Finite Group Databasebeta

← C2×#23774107 #35158190

Subgroups — C2×#23774107 #35158190

Order 20224.

1998 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×#19099117C211yesmaximal, characteristic, complemented
2C2×#19099100C211yesmaximal, characteristic
3#23774107C2116yesmaximal, direct product factor
4C2×#19098970C211yesmaximal, characteristic, complemented
5C2×#19098956C211yesmaximal, characteristic, complemented
6C2×#19098930C211yesmaximal, characteristic, complemented
7C2×#19098924C211yesmaximal, characteristic, complemented
8C2×#19098803C211yesmaximal, characteristic, complemented
9C2×#19098801C211yesmaximal, characteristic, complemented
10C2×#19098795C211yesmaximal, characteristic
11C2×#19098793C211yesmaximal, characteristic
12C2×#19098668C211yesmaximal, characteristic, complemented
13C2×#19098665C211yesmaximal, characteristic, complemented
14C2×#19098661C211yesmaximal, characteristic, complemented
15C2×#97×D79C211yesmaximal, characteristic, complemented
16C2×#441×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929613C2211yescharacteristic
19C22×#11929611C2211yescharacteristic
20C22×C8×D79C2211yescharacteristic
21C22×C8×D79C2211yescharacteristic
22#19099117—24no—
23#19099117C2218yescomplemented
24C2×#14579160C2211yescharacteristic
25C2×#14579159C2211yescharacteristic
26#19099100—24no—
27#19099100C2218yes—
28C2×#14579156—21no—
29C2×#14579152C2211yescharacteristic
30C2×#14579151—21no—
31C2×#14579150C2211yescharacteristic
32C2×#14579146—21no—
33C2×#14579141C2211yescharacteristic
34C2×#14579139—21no—
35C2×#14579137C2211yescharacteristic
36C2×#14579137C2211yescharacteristic
37C2×#14579136C2211yescharacteristic
38C2×C4×Dic158—21no—
39C2×C4×Dic158C2211yescharacteristic
40C2×C4×D316—21no—
41C2×C4×D316C2211yescharacteristic
42C2×#14579118—21no—
43C2×#14579118—21no—
44C2×C42×D79C2211yescharacteristic
45#19098970C2218yescomplemented
46#19098956C2218yescomplemented
47#19098930C2218yescomplemented
48#19098924C2218yescomplemented
49#19098803C2218yescomplemented
50#19098801C2218yescomplemented
51#19098795C2218yes—
52#19098793C2218yes—
53#19098668C2218yescomplemented
54#19098665C2218yescomplemented
55#19098661C2218yescomplemented
56C2×#14579095C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579081C2211yescharacteristic
65C2×#14579072C2211yescharacteristic
66C2×#14579071C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68#97×D79C2218yescomplemented
69C22×Q16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71C2×C4×Q8×C79C2211yescharacteristic
72#441×C79C2218yescomplemented
73C2×#106×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×D316—21no—
80C22×D316C2311yescharacteristic
81C22×C4×D79—21no—
82C22×C4×D79D411yescharacteristic
83C22×C4×D79D411yescharacteristic
84C22×C4×D79C2311yescharacteristic
85C2×#11929614—24no—
86C2×#11929614C2314yes—
87C2×#11929613—24no—
88C2×#11929613C2314yes—
89C2×#11929611—24no—
90C2×#11929611C2314yes—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93C2×C8×D79—24no—
