Finite Group Databasebeta

← #35197386

Subgroups — #35197386

Order 20224.

11222 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099399C212yesmaximal, complemented
2#23777166C214yesmaximal, complemented
3#23777162C214yesmaximal, complemented
4#23777161C218yesmaximal, complemented
5#23777078C218yesmaximal, complemented
6#23777072C218yesmaximal, complemented
7#23777067C218yesmaximal, complemented
8#23777061C218yesmaximal, complemented
9#23776733C211yesmaximal, characteristic, complemented
10#23776728C214yesmaximal, complemented
11C2×#19099141C212yesmaximal, complemented
12#537×D79C214yesmaximal, complemented
13C2×#19099043C211yesmaximal, characteristic, complemented
14C79×#3449C211yesmaximal, 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#19099234C2218yescomplemented
29#19099233C2218yescomplemented
30D4×Dic158C2218yescomplemented
31#19099228C2218yescomplemented
32#19099222C22116yescomplemented
33#19099221C22116yescomplemented
34#19099218C2218yescomplemented
35#19099216C2218yescomplemented
36#19099211C22132yescomplemented
37#19099209C22116yescomplemented
38#19099206C22116yescomplemented
39#19099205C22132yescomplemented
40#19099200C22132yescomplemented
41D4×D316C2218yescomplemented
42#19099198C2218yescomplemented
43#19099195C22132yescomplemented
44#19099144C2212yescomplemented
45#19099144C2212yescomplemented
46#19099143C22116yescomplemented
47#19099142C22116yescomplemented
48#19099141C2218yescomplemented
49#19099141C2218yescomplemented
50#19099141C2218yescomplemented
51#19099141C2218yescomplemented
52#19099140C22116yescomplemented
53#19099139C2214yescomplemented
54#19099136C22116yescomplemented
55#19099132C2214yescomplemented
56#19099129C22116yescomplemented
57#19099125C2214yescomplemented
58#19099121C22116yescomplemented
59#19099113C2214yescomplemented
60#19099108C22116yescomplemented
61#19099076C22116yescomplemented
62#19099075C2218yescomplemented
63#19099073C22116yescomplemented
64C2×#14579140C2214yescomplemented
65C2×#14579137C2214yescomplemented
66C22⋊Q8×D79C22116yescomplemented
67C2×#14579135C2214yescomplemented
68C2×#14579133C2218yescomplemented
69C2×#14579132C2214yescomplemented
70#121×D79C22116yescomplemented
71#121×D79C22116yescomplemented
72#19099043C2218yescomplemented
73#19099043C2218yescomplemented
74C2×C4×Dic158C2212yescomplemented
75C2×C4×D316C2212yescomplemented
76C2×(C22⋊D79)⋊C4C2214yescomplemented
77C2×#14579119C2212yescomplemented
78C22×C4⋊Dic79C2211yescharacteristic, complemented
79C2×C4⋊C4×D79C2212yescomplemented
80C22×#41×C79C2212yescomplemented
81#537×C79C2212yescomplemented
82#537×C79C2212yescomplemented
83#536×C79C2214yescomplemented
84#535×C79C2214yescomplemented
85#534×C79C2214yescomplemented
86#532×C79C2214yescomplemented
87#525×C79C2218yescomplemented
88C2×#117×C79C2211yescharacteristic, complemented
