Finite Group Databasebeta

← C2×#23773631 #35156550

Subgroups — C2×#23773631 #35156550

Order 20224.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099184C211yesmaximal, characteristic
2C2×#19099040C211yesmaximal, characteristic, complemented
3#23773631C2116yesmaximal, direct product factor
4C2×#19098905C211yesmaximal, characteristic, complemented
5C2×#19098888C211yesmaximal, characteristic
6C2×#19098859C211yesmaximal, characteristic, complemented
7C2×#19098849C211yesmaximal, characteristic, complemented
8C2×#19098786C211yesmaximal, characteristic, complemented
9C2×#19098786C211yesmaximal, characteristic, complemented
10C2×#19098721C211yesmaximal, characteristic, complemented
11C2×#19098704C211yesmaximal, characteristic
12C2×#19098671C211yesmaximal, characteristic, complemented
13C2×#19098665C211yesmaximal, characteristic, complemented
14C2×C4×Dic316C211yesmaximal, characteristic, complemented
15C2×C4×#11929613C211yesmaximal, characteristic, complemented
16C2×#433×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C22×Dic316C2211yescharacteristic
19C22×Dic316C2211yescharacteristic
20C22×#11929613C2211yescharacteristic
21C22×#11929613C2211yescharacteristic
22#19099184—24no—
23#19099184C2218yes—
24C2×#14579161C2211yescharacteristic
25C2×#14579156—21no—
26C2×#14579149C2211yescharacteristic
27C2×#14579147—21no—
28C2×#14579143—21no—
29C2×#14579140C2211yescharacteristic
30C2×#14579139—21no—
31C2×#14579135C2211yescharacteristic
32#19099040—24no—
33#19099040C2218yescomplemented
34C2×C4×Dic158C2211yescharacteristic
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×Dic158C2211yescharacteristic
37C2×C4×Dic158C2211yescharacteristic
38C2×C4×Dic158C2211yescharacteristic
39C2×#14579126—21no—
40C2×#14579126—21no—
41C2×C4×D316C2211yescharacteristic
42C2×#14579120C2211yescharacteristic
43C2×#14579117—21no—
44C2×#14579117—21no—
45#19098905C2218yescomplemented
46#19098888C2218yes—
47#19098859C2218yescomplemented
48#19098849C2218yescomplemented
49#19098786C2218yescomplemented
50#19098786C2218yescomplemented
51#19098721C2218yescomplemented
52#19098704C2218yes—
53#19098671C2218yescomplemented
54#19098665C2218yescomplemented
55C4×Dic316C2218yescomplemented
56C4×#11929613C2218yescomplemented
57C2×#14579095C2211yescharacteristic
58C2×#14579095C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579093C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579086C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579086C2211yescharacteristic
66C2×#14579086C2211yescharacteristic
67C2×#14579083C2211yescharacteristic
68C2×#14579083C2211yescharacteristic
69C2×#117×C79C2211yescharacteristic
70#433×C79C2218yescomplemented
71C2×C4⋊C8×C79C2211yescharacteristic
72C2×C4⋊C8×C79C2211yescharacteristic
73C2×C22⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×#97×C79C2211yescharacteristic