94C2×C8×D79—24no—
95C2×C8×D79C2314yes—
96C2×C8×D79C2314yes—
97#14579160—22no—
98#14579160C2314yes—
99#14579159—22no—
100#14579159C2314yes—
101#14579156—28no—
102#14579152—22no—
103#14579152C2314yes—
104#14579151—28no—
105#14579150—22no—
106#14579150C2314yes—
107#14579146—28no—
108#14579141—22no—
109#14579141C2314yes—
110#14579139—28no—
111#14579137—22no—
112#14579137—22no—
113#14579137C2314yes—
114#14579137C2314yes—
115#14579136—22no—
116#14579136C2314yes—
117C4×Dic158—22no—
118C4×Dic158—28no—
119C4×Dic158C2314yes—
120C4×D316—22no—
121C4×D316—28no—
122C4×D316C2314yes—
123#14579118—28no—
124#14579118—28no—
125C2×C4⋊Dic79—21no—
126C2×C4⋊Dic79—21no—
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×Dic79⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79D411yescharacteristic
145C2×C4×Dic79D411yescharacteristic
146C2×C4×Dic79C2311yescharacteristic
147C42×D79D414yes—
148C42×D79C2314yes—
149#14579095C2314yes—
150#14579094C2314yes—
151#14579092C2314yes—
152#14579086C2314yes—
153#14579085C2314yes—
154#14579085C2314yes—
155#14579084C2314yes—
156#14579083C2314yes—
157#14579081C2314yes—
158#14579072C2314yes—
159#14579071C2314yes—
160#14579071C2314yes—
161C22×Q8×C79C2311yescharacteristic
162C22×Q8×C79C2311yescharacteristic
163C2×Q16×C79—24no—
164C2×Q16×C79C2314yes—
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C4×Q8×C79—22no—
168C4×Q8×C79—22no—
169C4×Q8×C79C2314yes—
170C4×Q8×C79C2314yes—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79—21no—
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C42×C79—21no—
176C2×C42×C79—21no—
177C2×C42×C79C2311yescharacteristic
178#106×C79C2314yes—
179#103×C79C2314yes—
180#103×C79C2314yes—
181#97×C79C2314yes—
182C23×D79—21no—
183C23×D79C2×D411yescharacteristic
184C2×Dic158—24no—
185C2×Dic158—21no—
186C2×Dic158—22no—
187C2×Dic158—22no—
188C2×Dic158—44no—
189C2×Dic158C2412yes—
190C2×D316—24no—
191C2×D316—21no—
192C2×D316—22no—
193C2×D316—22no—
194C2×D316—44no—
195C2×D316C2412yes—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C2×C4×D79—24no—
203C2×C4×D79—24no—
204C2×C4×D79—22no—
205C2×C4×D79—22no—
206C2×C4×D79—42no—
207C2×C4×D79—44no—
208C2×C4×D79C2×D412yes—
209C2×C4×D79C2×D414yes—
210C2×C4×D79C2×D414yes—
211C2×C4×D79C2412yes—
212#11929614—28no—
213#11929613—28no—
214#11929611—28no—
215C2×C79⋊C8—22no—
216C2×C79⋊C8#4114yes—
217C2×C79⋊C8C2412yes—
218C2×C79⋊C8C2412yes—
219C8×D79—28no—
220C8×D79—28no—
221C4⋊Dic79—24no—
222C4⋊Dic79—24no—
223C4⋊Dic79—21no—
224C4⋊Dic79—21no—
225C4⋊Dic79C2412yes—
226C4⋊Dic79C2412yes—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4—24no—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4—24no—
241C4×Dic79—24no—
242C4×Dic79C2×D412yes—
243C4×Dic79C2×D414yes—
244C4×Dic79C2×D414yes—
245C4×Dic79C2412yes—
246C2×Q8×C79—21no—
247C2×Q8×C79—21no—
248C2×Q8×C79—22no—
249C2×Q8×C79—22no—
250C2×Q8×C79—22no—
251C2×Q8×C79—22no—
252C2×Q8×C79C2412yes—
