Q8—13412no—
720C2×Q8—13412no—
721C2×Q8—13412no—
722C2×Q8—13412no—
723C2×Q8—1344no—
724C2×Q8C2×C4×D6713yes—
725C2×Q8C2×C4×D6711yescharacteristic
726C2×D4—212no—
727C2×D4—676no—
728C2×D4—6724no—
729C2×D4—673no—
730C2×D4—673no—
731C2×D4—671no—
732C2×D4—673no—
733C2×D4—673no—
734C2×D4—673no—
735C2×D4—671no—
736C2×D4—673no—
737C2×D4—676no—
738C2×D4—673no—
739C2×D4—673no—
740C2×D4—673no—
741C2×D4—671no—
742C2×D4—673no—
743C2×D4—673no—
744C2×D4—13412no—
745C2×D4—13412no—
746C2×D4—13412no—
747C2×D4—13412no—
748C2×D4—13424no—
749C2×D4—13412no—
750C2×D4—13424no—
751C2×D4—13424no—
752C2×D4—13412no—
753C2×D4—13412no—
754C2×D4C2×C4×D6716yes—
755C2×D4C2×C4×D6713yes—
756C2×D4C2×C4×D6713yes—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—673no—
760C22×C4—673no—
761C22×C4—673no—
762C22×C4—6712no—
763C22×C4—6712no—
764C22×C4—671no—
765C22×C4—673no—
766C22×C4—676no—
767C22×C4—673no—
768C22×C4—676no—
769C22×C4—676no—
770C22×C4—673no—
771C22×C4—673no—
772C22×C4—673no—
773C22×C4—671no—
774C22×C4—13412no—
775C22×C4—13412no—
776C22×C4—1346no—
777C22×C4—1346no—
778C22×C4C2×C4×D6713yes—
779C22×C4C2×C4×D6713yes—
780C22×C4C2×C4×D6713yes—
781C22×C4C23×D6713yes—
782C22×C4C23×D6711yescharacteristic
783C22×C4C23×D6713yes—
784M16—26no—
785M16—26no—
786M16—1342no—
787M16—1346no—
788M16—1346no—
789M16—1346no—
790M16—13412no—
791M16—1346no—
792M16—1346no—
793C2×C8—26no—
794C2×C8—26no—
795C2×C8—671no—
796C2×C8—671no—
797C2×C8—673no—
798C2×C8—673no—
799C2×C8—1342no—
800C2×C8—1346no—
801C2×C8—1346no—
802C2×C8—1346no—
803C2×C8—13412no—
804C2×C8—1346no—
805C2×C8—1346no—
806C2×C8C23×D6711yescharacteristic
807C2×C8C23×D6713yes—
808C2×C8C23×D6713yes—
809C2×C8C23×D6711yescharacteristic
810C23—26no—
811C23—43no—
812C23—43no—
813C23—2683no—
814C23—2683no—
815C23—2683no—
816C23—2683no—
817C23—2686no—
818C23—2686no—
819C23—6712no—
820C23—671no—
821C23—673no—
822C23—673no—
823C23—671no—
824C23—13412no—
825C23—1346no—
826C23C22×C4×D6713yes—
827C23C22×C4×D6711yescharacteristic
828C23C22×C4×D6713yes—
829Q8—26no—
830Q8—6712no—
831Q8—1342no—
832Q8—1346no—
833Q8—1346no—
834Q8—1346no—
835Q8—1346no—
836Q8C22⋊C4×D6714yes—
837D4—212no—
838D4—26no—
839D4—6724no—
840D4—6712no—
841D4—1342no—
842D4—1346no—
843D4—1346no—
844D4—1346no—
845D4—1342no—
846D4—1346no—
847D4—1346no—
848D4—1346no—
849D4—1342no—
850D4—1346no—
851D4—1346no—
852D4—1346no—
853D4—13412no—
854D4—1346no—
855D4C22⋊C4×D67112yes—
856C2×C4—26no—
857C2×C4—26no—
858C2×C4—26no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—23no—
862C2×C4—23no—
863C2×C4—6712no—
864C2×C4—671no—
865C2×C4—673no—
866C2×C4—6712no—
867C2×C4—6712no—
868C2×C4—672no—
869C2×C4—676no—
870C2×C4—676no—
871C2×C4—672no—
872C2×C4—673no—
873C2×C4—671no—
874C2×C4—13412no—
875C2×C4—13412no—
876C2×C4—13412no—
877C2×C4—1346no—
878C2×C4—1346no—
879C2×C4—1346no—
880C2×C4—1343no—
881C2×C4—1343no—
882C2×C4—1341no—
883C2×C4—1341no—
884C2×C4C22×C4×D6713yes—
885C2×C4C22×C4×D6711yescharacteristic
886C2×C4C22×C4×D6713yes—
887C2×C4C2×D4×D6716yes—
888C2×C4C2×D4×D6716yes—
889C2×C4C24×D6711yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—1341no—