89#14579209—232no—
90#14579208—232no—
91#14579208—232no—
92#14579207—232no—
93#14579207—232no—
94#14579206—232no—
95#14579206—264no—
96C2×#11929625C2318yes—
97C2×#11929625C2318yes—
98C2×#11929624—216no—
99C2×#11929624—264no—
100C2×#11929624D4116yescomplemented
101C2×#11929624C23116yes—
102C2×#11929624C2314yes—
103C2×#11929624C23116yes—
104C2×#11929624C2314yes—
105C2×#11929624C2318yes—
106C2×#11929624C2318yes—
107C2×#11929624C2314yes—
108C2×#11929624C2314yes—
109C2×#11929624C2314yes—
110C2×#11929624C2314yes—
111C2×#11929623C23116yes—
112C2×#11929623C2318yes—
113C2×#11929623C23116yes—
114C2×#11929623C2318yes—
115#41×D79—264no—
116#41×D79—264no—
117C22×Dic158C2312yes—
118C22×Dic158C2318yes—
119C22×Dic158C2311yescharacteristic
120C2×Q8×D79C2318yes—
121C2×Q8×D79C2318yes—
122C22×D316C2318yes—
123C22×D316C2312yes—
124C22×D316C2311yescharacteristic
125C22×C22⋊D79C23116yes—
126C22×C22⋊D79C2314yes—
127C22×C22⋊D79C2318yes—
128C22×C22⋊D79C2312yes—
129C2×D4×D79C23116yes—
130C2×D4×D79C2318yes—
131C2×D4×D79C23116yes—
132C2×D4×D79C2318yes—
133C2×D4×D79C23116yes—
134C23×Dic79C2312yes—
135C22×C4×D79C23116yes—
136C22×C4×D79C2314yes—
137C22×C4×D79C2314yes—
138C22×C4×D79C2312yes—
139#14579161C2314yes—
140#14579160C23116yes—
141#14579158C2314yes—
142#14579157C23116yes—
143#14579149C2318yes—
144#14579147C23132yes—
145#14579146C23132yes—
146#14579145C23116yes—
147#14579143C23132yes—
148#14579141C2318yes—
149#14579141C2318yes—
150#14579140C23116yes—
151#14579140C23116yes—
152#14579139C23132yes—
153#14579138C23132yes—
154#14579137C23116yes—
155#14579137C23116yes—
156#14579136C2318yes—
157#14579136C23116yes—
158#14579136C2318yes—
159#14579135C2318yes—
160#14579135C23116yes—
161#14579135C23116yes—
162#14579135C2318yes—
163#14579134C23132yes—
164#14579134C23132yes—
165#14579133C23132yes—
166#14579133C23132yes—
167#14579133C23132yes—
168#14579132C23116yes—
169#14579132C23116yes—
170#14579132C23116yes—
171#14579131C23116yes—
172#14579131C23132yes—
173#14579129C23132yes—
174C4×Dic158C2318yes—
175C4×Dic158C2318yes—
176C4×D316C2318yes—
177C4×D316C2318yes—
178C4×D316C2318yes—
179C4×D316C2318yes—
180D4×Dic79C23116yes—
181#14579123C23116yes—
182(C22⋊D79)⋊C4C23132yes—
183(C22⋊D79)⋊C4C23132yes—
184#14579119C23116yes—
185C2×C4⋊Dic79C2312yes—
186C2×C4⋊Dic79C2312yes—
187C2×C4⋊Dic79C2314yes—
188C2×C4⋊Dic79C2314yes—
189C2×Dic79⋊C4C2314yes—
190C2×Dic79⋊C4C2318yes—
191C4⋊C4×D79C23116yes—
192C4⋊C4×D79C23116yes—
193C2×C22⋊Dic79C2318yes—
194C2×(C2×D79)⋊C4C2318yes—
195C2×(C2×D79)⋊C4C2314yes—
196C22⋊C4×D79C23132yes—
197C2×C4×Dic79C2314yes—
198C2×#41×C79—216no—
199C2×#41×C79C2314yes—
200C2×#41×C79C2314yes—
201C2×#41×C79C2314yes—
202C2×#41×C79C2314yes—
203C22×Q8×C79C2312yes—
204C22×D4×C79C2314yes—
205C22×D4×C79C2312yes—
206C23×C4×C79C2314yes—
207C23×C4×C79C2311yescharacteristic
