Finite Group Databasebeta

← C2×#23773999 #35158039

Subgroups — C2×#23773999 #35158039

Order 20224.

1986 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099115C211yesmaximal, characteristic, complemented
2C2×#19099094C211yesmaximal, characteristic
3#23773999C2116yesmaximal, direct product factor
4C2×#19098971C211yesmaximal, characteristic, complemented
5C2×#19098954C211yesmaximal, characteristic, complemented
6C2×#19098930C211yesmaximal, characteristic, complemented
7C2×#19098921C211yesmaximal, characteristic, complemented
8C2×#19098821C211yesmaximal, characteristic, complemented
9C2×#19098819C211yesmaximal, characteristic, complemented
10C2×#19098807C211yesmaximal, characteristic
11C2×#19098657C211yesmaximal, characteristic, complemented
12C2×#19098655C211yesmaximal, characteristic, complemented
13C2×#19098654C211yesmaximal, characteristic, complemented
14C2×SD16×Dic79C211yesmaximal, characteristic, complemented
15C2×M16×Dic79C211yesmaximal, characteristic, complemented
16C2×#468×C79C211yesmaximal, characteristic
17C22×Dic316C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929612C2211yescharacteristic
20C22×#11929608C2211yescharacteristic
21#19099115—24no—
22#19099115C2218yescomplemented
23C2×#14579160C2211yescharacteristic
24C2×#14579159C2211yescharacteristic
25#19099094—24no—
26#19099094C2218yes—
27C2×#14579154—21no—
28C2×#14579152C2211yescharacteristic
29C2×#14579151—21no—
30C2×#14579148C2211yescharacteristic
31C2×#14579142—21no—
32C2×#14579140C2211yescharacteristic
33C2×#14579140C2211yescharacteristic
34C2×#14579138—21no—
35C2×Q8×Dic79C2211yescharacteristic
36C2×#14579126—21no—
37C2×#14579126C2211yescharacteristic
38C2×#14579126C2211yescharacteristic
39C2×D4×Dic79—21no—
40C2×D4×Dic79C2211yescharacteristic
41C2×#14579117—21no—
42C2×#14579117—21no—
43C22×C4×Dic79C2211yescharacteristic
44#19098971C2218yescomplemented
45#19098954C2218yescomplemented
46#19098930C2218yescomplemented
47#19098921C2218yescomplemented
48#19098821C2218yescomplemented
49#19098819C2218yescomplemented
50#19098807C2218yes—
51#19098657C2218yescomplemented
52#19098655C2218yescomplemented
53#19098654C2218yescomplemented
54SD16×Dic79C2218yescomplemented
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×#14579086C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579084C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579082C2211yescharacteristic
64M16×Dic79C2218yescomplemented
65C2×#14579071C2211yescharacteristic
66C2×#14579071C2211yescharacteristic
67C2×C8×Dic79C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C22×M16×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73#468×C79C2218yes—
74C2×#107×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×Dic158C2311yescharacteristic
80C23×Dic79—21no—
81C23×Dic79D411yescharacteristic
82C23×Dic79D411yescharacteristic
83C2×Dic316—24no—
84C2×Dic316C2314yes—
85C2×#11929614—24no—
86C2×#11929614C2314yes—
87C2×#11929612—24no—
88C2×#11929612C2314yes—
89C2×#11929608—24no—
90C2×#11929608C2314yes—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93#14579160—22no—
94#14579160C2314yes—
95#14579159—22no—
96#14579159C2314yes—
97#14579154—28no—
