Finite Group Databasebeta

← C2×#23777053 #35196510

Subgroups — C2×#23777053 #35196510

Order 20224.

11510 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579208C211yesmaximal, characteristic, complemented
2C22×#41×D79C211yesmaximal, characteristic, complemented
3#23777053C2132yesmaximal, direct product factor
4C2×#19099233C213yesmaximal, complemented
5C2×#19099232C211yesmaximal, characteristic, complemented
6C2×#19099231C213yesmaximal, complemented
7C2×#19099225C211yesmaximal, characteristic, complemented
8C2×#19099222C213yesmaximal, complemented
9C2×#19099220C211yesmaximal, characteristic, complemented
10C2×#19099219C213yesmaximal, complemented
11C2×#19099129C213yesmaximal, complemented
12C2×#19099126C213yesmaximal, complemented
13C2×#19099073C213yesmaximal, complemented
14C2×#19099072C213yesmaximal, complemented
15C2×#19099039C211yesmaximal, characteristic, complemented
16C2×#550×C79C211yesmaximal, characteristic, complemented
17C2×#14579208—216no—
18C2×#14579208C22116yescomplemented
19C22×#11929625C2211yescharacteristic
20C22×#11929624C2213yes—
21C22×#11929624C2213yes—
22C22×#11929623C2213yes—
23C22×#11929623C2213yes—
24C22×#11929623C2213yescomplemented
25C2×#41×D79—216no—
26C2×#41×D79C22116yescomplemented
27C23×Dic158C2213yescomplemented
28C22×Q8×D79C2211yescharacteristic
29C22×Q8×D79C2211yescharacteristic, complemented
30C22×D4×D79C2213yes—
31C23×C4×D79C2213yes—
32#19099233C22148yescomplemented
33#19099232C22116yescomplemented
34#19099231C22148yescomplemented
35#19099225C22116yescomplemented
36#19099222C22148yescomplemented
37#19099220C22116yescomplemented
38#19099219C22148yescomplemented
39#19099129C22148yescomplemented
40#19099126C22148yescomplemented
41C2×#14579157C2213yescomplemented
42C2×#14579157C2216yescomplemented
43C2×#14579149C2213yescomplemented
44C2×#14579148C2213yescomplemented
45C2×#14579147C2216yescomplemented
46#19099073C22148yescomplemented
47#19099072C22148yescomplemented
48C2×#14579146C2211yescharacteristic
49C2×#14579143C2213yes—
50C2×#14579141C2213yescomplemented
51C2×#14579140C2213yescomplemented
52C2×#14579139C2213yescomplemented
53C2×#14579138C2213yescomplemented
54C2×#14579136C2213yescomplemented
55C2×#14579135C2213yescomplemented
56C2×#14579134C2213yescomplemented
57C2×#14579133C2216yescomplemented
58C2×#14579133C2216yescomplemented
59C2×#14579133C2213yescomplemented
60C2×#14579132C2213yescomplemented
61C2×#14579132C2213yescomplemented
62C2×#14579131C2213yes—
63C2×#14579129C2213yes—
64C2×#14579129C2216yes—
65#19099039C22116yescomplemented
66C2×Q8×Dic79C2211yescharacteristic, complemented
67C2×C4×Dic158C2213yescomplemented
68C2×#14579126C2213yescomplemented
69C2×C4×D316C2213yescomplemented
70C2×D4×Dic79C2216yescomplemented
71C2×C4×C22⋊D79C2213yescomplemented
72C2×C4×C22⋊D79C2213yescomplemented
73C2×(C22⋊D79)⋊C4C2216yescomplemented