208C4⋊Q8×C79C2314yes—
209#127×C79C2314yes—
210#124×C79C2318yes—
211#123×C79C23116yes—
212C22⋊Q8×C79C2318yes—
213C22⋊Q8×C79C2318yes—
214#121×C79C2318yes—
215#121×C79C2318yes—
216#121×C79C2318yes—
217#121×C79C2318yes—
218#120×C79C23116yes—
219C4×D4×C79C2318yes—
220C4×D4×C79C2318yes—
221#117×C79C2314yes—
222#117×C79C2314yes—
223C2×C4⋊C4×C79C2311yescharacteristic
224C2×C4⋊C4×C79C2311yescharacteristic
225C2×C22⋊C4×C79C2312yes—
226C2×C42×C79C2312yes—
227C23×D79C24116yes—
228C23×D79C2414yes—
229C23×D79C2412yes—
230#11929625—232no—
231#11929625—232no—
232#11929624—232no—
233#11929624—264no—
234#11929624—232no—
235#11929624—216no—
236#11929624—216no—
237#11929624—216no—
238#11929624—216no—
239#11929624—264no—
240#11929624C2×D4132yescomplemented
241#11929624C2×D4132yescomplemented
242#11929623—264no—
243#11929623—232no—
244#11929623—232no—
245#11929623—264no—
246C2×Dic158—232no—
247C2×Dic158—28no—
248C2×Dic158C2×D418yescomplemented
249C2×Dic158C24116yes—
250C2×Dic158C2414yes—
251C2×Dic158C2414yes—
252C2×Dic158C2412yes—
253C2×Dic158C2412yes—
254Q8×D79—232no—
255Q8×D79—232no—
256C2×D316—232no—
257C2×D316—28no—
258C2×D316C2×D418yescomplemented
259C2×D316C2414yes—
260C2×D316C24116yes—
261C2×D316C2414yes—
262C2×D316C2418yes—
263C2×D316C2418yes—
264C2×D316C2412yes—
265C2×D316C2412yes—
266C2×C22⋊D79—216no—
267C2×C22⋊D79—264no—
268C2×C22⋊D79—88no—
269C2×C22⋊D79C2×D4116yescomplemented
270C2×C22⋊D79C24116yes—
271C2×C22⋊D79C2418yes—
272C2×C22⋊D79C24116yes—
273C2×C22⋊D79C2418yes—
274C2×C22⋊D79C24132yes—
275C2×C22⋊D79C2418yes—
276D4×D79—232no—
277D4×D79—232no—
278D4×D79—264no—
279D4×D79—264no—
280D4×D79—816no—
281C22×Dic79—82no—
282C22×Dic79C2414yes—
283C22×Dic79C24116yes—
284C22×Dic79C2414yes—
285C22×Dic79C2418yes—
286C22×Dic79C2412yes—
287C2×C4×D79—264no—
288C2×C4×D79—216no—
289C2×C4×D79—84no—
290C2×C4×D79C2×D4116yescomplemented
291C2×C4×D79C24116yes—
292C2×C4×D79C24116yes—
293C2×C4×D79C2418yes—
294C2×C4×D79C2418yes—
295C2×C4×D79C24116yes—
296C2×C4×D79C2418yes—
297C4⋊Dic79C2418yes—
298C4⋊Dic79C2418yes—
299C4⋊Dic79C2414yes—
300C4⋊Dic79C2414yes—
301C4⋊Dic79C2418yes—
302Dic79⋊C4C24116yes—
303Dic79⋊C4C24132yes—
304C22⋊Dic79C24132yes—
305(C2×D79)⋊C4C24116yes—
306(C2×D79)⋊C4C24132yes—
307(C2×D79)⋊C4C24116yes—
308(C2×D79)⋊C4C24116yes—
309C4×Dic79C24116yes—
310C24×C79C2414yes—
311C24×C79C2411yescharacteristic
312#41×C79—216no—
313#41×C79—216no—
314#41×C79—216no—
315#41×C79—216no—
316C2×Q8×C79—28no—
317C2×Q8×C79C2414yes—
318C2×Q8×C79C2414yes—
319C2×D4×C79—216no—
320C2×D4×C79—28no—
321C2×D4×C79C2418yes—
322C2×D4×C79C2414yes—
323C2×D4×C79C2418yes—
324C2×D4×C79C2414yes—
325C2×D4×C79C2418yes—
326C2×D4×C79C2418yes—
327C22×C4×C79—216no—
328C22×C4×C79C2×D418yescomplemented
329C22×C4×C79C2418yes—
330C22×C4×C79C2414yes—
331C22×C4×C79C2418yes—
332C22×C4×C79C2412yes—