98#14579152—22no—
99#14579152C2314yes—
100#14579151—28no—
101#14579148—22no—
102#14579148C2314yes—
103#14579142—28no—
104#14579140—22no—
105#14579140—22no—
106#14579140C2314yes—
107#14579140C2314yes—
108#14579138—28no—
109Q8×Dic79—22no—
110Q8×Dic79C2314yes—
111#14579126—28no—
112#14579126—22no—
113#14579126—22no—
114#14579126C2314yes—
115#14579126C2314yes—
116D4×Dic79—28no—
117D4×Dic79—22no—
118D4×Dic79C2314yes—
119#14579117—28no—
120#14579117—28no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×C22⋊Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79D411yescharacteristic
142C2×C4×Dic79D411yescharacteristic
143C2×C4×Dic79D414yes—
144C2×C4×Dic79C2311yescharacteristic
145C2×C4×Dic79C2311yescharacteristic
146C2×C4×Dic79C2314yes—
147#14579094C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150#14579086C2314yes—
151#14579086C2314yes—
152#14579085C2314yes—
153#14579084C2314yes—
154#14579084C2314yes—
155#14579082C2314yes—
156#14579071C2314yes—
157#14579071C2314yes—
158C8×Dic79C2314yes—
159C8×Dic79C2314yes—
160C22×Q8×C79C2311yescharacteristic
161C22×D4×C79—21no—
162C22×D4×C79C2311yescharacteristic
163C23×C4×C79C2311yescharacteristic
164C2×SD16×C79—24no—
165C2×SD16×C79C2314yes—
166C2×M16×C79—24no—
167C2×M16×C79C2314yes—
168C22×C8×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170C22⋊Q8×C79—22no—
171C22⋊Q8×C79C2314yes—
172#121×C79—22no—
173#121×C79C2314yes—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179#107×C79C2314yes—
180#103×C79C2314yes—
181#102×C79C2314yes—
182C2×Dic158—24no—
183C2×Dic158—21no—
184C2×Dic158—21no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—22no—
188C2×Dic158—22no—
189C2×Dic158—44no—
190C2×Dic158C2412yes—
191C2×Dic158C2412yes—
192C22×Dic79—24no—
193C22×Dic79—24no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—42no—
199C22×Dic79—44no—
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D414yes—
204C22×Dic79C2×D414yes—
205C22×Dic79C2×D411yescharacteristic
206Dic316—28no—
207#11929614—28no—
208#11929612—28no—
209#11929608—28no—
210C2×C79⋊C8—22no—
211C2×C79⋊C8#4114yes—
212C2×C79⋊C8C2412yes—
213C2×C79⋊C8C2412yes—
214C4⋊Dic79—24no—
215C4⋊Dic79—24no—
216C4⋊Dic79—21no—
217C4⋊Dic79—21no—
218C4⋊Dic79C2412yes—
219C4⋊Dic79C2412yes—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228C22⋊Dic79—24no—
229C22⋊Dic79—24no—
230C22⋊Dic79—24no—
231C22⋊Dic79—24no—
232C22⋊Dic79—24no—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79C2×D414yes—
237C4×Dic79C2×D412yes—
238C4×Dic79C2×D412yes—
239C4×Dic79C2×D414yes—
240C4×Dic79C2412yes—
241C4×Dic79C2412yes—
242C24×C79—21no—
243C24×C79C2×D411yescharacteristic
244C2×Q8×C79—21no—
245C2×Q8×C79—22no—
246C2×Q8×C79—22no—
247C2×Q8×C79C2412yes—
248C2×D4×C79—24no—
249C2×D4×C79—21no—
250C2×D4×C79—22no—
251C2×D4×C79—22no—
252C2×D4×C79—44no—
253C2×D4×C79C2412yes—
254C22×C4×C79—22no—
255C22×C4×C79—22no—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79—21no—
259C22×C4×C79C2×D411yescharacteristic
260C22×C4×C79C2×D412yes—
261C22×C4×C79C2412yes—
262C22×C4×C79C2411yescharacteristic
263SD16×C79—28no—
264M16×C79—28no—
265C2×C8×C79—22no—
266C2×C8×C79#4114yes—
267C2×C8×C79C2412yes—
268C2×C8×C79C2412yes—