76C2×C4×C8×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—22no—
79C22×Dic158—24no—
80C22×Dic158—24no—
81C22×Dic158—21no—
82C22×Dic158C2314yes—
83C22×Dic158C2311yescharacteristic
84C22×Dic158C2311yescharacteristic
85C22×Dic158C2311yescharacteristic
86C22×D316C2311yescharacteristic
87C22×C22⋊D79—21no—
88C23×Dic79—21no—
89C22×C4×D79—21no—
90C2×Dic316—24no—
91C2×Dic316—24no—
92C2×Dic316C2314yes—
93C2×Dic316C2314yes—
94C2×#11929613—24no—
95C2×#11929613—24no—
96C2×#11929613C2314yes—
97C2×#11929613C2314yes—
98#14579161—22no—
99#14579161C2314yes—
100#14579156—28no—
101#14579149—22no—
102#14579149C2314yes—
103#14579147—28no—
104#14579143—28no—
105#14579140—22no—
106#14579140C2314yes—
107#14579139—28no—
108#14579135—22no—
109#14579135C2314yes—
110C4×Dic158—22no—
111C4×Dic158—22no—
112C4×Dic158—22no—
113C4×Dic158—22no—
114C4×Dic158—22no—
115C4×Dic158C2314yes—
116C4×Dic158C2314yes—
117C4×Dic158C2314yes—
118C4×Dic158C2314yes—
119C4×Dic158C2314yes—
120#14579126—28no—
121#14579126—28no—
122C4×D316—22no—
123C4×D316C2314yes—
124#14579120—22no—
125#14579120C2314yes—
126#14579117—28no—
127#14579117—28no—
128C2×C4⋊Dic79—21no—
129C2×C4⋊Dic79C2311yescharacteristic
130C2×C4⋊Dic79C2311yescharacteristic
131C2×C4⋊Dic79C2311yescharacteristic
132C2×C4⋊Dic79C2311yescharacteristic
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×Dic79⋊C4—21no—
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C2×C22⋊Dic79—21no—
140C2×C22⋊Dic79—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×(C2×D79)⋊C4—21no—
144C2×(C2×D79)⋊C4—21no—
145C2×C4×Dic79—21no—
146C2×C4×Dic79—21no—
147C2×C4×Dic79—21no—
148C2×C4×Dic79—21no—
149C2×C4×Dic79—21no—
150C2×C4×Dic79—21no—
151#14579095C2314yes—
152#14579095C2314yes—
153#14579093C2314yes—
154#14579093C2314yes—
155#14579086C2314yes—
156#14579086C2314yes—
157#14579086C2314yes—
158#14579086C2314yes—
159#14579086C2314yes—
160#14579086C2314yes—
161#14579083C2314yes—
162#14579083C2314yes—
163C23×C4×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168#117×C79D414yes—
169#117×C79C2314yes—
170C2×C4⋊C4×C79D411yescharacteristic
171C2×C4⋊C4×C79D411yescharacteristic
172C2×C22⋊C4×C79D411yescharacteristic
173C2×C22⋊C4×C79D411yescharacteristic
174C2×C42×C79C2311yescharacteristic
175C2×C42×C79C2311yescharacteristic
176C4⋊C8×C79C2314yes—
177C4⋊C8×C79C2314yes—
178C22⋊C8×C79C2314yes—
179C22⋊C8×C79C2314yes—
180#97×C79C2314yes—
181C4×C8×C79C2314yes—
182C23×D79—21no—
183C2×Dic158—28no—
184C2×Dic158—216no—
185C2×Dic158—28no—
186C2×Dic158—28no—
187C2×Dic158—24no—
188C2×Dic158—21no—
189C2×Dic158—21no—
190C2×Dic158—21no—
191C2×Dic158—24no—
192C2×Dic158—22no—
193C2×Dic158—22no—
194C2×Dic158—22no—
195C2×Dic158—22no—
196C2×Dic158—82no—
197C2×Dic158#4114yes—
198C2×Dic158#4114yes—
199C2×Dic158C2412yes—
200C2×Dic158C2412yes—
201C2×Dic158C2412yes—