333C22×C4×C79C2412yes—
334C22×C4×C79C2411yescharacteristic
335C22×C4×C79C2412yes—
336C22×C4×C79C2411yescharacteristic
337C22×C4×C79C2412yes—
338C4⋊C4×C79C2414yes—
339C4⋊C4×C79C2414yes—
340C4⋊C4×C79C2418yes—
341C4⋊C4×C79C2418yes—
342C22⋊C4×C79C2418yes—
343C22⋊C4×C79C24116yes—
344C22⋊C4×C79C24116yes—
345C42×C79C2414yes—
346C42×C79C2414yes—
347C23×C79—28no—
348C23×C79—41no—
349C23×C79—41no—
350C23×C79—44no—
351C23×C79—44no—
352C23×C79C22×D414yes—
353C23×C79C2518yes—
354C23×C79C2512yes—
355C23×C79C2511yescharacteristic
356C22×D79—28no—
357C22×D79—232no—
358C22×D79—42no—
359C22×D79—42no—
360C22×D79—416no—
361C22×D79—44no—
362C22×D79—416no—
363C22×D79—44no—
364C22×D79C22×D418yes—
365C22×D79C2518yes—
366C22×D79C2514yes—
367Q8×C79—28no—
368Q8×C79—28no—
369D4×C79—216no—
370D4×C79—216no—
371D4×C79—28no—
372D4×C79—28no—
373D4×C79—48no—
374D4×C79—48no—
375C2×C4×C79—28no—
376C2×C4×C79—216no—
377C2×C4×C79—216no—
378C2×C4×C79—42no—
379C2×C4×C79—42no—
380C2×C4×C79C22×D418yes—
381C2×C4×C79C22×D414yes—
382C2×C4×C79C22×D418yes—
383C2×C4×C79C22×D414yes—
384C2×C4×C79C2514yes—
385C2×C4×C79C2514yes—
386C2×C4×C79C2518yes—
387C2×C4×C79C2511yescharacteristic
388C2×C4×C79C2512yes—
389C2×C4×C79C2511yescharacteristic
390C22⋊D79—216no—
391C22⋊D79—216no—
392C22⋊D79—232no—
393C22⋊D79—232no—
394C22⋊D79—432no—
395C22⋊D79C22×D4132yes—
396C2×Dic79—28no—
397C2×Dic79—232no—
398C2×Dic79—44no—
399C2×Dic79—48no—
400C2×Dic79C22×D418yes—
401C2×Dic79C2518yes—
402C2×Dic79C2518yes—
403C2×Dic79C2514yes—
404D316—232no—
405D316—28no—
406D316—28no—
407D316—48no—
408D316—48no—
409D316C22×D418yes—
410D316C22×D418yes—
411C4×D79—232no—
412C4×D79—216no—
413C4×D79—216no—
414C4×D79—232no—
415C4×D79—416no—
416C4×D79C22×D4132yes—
417Dic158—28no—
418Dic158—28no—
419Dic158—232no—
420Dic158C22×D418yes—
421Dic158C22×D418yes—
422C22×C79—21no—
423C22×C79—22no—
424C22×C79—21no—
425C22×C79—22no—
426C22×C79—28no—
427C22×C79—28no—
428C22×C79—28no—
429C22×C79—44no—
430C22×C79—88no—
431C22×C79C23×D412yes—
432C22×C79C23×D414yes—
433C22×C79C2611yescharacteristic
434C2×D79—24no—
435C2×D79—24no—
436C2×D79—28no—
437C2×D79—28no—
438C2×D79—28no—
439C2×D79—48no—
440C2×D79—832no—
441C2×D79—88no—
442C2×D79C23×D418yes—
443C4×C79—28no—
444C4×C79—24no—
445C4×C79—24no—
446C4×C79C23×D412yes—
447C4×C79C23×D414yes—
448C4×C79C23×D412yes—
449Dic79—28no—
450Dic79—28no—
451Dic79C23×D418yes—
452#62853—791nomaximal, Sylow
453C2×C79—22no—
454C2×C79—24no—
455C2×C79—48no—
456C2×C79C24×D411yescharacteristic
457C2×C79H(7,𝔽2)11yescharacteristic
458C2×C792−1+611yescharacteristic
459D79—28no—
460D79—48no—
461C2×#585—792no—
462#3497—794no—
463#3496—798no—
464#3496—794no—
465#3489—798no—
466#3489—798no—
467#3488—798no—
468#3488—798no—
469#3449—794no—
470#3449—791no—
471#3449D7911yescharacteristic, complemented
472C2×#537—792no—
