Finite Group Databasebeta

← #35197384

Subgroups — #35197384

Order 20224.

11222 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099399C212yesmaximal, complemented
2#23777169C214yesmaximal, complemented
3#23777163C214yesmaximal, complemented
4#23777157C218yesmaximal, complemented
5#23777076C218yesmaximal, complemented
6#23777075C218yesmaximal, complemented
7#23777065C218yesmaximal, complemented
8#23777064C218yesmaximal, complemented
9#23776729C212yesmaximal, complemented
10#23776728C214yesmaximal, complemented
11C2×#19099144C211yesmaximal, characteristic, complemented
12#537×D79C214yesmaximal, complemented
13C2×#19099044C211yesmaximal, characteristic, complemented
14C2×#537×C79C211yesmaximal, characteristic, complemented
15#19099399—232no—
16C2×#14579209C2214yescomplemented
17C2×#14579208C2214yescomplemented
18C2×#14579208C2214yescomplemented
19C2×#14579207C2214yescomplemented
20C2×#14579207C2214yescomplemented
21C2×#14579206C2214yescomplemented
22C2×#14579206C2218yescomplemented
23C22×#11929624C2211yescharacteristic
24C22×#11929624C2218yescomplemented
25C22×#11929624C2212yescomplemented
26C2×#41×D79C2218yescomplemented
27C2×#41×D79C2218yescomplemented
28#19099231C22116yescomplemented
29#19099226C22116yescomplemented
30#19099223C22116yescomplemented
31#19099219C22116yescomplemented
32#19099215C22116yescomplemented
33#19099214C22116yescomplemented
34#19099213C22116yescomplemented
35#19099210C22116yescomplemented
36#19099204C22116yescomplemented
37#19099203C22132yescomplemented
38#19099202C22132yescomplemented
39#19099197C22116yescomplemented
40#19099197C22116yescomplemented
41D4×C22⋊D79C22116yescomplemented
42#19099144C2218yescomplemented
43#19099144C2214yescomplemented
44#19099144C2214yescomplemented
45#19099143C22116yescomplemented
46#19099142C22116yescomplemented
47#19099141C2214yescomplemented
48#19099141C2214yescomplemented
49#19099140C22116yescomplemented
50#19099137C2214yescomplemented
51#19099136C22116yescomplemented
52#19099134C2214yescomplemented
53#19099130C2214yescomplemented
54#19099129C22116yescomplemented
55#19099127C2214yescomplemented
56#19099122C2218yescomplemented
57#19099121C22116yescomplemented
58#19099109C2218yescomplemented
59#19099108C22116yescomplemented
60#19099076C22116yescomplemented
61#19099074C2218yescomplemented
62#19099073C22116yescomplemented
63#19099070C2218yescomplemented
64C2×#14579141C2214yescomplemented
65C22⋊Q8×D79C22116yescomplemented
66C2×#14579136C2214yescomplemented
67C2×#14579135C2214yescomplemented
68#121×D79C22116yescomplemented
69#121×D79C22116yescomplemented
70#19099044C2218yescomplemented
71#19099044C2218yescomplemented
72C2×#14579126C2212yescomplemented
73C2×#14579123C2212yescomplemented
74C2×C4×C22⋊D79C2214yescomplemented
75C2×#14579120C2211yescharacteristic, complemented
76C2×#14579119C2212yescomplemented