269C4⋊C4×C79—24no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79C2412yes—
273C4⋊C4×C79C2412yes—
274C22⋊C4×C79—24no—
275C22⋊C4×C79—24no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—22no—
280C23×C79—42no—
281C23×C79—42no—
282C23×C79—42no—
283C23×C79C22×D412yes—
284C23×C79C22×D411yescharacteristic
285Q8×C79—22no—
286Q8×C79—22no—
287Q8×C79—42no—
288D4×C79—22no—
289D4×C79—22no—
290D4×C79—48no—
291D4×C79—42no—
292C2×C4×C79—22no—
293C2×C4×C79—24no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—42no—
300C2×C4×C79—42no—
301C2×C4×C79—42no—
302C2×C4×C79C22×D412yes—
303C2×C4×C79C22×D411yescharacteristic
304C2×C4×C79C2×#4112yes—
305C2×C4×C79C2×#4112yes—
306C2×C4×C79C2511yescharacteristic
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—28no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—44no—
316C2×Dic79—42no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—48no—
321C2×Dic79#13714yes—
322C2×Dic79C22×D412yes—
323C2×Dic79C22×D412yes—
324C2×Dic79C22×D412yes—
325C2×Dic79C22×D412yes—
326Dic158—22no—
327Dic158—22no—
328Dic158—22no—
329Dic158—22no—
330Dic158—48no—
331Dic158—42no—
332Dic158—42no—
333C8×C79—22no—
334C8×C79C2×#4114yes—
335C79⋊C8—22no—
336C79⋊C8C2×#4114yes—
337C22×C79—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—44no—
341C22×C79—42no—
342C22×C79—42no—
343C22×C79—42no—
344C22×C79—84no—
345C22×C79#53212yes—
346C22×C79C2×#13712yes—
347C22×C79#57512yes—
348C22×C79C23×D411yescharacteristic
349C4×C79—22no—
350C4×C79—42no—
351C4×C79—42no—
352C4×C79—42no—
353C4×C79#53212yes—
354C4×C79C22×#4111yescharacteristic
355C4×C79C22×#4111yescharacteristic
356Dic79—22no—
357Dic79—22no—
358Dic79—22no—
359Dic79—42no—
360Dic79—42no—
361Dic79—42no—
362Dic79—42no—
363Dic79C2×#13714yes—
364C2×#3172—791nomaximal, Sylow
365C2×C79—42no—
366C2×C79—82no—
367C2×C79#317214yescomplemented
368C2×C79C2×#53211yescharacteristic
369C2×C79C22×#13711yescharacteristic
370C2×C79C2×#57511yescharacteristic
371C2×#533—791no—
372C2×#529—791no—
373#3172—7916no—
374C2×#501—791no—
375C2×#497—791no—
376C2×#491—791no—
377C2×#489—791no—
378C2×#470—791no—
379C2×#470—791no—
380C2×#468—791no—
381C2×#468D7911yescharacteristic
382C2×C4×Q16—791no—
383C2×C4×Q16—791no—
384C2×C4×SD16—791no—
385C2×C4×SD16—791no—
386C2×C4×M16—791no—
387C79C2×#317211yescharacteristic, complemented, Sylow
388C22×Q16—791no—
389C22×Q16—791no—
390C22×SD16—791no—
391C22×SD16C2×D7911yescharacteristic
392C22×M16—791no—
393C22×M16C2×D7911yescharacteristic
394#533—798no—
395#533—1584no—
396C2×C4⋊Q8—791no—
397C2×C4⋊Q8—791no—
398#529—798no—
399#529—1584no—
400C2×#126—1581no—
401C2×#125—791no—
402C2×#125—1581no—
403C2×#124—791no—
404C2×#123—1581no—
405C2×C22⋊Q8—791no—
406C2×C22⋊Q8—791no—
407C2×C22⋊Q8—1581no—
408C2×C22⋊Q8C2×D7911yescharacteristic
409C2×#121C2×D7911yescharacteristic
410C2×C4×Q8—791no—
411C2×C4×Q8—791no—
412C2×C4×Q8—791no—
413C2×C4×Q8—1581no—
414C2×C4×D4—791no—
415C2×C4×D4—1581no—
416C2×#117—1581no—
417C2×#117—1581no—
418C22×C42—791no—
419#501—798no—
420#497—798no—
421#491—798no—
422#489—798no—
423#470—798no—
424#470—798no—
425#468—798no—
426#468C2×D7918yes—
427C4×Q16—798no—
428C4×Q16—798no—
429C4×SD16—798no—