473C2×#537—794no—
474C2×#520—791no—
475C79#6285311yescharacteristic, complemented, Sylow
476#585—15832no—
477C2×2−1+4—794no—
478C2×2−1+4—794no—
479C2×2−1+4—794no—
480C2×H(5,𝔽2)—794no—
481C2×H(5,𝔽2)—794no—
482C2×H(5,𝔽2)—794no—
483C2×H(5,𝔽2)—798no—
484C22×#41—798no—
485C22×#41—798no—
486C22×#41—791no—
487C22×#41—792no—
488C22×#41—798no—
489C22×#41C2×D7912yescomplemented
490#550—798no—
491#550—798no—
492D4×Q8—798no—
493D4×Q8—798no—
494#548—7916no—
495#548—7916no—
496#547—798no—
497#547—7932no—
498#547—798no—
499#546—7916no—
500#546—7932no—
501#546—7932no—
502#546—7916no—
503D42—798no—
504D42—7932no—
505D42—798no—
506#537—798no—
507#537—798no—
508#537—798no—
509#537—798no—
510#537—7916no—
511#537—7916no—
512#537—7916no—
513#537—792no—
514#537—792no—
515#537C2×D7912yescomplemented
516#537C2×D7912yescomplemented
517#536—7916no—
518#536—794no—
519#536C2×D7914yescomplemented
520#535—7916no—
521#535—794no—
522#535C2×D7914yescomplemented
523#534—7916no—
524#534—794no—
525#534C2×D7914yescomplemented
526#532—7916no—
527#532—794no—
528#532C2×D7914yescomplemented
529#525—7916no—
530#525—7916no—
531#525—798no—
532#525C2×D7918yescomplemented
533C2×C22⋊Q8—794no—
534C2×C22⋊Q8—794no—
535C2×C22⋊Q8—7916no—
536C2×#121—794no—
537C2×#121—798no—
538C2×#121—794no—
539C2×#121—7916no—
540C2×#121—7916no—
541#520—798no—
542#520—798no—
543C2×C4×Q8—792no—
544C2×C4×D4—794no—
545C2×C4×D4—792no—
546C2×#117—792no—
547C2×#117C2×D7911yescharacteristic, complemented
548C22×C4⋊C4—791no—
549C22×C4⋊C4—792no—
5502−1+4—15832no—
5512−1+4—15832no—
5522−1+4—15832no—
553H(5,𝔽2)—15864no—
554H(5,𝔽2)—15832no—
555H(5,𝔽2)—15832no—
556H(5,𝔽2)—15832no—
557C2×#41—216no—
558C2×#41—798no—
559C2×#41—798no—
560C2×#41—798no—
561C2×#41—7916no—
562C2×#41—7916no—
563C2×#41—798no—
564C2×#41—7916no—
565C2×#41—794no—
566C2×#41—794no—
567C2×#41—794no—
568C2×#41—794no—
569C2×#41—7916no—
570C2×#41—794no—
571C2×#41—794no—
572C2×#41—798no—
573C2×#41—7916no—
574C2×#41—798no—
575C2×#41—15864no—
576C2×#41—15864no—
577C2×#41—15864no—
578C2×#41—15816no—
579C2×#41C22×D7914yes—
580C2×#41C22×D7914yes—
581C2×#41C22×D7914yes—
582C2×#41C22×D7914yes—
583C22×Q8—798no—
584C22×Q8—798no—
585C22×Q8—791no—
586C22×Q8—792no—
587C22×Q8—798no—
588C22×Q8C22×D7912yes—
589C22×D4—792no—
590C22×D4—798no—
591C22×D4—794no—
592C22×D4—7916no—
593C22×D4—7916no—
594C22×D4—7916no—
595C22×D4—798no—
596C22×D4—7916no—
597C22×D4—798no—
598C22×D4—791no—
599C22×D4—792no—
600C22×D4—798no—
601C22×D4C22×D7914yes—
602C22×D4C22×D7912yes—
603C23×C4—792no—
604C23×C4—792no—
605C23×C4—794no—
606C23×C4—7916no—
607C23×C4—794no—
608C23×C4C22×D7914yes—
609C23×C4C22×D7911yescharacteristic
610C4⋊Q8—7916no—
611C4⋊Q8—794no—
612C4⋊Q8C22×D7914yes—
613#127—7916no—
614#127—794no—
615#127C22×D7914yes—
616#124—7932no—
617#124—798no—
618#124C22×D7918yes—
619#123—7932no—