253C2×Q8×C79C2412yes—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2×D411yescharacteristic
260C22×C4×C79C2411yescharacteristic
261Q16×C79—28no—
262C2×C8×C79—22no—
263C2×C8×C79#4114yes—
264C2×C8×C79C2412yes—
265C2×C8×C79C2412yes—
266C4⋊C4×C79—24no—
267C4⋊C4×C79—24no—
268C4⋊C4×C79—21no—
269C4⋊C4×C79—21no—
270C4⋊C4×C79C2412yes—
271C4⋊C4×C79C2412yes—
272C42×C79—24no—
273C42×C79—24no—
274C42×C79C2×D412yes—
275C42×C79C2412yes—
276C23×C79C22×D411yescharacteristic
277C22×D79—22no—
278C22×D79—22no—
279C22×D79—22no—
280C22×D79—42no—
281C22×D79—42no—
282C22×D79—42no—
283C22×D79#13714yes—
284C22×D79C22×D412yes—
285Q8×C79—22no—
286Q8×C79—22no—
287Q8×C79—22no—
288Q8×C79—22no—
289Q8×C79—42no—
290Q8×C79—42no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—42no—
298C2×C4×C79—42no—
299C2×C4×C79—42no—
300C2×C4×C79—42no—
301C2×C4×C79C22×D412yes—
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—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—42no—
314C2×Dic79—42no—
315C2×Dic79—42no—
316C2×Dic79C22×D412yes—
317C2×Dic79C22×D412yes—
318C2×Dic79C22×D412yes—
319D316—22no—
320D316—22no—
321D316—48no—
322D316—42no—
323C4×D79—28no—
324C4×D79—24no—
325C4×D79—22no—
326C4×D79—22no—
327C4×D79—44no—
328C4×D79—48no—
329Dic158—22no—
330Dic158—22no—
331Dic158—48no—
332Dic158—42no—
333C8×C79—22no—
334C8×C79C2×#4114yes—
335C79⋊C8—22no—
336C79⋊C8C2×#4114yes—
337C22×C79#53212yes—
338C22×C79C2×#13712yes—
339C22×C79#57512yes—
340C22×C79C23×D411yescharacteristic
341C2×D79—28no—
342C2×D79—22no—
343C2×D79—22no—
344C2×D79—42no—
345C2×D79—42no—
346C2×D79—42no—
347C2×D79—84no—
348C2×D79C2×#13714yes—
349C4×C79—22no—
350C4×C79—22no—
351C4×C79—42no—
352C4×C79—42no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79#53212yes—
356C4×C79C22×#4111yescharacteristic
357C4×C79C22×#4111yescharacteristic
358Dic79—22no—
359Dic79—22no—
360Dic79—22no—
361Dic79—42no—
362Dic79—42no—
363Dic79—42no—
364C2×#3181—791nomaximal, Sylow
365C2×C79#318114yescomplemented
366C2×C79C2×#53211yescharacteristic
367C2×C79C22×#13711yescharacteristic
368C2×C79C2×#57511yescharacteristic
369D79—24no—
370D79—82no—
371C2×#533—791no—
372C2×#529—791no—
373#3181—7916no—
374C2×#501—791no—
375C2×#497—791no—
376C2×#491—791no—
377C2×#489—791no—
378C2×#467—791no—
379C2×#467—791no—
380C2×#465—791no—
381C2×#465—791no—
382C2×#441—791no—
383C2×#441D7911yescharacteristic, complemented
384C2×#440—791no—
385C2×#440—791no—
386C22×#97—791no—
387C79C2×#318111yescharacteristic, complemented, Sylow
388C22×Q16—791no—
389C22×Q16C2×D7911yescharacteristic
390C22×SD16—791no—
391C22×SD16—791no—
392C23×C8—791no—
393C23×C8—791no—
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—791no—
408C2×C22⋊Q8—1581no—
409C2×#121—791no—
410C2×C4×Q8—791no—
411C2×C4×Q8—1581no—
412C2×C4×Q8C2×D7911yescharacteristic
413C2×C4×Q8C2×D7911yescharacteristic
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#467—798no—
424#467—798no—
425#465—798no—
426#465—798no—
427#441—798no—
428#441C2×D7918yescomplemented
429#440—798no—
430#440—798no—
