Finite Group Databasebeta

← C2×#23774700 #35160508

Subgroups — C2×#23774700 #35160508

Order 20224.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099191C211yesmaximal, characteristic, complemented
2C2×#19099184C211yesmaximal, characteristic
3#23774700C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098961C211yesmaximal, characteristic, complemented
6C2×#19098923C211yesmaximal, characteristic, complemented
7C2×#19098918C211yesmaximal, characteristic, complemented
8C2×#19098882C211yesmaximal, characteristic
9C2×#19098905C211yesmaximal, characteristic, complemented
10C2×#19098888C211yesmaximal, characteristic
11C2×#19098894C211yesmaximal, characteristic, complemented
12C2×#19098871C211yesmaximal, characteristic, complemented
13C2×#19098849C211yesmaximal, characteristic, complemented
14C2×#19098864C211yesmaximal, characteristic, complemented
15C2×#19098854C211yesmaximal, characteristic, complemented
16C2×#433×C79C211yesmaximal, characteristic, complemented
17#19099191—24no—
18#19099191C2218yescomplemented
19#19099184—24no—
20#19099184C2218yes—
21C2×#14579161C2211yescharacteristic
22C2×#14579161C2211yescharacteristic
23C2×#14579161C2211yescharacteristic
24C2×#14579160—21no—
25C2×#14579156—21no—
26C2×#14579153C2211yescharacteristic
27C2×#14579153C2211yescharacteristic
28C2×#14579152—21no—
29C2×#14579149C2211yescharacteristic
30C2×#14579147—21no—
31C2×#14579143—21no—
32C2×#14579140C2211yescharacteristic
33C2×#14579139—21no—
34C2×#14579138—21no—
35C2×#14579138—21no—
36C2×#14579135C2211yescharacteristic
37C2×C4×Dic158C2211yescharacteristic
38C2×C4×D316C2211yescharacteristic
39C2×#14579120C2211yescharacteristic
40C22×C4⋊Dic79C2211yescharacteristic
41#19098972C2218yescomplemented
42#19098961C2218yescomplemented
43#19098923C2218yescomplemented
44#19098918C2218yescomplemented
45#19098905C2218yescomplemented
46#19098894C2218yescomplemented
47#19098888C2218yes—
48#19098882C2218yes—
49#19098871C2218yescomplemented
50#19098864C2218yescomplemented
51#19098854C2218yescomplemented
52#19098849C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579093C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579093C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579093C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579086C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579083C2211yescharacteristic
66C2×#14579083C2211yescharacteristic
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—21no—
79C22×Dic158—21no—
80C22×Dic158C2311yescharacteristic
81C22×D316C2311yescharacteristic
82C22×C22⋊D79—21no—
83C23×Dic79—21no—
84C22×C4×D79—21no—
85#14579161—22no—
86#14579161—22no—
87#14579161—22no—
88#14579161C2314yes—
89#14579161C2314yes—
90#14579161C2314yes—
91#14579160—28no—
92#14579156—28no—
93#14579153—22no—
94#14579153—22no—
95#14579153C2314yes—
96#14579153C2314yes—
97#14579152—28no—
98#14579149—22no—
99#14579149C2314yes—
100#14579147—28no—
101#14579143—28no—
102#14579140—22no—
103#14579140C2314yes—
104#14579139—28no—
105#14579138—28no—
106#14579138—28no—
107#14579135—22no—
108#14579135C2314yes—
109C4×Dic158—22no—
110C4×Dic158C2314yes—
111C4×D316—22no—
112C4×D316C2314yes—
113#14579120—22no—
114#14579120C2314yes—
115C2×C4⋊Dic79—22no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79C2314yes—
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