202C2×D316—21no—
203C2×D316—22no—
204C2×D316—22no—
205C2×D316C2412yes—
206C2×C22⋊D79—24no—
207C2×C22⋊D79—82no—
208C22×Dic79—28no—
209C22×Dic79—21no—
210C22×Dic79—21no—
211C22×Dic79—24no—
212C22×Dic79—21no—
213C22×Dic79—21no—
214C22×Dic79—21no—
215C22×Dic79—21no—
216C22×Dic79—21no—
217C2×C4×D79—24no—
218C2×C4×D79—82no—
219Dic316—28no—
220Dic316—28no—
221#11929613—28no—
222#11929613—28no—
223C4⋊Dic79—24no—
224C4⋊Dic79—21no—
225C4⋊Dic79—21no—
226C4⋊Dic79—21no—
227C4⋊Dic79—21no—
228C4⋊Dic79C2412yes—
229C4⋊Dic79C2412yes—
230C4⋊Dic79C2412yes—
231C4⋊Dic79C2412yes—
232Dic79⋊C4—24no—
233Dic79⋊C4—24no—
234Dic79⋊C4—24no—
235Dic79⋊C4—24no—
236Dic79⋊C4—24no—
237Dic79⋊C4—24no—
238C22⋊Dic79—24no—
239C22⋊Dic79—24no—
240(C2×D79)⋊C4—24no—
241(C2×D79)⋊C4—24no—
242(C2×D79)⋊C4—24no—
243(C2×D79)⋊C4—24no—
244C4×Dic79—24no—
245C4×Dic79—24no—
246C4×Dic79—24no—
247C4×Dic79—24no—
248C4×Dic79—24no—
249C4×Dic79—24no—
250C24×C79C2×D411yescharacteristic
251C22×C4×C79—22no—
252C22×C4×C79—22no—
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D412yes—
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2412yes—
260C22×C4×C79C2411yescharacteristic
261C2×C8×C79—22no—
262C2×C8×C79—22no—
263C2×C8×C79—22no—
264C2×C8×C79—22no—
265C2×C8×C79C2412yes—
266C2×C8×C79C2412yes—
267C2×C8×C79C2412yes—
268C2×C8×C79C2412yes—
269C4⋊C4×C79C2×D414yes—
270C4⋊C4×C79C2×D414yes—
271C22⋊C4×C79C2×D414yes—
272C22⋊C4×C79C2×D414yes—
273C42×C79C2×D412yes—
274C42×C79C2×D412yes—
275C42×C79C2412yes—
276C42×C79C2412yes—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—22no—
280C23×C79C22×D412yes—
281C23×C79C22×D411yescharacteristic
282C22×D79—22no—
283C22×D79—42no—
284C22×D79—42no—
285C22×D79—42no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—24no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79C22×D412yes—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D412yes—
297C2×C4×C79C22×D412yes—
298C2×C4×C79C22×D412yes—
299C2×C4×C79C22×D411yescharacteristic
300C2×C4×C79C2×#4112yes—
301C2×C4×C79C2×#4112yes—
302C2×C4×C79C2511yescharacteristic
303C22⋊D79—84no—
304C2×Dic79—216no—
305C2×Dic79—24no—
306C2×Dic79—24no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—42no—
315C2×Dic79—42no—
316C2×Dic79—42no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319D316—22no—
320D316—22no—
321D316—42no—
322C4×D79—84no—
323Dic158—216no—
324Dic158—24no—
325Dic158—24no—
326Dic158—22no—
327Dic158—22no—
328Dic158—22no—
329Dic158—22no—
330Dic158—42no—
331Dic158—84no—
332Dic158C2×#4114yes—
333Dic158C2×#4114yes—
334C8×C79—22no—
335C8×C79—22no—
336C8×C79—22no—
337C8×C79—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—44no—
342C22×C79#52512yes—
343C22×C79#57712yes—
344C22×C79#57812yes—
345C22×C79C23×D411yescharacteristic
346C2×D79—42no—
347C2×D79—42no—
348C2×D79—42no—
349C2×D79—84no—
350C4×C79—22no—
351C4×C79—22no—