74C2×#14579119C2213yes—
75C2×#14579118C2213yes—
76C22×#41×C79C2211yescharacteristic
77C22×#41×C79C2211yescharacteristic, complemented
78#550×C79C22116yescomplemented
79C2×#127×C79C2213yescomplemented
80C2×#121×C79C2213yescomplemented
81C2×#121×C79C2213yescomplemented
82C2×C4×Q8×C79C2211yescharacteristic, complemented
83C2×C4×D4×C79C2213yescomplemented
84C24×D79C2313yes—
85#14579208—2128no—
86C2×#11929625—28no—
87C2×#11929625C2318yes—
88C2×#11929624—224no—
89C2×#11929624—224no—
90C2×#11929624C23124yes—
91C2×#11929624C23124yes—
92C2×#11929623—224no—
93C2×#11929623—224no—
94C2×#11929623—224no—
95C2×#11929623C23124yes—
96C2×#11929623C23124yes—
97C2×#11929623C23124yescomplemented
98#41×D79—2128no—
99C22×Dic158—224no—
100C22×Dic158C2313yes—
101C22×Dic158C2313yes—
102C22×Dic158C2313yes—
103C22×Dic158C23124yescomplemented
104C2×Q8×D79—28no—
105C2×Q8×D79D4116yescomplemented
106C2×Q8×D79C2318yes—
107C2×Q8×D79C2318yescomplemented
108C22×D316C2311yescharacteristic
109C22×D316C2313yes—
110C22×D316C2313yes—
111C22×C22⋊D79C2313yes—
112C22×C22⋊D79C2316yes—
113C22×C22⋊D79C2313yes—
114C22×C22⋊D79C2316yes—
115C22×C22⋊D79C2313yes—
116C22×C22⋊D79C2313yes—
117C2×D4×D79—224no—
118C2×D4×D79C23124yes—
119C23×Dic79C2316yes—
120C23×Dic79C2313yes—
121C22×C4×D79—224no—
122C22×C4×D79C2313yes—
123C22×C4×D79C2313yes—
124C22×C4×D79C2313yes—
125C22×C4×D79C2311yescharacteristic
126C22×C4×D79C23124yes—
127C22×C4×D79C2313yes—
128#14579157C23124yescomplemented
129#14579157C23148yescomplemented
130#14579149C23124yescomplemented
131#14579148C23124yescomplemented
132#14579147C23148yescomplemented
133#14579146C2318yes—
134#14579143C23124yes—
135#14579141C23124yescomplemented
136#14579140C23124yescomplemented
137#14579139C23124yescomplemented
138#14579138C23124yescomplemented
139#14579136C23124yescomplemented
140#14579135C23124yescomplemented
141#14579134C23124yescomplemented
142#14579133C23148yescomplemented
143#14579133C23148yescomplemented
144#14579133C23124yescomplemented
145#14579132C23124yescomplemented
146#14579132C23124yescomplemented
147#14579131C23124yes—
148#14579129C23124yes—
149#14579129C23148yes—
150Q8×Dic79C2318yescomplemented
151C4×Dic158C23124yescomplemented
152#14579126C23124yescomplemented
153C4×D316C23124yescomplemented
154D4×Dic79C23148yescomplemented
155C4×C22⋊D79C23124yescomplemented
156C4×C22⋊D79C23124yescomplemented
157(C22⋊D79)⋊C4C23148yescomplemented
158#14579119C23124yes—
159#14579118C23124yes—
160C2×C4⋊Dic79C2313yes—
161C2×C4⋊Dic79C2313yes—
162C2×Dic79⋊C4C2313yes—
163C2×Dic79⋊C4C2313yes—
164C2×Dic79⋊C4C2313yes—
165C2×Dic79⋊C4C2311yescharacteristic
166C2×C22⋊Dic79C2313yes—
167C2×C22⋊Dic79C2313yes—
168C2×C22⋊Dic79C2316yes—
169C2×(C2×D79)⋊C4C2311yescharacteristic
170C2×(C2×D79)⋊C4C2313yes—
171C2×(C2×D79)⋊C4C2316yes—
172C2×(C2×D79)⋊C4C2311yescharacteristic
173C2×(C2×D79)⋊C4C2313yes—