430C4×SD16—798no—
431C2×#107—791no—
432C2×#107C2×D7911yescharacteristic
433C2×#106—791no—
434C2×#106—791no—
435C2×#103—791no—
436C2×#103—791no—
437C2×#103—791no—
438C2×#103—791no—
439C2×#103—791no—
440C2×#103C2×D7911yescharacteristic
441C2×#102—791no—
442C2×#102C2×D7911yescharacteristic
443C4×M16—798no—
444C2×#97—791no—
445C2×#97—791no—
446C2×C4×C8—791no—
447C2×C4×C8—791no—
448C22×Q8—791no—
449C22×Q8—791no—
450C22×Q8—1581no—
451C22×Q8C22×D7911yescharacteristic
452C22×D4—21no—
453C22×D4C22×D7911yescharacteristic
454C23×C4—791no—
455C23×C4—791no—
456C23×C4—1581no—
457C23×C4C22×D7911yescharacteristic
458C2×Q16—794no—
459C2×Q16—794no—
460C2×Q16—1584no—
461C2×Q16—1584no—
462C2×SD16—24no—
463C2×SD16—794no—
464C2×SD16—1584no—
465C2×SD16C22×D7914yes—
466C2×M16—24no—
467C2×M16—794no—
468C2×M16—1584no—
469C2×M16C22×D7914yes—
470C22×C8—791no—
471C22×C8—791no—
472C22×C8C22×D7911yescharacteristic
473C22×C8C22×D7911yescharacteristic
474C4⋊Q8—794no—
475C4⋊Q8—794no—
476C4⋊Q8—1582no—
477C4⋊Q8—1582no—
478#126—1588no—
479#125—794no—
480#125—1582no—
481#125—1588no—
482#124—794no—
483#124—1582no—
484#123—1588no—
485C22⋊Q8—22no—
486C22⋊Q8—794no—
487C22⋊Q8—794no—
488C22⋊Q8—1588no—
489C22⋊Q8—1582no—
490C22⋊Q8—1582no—
491C22⋊Q8C22×D7914yes—
492#121—22no—
493#121C22×D7914yes—
494C4×Q8—794no—
495C4×Q8—794no—
496C4×Q8—794no—
497C4×Q8—1582no—
498C4×Q8—1582no—
499C4×Q8—1588no—
500C4×Q8—1582no—
501C4×D4—794no—
502C4×D4—1582no—
503C4×D4—1588no—
504#117—1588no—
505#117—1588no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4—1581no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4C22×D7911yescharacteristic
520C2×C4⋊C4C22×D7911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C42—791no—
529C2×C42—791no—
530C2×C42—794no—
531C2×C42—791no—
532C2×C42—791no—
533C2×C42—794no—
534C2×C42—1581no—
535C2×C42—1581no—
536C2×C42—1581no—
537#107—794no—
538#107C22×D7914yes—
539#106—794no—
540#106—794no—
541#103—794no—
542#103—794no—
543#103—794no—
544#103—794no—
545#103—794no—
546#103C22×D7914yes—
547#102—794no—
548#102C22×D7914yes—
549#97—794no—
550#97—794no—
551C4×C8—794no—
552C4×C8—794no—
553C24—21no—
554C24D4×D7911yescharacteristic
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—3164no—
559C2×Q8—792no—
560C2×Q8—792no—
561C2×Q8—1584no—
562C2×Q8—1582no—
563C2×Q8—1582no—
564C2×Q8—1582no—
565C2×Q8—1582no—
566C2×Q8—1581no—
567C2×Q8—1581no—
568C2×Q8C23×D7912yes—
569C2×D4—24no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—44no—
574C2×D4C23×D7912yes—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—3164no—
581C22×C4—3162no—
582C22×C4—794no—
583C22×C4—791no—
584C22×C4—794no—
585C22×C4—791no—
586C22×C4—791no—
587C22×C4—791no—
588C22×C4—1584no—
589C22×C4—1581no—
590C22×C4—1581no—
591C22×C4—1581no—
592C22×C4—1581no—
593C22×C4—1584no—
594C22×C4D4×D7912yes—
595C22×C4D4×D7911yescharacteristic
596C22×C4C23×D7912yes—
597C22×C4C23×D7911yescharacteristic
598Q16—1588no—
599Q16—1588no—
600SD16—28no—
601SD16—1588no—
602M16—28no—
603M16—1588no—
604C2×C8—22no—
605C2×C8—794no—
606C2×C8—792no—
607C2×C8—792no—
608C2×C8—1582no—
609C2×C8#1192962314yes—
610C2×C8C23×D7912yes—
611C2×C8C23×D7912yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—792no—