352C4×C79—22no—
353C4×C79—22no—
354C4×C79—22no—
355C4×C79#52512yes—
356C4×C79C22×#4111yescharacteristic
357C4×C79C22×#4111yescharacteristic
358Dic79—24no—
359Dic79—24no—
360Dic79—42no—
361Dic79—42no—
362Dic79—42no—
363Dic79—42no—
364Dic79—42no—
365C2×#3121—791nomaximal, Sylow
366C2×C79—42no—
367C2×C79#312114yescomplemented
368C2×C79C2×#52511yescharacteristic
369C2×C79C2×#57711yescharacteristic
370C2×C79C2×#57811yescharacteristic
371D79—82no—
372C2×#542—791no—
373C2×#519—791no—
374#3121—7916no—
375C2×#485—791no—
376C2×#482—791no—
377C2×#477—791no—
378C2×#475—791no—
379C2×#464—791no—
380C2×#464—791no—
381C2×#451—791no—
382C2×#448—791no—
383C2×#441—791no—
384C2×#440—791no—
385C2×C4×Q16—791no—
386C2×C4×SD16—791no—
387C2×#433D7911yescharacteristic, complemented
388C79C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8—791no—
390C22×Q16—791no—
391C22×Q16—791no—
392C22×SD16—791no—
393C22×SD16—791no—
394#542—798no—
395#542—1584no—
396C2×C4⋊Q8—791no—
397C2×#126—1581no—
398C2×#124—791no—
399C2×#124—1581no—
400C2×#123—1581no—
401C2×C22⋊Q8—791no—
402C2×C22⋊Q8—1581no—
403C2×#121—791no—
404#519—798no—
405#519—1584no—
406C2×C4×Q8—791no—
407C2×C4×Q8—791no—
408C2×C4×Q8—791no—
409C2×C4×Q8—791no—
410C2×C4×Q8—791no—
411C2×C4×Q8—1581no—
412C2×C4×Q8—1581no—
413C2×C4×D4—791no—
414C2×#117—791no—
415C2×#117—1581no—
416C2×#117—1581no—
417C2×#117C2×D7911yescharacteristic
418#485—798no—
419#482—798no—
420#477—798no—
421#475—798no—
422#464—798no—
423#464—798no—
424#451—798no—
425#448—798no—
426#441—798no—
427#440—798no—
428C4×Q16—798no—
429C4×SD16—798no—
430#433C2×D7918yescomplemented
431C2×#107—791no—
432C2×#107—791no—
433C2×#106—791no—
434C2×#106—791no—
435C2×C4⋊C8C2×D7911yescharacteristic
436C2×C4⋊C8C2×D7911yescharacteristic
437C2×#103—791no—
438C2×#103—791no—
439C2×#103—791no—
440C2×#103—791no—
441C2×#103—791no—
442C2×#103—791no—
443C2×#102—791no—
444C2×#102—791no—
445C2×C22⋊C8C2×D7911yescharacteristic
446C2×C22⋊C8C2×D7911yescharacteristic
447C2×#97C2×D7911yescharacteristic
448C2×C4×C8C2×D7911yescharacteristic
449C22×Q8—791no—
450C22×Q8—791no—
451C22×Q8—791no—
452C22×Q8—794no—
453C22×Q8—1584no—
454C22×Q8—1584no—
455C22×Q8—1581no—
456C22×Q8—1581no—
457C22×Q8—1582no—
458C22×D4—791no—
459C22×D4—1581no—
460C23×C4—1581no—
461C23×C4—1581no—
462C23×C4C22×D7911yescharacteristic
463C2×Q16—794no—
464C2×Q16—794no—
465C2×Q16—1584no—
466C2×Q16—1584no—
467C2×SD16—794no—
468C2×SD16—794no—
469C2×SD16—1584no—
470C2×SD16—1584no—
471C22×C8C22×D7911yescharacteristic
472C22×C8C22×D7911yescharacteristic
473C22×C8C22×D7911yescharacteristic
474C22×C8C22×D7911yescharacteristic
475C4⋊Q8—794no—
476C4⋊Q8—1582no—
477#126—1588no—
478#124—794no—
479#124—1588no—
480#124—1582no—
481#123—1588no—
482C22⋊Q8—794no—
483C22⋊Q8—1582no—
484C22⋊Q8—1588no—
485#121—794no—
486#121—1582no—
487C4×Q8—794no—
488C4×Q8—794no—