174C2×(C2×D79)⋊C4C2311yescharacteristic
175C2×(C2×D79)⋊C4C2313yes—
176C2×C4×Dic79C2313yes—
177C2×C4×Dic79C2316yes—
178C2×#41×C79—28no—
179C2×#41×C79—28no—
180C2×#41×C79C2318yes—
181C2×#41×C79C2318yescomplemented
182C22×Q8×C79C2311yescharacteristic
183C22×D4×C79C2313yes—
184C22×D4×C79C2313yes—
185C22×D4×C79C2313yes—
186C22×D4×C79C2316yes—
187C23×C4×C79C2313yes—
188C23×C4×C79C2313yes—
189#127×C79C23124yescomplemented
190#121×C79C23124yescomplemented
191#121×C79C23124yescomplemented
192C4×Q8×C79C2318yescomplemented
193C4×D4×C79C23124yescomplemented
194C2×C4⋊C4×C79C2311yescharacteristic
195C2×C4⋊C4×C79C2313yes—
196C2×C22⋊C4×C79C2313yes—
197C2×C22⋊C4×C79C2313yes—
198C2×C42×C79C2313yes—
199C23×D79—212no—
200C23×D79—46no—
201C23×D79—46no—
202C23×D79C2413yes—
203C23×D79C2411yescharacteristic
204C23×D79C2411yescharacteristic
205C23×D79C24112yes—
206#11929625—232no—
207#11929624—296no—
208#11929624—296no—
209#11929623—296no—
210#11929623—296no—
211#11929623—296no—
212C2×Dic158—212no—
213C2×Dic158—296no—
214C2×Dic158—212no—
215C2×Dic158C2×D4124yes—
216C2×Dic158C24112yes—
217C2×Dic158C24112yes—
218C2×Dic158C24112yes—
219Q8×D79—232no—
220Q8×D79C2×D4164yescomplemented
221C2×D316—24no—
222C2×D316—212no—
223C2×D316—46no—
224C2×D316C2414yes—
225C2×D316C24112yes—
226C2×D316C24112yes—
227C2×C22⋊D79—212no—
228C2×C22⋊D79—224no—
229C2×C22⋊D79—212no—
230C2×C22⋊D79—46no—
231C2×C22⋊D79—412no—
232C2×C22⋊D79—46no—
233C2×C22⋊D79C24112yes—
234C2×C22⋊D79C24124yes—
235C2×C22⋊D79C24112yes—
236C2×C22⋊D79C24124yes—
237C2×C22⋊D79C24112yes—
238C2×C22⋊D79C24112yes—
239D4×D79—296no—
240C22×Dic79—224no—
241C22×Dic79—212no—
242C22×Dic79C2413yes—
243C22×Dic79C24124yes—
244C22×Dic79C24112yes—
245C22×Dic79C2411yescharacteristic
246C22×Dic79C2413yes—
247C22×Dic79C2411yescharacteristic
248C22×Dic79C2413yes—
249C2×C4×D79—212no—
250C2×C4×D79—296no—
251C2×C4×D79—24no—
252C2×C4×D79—212no—
253C2×C4×D79—212no—
254C2×C4×D79C2×D4124yes—
255C2×C4×D79C24112yes—
256C2×C4×D79C24112yes—
257C2×C4×D79C24112yes—
258C2×C4×D79C2414yes—
259C2×C4×D79C24112yes—
260C4⋊Dic79C24112yes—
261C4⋊Dic79C24112yes—
262Dic79⋊C4C24112yes—
263Dic79⋊C4C24112yes—
264Dic79⋊C4C24112yes—
265Dic79⋊C4C2414yes—
266C22⋊Dic79C24112yes—
267C22⋊Dic79C24112yes—
268C22⋊Dic79C24124yes—
269(C2×D79)⋊C4C2414yes—
270(C2×D79)⋊C4C24112yes—
271(C2×D79)⋊C4C24124yes—
272(C2×D79)⋊C4C2414yes—
273(C2×D79)⋊C4C24112yes—
274(C2×D79)⋊C4C2414yes—
275(C2×D79)⋊C4C24112yes—
276C4×Dic79C24112yes—
277C4×Dic79C24124yes—
278C24×C79C2413yes—
279C24×C79C2413yes—
280#41×C79—232no—
281#41×C79—232no—
282C2×Q8×C79C2×D418yes—
283C2×Q8×C79C2414yes—
284C2×D4×C79—212no—
285C2×D4×C79—212no—
286C2×D4×C79—412no—
287C2×D4×C79—46no—
288C2×D4×C79C24112yes—
289C2×D4×C79C24112yes—
290C2×D4×C79C24112yes—
291C2×D4×C79C24124yes—
292C22×C4×C79—212no—
293C22×C4×C79—212no—
294C22×C4×C79C2411yescharacteristic