431C2×#107—791no—
432C2×#107—791no—
433C2×#106—791no—
434C2×#106C2×D7911yescharacteristic
435C2×#103—791no—
436C2×#103—791no—
437C2×#103—791no—
438C2×#103—791no—
439C2×#103C2×D7911yescharacteristic
440C2×#103C2×D7911yescharacteristic
441C2×#102—791no—
442C2×#102—791no—
443C2×#97—791no—
444C2×#97—791no—
445C2×#97—791no—
446C2×#97—798no—
447C2×#97C2×D7911yescharacteristic
448C22×Q8—791no—
449C22×Q8—1581no—
450C22×Q8C22×D7911yescharacteristic
451C22×Q8C22×D7911yescharacteristic
452C22×D4—791no—
453C22×D4—1581no—
454C23×C4—791no—
455C23×C4—791no—
456C23×C4—791no—
457C23×C4—1581no—
458C2×Q16—24no—
459C2×Q16—794no—
460C2×Q16—1584no—
461C2×Q16C22×D7914yes—
462C2×SD16—794no—
463C2×SD16—794no—
464C2×SD16—1584no—
465C2×SD16—1584no—
466C22×C8—791no—
467C22×C8—791no—
468C22×C8—794no—
469C22×C8—794no—
470C22×C8—1584no—
471C22×C8—1584no—
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—794no—
486C22⋊Q8—794no—
487C22⋊Q8—794no—
488C22⋊Q8—1582no—
489C22⋊Q8—1588no—
490C22⋊Q8—1582no—
491C22⋊Q8—1582no—
492#121—794no—
493#121—1582no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—794no—
497C4×Q8—1588no—
498C4×Q8—1582no—
499C4×Q8C22×D7914yes—
500C4×Q8C22×D7914yes—
501C4×D4—794no—
502C4×D4—1588no—
503C4×D4—1582no—
504#117—1588no—
505#117—1588no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
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—1581no—
522C2×C22⋊C4—1581no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—791no—
531C2×C42—791no—
532C2×C42—791no—
533C2×C42—794no—
534C2×C42—794no—
535C2×C42—1581no—
536C2×C42C22×D7911yescharacteristic
537#107—794no—
538#107—794no—
539#106—794no—
540#106C22×D7914yes—
541#103—794no—
542#103—794no—
543#103—794no—
544#103—794no—
545#103C22×D7914yes—
546#103C22×D7914yes—
547#102—794no—
548#102—794no—
549#97—794no—
550#97—794no—
551#97—794no—
552#97C22×D7914yes—
553C24—791no—
554C24—1581no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—3164no—
562C2×Q8—792no—
563C2×Q8—1584no—
564C2×Q8—1582no—
565C2×Q8—1582no—
566C2×Q8—1581no—
567C2×Q8C23×D7912yes—
568C2×Q8C23×D7912yes—
569C2×D4—3164no—
570C2×D4—792no—
571C2×D4—1584no—
572C2×D4—1582no—
573C2×D4—1582no—
574C2×D4—1581no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—3164no—
580C22×C4—3162no—
581C22×C4—794no—
582C22×C4—791no—
583C22×C4—791no—
584C22×C4—791no—
585C22×C4—792no—
586C22×C4—794no—
587C22×C4—792no—
588C22×C4—1584no—
589C22×C4—1581no—
590C22×C4—1581no—
591C22×C4—1581no—
592C22×C4—1584no—
593C22×C4—1582no—
594C22×C4—1582no—
595C22×C4D4×D7911yescharacteristic
596C22×C4D4×D7911yescharacteristic
597C22×C4C23×D7911yescharacteristic
598Q16—28no—
599Q16—1588no—
600SD16—1588no—
601SD16—1588no—
602C2×C8—22no—
603C2×C8—794no—
604C2×C8—792no—
605C2×C8—792no—
606C2×C8—1588no—
607C2×C8—1582no—
608C2×C8—1588no—
609C2×C8#1192962414yes—
610C2×C8C23×D7912yes—
611C2×C8C23×D7912yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—792no—
617C4⋊C4—792no—
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—1584no—