489C4×Q8—794no—
490C4×Q8—794no—
491C4×Q8—794no—
492C4×Q8—1588no—
493C4×Q8—1588no—
494C4×Q8—1582no—
495C4×Q8—1582no—
496C4×Q8—1582no—
497C4×Q8—1582no—
498C4×Q8—1582no—
499C4×D4—794no—
500C4×D4—1582no—
501#117—794no—
502#117—1582no—
503#117—1588no—
504#117—1588no—
505#117D31614yes—
506#117C22×D7914yes—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—791no—
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⋊C4D31611yescharacteristic
519C2×C4⋊C4D31611yescharacteristic
520C2×C22⋊C4—1581no—
521C2×C22⋊C4—1581no—
522C2×C22⋊C4—1581no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4D31611yescharacteristic
527C2×C22⋊C4D31611yescharacteristic
528C2×C42—1581no—
529C2×C42—1581no—
530C2×C42—1581no—
531C2×C42—1581no—
532C2×C42—1581no—
533C2×C42—1581no—
534C2×C42C22×D7911yescharacteristic
535C2×C42C22×D7911yescharacteristic
536#107—794no—
537#107—794no—
538#106—794no—
539#106—794no—
540C4⋊C8C22×D7914yes—
541C4⋊C8C22×D7914yes—
542#103—794no—
543#103—794no—
544#103—794no—
545#103—794no—
546#103—794no—
547#103—794no—
548#102—794no—
549#102—794no—
550C22⋊C8C22×D7914yes—
551C22⋊C8C22×D7914yes—
552#97C22×D7914yes—
553C4×C8C22×D7914yes—
554C24—1581no—
555C24C2×D31611yescharacteristic
556C2×Q8—794no—
557C2×Q8—794no—
558C2×Q8—792no—
559C2×Q8—792no—
560C2×Q8—792no—
561C2×Q8—6322no—
562C2×Q8—1588no—
563C2×Q8—1588no—
564C2×Q8—1588no—
565C2×Q8—15816no—
566C2×Q8—1582no—
567C2×Q8—1582no—
568C2×Q8—1582no—
569C2×Q8—1582no—
570C2×Q8—1581no—
571C2×Q8—1584no—
572C2×Q8—1584no—
573C2×Q8—1581no—
574C2×Q8—1581no—
575C2×D4—792no—
576C2×D4—6322no—
577C2×D4—1584no—
578C2×D4—1582no—
579C2×D4—1582no—
580C2×D4—1581no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—6322no—
584C22×C4—1581no—
585C22×C4—1581no—
586C22×C4—1581no—
587C22×C4—1581no—
588C22×C4—1581no—
589C22×C4—1584no—
590C22×C4—1588no—
591C22×C4—1584no—
592C22×C4—1581no—
593C22×C4—1581no—
594C22×C4C2×D31612yes—
595C22×C4C2×D31611yescharacteristic
596C22×C4C2×D31611yescharacteristic
597C22×C4C2×D31611yescharacteristic
598C22×C4C2×D31611yescharacteristic
599C22×C4C2×D31611yescharacteristic
600C22×C4C23×D7912yes—
601C22×C4C23×D7911yescharacteristic
602Q16—1588no—
603Q16—1588no—
604SD16—1588no—
605SD16—1588no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C23×D7912yes—
611C2×C8C23×D7912yes—
612C2×C8C23×D7912yes—
613C2×C8C23×D7912yes—
614C4⋊C4—792no—
615C4⋊C4—792no—
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—1581no—
625C4⋊C4—1581no—
626C4⋊C4—1581no—
627C4⋊C4—1581no—
628C4⋊C4—1584no—
629C4⋊C4C2×D31614yes—
630C4⋊C4C2×D31614yes—
631C22⋊C4—1584no—
632C22⋊C4—1584no—
633C22⋊C4—1584no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4C2×D31614yes—
638C22⋊C4C2×D31614yes—
639C42—1584no—
640C42—1584no—
641C42—1584no—
642C42—1584no—
643C42—1584no—
644C42—1584no—
645C42C2×D31612yes—
646C42C2×D31612yes—