620#123—7932no—
621#123—7916no—
622#123C22×D79116yes—
623C22⋊Q8—7916no—
624C22⋊Q8—7916no—
625C22⋊Q8—7916no—
626C22⋊Q8—7916no—
627C22⋊Q8—798no—
628C22⋊Q8—7932no—
629C22⋊Q8—798no—
630C22⋊Q8—7932no—
631C22⋊Q8C22×D7918yes—
632C22⋊Q8C22×D7918yes—
633#121—7916no—
634#121—7932no—
635#121—7916no—
636#121—7932no—
637#121—7916no—
638#121—7932no—
639#121—7916no—
640#121—798no—
641#121—7916no—
642#121—798no—
643#121—798no—
644#121—7916no—
645#121—798no—
646#121—7932no—
647#121—7932no—
648#121C22×D7918yes—
649#121C22×D7918yes—
650#121C22×D7918yes—
651#121C22×D7918yes—
652#120—7932no—
653#120—7932no—
654#120—7916no—
655#120C22×D79116yes—
656C4×Q8—798no—
657C4×Q8—798no—
658C4×D4—7916no—
659C4×D4—7916no—
660C4×D4—7932no—
661C4×D4—7932no—
662C4×D4—798no—
663C4×D4—798no—
664C4×D4—798no—
665C4×D4—798no—
666C4×D4C22×D7918yes—
667C4×D4C22×D7918yes—
668#117—7916no—
669#117C22×D7914yes—
670#117C22×D7914yes—
671C2×C4⋊C4—792no—
672C2×C4⋊C4—794no—
673C2×C4⋊C4—792no—
674C2×C4⋊C4—794no—
675C2×C4⋊C4—794no—
676C2×C4⋊C4—798no—
677C2×C4⋊C4—7916no—
678C2×C4⋊C4—7916no—
679C2×C4⋊C4C22×D7911yescharacteristic
680C2×C4⋊C4C22×D7911yescharacteristic
681C2×C22⋊C4—798no—
682C2×C22⋊C4—794no—
683C2×C22⋊C4—798no—
684C2×C22⋊C4—7932no—
685C2×C22⋊C4C22×D7912yes—
686C2×C42—794no—
687C2×C42C22×D7912yes—
688C24—792no—
689C24—7916no—
690C24—794no—
691C24C23×D7914yes—
692C24C23×D7911yescharacteristic
693#41—216no—
694#41—216no—
695#41—216no—
696#41—216no—
697#41—7932no—
698#41—7932no—
699#41—15864no—
700#41—15864no—
701#41—15832no—
702#41—15832no—
703#41—15864no—
704#41—15832no—
705#41—15832no—
706#41—15864no—
707#41—15832no—
708#41—15832no—
709#41—15816no—
710#41—15816no—
711#41—15816no—
712#41—15816no—
713C2×Q8—28no—
714C2×Q8—792no—
715C2×Q8—792no—
716C2×Q8—794no—
717C2×Q8—7916no—
718C2×Q8—794no—
719C2×Q8—798no—
720C2×Q8—15832no—
721C2×Q8—15832no—
722C2×Q8—15832no—
723C2×Q8—1588no—
724C2×Q8C23×D7914yes—
725C2×Q8C23×D7914yes—
726C2×D4—216no—
727C2×D4—28no—
728C2×D4—7932no—
729C2×D4—798no—
730C2×D4—7916no—
731C2×D4—7916no—
732C2×D4—798no—
733C2×D4—798no—
734C2×D4—7916no—
735C2×D4—798no—
736C2×D4—798no—
737C2×D4—792no—
738C2×D4—792no—
739C2×D4—7916no—
740C2×D4—794no—
741C2×D4—794no—
742C2×D4—798no—
743C2×D4—63216no—
744C2×D4—6328no—
745C2×D4—15832no—
746C2×D4—15832no—
747C2×D4—15864no—
748C2×D4—15832no—
749C2×D4—15864no—
750C2×D4—15864no—
751C2×D4—15816no—
752C2×D4—1588no—
753C2×D4C23×D7918yes—
754C2×D4C23×D7918yes—
755C2×D4C23×D7914yes—
756C2×D4C23×D7914yes—
757C2×D4C23×D7918yes—
758C2×D4C23×D7918yes—
759C22×C4—216no—
760C22×C4—794no—
761C22×C4—798no—
762C22×C4—7916no—
763C22×C4—792no—
764C22×C4—798no—
765C22×C4—7916no—
766C22×C4—794no—
767C22×C4—7916no—
768C22×C4—7916no—
769C22×C4—7916no—
770C22×C4—798no—
771C22×C4—798no—
772C22×C4—6324no—
773C22×C4—6322no—
774C22×C4—15864no—