77C2×C4⋊C4×D79C2212yescomplemented
78C22×#41×C79C2212yescomplemented
79#537×C79C2218yescomplemented
80#537×C79C2214yescomplemented
81#537×C79C2214yescomplemented
82C2×C22⋊Q8×C79C2214yescomplemented
83C2×#121×C79C2214yescomplemented
84C2×#121×C79C2214yescomplemented
85C22×C4⋊C4×C79C2211yescharacteristic, complemented
86#14579209—232no—
87#14579208—232no—
88#14579208—232no—
89#14579207—232no—
90#14579207—232no—
91#14579206—232no—
92#14579206—264no—
93C2×#11929625C2318yes—
94C2×#11929625C2318yes—
95C2×#11929624—216no—
96C2×#11929624—264no—
97C2×#11929624D4116yescomplemented
98C2×#11929624C23116yes—
99C2×#11929624C2314yes—
100C2×#11929624C2314yes—
101C2×#11929624C23116yes—
102C2×#11929624C2314yes—
103C2×#11929624C2318yes—
104C2×#11929624C2318yes—
105C2×#11929624C2314yes—
106C2×#11929624C2314yes—
107C2×#11929624C2314yes—
108C2×#11929623C23116yes—
109C2×#11929623C2318yes—
110C2×#11929623C23116yes—
111C2×#11929623C2318yes—
112#41×D79—264no—
113#41×D79—264no—
114C22×Dic158C2318yes—
115C22×Dic158C2312yes—
116C22×Dic158C2311yescharacteristic
117C2×Q8×D79C2318yes—
118C2×Q8×D79C2318yes—
119C22×D316C2318yes—
120C22×D316C2312yes—
121C22×D316C2314yes—
122C22×D316C2311yescharacteristic
123C22×C22⋊D79C23116yes—
124C22×C22⋊D79C2314yes—
125C22×C22⋊D79C2312yes—
126C2×D4×D79C23116yes—
127C2×D4×D79C2318yes—
128C2×D4×D79C23116yes—
129C2×D4×D79C2318yes—
130C2×D4×D79C23116yes—
131C22×C4×D79C23116yes—
132C22×C4×D79C2314yes—
133C22×C4×D79C2314yes—
134C22×C4×D79C2312yes—
135#14579160C23116yes—
136#14579159C2318yes—
137#14579157C23116yes—
138#14579157C2318yes—
139#14579150C2318yes—
140#14579148C2318yes—
141#14579147C23132yes—
142#14579146C23132yes—
143#14579144C23116yes—
144#14579143C23132yes—
145#14579142C23116yes—
146#14579141C23116yes—
147#14579141C23116yes—
148#14579140C2318yes—
149#14579140C2318yes—
150#14579139C23132yes—
151#14579138C23132yes—
152#14579137C2318yes—
153#14579137C2318yes—
154#14579136C23116yes—
155#14579136C23116yes—
156#14579136C23116yes—
157#14579135C23116yes—
158#14579135C2318yes—
159#14579135C2318yes—
160#14579135C23116yes—
161#14579134C23132yes—
162#14579134C23132yes—
163#14579133C23116yes—
164#14579133C23132yes—
165#14579133C23116yes—
166#14579132C2318yes—
167#14579132C2318yes—
168#14579132C23116yes—
169#14579131C23132yes—
170#14579130C23116yes—
171#14579129C23132yes—
172#14579129C23116yes—
173#14579126C23116yes—
174D4×Dic79C23116yes—
175#14579123C23116yes—
176#14579123C23116yes—
177C4×C22⋊D79C23116yes—
178C4×C22⋊D79C23116yes—
179C4×C22⋊D79C23116yes—
180C4×C22⋊D79C23116yes—
181(C22⋊D79)⋊C4C23132yes—
182#14579120C2314yes—
183#14579120C2314yes—
184#14579119C23116yes—
185C2×C4⋊Dic79C2311yescharacteristic
186C2×C4⋊Dic79C2311yescharacteristic
187C2×C4⋊Dic79C2314yes—
188C2×Dic79⋊C4C2314yes—
189C4⋊C4×D79C23116yes—
190C4⋊C4×D79C23116yes—
191C2×C22⋊Dic79C2312yes—
192C2×(C2×D79)⋊C4C2318yes—