295C22×C4×C79C24112yes—
296C22×C4×C79C24112yes—
297C22×C4×C79C2411yescharacteristic
298C22×C4×C79C2413yes—
299C22×C4×C79C2411yescharacteristic
300C22×C4×C79C2413yes—
301C4⋊C4×C79C2414yes—
302C4⋊C4×C79C24112yes—
303C22⋊C4×C79C24112yes—
304C22⋊C4×C79C24112yes—
305C42×C79C24112yes—
306C23×C79—26no—
307C23×C79—26no—
308C23×C79—26no—
309C23×C79—26no—
310C23×C79—26no—
311C23×C79—26no—
312C23×C79C2516yes—
313C23×C79C2516yes—
314C23×C79C2511yescharacteristic
315C22×D79—22no—
316C22×D79—22no—
317C22×D79—22no—
318C22×D79—26no—
319C22×D79—22no—
320C22×D79—26no—
321C22×D79—26no—
322C22×D79—22no—
323C22×D79—224no—
324C22×D79—412no—
325C22×D79—412no—
326C22×D79—448no—
327C22×D79C22×D414yes—
328C22×D79C2516yes—
329C22×D79C2512yes—
330C22×D79C2512yes—
331Q8×C79C22×D4116yes—
332D4×C79—224no—
333D4×C79—224no—
334D4×C79—412no—
335D4×C79—424no—
336C2×C4×C79—22no—
337C2×C4×C79—22no—
338C2×C4×C79—26no—
339C2×C4×C79—22no—
340C2×C4×C79—224no—
341C2×C4×C79—224no—
342C2×C4×C79C22×D4112yes—
343C2×C4×C79C2516yes—
344C2×C4×C79C2512yes—
345C2×C4×C79C2512yes—
346C2×C4×C79C2512yes—
347C2×C4×C79C2516yes—
348C22⋊D79—224no—
349C22⋊D79—248no—
350C22⋊D79—224no—
351C22⋊D79—412no—
352C22⋊D79—424no—
353C22⋊D79—412no—
354C2×Dic79—22no—
355C2×Dic79—26no—
356C2×Dic79—22no—
357C2×Dic79—26no—
358C2×Dic79—224no—
359C2×Dic79—248no—
360C2×Dic79C22×D4112yes—
361C2×Dic79C2512yes—
362C2×Dic79C2516yes—
363C2×Dic79C2516yes—
364C2×Dic79C2512yes—
365C2×Dic79C2516yes—
366D316—28no—
367D316—224no—
368D316—412no—
369C4×D79—28no—
370C4×D79—224no—
371C4×D79—224no—
372C4×D79—224no—
373C4×D79C22×D4148yes—
374Dic158—224no—
375Dic158—224no—
376Dic158C22×D4148yes—
377C22×C79—26no—
378C22×C79—26no—
379C22×C79—26no—
380C22×C79—26no—
381C22×C79—26no—
382C22×C79—26no—
383C22×C79—412no—
384C22×C79—412no—
385C22×C79C23×D412yes—
386C22×C79#58512yes—
387C22×C79#58512yes—
388C22×C79C2611yescharacteristic
389C2×D79—22no—
390C2×D79—22no—
391C2×D79—28no—
392C2×D79—22no—
393C2×D79—26no—
394C2×D79—22no—
395C2×D79—26no—
396C2×D79—26no—
397C2×D79—22no—
398C2×D79—448no—
399C2×D79—44no—
400C2×D79—412no—
401C2×D79C23×D414yes—
402C4×C79—22no—
403C4×C79—22no—
404C4×C79—22no—
405C4×C79—26no—
406C4×C79C23×D4112yes—
407Dic79—26no—
408Dic79—22no—
409Dic79—22no—
410Dic79—26no—
411Dic79C23×D4112yes—
412C2×#3487—791nomaximal, Sylow
413C2×C79—46no—
414C2×C79—46no—
415C2×C79#348714yescomplemented
416C2×C79C24×D411yescharacteristic
417C2×C79C2×#58511yescharacteristic
418C2×C79C2×#58511yescharacteristic
419D79—24no—
420D79—42no—
421D79—46no—
422C22×2−1+4—791no—
423C23×#41—791no—
424#3487—7932no—
425C2×#550—791no—
426C2×#550—793no—
427C2×#550—793no—
428C2×#550D7911yescharacteristic, complemented
429C2×#548—791no—
430C2×#548—793no—
431C2×#548—791no—
432C2×#548—793no—
433C2×#535—793no—
434C2×#535—793no—
435C2×#525—793no—
436C2×#525—793no—
437C2×#519—791no—