775C22×C4—15816no—
776C22×C4D4×D7918yescomplemented
777C22×C4C23×D7914yes—
778C22×C4C23×D7918yes—
779C22×C4C23×D7918yes—
780C22×C4C23×D7912yes—
781C22×C4C23×D7912yes—
782C22×C4C23×D7911yescharacteristic
783C22×C4C23×D7911yescharacteristic
784C22×C4C23×D7912yes—
785C22×C4C23×D7912yes—
786C4⋊C4—7916no—
787C4⋊C4—7932no—
788C4⋊C4—798no—
789C4⋊C4—794no—
790C4⋊C4—794no—
791C4⋊C4—798no—
792C4⋊C4—798no—
793C4⋊C4C23×D7914yes—
794C4⋊C4C23×D7918yes—
795C4⋊C4C23×D7914yes—
796C4⋊C4C23×D7918yes—
797C22⋊C4—7932no—
798C22⋊C4—7932no—
799C22⋊C4—7916no—
800C22⋊C4—7916no—
801C22⋊C4—7916no—
802C22⋊C4C23×D79116yes—
803C22⋊C4C23×D7918yes—
804C22⋊C4C23×D79116yes—
805C42—7916no—
806C42C23×D7914yes—
807C42C23×D7914yes—
808C23—28no—
809C23—41no—
810C23—41no—
811C23—44no—
812C23—44no—
813C23—3162no—
814C23—3162no—
815C23—3164no—
816C23—31616no—
817C23—3164no—
818C23—31616no—
819C23—798no—
820C23—794no—
821C23—798no—
822C23—15832no—
823C23—1588no—
824C23C2×D4×D7914yes—
825C23C24×D7918yes—
826C23C24×D7912yes—
827C23C24×D7911yescharacteristic
828Q8—28no—
829Q8—28no—
830Q8—798no—
831Q8—798no—
832Q8—15832no—
833Q8—1588no—
834Q8—1588no—
835D4—216no—
836D4—216no—
837D4—28no—
838D4—28no—
839D4—48no—
840D4—48no—
841D4—3168no—
842D4—3168no—
843D4—31632no—
844D4—7932no—
845D4—798no—
846D4—798no—
847D4—15832no—
848D4—15832no—
849D4—15832no—
850D4—15816no—
851D4—15816no—
852D4—1588no—
853D4—1588no—
854C2×C4—28no—
855C2×C4—216no—
856C2×C4—216no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—31616no—
860C2×C4—3164no—
861C2×C4—3168no—
862C2×C4—794no—
863C2×C4—798no—
864C2×C4—7932no—
865C2×C4—798no—
866C2×C4—798no—
867C2×C4—15832no—
868C2×C4—15832no—
869C2×C4—15832no—
870C2×C4—1588no—
871C2×C4—15816no—
872C2×C4—15816no—
873C2×C4C2×D4×D7918yes—
874C2×C4C2×D4×D7914yes—
875C2×C4C2×D4×D7918yes—
876C2×C4C2×D4×D7914yes—
877C2×C4C24×D7914yes—
878C2×C4C24×D7914yes—
879C2×C4C24×D7918yes—
880C2×C4C24×D7911yescharacteristic
881C2×C4C24×D7911yescharacteristic
882C2×C4C24×D7912yes—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—22no—
887C22—28no—
888C22—28no—
889C22—28no—
890C22—44no—
891C22—88no—
892C22—3168no—
893C22—798no—
894C22—6328no—
895C22—63232no—
896C22—1588no—
897C22—1588no—
898C22—1588no—
899C22—1584no—
900C22—1584no—
901C22C22×D4×D7914yes—
902C22C22×D4×D7912yes—
903C22C25×D7911yescharacteristic
904C4—28no—
905C4—24no—
906C4—24no—
907C4—798no—
908C4—1588no—
909C4—1588no—
910C4C22×D4×D7912yes—
911C4C22×D4×D7914yes—
912C4C22×D4×D7912yes—
913C2—24no—
914C2—22no—
915C2—48no—
916C2—3168no—
917C2—1588no—
918C2C23×D4×D7911yescharacteristic
919C2#2377821111yescharacteristic
920C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3449C2
hypercenter#3449D79
hypocenterC79#62853
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#19099399C2semidirect
2. #23777166C2semidirect