193C2×(C2×D79)⋊C4C2314yes—
194C22⋊C4×D79C23132yes—
195C2×C4×Dic79C2314yes—
196C2×C4×Dic79C2312yes—
197C2×#41×C79—216no—
198C2×#41×C79C2314yes—
199C2×#41×C79C2314yes—
200C2×#41×C79C2314yes—
201C2×#41×C79C2314yes—
202C22×Q8×C79C2312yes—
203C22×D4×C79C2314yes—
204C22×D4×C79C2312yes—
205C22×D4×C79C2314yes—
206C23×C4×C79C2314yes—
207C23×C4×C79C2312yes—
208C23×C4×C79C2311yescharacteristic
209C22⋊Q8×C79C23116yes—
210C22⋊Q8×C79C23116yes—
211#121×C79C23116yes—
212#121×C79C23116yes—
213#121×C79C23116yes—
214#121×C79C23116yes—
215C2×C4⋊C4×C79C2314yes—
216C2×C4⋊C4×C79C2312yes—
217C2×C4⋊C4×C79C2312yes—
218C2×C4⋊C4×C79C2314yes—
219C2×C4⋊C4×C79C2314yes—
220C2×C22⋊C4×C79C2318yes—
221C23×D79C24116yes—
222C23×D79C2414yes—
223C23×D79C2412yes—
224#11929625—232no—
225#11929625—232no—
226#11929624—232no—
227#11929624—264no—
228#11929624—232no—
229#11929624—216no—
230#11929624—216no—
231#11929624—216no—
232#11929624—216no—
233#11929624—264no—
234#11929624C2×D4132yescomplemented
235#11929624C2×D4132yescomplemented
236#11929623—264no—
237#11929623—232no—
238#11929623—232no—
239#11929623—264no—
240C2×Dic158—232no—
241C2×Dic158—28no—
242C2×Dic158C2×D418yescomplemented
243C2×Dic158C24116yes—
244C2×Dic158C2414yes—
245C2×Dic158C2414yes—
246C2×Dic158C2414yes—
247Q8×D79—232no—
248Q8×D79—232no—
249C2×D316—232no—
250C2×D316—28no—
251C2×D316—84no—
252C2×D316C2×D418yescomplemented
253C2×D316C2414yes—
254C2×D316C24116yes—
255C2×D316C2414yes—
256C2×D316C24116yes—
257C2×D316C2414yes—
258C2×C22⋊D79—216no—
259C2×C22⋊D79—264no—
260C2×C22⋊D79C2×D4116yescomplemented
261C2×C22⋊D79C24116yes—
262C2×C22⋊D79C2418yes—
263C2×C22⋊D79C24116yes—
264C2×C22⋊D79C2418yes—
265C2×C22⋊D79C24116yes—
266C2×C22⋊D79C24116yes—
267C2×C22⋊D79C2414yes—
268C2×C22⋊D79C2414yes—
269D4×D79—232no—
270D4×D79—232no—
271D4×D79—264no—
272D4×D79—264no—
273D4×D79—816no—
274C22×Dic79C2414yes—
275C22×Dic79C24116yes—
276C22×Dic79C2412yes—
277C22×Dic79C2412yes—
278C22×Dic79C2412yes—
279C2×C4×D79—264no—
280C2×C4×D79—216no—
281C2×C4×D79—84no—
282C2×C4×D79C2×D4116yescomplemented
283C2×C4×D79C24116yes—
284C2×C4×D79C24116yes—
285C2×C4×D79C2418yes—
286C2×C4×D79C2418yes—
287C2×C4×D79C24116yes—
288C2×C4×D79C2418yes—
289C4⋊Dic79C2414yes—
290C4⋊Dic79C24116yes—
291C4⋊Dic79C2414yes—
292Dic79⋊C4C24116yes—
293Dic79⋊C4C24116yes—
294Dic79⋊C4C24116yes—
295C22⋊Dic79C24116yes—
296C22⋊Dic79C2414yes—
297C22⋊Dic79C2414yes—
298C22⋊Dic79C24116yes—
299(C2×D79)⋊C4C24116yes—
300(C2×D79)⋊C4C24132yes—
301(C2×D79)⋊C4C24116yes—
302(C2×D79)⋊C4C24116yes—
303C4×Dic79C24116yes—
304C4×Dic79C2418yes—
305C24×C79C2414yes—
306C24×C79C2411yescharacteristic
307#41×C79—216no—
308#41×C79—216no—
309#41×C79—216no—
310#41×C79—216no—
311C2×Q8×C79—28no—
312C2×Q8×C79C2414yes—
313C2×Q8×C79C2414yes—
314C2×D4×C79—216no—
315C2×D4×C79—28no—
316C2×D4×C79—84no—
317C2×D4×C79C2418yes—
318C2×D4×C79C2414yes—