438C79C2×#348711yescharacteristic, complemented, Sylow
439C2×2−1+4—7916no—
440C2×2−1+4—15816no—
441C22×#41—7916no—
442C22×#41—791no—
443C22×#41—793no—
444C22×#41—793no—
445C22×#41—793no—
446C22×#41—793no—
447C22×#41—793no—
448C22×#41—15816no—
449C22×#41C2×D7911yescharacteristic
450C22×#41C2×D7911yescharacteristic, complemented
451C23×Q8—791no—
452C23×Q8—791no—
453C23×Q8—793no—
454C23×D4—793no—
455C24×C4—793no—
456#550—7916no—
457#550—7948no—
458#550—7948no—
459#550C2×D79116yescomplemented
460#548—7916no—
461#548—7948no—
462#548—7916no—
463#548—7948no—
464#535—7948no—
465#535—7948no—
466C2×#127—793no—
467C2×#127—796no—
468C2×#127C2×D7913yescomplemented
469C2×#124—793no—
470C2×#124—796no—
471C2×#124—793no—
472#525—7948no—
473#525—7948no—
474C2×#123—791no—
475C2×#123—793no—
476C2×C22⋊Q8—793no—
477C2×C22⋊Q8—793no—
478C2×C22⋊Q8—793no—
479C2×C22⋊Q8—793no—
480C2×#121—793no—
481C2×#121—793no—
482C2×#121—793no—
483C2×#121—796no—
484C2×#121—796no—
485C2×#121—793no—
486C2×#121—793no—
487C2×#121—793no—
488C2×#121C2×D7913yescomplemented
489C2×#121C2×D7913yescomplemented
490C2×#120—796no—
491C2×#120—793no—
492C2×#120—793no—
493#519—7916no—
494C2×C4×Q8—791no—
495C2×C4×Q8—793no—
496C2×C4×Q8—793no—
497C2×C4×Q8C2×D7911yescharacteristic, complemented
498C2×C4×D4—796no—
499C2×C4×D4—793no—
500C2×C4×D4—793no—
501C2×C4×D4—796no—
502C2×C4×D4—793no—
503C2×C4×D4C2×D7913yescomplemented
504C2×#117—793no—
505C2×#117—793no—
506C25—793no—
5072−1+4—158128no—
508C2×#41—28no—
509C2×#41—28no—
510C2×#41—798no—
511C2×#41—7924no—
512C2×#41—7924no—
513C2×#41—7924no—
514C2×#41—7924no—
515C2×#41—7924no—
516C2×#41—15824no—
517C2×#41—15824no—
518C2×#41—15824no—
519C2×#41—15824no—
520C2×#41—15824no—
521C2×#41—158128no—
522C2×#41—1588no—
523C2×#41C22×D7918yes—
524C2×#41C22×D7918yescomplemented
525C22×Q8—7916no—
526C22×Q8—798no—
527C22×Q8—798no—
528C22×Q8—793no—
529C22×Q8—793no—
530C22×Q8—793no—
531C22×Q8—7924no—
532C22×Q8—15824no—
533C22×Q8—1588no—
534C22×Q8C22×D7911yescharacteristic
535C22×D4—793no—
536C22×D4—796no—
537C22×D4—793no—
538C22×D4—793no—
539C22×D4—796no—
540C22×D4—793no—
541C22×D4—7924no—
542C22×D4—793no—
543C22×D4—791no—
544C22×D4—793no—
545C22×D4—15824no—
546C22×D4C22×D7913yes—
547C22×D4C22×D7913yes—
548C22×D4C22×D7916yes—
549C22×D4C22×D7913yes—
550C23×C4—793no—
551C23×C4—796no—
552C23×C4—793no—
553C23×C4—793no—
554C23×C4—793no—
555C23×C4—793no—
556C23×C4—791no—
557C23×C4—7924no—
558C23×C4—15824no—
559C23×C4C22×D7913yes—
560C23×C4C22×D7913yes—
561#127—7924no—
562#127—7948no—
563#127C22×D79124yescomplemented
564#124—7924no—
565#124—7948no—
566#124—7924no—
567#123—798no—
568#123—7924no—
569C22⋊Q8—7924no—
570C22⋊Q8—7924no—
571C22⋊Q8—7924no—
572C22⋊Q8—7924no—
573#121—7924no—
574#121—7924no—
575#121—7924no—
576#121—7948no—
577#121—7948no—
578#121—7924no—
579#121—7924no—
580#121—7924no—
581#121C22×D79124yescomplemented