647C42C23×D7912yes—
648C42C23×D7912yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—3162no—
653C23—3162no—
654C23—3162no—
655C23—1582no—
656C23C22×D31612yes—
657C23C22×D31611yescharacteristic
658Q8—3162no—
659Q8—794no—
660Q8—794no—
661Q8—6324no—
662Q8—15816no—
663Q8—1582no—
664Q8—1582no—
665Q8—1584no—
666Q8—1584no—
667Q8—1582no—
668Q8—1582no—
669D4—3162no—
670D4—6324no—
671D4—1582no—
672D4—1582no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—3162no—
682C2×C4—3162no—
683C2×C4—3162no—
684C2×C4—3162no—
685C2×C4—3162no—
686C2×C4—6324no—
687C2×C4—1582no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—15816no—
693C2×C4—1584no—
694C2×C4—1584no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4C22×D31612yes—
698C2×C4C22×D31612yes—
699C2×C4C22×D31612yes—
700C2×C4C22×D31612yes—
701C2×C4C22×D31612yes—
702C2×C4C22×D31611yescharacteristic
703C2×C4#41×D7912yes—
704C2×C4#41×D7912yes—
705C2×C4C24×D7911yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—3162no—
715C22—3162no—
716C22—3162no—
717C22—6324no—
718C22#1909907512yes—
719C22#1909937512yes—
720C22#1909938012yes—
721C22C23×D31611yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—3162no—
728C4—3162no—
729C4—3162no—
730C4—3162no—
731C4—3162no—
732C4—1584no—
733C4—1584no—
734C4#1909907512yes—
735C4C2×#41×D7911yescharacteristic
736C4C2×#41×D7911yescharacteristic
737C2—42no—
738C2—6322no—
739C2#2377363114yesdirect product factor
740C2C2×#1909907511yescharacteristic
741C2C2×#1909937511yescharacteristic
742C2C2×#1909938011yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#433×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
hypercenterC2×#433D79
hypocenterC79C2×#3121
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. C2×#19099040C2semidirect
3. #23773631C2direct (N × H)
4. C2×#19098905C2semidirect
6. C2×#19098859C2semidirect
7. C2×#19098849C2semidirect
8. C2×#19098786C2semidirect
9. C2×#19098786C2semidirect
10. C2×#19098721C2semidirect
12. C2×#19098671C2semidirect
13. C2×#19098665C2semidirect
14. C2×C4×Dic316C2semidirect
15. C2×C4×#11929613C2semidirect
16. C2×#433×C79C2semidirect
33. #19099040C22semidirect
45. #19098905C22semidirect
47. #19098859C22semidirect
48. #19098849C22semidirect
49. #19098786C22semidirect
50. #19098786C22semidirect
51. #19098721C22semidirect
53. #19098671C22semidirect
54. #19098665C22semidirect
55. C4×Dic316C22semidirect
56. C4×#11929613C22semidirect
70. #433×C79C22semidirect
367. C2×C79#3121semidirect
387. C2×#433D79semidirect
388. C79C2×#3121semidirect
430. #433C2×D79semidirect
739. C2#23773631direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991842
C2×#190990402
#237736312
C2×#190989052
C2×#190988882
C2×#190988592
C2×#190988492
C2×#190987862
C2×#190987212
C2×#190987042
C2×#190986712
C2×#190986652
C2×C4×Dic3162
C2×C4×#119296132
C2×#433×C792
C2×#312179