3. #23777162C2semidirect
4. #23777161C2semidirect
5. #23777078C2semidirect
6. #23777072C2semidirect
7. #23777067C2semidirect
8. #23777061C2semidirect
9. #23776733C2semidirect
10. #23776728C2semidirect
11. C2×#19099141C2semidirect
12. #537×D79C2semidirect
13. C2×#19099043C2semidirect
14. C79×#3449C2semidirect
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. #19099234C22semidirect
29. #19099233C22semidirect
30. D4×Dic158C22semidirect
31. #19099228C22semidirect
32. #19099222C22semidirect
33. #19099221C22semidirect
34. #19099218C22semidirect
35. #19099216C22semidirect
36. #19099211C22semidirect
37. #19099209C22semidirect
38. #19099206C22semidirect
39. #19099205C22semidirect
40. #19099200C22semidirect
41. D4×D316C22semidirect
42. #19099198C22semidirect
43. #19099195C22semidirect
44. #19099144C22semidirect
45. #19099144C22semidirect
46. #19099143C22semidirect
47. #19099142C22semidirect
48. #19099141C22semidirect
49. #19099141C22semidirect
50. #19099141C22semidirect
51. #19099141C22semidirect
52. #19099140C22semidirect
53. #19099139C22semidirect
54. #19099136C22semidirect
55. #19099132C22semidirect
56. #19099129C22semidirect
57. #19099125C22semidirect
58. #19099121C22semidirect
59. #19099113C22semidirect
60. #19099108C22semidirect
61. #19099076C22semidirect
62. #19099075C22semidirect
63. #19099073C22semidirect
64. C2×#14579140C22semidirect
65. C2×#14579137C22semidirect
66. C22⋊Q8×D79C22semidirect
67. C2×#14579135C22semidirect
68. C2×#14579133C22semidirect
69. C2×#14579132C22semidirect
70. #121×D79C22semidirect
71. #121×D79C22semidirect
72. #19099043C22semidirect
73. #19099043C22semidirect
74. C2×C4×Dic158C22semidirect
75. C2×C4×D316C22semidirect
76. C2×(C22⋊D79)⋊C4C22semidirect
77. C2×#14579119C22semidirect
78. C22×C4⋊Dic79C22semidirect
79. C2×C4⋊C4×D79C22semidirect
80. C22×#41×C79C22semidirect
81. #537×C79C22semidirect
82. #537×C79C22semidirect
83. #536×C79C22semidirect
84. #535×C79C22semidirect
85. #534×C79C22semidirect
86. #532×C79C22semidirect
87. #525×C79C22semidirect
88. C2×#117×C79C22semidirect
100. C2×#11929624D4semidirect
240. #11929624C2×D4semidirect
241. #11929624C2×D4semidirect
248. C2×Dic158C2×D4semidirect
258. C2×D316C2×D4semidirect
269. C2×C22⋊D79C2×D4semidirect
290. C2×C4×D79C2×D4semidirect
328. C22×C4×C79C2×D4semidirect
471. #3449D79semidirect
475. C79#62853semidirect
489. C22×#41C2×D79semidirect
515. #537C2×D79semidirect
516. #537C2×D79semidirect
519. #536C2×D79semidirect
522. #535C2×D79semidirect
525. #534C2×D79semidirect
528. #532C2×D79semidirect
532. #525C2×D79semidirect
547. C2×#117C2×D79semidirect
776. 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
#237771662
#237771622
#237771612
#237770782
#237770722
#237770672
#237770612
#237767332
#237767282
C2×#190991412
#537×D792
C2×#190990432
C79×#34492
#6285379