582#121C22×D79124yescomplemented
583#120—7948no—
584#120—7924no—
585#120—7924no—
586C4×Q8—798no—
587C4×Q8—7924no—
588C4×Q8—7924no—
589C4×Q8C22×D7918yescomplemented
590C4×D4—7948no—
591C4×D4—7924no—
592C4×D4—7924no—
593C4×D4—7948no—
594C4×D4—7924no—
595C4×D4C22×D79124yescomplemented
596#117—7924no—
597#117—7924no—
598C2×C4⋊C4—793no—
599C2×C4⋊C4—793no—
600C2×C4⋊C4—793no—
601C2×C4⋊C4—793no—
602C2×C4⋊C4—791no—
603C2×C4⋊C4—793no—
604C2×C4⋊C4C22×D7913yes—
605C2×C4⋊C4C22×D7911yescharacteristic
606C2×C22⋊C4—793no—
607C2×C22⋊C4—796no—
608C2×C22⋊C4—793no—
609C2×C22⋊C4—793no—
610C2×C22⋊C4—791no—
611C2×C22⋊C4—791no—
612C2×C22⋊C4—791no—
613C2×C22⋊C4—793no—
614C2×C22⋊C4—796no—
615C2×C22⋊C4—793no—
616C2×C22⋊C4C22×D7913yes—
617C2×C22⋊C4C22×D7913yes—
618C2×C42—796no—
619C2×C42—793no—
620C2×C42C22×D7913yes—
621C24—3166no—
622C24—3166no—
623C24—7912no—
624C24—791no—
625C24—793no—
626C24—791no—
627C24—15812no—
628C24C23×D7913yes—
629C24C23×D7913yes—
630#41—232no—
631#41—232no—
632#41—15896no—
633#41—15896no—
634#41—15896no—
635#41—15896no—
636#41—15896no—
637#41—15832no—
638C2×Q8—7964no—
639C2×Q8—7912no—
640C2×Q8—7912no—
641C2×Q8—7912no—
642C2×Q8—7924no—
643C2×Q8—15812no—
644C2×Q8—15896no—
645C2×Q8—15832no—
646C2×Q8—15812no—
647C2×Q8D4×D7918yes—
648C2×Q8C23×D7914yes—
649C2×D4—212no—
650C2×D4—212no—
651C2×D4—412no—
652C2×D4—46no—
653C2×D4—3166no—
654C2×D4—3166no—
655C2×D4—31612no—
656C2×D4—3166no—
657C2×D4—7924no—
658C2×D4—7912no—
659C2×D4—7912no—
660C2×D4—7912no—
661C2×D4—7924no—
662C2×D4—7912no—
663C2×D4—7912no—
664C2×D4—794no—
665C2×D4—7912no—
666C2×D4—1584no—
667C2×D4—15896no—
668C2×D4—15824no—
669C2×D4—15812no—
670C2×D4—15812no—
671C2×D4—15812no—
672C2×D4C23×D79112yes—
673C2×D4C23×D79112yes—
674C2×D4C23×D79124yes—
675C2×D4C23×D79112yes—
676C22×C4—212no—
677C22×C4—212no—
678C22×C4—793no—
679C22×C4—7912no—
680C22×C4—7924no—
681C22×C4—7924no—
682C22×C4—7912no—
683C22×C4—791no—
684C22×C4—793no—
685C22×C4—793no—
686C22×C4—791no—
687C22×C4—7912no—
688C22×C4—7912no—
689C22×C4—7912no—
690C22×C4—794no—
691C22×C4—15812no—
692C22×C4—15896no—
693C22×C4—1584no—
694C22×C4—15812no—
695C22×C4—15824no—
696C22×C4—15812no—
697C22×C4—15812no—
698C22×C4C23×D79112yes—
699C22×C4C23×D79112yes—
700C22×C4C23×D7913yes—
701C22×C4C23×D7911yescharacteristic
702C22×C4C23×D7911yescharacteristic
703C22×C4C23×D7911yescharacteristic
704C22×C4C23×D7913yes—
705C4⋊C4—7912no—
706C4⋊C4—7912no—
707C4⋊C4—7912no—
708C4⋊C4—794no—
709C4⋊C4—7912no—
710C4⋊C4—7912no—
711C4⋊C4C23×D79112yes—
712C4⋊C4C23×D7914yes—
713C22⋊C4—7912no—
714C22⋊C4—7912no—
715C22⋊C4—7924no—
716C22⋊C4—7912no—
717C22⋊C4—794no—
718C22⋊C4—794no—
719C22⋊C4—794no—
720C22⋊C4—7912no—
721C22⋊C4—7924no—
722C22⋊C4—7912no—
723C22⋊C4C23×D79112yes—
724C22⋊C4C23×D79112yes—
725C42—7924no—
726C42—7912no—
727C42C23×D79112yes—
728C23—26no—
729C23—26no—
730C23—26no—
731C23—26no—