319C2×D4×C79C2418yes—
320C2×D4×C79C2414yes—
321C2×D4×C79C24116yes—
322C22×C4×C79—216no—
323C22×C4×C79—82no—
324C22×C4×C79C2×D418yescomplemented
325C22×C4×C79C2418yes—
326C22×C4×C79C2414yes—
327C22×C4×C79C2418yes—
328C22×C4×C79C2414yes—
329C22×C4×C79C2414yes—
330C22×C4×C79C2414yes—
331C22×C4×C79C2411yescharacteristic
332C22×C4×C79C2412yes—
333C22×C4×C79C2412yes—
334C22×C4×C79C2411yescharacteristic
335C4⋊C4×C79C2418yes—
336C4⋊C4×C79C2418yes—
337C4⋊C4×C79C24116yes—
338C22⋊C4×C79C24132yes—
339C23×C79—28no—
340C23×C79—41no—
341C23×C79—41no—
342C23×C79—44no—
343C23×C79—44no—
344C23×C79C22×D414yes—
345C23×C79C2518yes—
346C23×C79C2511yescharacteristic
347C23×C79C2511yescharacteristic
348C23×C79C2511yescharacteristic
349C22×D79—28no—
350C22×D79—232no—
351C22×D79—42no—
352C22×D79—42no—
353C22×D79—416no—
354C22×D79—44no—
355C22×D79—416no—
356C22×D79—44no—
357C22×D79C22×D418yes—
358C22×D79C2518yes—
359C22×D79C2514yes—
360Q8×C79—28no—
361Q8×C79—28no—
362D4×C79—216no—
363D4×C79—216no—
364D4×C79—28no—
365D4×C79—28no—
366D4×C79—416no—
367C2×C4×C79—28no—
368C2×C4×C79—216no—
369C2×C4×C79—216no—
370C2×C4×C79—44no—
371C2×C4×C79—44no—
372C2×C4×C79—44no—
373C2×C4×C79C22×D418yes—
374C2×C4×C79C22×D414yes—
375C2×C4×C79C22×D414yes—
376C2×C4×C79C22×D418yes—
377C2×C4×C79C2518yes—
378C2×C4×C79C2518yes—
379C2×C4×C79C2512yes—
380C2×C4×C79C2512yes—
381C22⋊D79—216no—
382C22⋊D79—216no—
383C22⋊D79—232no—
384C22⋊D79—232no—
385C22⋊D79—416no—
386C22⋊D79—416no—
387C22⋊D79C22×D4116yes—
388C22⋊D79C22×D4116yes—
389C2×Dic79—28no—
390C2×Dic79—232no—
391C2×Dic79—42no—
392C2×Dic79—42no—
393C2×Dic79C22×D418yes—
394C2×Dic79C2514yes—
395C2×Dic79C2514yes—
396C2×Dic79C2518yes—
397C2×Dic79C2514yes—
398D316—232no—
399D316—28no—
400D316—28no—
401D316—416no—
402D316C22×D4116yes—
403C4×D79—232no—
404C4×D79—216no—
405C4×D79—216no—
406C4×D79—232no—
407C4×D79—416no—
408C4×D79C22×D4132yes—
409Dic158—28no—
410Dic158—28no—
411Dic158—232no—
412Dic158C22×D4116yes—
413C22×C79—21no—
414C22×C79—21no—
415C22×C79—21no—
416C22×C79—21no—
417C22×C79—21no—
418C22×C79—21no—
419C22×C79—28no—
420C22×C79—28no—
421C22×C79—28no—
422C22×C79—44no—
423C22×C79—88no—
424C22×C79C23×D412yes—
425C22×C79C23×D412yes—
426C22×C79C23×D412yes—
427C22×C79C2611yescharacteristic
428C2×D79—24no—
429C2×D79—24no—
430C2×D79—28no—
431C2×D79—28no—
432C2×D79—28no—
433C2×D79—48no—
434C2×D79—832no—
435C2×D79—88no—
436C2×D79C23×D418yes—
437C4×C79—28no—
438C4×C79—28no—
439C4×C79C23×D414yes—
440C4×C79C23×D414yes—
441Dic79—28no—
442Dic79—24no—
443Dic79—24no—
444Dic79C23×D418yes—
445#62853—791nomaximal, Sylow
446C2×C79—22no—
447C2×C79—22no—
448C2×C79—22no—
449C2×C79—48no—
450C2×C79C24×D411yescharacteristic
451C2×C79H(7,𝔽2)11yescharacteristic
452C2×C792−1+611yescharacteristic
453D79—28no—
454D79—48no—
455C2×#585—792no—
456#3497—794no—
457#3496—794no—
458#3496—798no—
459#3489—798no—