895C8—1343no—
896C8—1343no—
897C8—1341no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—26812no—
908C22—5366no—
909C22—53612no—
910C22—672no—
911C22—676no—
912C22—1343no—
913C22—1341no—
914C22—1341no—
915C22—1343no—
916C22—1341no—
917C22—1343no—
918C22—1341no—
919C22—1343no—
920C22—1341no—
921C22—1343no—
922C22C2×C22⋊C4×D6716yes—
923C22C23×C4×D6711yescharacteristic
924C4—21no—
925C4—23no—
926C4—672no—
927C4—676no—
928C4—1343no—
929C4—1341no—
930C4C2×C22⋊C4×D6716yes—
931C4C22×D4×D6711yescharacteristic
932C4C22×D4×D6711yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—2681no—
937C2—2683no—
938C2—1342no—
939C2—1346no—
940C2C22×C22⋊C4×D6711yescharacteristic
941C2#2257492011yescharacteristic
942C2#2257492211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D67
commutator, socleC22×C67C24×C4
FittingC67×#2880C2
prime radicalC2×#16864232C2
cosocleC2×C4×C67C25
hypercenter#2880D67
hypocenterC67#60065
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#16864161C2semidirect
3. C2×#131×D67C2semidirect
4. #22568659C2semidirect
5. #22568658C2semidirect
6. #22568657C2semidirect
7. #22568657C2semidirect
8. #22568656C2semidirect
9. #22568656C2semidirect
10. #22568655C2semidirect
11. #22568652C2semidirect
12. #22568651C2semidirect
13. C2×#16863361C2semidirect
14. #408×D67C2semidirect
15. C67×#2880C2semidirect
33. C2×#14524051C22semidirect
34. C2×#14524051C22semidirect
35. C2×#14524050C22semidirect
36. C2×#14524050C22semidirect
37. C2×#14524049C22semidirect
38. C2×#14524049C22semidirect
40. C22×#11761611C22semidirect
41. C2×M16×D67C22semidirect
42. C2×M16×D67C22semidirect
43. C22×C8×D67C22semidirect
44. #16863364C22semidirect
45. #16863364C22semidirect
46. #16863363C22semidirect
47. #16863363C22semidirect
48. #16863362C22semidirect
49. #16863362C22semidirect
50. #16863361C22semidirect
51. #16863361C22semidirect
52. #16863361C22semidirect
53. #16863361C22semidirect
54. #16863361C22semidirect
55. #16863361C22semidirect
56. #16863361C22semidirect
57. #16863361C22semidirect
58. #16863361C22semidirect
59. #16863361C22semidirect
60. #16863361C22semidirect
61. #16863360C22semidirect
62. #16863359C22semidirect
63. #16863359C22semidirect
64. #16863358C22semidirect
65. #16863358C22semidirect
66. C2×C22⋊(C67⋊C8)C22semidirect
67. C2×(C2×D67)⋊C8C22semidirect
68. C2×(C2×D67)⋊C8C22semidirect
69. C22⋊C8×D67C22semidirect
70. C22⋊C8×D67C22semidirect
72. C2×#131×C67C22semidirect
73. C2×#131×C67C22semidirect
74. #408×C67C22semidirect
75. #408×C67C22semidirect
76. #407×C67C22semidirect
77. C2×C22⋊C8×C67C22semidirect
482. #2880D67semidirect
487. C67#60065semidirect
513. C2×#131C2×D67semidirect
514. C2×#131C2×D67semidirect
536. #408C2×D67semidirect
537. #408C2×D67semidirect
543. #407C2×D67semidirect
549. C2×C22⋊C8C2×D67semidirect

Maximal subgroups

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

subgroupindex
C2×#168642322
C2×#168641612
C2×#131×D672
#225686592
#225686582
#225686572
#225686562
#225686552
#225686522
#225686512
C2×#168633612
#408×D672
C67×#28802
#6006567