732C23—26no—
733C23—26no—
734C23—31612no—
735C23—31612no—
736C23—31648no—
737C23—792no—
738C23—794no—
739C23—796no—
740C23—792no—
741C23—15824no—
742C23—1582no—
743C23—1586no—
744C23—1582no—
745C23—1586no—
746C23—1582no—
747C23—1586no—
748C23—1582no—
749C23—1582no—
750C23C24×D7916yes—
751C23C24×D7916yes—
752C23C24×D7911yescharacteristic
753Q8—7948no—
754Q8—15824no—
755Q8—15824no—
756Q8C2×D4×D79116yes—
757D4—224no—
758D4—224no—
759D4—424no—
760D4—412no—
761D4—31612no—
762D4—31612no—
763D4—31624no—
764D4—31612no—
765D4—1588no—
766D4—15848no—
767D4—15824no—
768D4—15824no—
769D4—15824no—
770C2×C4—26no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—224no—
775C2×C4—224no—
776C2×C4—796no—
777C2×C4—7912no—
778C2×C4—7948no—
779C2×C4—792no—
780C2×C4—796no—
781C2×C4—796no—
782C2×C4—792no—
783C2×C4—15824no—
784C2×C4—1588no—
785C2×C4—15824no—
786C2×C4—15848no—
787C2×C4—1582no—
788C2×C4—1586no—
789C2×C4—1582no—
790C2×C4—1586no—
791C2×C4—15824no—
792C2×C4—15824no—
793C2×C4C2×D4×D79112yes—
794C2×C4C24×D7916yes—
795C2×C4C24×D7912yes—
796C2×C4C24×D7912yes—
797C2×C4C24×D7912yes—
798C2×C4C24×D7916yes—
799C22—26no—
800C22—26no—
801C22—26no—
802C22—26no—
803C22—26no—
804C22—26no—
805C22—412no—
806C22—412no—
807C22—31648no—
808C22—31612no—
809C22—3164no—
810C22—794no—
811C22—1582no—
812C22—1586no—
813C22—1582no—
814C22—1586no—
815C22—1582no—
816C22—1586no—
817C22—1588no—
818C22—1582no—
819C22—1582no—
820C22C22×D4×D7912yes—
821C22#1909939812yes—
822C22#1909939912yes—
823C22C25×D7911yescharacteristic
824C4—22no—
825C4—22no—
826C4—26no—
827C4—22no—
828C4—7912no—
829C4—1582no—
830C4—1586no—
831C4—1582no—
832C4—1586no—
833C4C22×D4×D79112yes—
834C2—46no—
835C2—46no—
836C2—3166no—
837C2—3162no—
838C2—1584no—
839C2#2377705314yesdirect product factor
840C2C23×D4×D7911yescharacteristic
841C2C2×#1909939811yescharacteristic
842C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#550×C79C2
socleC23×C79C25
hypercenterC2×#550D79
hypocenterC79C2×#3487
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#14579208C2semidirect
2. C22×#41×D79C2semidirect
3. #23777053C2direct (N × H)
4. C2×#19099233C2semidirect
5. C2×#19099232C2semidirect
6. C2×#19099231C2semidirect
7. C2×#19099225C2semidirect
8. C2×#19099222C2semidirect
9. C2×#19099220C2semidirect
10. C2×#19099219C2semidirect
11. C2×#19099129C2semidirect
12. C2×#19099126C2semidirect
13. C2×#19099073C2semidirect
14. C2×#19099072C2semidirect
15. C2×#19099039C2semidirect
16. C2×#550×C79C2semidirect
18. C2×#14579208C22semidirect
24. C22×#11929623C22semidirect
26. C2×#41×D79C22semidirect
27. C23×Dic158C22semidirect
29. C22×Q8×D79C22semidirect
32. #19099233C22semidirect
33. #19099232C22semidirect
34. #19099231C22semidirect
35. #19099225C22semidirect
36. #19099222C22semidirect
37. #19099220C22semidirect
38. #19099219C22semidirect
39. #19099129C22semidirect