460#3489—798no—
461#3488—798no—
462#3488—798no—
463#3449—792no—
464#3449—794no—
465C2×#537—794no—
466C2×#537—791no—
467C2×#537D7911yescharacteristic, complemented
468C2×#520—791no—
469C79#6285311yescharacteristic, complemented, Sylow
470#585—15832no—
471C2×2−1+4—794no—
472C2×2−1+4—794no—
473C2×2−1+4—794no—
474C2×H(5,𝔽2)—794no—
475C2×H(5,𝔽2)—794no—
476C2×H(5,𝔽2)—794no—
477C2×H(5,𝔽2)—798no—
478C22×#41—798no—
479C22×#41—798no—
480C22×#41—791no—
481C22×#41—792no—
482C22×#41—798no—
483C22×#41C2×D7912yescomplemented
484#550—7916no—
485D4×Q8—7916no—
486#548—7916no—
487#548—7916no—
488#547—7916no—
489#547—7916no—
490#547—7916no—
491#546—7916no—
492#546—7932no—
493#546—7916no—
494#546—7932no—
495D42—7916no—
496D42—7916no—
497D42—7916no—
498#537—794no—
499#537—794no—
500#537—7916no—
501#537—7916no—
502#537—7916no—
503#537—794no—
504#537—798no—
505#537—794no—
506#537C2×D7914yescomplemented
507#537C2×D7918yescomplemented
508#537C2×D7914yescomplemented
509#536—794no—
510#536—794no—
511#536—7916no—
512#535—794no—
513#535—794no—
514#535—7916no—
515#534—798no—
516#534—7916no—
517#532—798no—
518#532—7916no—
519#525—798no—
520#525—798no—
521#525—7916no—
522#525—7916no—
523C2×C22⋊Q8—7916no—
524C2×C22⋊Q8—794no—
525C2×C22⋊Q8C2×D7914yescomplemented
526C2×#121—794no—
527C2×#121—7916no—
528C2×#121—7916no—
529C2×#121—794no—
530C2×#121C2×D7914yescomplemented
531C2×#121C2×D7914yescomplemented
532#520—798no—
533#520—798no—
534C2×C4×Q8—792no—
535C2×C4×D4—794no—
536C2×C4×D4—792no—
537C2×#117—791no—
538C2×#117—792no—
539C22×C4⋊C4—792no—
540C22×C4⋊C4C2×D7911yescharacteristic, complemented
5412−1+4—15832no—
5422−1+4—15832no—
5432−1+4—15832no—
544H(5,𝔽2)—15864no—
545H(5,𝔽2)—15832no—
546H(5,𝔽2)—15832no—
547H(5,𝔽2)—15832no—
548C2×#41—216no—
549C2×#41—798no—
550C2×#41—798no—
551C2×#41—798no—
552C2×#41—7916no—
553C2×#41—7916no—
554C2×#41—798no—
555C2×#41—7916no—
556C2×#41—794no—
557C2×#41—794no—
558C2×#41—794no—
559C2×#41—794no—
560C2×#41—7916no—
561C2×#41—794no—
562C2×#41—794no—
563C2×#41—798no—
564C2×#41—7916no—
565C2×#41—798no—
566C2×#41—15864no—
567C2×#41—15864no—
568C2×#41—15864no—
569C2×#41—15816no—
570C2×#41C22×D7914yes—
571C2×#41C22×D7914yes—
572C2×#41C22×D7914yes—
573C2×#41C22×D7914yes—
574C22×Q8—798no—
575C22×Q8—798no—
576C22×Q8—791no—
577C22×Q8—792no—
578C22×Q8—798no—
579C22×Q8C22×D7912yes—
580C22×D4—792no—
581C22×D4—794no—
582C22×D4—7916no—
583C22×D4—7916no—
584C22×D4—7916no—
585C22×D4—798no—
586C22×D4—7916no—
587C22×D4—798no—
588C22×D4—791no—
589C22×D4—794no—
590C22×D4—792no—
591C22×D4—798no—
592C22×D4C22×D7914yes—
593C22×D4C22×D7912yes—
594C22×D4C22×D7914yes—
595C23×C4—792no—
596C23×C4—794no—
597C23×C4—7916no—
598C23×C4—794no—
599C23×C4C22×D7914yes—
600C23×C4C22×D7912yes—
601C23×C4C22×D7911yescharacteristic
602C4⋊Q8—798no—
603C4⋊Q8—7916no—
604#127—798no—
605#127—7916no—
606#124—798no—
607#124—798no—