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×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141#14579095C2314yes—
142#14579095C2314yes—
143#14579093C2314yes—
144#14579093C2314yes—
145#14579093C2314yes—
146#14579093C2314yes—
147#14579093C2314yes—
148#14579093C2314yes—
149#14579086C2314yes—
150#14579086C2314yes—
151#14579086C2314yes—
152#14579086C2314yes—
153#14579083C2314yes—
154#14579083C2314yes—
155#14579083C2314yes—
156#14579083C2314yes—
157C23×C4×C79C2311yescharacteristic
158C22×C8×C79C2311yescharacteristic
159C22×C8×C79C2311yescharacteristic
160C22×C8×C79C2311yescharacteristic
161C22×C8×C79C2311yescharacteristic
162#117×C79D414yes—
163#117×C79C2314yes—
164C2×C4⋊C4×C79D411yescharacteristic
165C2×C4⋊C4×C79D411yescharacteristic
166C2×C22⋊C4×C79D411yescharacteristic
167C2×C22⋊C4×C79D411yescharacteristic
168C2×C42×C79C2311yescharacteristic
169C2×C42×C79C2311yescharacteristic
170C4⋊C8×C79C2314yes—
171C4⋊C8×C79C2314yes—
172C22⋊C8×C79C2314yes—
173C22⋊C8×C79C2314yes—
174#97×C79C2314yes—
175C4×C8×C79C2314yes—
176C23×D79—21no—
177C2×Dic158—21no—
178C2×Dic158—24no—
179C2×Dic158—24no—
180C2×Dic158—24no—
181C2×Dic158—22no—
182C2×Dic158—22no—
183C2×Dic158—82no—
184C2×Dic158—82no—
185C2×Dic158—82no—
186C2×Dic158C2412yes—
187C2×D316—21no—
188C2×D316—22no—
189C2×D316—22no—
190C2×D316C2412yes—
191C2×C22⋊D79—24no—
192C2×C22⋊D79—82no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—24no—
201C22×Dic79—82no—
202C2×C4×D79—24no—
203C2×C4×D79—82no—
204C4⋊Dic79—24no—
205C4⋊Dic79—21no—
206C4⋊Dic79—21no—
207C4⋊Dic79—24no—
208C4⋊Dic79—24no—
209C4⋊Dic79—24no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216C4⋊Dic79C2412yes—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219C4⋊Dic79C2412yes—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226C22⋊Dic79—24no—
227C22⋊Dic79—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232C4×Dic79—24no—
233C4×Dic79—24no—
234C24×C79C2×D411yescharacteristic
235C22×C4×C79—22no—
236C22×C4×C79—22no—
237C22×C4×C79C2×D411yescharacteristic
238C22×C4×C79C2×D411yescharacteristic
239C22×C4×C79C2×D411yescharacteristic
240C22×C4×C79C2×D411yescharacteristic
241C22×C4×C79C2×D411yescharacteristic
242C22×C4×C79C2×D412yes—
243C22×C4×C79C2412yes—
244C22×C4×C79C2411yescharacteristic
245C2×C8×C79—22no—
246C2×C8×C79—22no—
247C2×C8×C79—22no—
248C2×C8×C79—22no—
249C2×C8×C79C2412yes—
250C2×C8×C79C2412yes—
251C2×C8×C79C2412yes—
252C2×C8×C79C2412yes—
253C4⋊C4×C79C2×D414yes—
254C4⋊C4×C79C2×D414yes—
255C22⋊C4×C79C2×D414yes—
256C22⋊C4×C79C2×D414yes—
257C42×C79C2×D412yes—
258C42×C79C2×D412yes—
259C42×C79C2412yes—
260C42×C79C2412yes—
261C23×C79—22no—
262C23×C79—22no—
263C23×C79—22no—
264C23×C79C22×D412yes—
265C23×C79C22×D411yescharacteristic
266C22×D79—22no—
267C22×D79—42no—
268C22×D79—42no—
269C22×D79—42no—
270C2×C4×C79—22no—
271C2×C4×C79—22no—
272C2×C4×C79—22no—
273C2×C4×C79—22no—
274C2×C4×C79—22no—
275C2×C4×C79—24no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79C22×D412yes—
279C2×C4×C79C22×D412yes—
280C2×C4×C79C22×D412yes—
281C2×C4×C79C22×D412yes—
282C2×C4×C79C22×D412yes—
283C2×C4×C79C22×D411yescharacteristic
284C2×C4×C792−1+412yes—
285C2×C4×C792−1+412yes—
286C2×C4×C79C2511yescharacteristic
287C22⋊D79—84no—
288C2×Dic79—22no—
289C2×Dic79—22no—
290C2×Dic79—22no—
291C2×Dic79—22no—
292C2×Dic79—22no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—42no—
296C2×Dic79—42no—
297C2×Dic79—42no—
298C2×Dic79—42no—