40. #19099126C22semidirect
41. C2×#14579157C22semidirect
42. C2×#14579157C22semidirect
43. C2×#14579149C22semidirect
44. C2×#14579148C22semidirect
45. C2×#14579147C22semidirect
46. #19099073C22semidirect
47. #19099072C22semidirect
50. C2×#14579141C22semidirect
51. C2×#14579140C22semidirect
52. C2×#14579139C22semidirect
53. C2×#14579138C22semidirect
54. C2×#14579136C22semidirect
55. C2×#14579135C22semidirect
56. C2×#14579134C22semidirect
57. C2×#14579133C22semidirect
58. C2×#14579133C22semidirect
59. C2×#14579133C22semidirect
60. C2×#14579132C22semidirect
61. C2×#14579132C22semidirect
65. #19099039C22semidirect
66. C2×Q8×Dic79C22semidirect
67. C2×C4×Dic158C22semidirect
68. C2×#14579126C22semidirect
69. C2×C4×D316C22semidirect
70. C2×D4×Dic79C22semidirect
71. C2×C4×C22⋊D79C22semidirect
72. C2×C4×C22⋊D79C22semidirect
73. C2×(C22⋊D79)⋊C4C22semidirect
77. C22×#41×C79C22semidirect
78. #550×C79C22semidirect
79. C2×#127×C79C22semidirect
80. C2×#121×C79C22semidirect
81. C2×#121×C79C22semidirect
82. C2×C4×Q8×C79C22semidirect
83. C2×C4×D4×C79C22semidirect
97. C2×#11929623C23semidirect
103. C22×Dic158C23semidirect
105. C2×Q8×D79D4semidirect
107. C2×Q8×D79C23semidirect
128. #14579157C23semidirect
129. #14579157C23semidirect
130. #14579149C23semidirect
131. #14579148C23semidirect
132. #14579147C23semidirect
135. #14579141C23semidirect
136. #14579140C23semidirect
137. #14579139C23semidirect
138. #14579138C23semidirect
139. #14579136C23semidirect
140. #14579135C23semidirect
141. #14579134C23semidirect
142. #14579133C23semidirect
143. #14579133C23semidirect
144. #14579133C23semidirect
145. #14579132C23semidirect
146. #14579132C23semidirect
150. Q8×Dic79C23semidirect
151. C4×Dic158C23semidirect
152. #14579126C23semidirect
153. C4×D316C23semidirect
154. D4×Dic79C23semidirect
155. C4×C22⋊D79C23semidirect
156. C4×C22⋊D79C23semidirect
157. (C22⋊D79)⋊C4C23semidirect
181. C2×#41×C79C23semidirect
189. #127×C79C23semidirect
190. #121×C79C23semidirect
191. #121×C79C23semidirect
192. C4×Q8×C79C23semidirect
193. C4×D4×C79C23semidirect
220. Q8×D79C2×D4semidirect
415. C2×C79#3487semidirect
428. C2×#550D79semidirect
438. C79C2×#3487semidirect
450. C22×#41C2×D79semidirect
459. #550C2×D79semidirect
468. C2×#127C2×D79semidirect
488. C2×#121C2×D79semidirect
489. C2×#121C2×D79semidirect
497. C2×C4×Q8C2×D79semidirect
503. C2×C4×D4C2×D79semidirect
524. C2×#41C22×D79semidirect
563. #127C22×D79semidirect
581. #121C22×D79semidirect
582. #121C22×D79semidirect
589. C4×Q8C22×D79semidirect
595. C4×D4C22×D79semidirect
839. C2#23777053direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145792082
C22×#41×D792
#237770532
C2×#190992332
C2×#190992322
C2×#190992312
C2×#190992252
C2×#190992222
C2×#190992202
C2×#190992192
C2×#190991292
C2×#190991262
C2×#190990732
C2×#190990722
C2×#190990392
C2×#550×C792
C2×#348779