608#124—7932no—
609#123—7916no—
610#123—7916no—
611#123—7932no—
612#123—7932no—
613C22⋊Q8—798no—
614C22⋊Q8—798no—
615C22⋊Q8—798no—
616C22⋊Q8—798no—
617C22⋊Q8—7916no—
618C22⋊Q8—7932no—
619C22⋊Q8—7916no—
620C22⋊Q8—7932no—
621C22⋊Q8C22×D79116yes—
622C22⋊Q8C22×D79116yes—
623#121—798no—
624#121—7916no—
625#121—7916no—
626#121—7932no—
627#121—798no—
628#121—7916no—
629#121—798no—
630#121—7916no—
631#121—7916no—
632#121—798no—
633#121—7916no—
634#121—7916no—
635#121—7916no—
636#121—7932no—
637#121—7932no—
638#121C22×D79116yes—
639#121C22×D79116yes—
640#121C22×D79116yes—
641#121C22×D79116yes—
642#120—7916no—
643#120—7916no—
644#120—7932no—
645#120—7932no—
646C4×Q8—7916no—
647C4×D4—7916no—
648C4×D4—7916no—
649C4×D4—7916no—
650C4×D4—7916no—
651C4×D4—7916no—
652C4×D4—7916no—
653C4×D4—7916no—
654C4×D4—7932no—
655#117—794no—
656#117—794no—
657#117—7916no—
658C2×C4⋊C4—791no—
659C2×C4⋊C4—794no—
660C2×C4⋊C4—791no—
661C2×C4⋊C4—794no—
662C2×C4⋊C4—7916no—
663C2×C4⋊C4—7916no—
664C2×C4⋊C4C22×D7912yes—
665C2×C4⋊C4C22×D7912yes—
666C2×C4⋊C4C22×D7914yes—
667C2×C4⋊C4C22×D7914yes—
668C2×C4⋊C4C22×D7914yes—
669C2×C22⋊C4—792no—
670C2×C22⋊C4—794no—
671C2×C22⋊C4—798no—
672C2×C22⋊C4—7932no—
673C2×C22⋊C4C22×D7918yes—
674C2×C42—792no—
675C2×C42—794no—
676C24—792no—
677C24—7916no—
678C24—794no—
679C24C23×D7914yes—
680C24C23×D7911yescharacteristic
681#41—216no—
682#41—216no—
683#41—216no—
684#41—216no—
685#41—7932no—
686#41—7932no—
687#41—15864no—
688#41—15864no—
689#41—15832no—
690#41—15832no—
691#41—15864no—
692#41—15832no—
693#41—15832no—
694#41—15864no—
695#41—15832no—
696#41—15832no—
697#41—15816no—
698#41—15816no—
699#41—15816no—
700#41—15816no—
701C2×Q8—28no—
702C2×Q8—794no—
703C2×Q8—794no—
704C2×Q8—7916no—
705C2×Q8—794no—
706C2×Q8—798no—
707C2×Q8—15832no—
708C2×Q8—15832no—
709C2×Q8—15832no—
710C2×Q8—1588no—
711C2×Q8C23×D7914yes—
712C2×Q8C23×D7914yes—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—84no—
716C2×D4—7916no—
717C2×D4—7916no—
718C2×D4—794no—
719C2×D4—794no—
720C2×D4—7916no—
721C2×D4—7916no—
722C2×D4—798no—
723C2×D4—798no—
724C2×D4—7916no—
725C2×D4—7916no—
726C2×D4—794no—
727C2×D4—7916no—
728C2×D4—794no—
729C2×D4—794no—
730C2×D4—798no—
731C2×D4—6324no—
732C2×D4—63216no—
733C2×D4—15832no—
734C2×D4—15832no—
735C2×D4—15864no—
736C2×D4—15832no—
737C2×D4—15864no—
738C2×D4—15864no—
739C2×D4—15816no—
740C2×D4—1588no—
741C2×D4C23×D7918yes—
742C2×D4C23×D7918yes—
743C2×D4C23×D7914yes—
744C2×D4C23×D7914yes—
745C2×D4C23×D79116yes—
746C22×C4—216no—
747C22×C4—82no—
748C22×C4—792no—
749C22×C4—792no—
750C22×C4—7916no—
751C22×C4—792no—
752C22×C4—798no—
753C22×C4—7916no—
754C22×C4—794no—
755C22×C4—7916no—
756C22×C4—7916no—
757C22×C4—7916no—
758C22×C4—798no—
759C22×C4—798no—
760C22×C4—6324no—
761C22×C4—15864no—
762C22×C4—15816no—
763C22×C4D4×D7918yescomplemented
764C22×C4C23×D7914yes—
765C22×C4C23×D7918yes—