632C22⋊C4—1584no—
633C22⋊C4—1584no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C42—24no—
639C42—24no—
640C42—792no—
641C42—794no—
642C42—794no—
643C42—792no—
644C42—1584no—
645C42D4×D7912yes—
646C42C23×D7912yes—
647C23—3162no—
648C23—3162no—
649C23—3162no—
650C23—794no—
651C23—792no—
652C23—1582no—
653C23—1582no—
654C23—1582no—
655C23C2×D4×D7911yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—3168no—
663Q8—3162no—
664Q8—1582no—
665Q8—1582no—
666D4—3168no—
667D4—3162no—
668D4—1582no—
669D4—1582no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—3168no—
681C2×C4—3164no—
682C2×C4—3162no—
683C2×C4—3162no—
684C2×C4—3162no—
685C2×C4—792no—
686C2×C4—792no—
687C2×C4—792no—
688C2×C4—1588no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1584no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4C2×D4×D7912yes—
699C2×C4C2×D4×D7912yes—
700C2×C4C2×D4×D7911yescharacteristic
701C2×C4#41×D7912yes—
702C2×C4C2×#1192962412yes—
703C2×C4C24×D7911yescharacteristic
704C8—22no—
705C8—794no—
706C8—1582no—
707C8C2×#1192962414yes—
708C22—3162no—
709C22—3162no—
710C22—3162no—
711C22—794no—
712C22—6324no—
713C22—1582no—
714C22—1588no—
715C22—1582no—
716C22#1909911012yes—
717C22#137×D7912yes—
718C22#1909936212yes—
719C22C22×D4×D7911yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—3162no—
727C4—3162no—
728C4—3162no—
729C4—1582no—
730C4—1582no—
731C4—1582no—
732C4#1909911012yes—
733C4C2×#41×D7911yescharacteristic
734C4C22×#1192962411yescharacteristic
735C2—6322no—
736C2—1584no—
737C2#2377410714yesdirect product factor
738C2C2×#1909911011yescharacteristic
739C2C2×#137×D7911yescharacteristic
740C2C2×#1909936211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#441×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579136C22
hypercenterC2×#441D79
hypocenterC79C2×#3181
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#19099117C2semidirect
3. #23774107C2direct (N × H)
4. C2×#19098970C2semidirect
5. C2×#19098956C2semidirect
6. C2×#19098930C2semidirect
7. C2×#19098924C2semidirect
8. C2×#19098803C2semidirect
9. C2×#19098801C2semidirect
12. C2×#19098668C2semidirect
13. C2×#19098665C2semidirect
14. C2×#19098661C2semidirect
15. C2×#97×D79C2semidirect
16. C2×#441×C79C2semidirect
23. #19099117C22semidirect
45. #19098970C22semidirect
46. #19098956C22semidirect
47. #19098930C22semidirect
48. #19098924C22semidirect
49. #19098803C22semidirect
50. #19098801C22semidirect
53. #19098668C22semidirect
54. #19098665C22semidirect
55. #19098661C22semidirect
68. #97×D79C22semidirect
72. #441×C79C22semidirect
365. C2×C79#3181semidirect
383. C2×#441D79semidirect
387. C79C2×#3181semidirect
428. #441C2×D79semidirect
737. C2#23774107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991172
C2×#190991002
#237741072
C2×#190989702
C2×#190989562
C2×#190989302
C2×#190989242
C2×#190988032
C2×#190988012
C2×#190987952
C2×#190987932
C2×#190986682
C2×#190986652
C2×#190986612
C2×#97×D792
C2×#441×C792
C2×#318179