616C4⋊C4—792no—
617C4⋊C4—1584no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1584no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1584no—
626C4⋊C4—1584no—
627C4⋊C4—1581no—
628C4⋊C4—1581no—
629C4⋊C4C23×D7912yes—
630C4⋊C4C23×D7912yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1584no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C42—792no—
639C42—792no—
640C42—794no—
641C42—792no—
642C42—792no—
643C42—794no—
644C42—1584no—
645C42—1584no—
646C42—1584no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23C2×D4×D7912yes—
655C23C2×D4×D7911yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—3168no—
660Q8—3162no—
661Q8—3162no—
662Q8—1582no—
663Q8—1582no—
664Q8—1582no—
665Q8—1582no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—3162no—
681C2×C4—3162no—
682C2×C4—3162no—
683C2×C4—3162no—
684C2×C4—3168no—
685C2×C4—3164no—
686C2×C4—794no—
687C2×C4—792no—
688C2×C4—792no—
689C2×C4—792no—
690C2×C4—792no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1588no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4C2×D4×D7912yes—
700C2×C4C2×D4×D7911yescharacteristic
701C2×C4#41×D7912yes—
702C2×C4C2×#1192962312yes—
703C2×C4C24×D7911yescharacteristic
704C8—22no—
705C8—794no—
706C8—1582no—
707C8C2×#1192962314yes—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—44no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—84no—
716C22#1909910812yes—
717C22#137×D7912yes—
718C22#1909935912yes—
719C22C22×D4×D7911yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—3162no—
725C4—3162no—
726C4—3162no—
727C4—3162no—
728C4—794no—
729C4—1582no—
730C4—1582no—
731C4—1582no—
732C4#1909910812yes—
733C4C2×#41×D7911yescharacteristic
734C4C22×#1192962311yescharacteristic
735C2—42no—
736C2—82no—
737C2#2377399914yesdirect product factor
738C2C2×#1909910811yescharacteristic
739C2C2×#137×D7911yescharacteristic
740C2C2×#1909935911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#468×C79C2
socleC23×C79C22×D4
prime radicalC2×#121×C79C22
hypercenterC2×#468D79
hypocenterC79C2×#3172
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#19099115C2semidirect
3. #23773999C2direct (N × H)
4. C2×#19098971C2semidirect
5. C2×#19098954C2semidirect
6. C2×#19098930C2semidirect
7. C2×#19098921C2semidirect
8. C2×#19098821C2semidirect
9. C2×#19098819C2semidirect
11. C2×#19098657C2semidirect
12. C2×#19098655C2semidirect
13. C2×#19098654C2semidirect
14. C2×SD16×Dic79C2semidirect
15. C2×M16×Dic79C2semidirect
22. #19099115C22semidirect
44. #19098971C22semidirect
45. #19098954C22semidirect
46. #19098930C22semidirect
47. #19098921C22semidirect
48. #19098821C22semidirect
49. #19098819C22semidirect
51. #19098657C22semidirect
52. #19098655C22semidirect
53. #19098654C22semidirect
54. SD16×Dic79C22semidirect
64. M16×Dic79C22semidirect
367. C2×C79#3172semidirect
387. C79C2×#3172semidirect
737. C2#23773999direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991152
C2×#190990942
#237739992
C2×#190989712
C2×#190989542
C2×#190989302
C2×#190989212
C2×#190988212
C2×#190988192
C2×#190988072
C2×#190986572
C2×#190986552
C2×#190986542
C2×SD16×Dic792
C2×M16×Dic792
C2×#468×C792
C2×#317279