766C22×C4C23×D7918yes—
767C22×C4C23×D7914yes—
768C22×C4C23×D7914yes—
769C22×C4C23×D7914yes—
770C22×C4C23×D7911yescharacteristic
771C22×C4C23×D7911yescharacteristic
772C22×C4C23×D7912yes—
773C22×C4C23×D7912yes—
774C4⋊C4—7916no—
775C4⋊C4—7916no—
776C4⋊C4—7916no—
777C4⋊C4—794no—
778C4⋊C4—7916no—
779C4⋊C4—794no—
780C4⋊C4C23×D7918yes—
781C4⋊C4C23×D79116yes—
782C4⋊C4C23×D7918yes—
783C22⋊C4—7916no—
784C22⋊C4—794no—
785C22⋊C4—794no—
786C22⋊C4—7916no—
787C22⋊C4—7916no—
788C22⋊C4—7932no—
789C22⋊C4—7916no—
790C22⋊C4—7916no—
791C22⋊C4C23×D79132yes—
792C42—7916no—
793C42—798no—
794C23—28no—
795C23—41no—
796C23—41no—
797C23—44no—
798C23—44no—
799C23—3162no—
800C23—3162no—
801C23—3164no—
802C23—31616no—
803C23—3164no—
804C23—31616no—
805C23—798no—
806C23—794no—
807C23—798no—
808C23—15832no—
809C23—1588no—
810C23C2×D4×D7914yes—
811C23C24×D7918yes—
812C23C24×D7911yescharacteristic
813C23C24×D7911yescharacteristic
814C23C24×D7911yescharacteristic
815Q8—28no—
816Q8—28no—
817Q8—7916no—
818Q8—15832no—
819Q8—1588no—
820Q8—1588no—
821D4—216no—
822D4—216no—
823D4—28no—
824D4—28no—
825D4—416no—
826D4—31616no—
827D4—31616no—
828D4—31616no—
829D4—7916no—
830D4—7916no—
831D4—7916no—
832D4—15832no—
833D4—15832no—
834D4—15832no—
835D4—15816no—
836D4—15816no—
837D4—1588no—
838D4—1588no—
839C2×C4—28no—
840C2×C4—216no—
841C2×C4—216no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—31616no—
846C2×C4—3162no—
847C2×C4—3162no—
848C2×C4—794no—
849C2×C4—798no—
850C2×C4—7932no—
851C2×C4—794no—
852C2×C4—794no—
853C2×C4—798no—
854C2×C4—15832no—
855C2×C4—15832no—
856C2×C4—15832no—
857C2×C4—1588no—
858C2×C4—15816no—
859C2×C4—15816no—
860C2×C4C2×D4×D7918yes—
861C2×C4C2×D4×D7914yes—
862C2×C4C2×D4×D7918yes—
863C2×C4C2×D4×D7914yes—
864C2×C4C24×D7918yes—
865C2×C4C24×D7918yes—
866C2×C4C24×D7912yes—
867C2×C4C24×D7912yes—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—28no—
875C22—28no—
876C22—28no—
877C22—44no—
878C22—88no—
879C22—3168no—
880C22—798no—
881C22—6328no—
882C22—63232no—
883C22—1588no—
884C22—1588no—
885C22—1588no—
886C22—1584no—
887C22—1584no—
888C22C22×D4×D7912yes—
889C22C22×D4×D7912yes—
890C22C22×D4×D7912yes—
891C22C25×D7911yescharacteristic
892C4—28no—
893C4—28no—
894C4—798no—
895C4—1588no—
896C4—1584no—
897C4—1584no—
898C4C22×D4×D7914yes—
899C4C22×D4×D7914yes—
900C2—22no—
901C2—22no—
902C2—22no—
903C2—48no—
904C2—3168no—
905C2—1588no—
906C2C23×D4×D7911yescharacteristic
907C2#2377821011yescharacteristic
908C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC2×#537×C79C2
hypercenterC2×#537D79
hypocenterC79#62853
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#19099399C2semidirect
2. #23777169C2semidirect
3. #23777163C2semidirect
4. #23777157C2semidirect
5. #23777076C2semidirect
6. #23777075C2semidirect
7. #23777065C2semidirect
8. #23777064C2semidirect
9. #23776729C2semidirect
10. #23776728C2semidirect
11. C2×#19099144C2semidirect
12. #537×D79C2semidirect
13. C2×#19099044C2semidirect
14. C2×#537×C79C2semidirect
16. C2×#14579209C22semidirect
17. C2×#14579208C22semidirect
18. C2×#14579208C22semidirect
19. C2×#14579207C22semidirect
20. C2×#14579207C22semidirect
21. C2×#14579206C22semidirect
22. C2×#14579206C22semidirect
24. C22×#11929624C22semidirect
25. C22×#11929624C22semidirect
26. C2×#41×D79C22semidirect
27. C2×#41×D79C22semidirect
28. #19099231C22semidirect
29. #19099226C22semidirect
30. #19099223C22semidirect
31. #19099219C22semidirect
32. #19099215C22semidirect
33. #19099214C22semidirect
34. #19099213C22semidirect
35. #19099210C22semidirect
36. #19099204C22semidirect
37. #19099203C22semidirect
38. #19099202C22semidirect
39. #19099197C22semidirect
40. #19099197C22semidirect
41. D4×C22⋊D79C22semidirect
42. #19099144C22semidirect
43. #19099144C22semidirect
44. #19099144C22semidirect
45. #19099143C22semidirect
46. #19099142C22semidirect
47. #19099141C22semidirect
48. #19099141C22semidirect
49. #19099140C22semidirect
50. #19099137C22semidirect
51. #19099136C22semidirect
52. #19099134C22semidirect
53. #19099130C22semidirect
54. #19099129C22semidirect
55. #19099127C22semidirect
56. #19099122C22semidirect
57. #19099121C22semidirect
58. #19099109C22semidirect
59. #19099108C22semidirect
60. #19099076C22semidirect
61. #19099074C22semidirect
62. #19099073C22semidirect
63. #19099070C22semidirect
64. C2×#14579141C22semidirect
65. C22⋊Q8×D79C22semidirect
66. C2×#14579136C22semidirect
67. C2×#14579135C22semidirect
68. #121×D79C22semidirect
69. #121×D79C22semidirect
70. #19099044C22semidirect
71. #19099044C22semidirect
72. C2×#14579126C22semidirect
73. C2×#14579123C22semidirect
74. C2×C4×C22⋊D79C22semidirect
75. C2×#14579120C22semidirect
76. C2×#14579119C22semidirect
77. C2×C4⋊C4×D79C22semidirect
78. C22×#41×C79C22semidirect
79. #537×C79C22semidirect
80. #537×C79C22semidirect
81. #537×C79C22semidirect
82. C2×C22⋊Q8×C79C22semidirect
83. C2×#121×C79C22semidirect
84. C2×#121×C79C22semidirect
85. C22×C4⋊C4×C79C22semidirect
97. C2×#11929624D4semidirect
234. #11929624C2×D4semidirect
235. #11929624C2×D4semidirect
242. C2×Dic158C2×D4semidirect
252. C2×D316C2×D4semidirect
260. C2×C22⋊D79C2×D4semidirect
282. C2×C4×D79C2×D4semidirect
324. C22×C4×C79C2×D4semidirect
467. C2×#537D79semidirect
469. C79#62853semidirect
483. C22×#41C2×D79semidirect
506. #537C2×D79semidirect
507. #537C2×D79semidirect
508. #537C2×D79semidirect
525. C2×C22⋊Q8C2×D79semidirect
530. C2×#121C2×D79semidirect
531. C2×#121C2×D79semidirect
540. C22×C4⋊C4C2×D79semidirect
763. C22×C4D4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190993992
#237771692
#237771632
#237771572
#237770762
#237770752
#237770652
#237770642
#237767292
#237767282
C2×#190991442
#537×D792
C2×#190990442
C2×#537×C792
#6285379