299C2×Dic79—42no—
300C2×Dic79—42no—
301C2×Dic79—42no—
302C2×Dic79—84no—
303D316—22no—
304D316—22no—
305D316—42no—
306C4×D79—84no—
307Dic158—22no—
308Dic158—22no—
309Dic158—42no—
310Dic158—84no—
311Dic158—84no—
312Dic158—84no—
313C8×C79—22no—
314C8×C79—22no—
315C8×C79—22no—
316C8×C79—22no—
317C22×C79—22no—
318C22×C79—22no—
319C22×C79—22no—
320C22×C79—44no—
321C22×C79#53612yes—
322C22×C79#57712yes—
323C22×C79#57712yes—
324C22×C79C23×D411yescharacteristic
325C2×D79—42no—
326C2×D79—42no—
327C2×D79—42no—
328C2×D79—84no—
329C4×C79—22no—
330C4×C79—22no—
331C4×C79—22no—
332C4×C79—22no—
333C4×C79—22no—
334C4×C79#53612yes—
335C4×C79C2×2−1+411yescharacteristic
336C4×C79C2×2−1+411yescharacteristic
337Dic79—42no—
338Dic79—42no—
339Dic79—42no—
340Dic79—42no—
341Dic79—42no—
342Dic79—42no—
343Dic79—42no—
344C2×#3244—791nomaximal, Sylow
345C2×C79—42no—
346C2×C79#324414yescomplemented
347C2×C79C2×#53611yescharacteristic
348C2×C79C2×#57711yescharacteristic
349C2×C79C2×#57711yescharacteristic
350D79—82no—
351C2×#544—791no—
352C2×#542—791no—
353#3244—7916no—
354C2×#501—791no—
355C2×#498—791no—
356C2×#489—791no—
357C2×#488—791no—
358C2×#481—791no—
359C2×#485—791no—
360C2×#482—791no—
361C2×#483—791no—
362C2×#479—791no—
363C2×#475—791no—
364C2×#478—791no—
365C2×#476—791no—
366C2×#433D7911yescharacteristic, complemented
367C79C2×#324411yescharacteristic, complemented, Sylow
368#544—798no—
369#544—1584no—
370#542—798no—
371#542—1584no—
372C2×C4⋊Q8—791no—
373C2×C4⋊Q8—791no—
374C2×C4⋊Q8—791no—
375C2×C4⋊Q8—1581no—
376C2×#126—1581no—
377C2×#125—791no—
378C2×#125—791no—
379C2×#125—1581no—
380C2×#124—791no—
381C2×#124—1581no—
382C2×#123—1581no—
383C2×C22⋊Q8—791no—
384C2×C22⋊Q8—1581no—
385C2×C22⋊Q8—1581no—
386C2×C22⋊Q8—1581no—
387C2×#121—791no—
388C2×C4×Q8—791no—
389C2×C4×D4—791no—
390C2×#117—791no—
391C2×#117C2×D7911yescharacteristic
392C22×C4⋊C4—791no—
393#501—798no—
394#498—798no—
395#489—798no—
396#488—798no—
397#485—798no—
398#483—798no—
399#482—798no—
400#481—798no—
401#479—798no—
402#478—798no—
403#476—798no—
404#475—798no—
405#433C2×D7918yescomplemented
406C2×#107—791no—
407C2×#107—791no—
408C2×#106—791no—
409C2×#106—791no—
410C2×#106—791no—
411C2×#106—791no—
412C2×#106—791no—
413C2×#106—791no—
414C2×C4⋊C8C2×D7911yescharacteristic
415C2×C4⋊C8C2×D7911yescharacteristic
416C2×#103—791no—
417C2×#103—791no—
418C2×#103—791no—
419C2×#103—791no—
420C2×#102—791no—
421C2×#102—791no—
422C2×#102—791no—
423C2×#102—791no—
424C2×C22⋊C8C2×D7911yescharacteristic
425C2×C22⋊C8C2×D7911yescharacteristic
426C2×#97C2×D7911yescharacteristic
427C2×C4×C8C2×D7911yescharacteristic
428C22×Q8—791no—
429C22×Q8—1581no—
430C22×Q8—1581no—
431C22×Q8—1581no—
432C22×D4—791no—
433C22×D4—1581no—
434C23×C4—1581no—
435C23×C4—1581no—
436C23×C4C22×D7911yescharacteristic
437C22×C8C22×D7911yescharacteristic
438C22×C8C22×D7911yescharacteristic
439C22×C8C22×D7911yescharacteristic
440C22×C8C22×D7911yescharacteristic
441C4⋊Q8—794no—
442C4⋊Q8—794no—
443C4⋊Q8—794no—
444C4⋊Q8—1588no—
445C4⋊Q8—1582no—
446C4⋊Q8—1582no—
447C4⋊Q8—1582no—
448#126—1588no—
449#125—794no—
450#125—794no—
451#125—1588no—
452#125—1582no—
453#125—1582no—
454#124—794no—
455#124—1588no—
456#124—1582no—
457#123—1588no—
458C22⋊Q8—794no—
459C22⋊Q8—1582no—
460C22⋊Q8—1588no—
461C22⋊Q8—1588no—
462C22⋊Q8—1588no—
463#121—794no—
464#121—1582no—
465C4×Q8—794no—
466C4×Q8—1582no—
467C4×D4—794no—
468C4×D4—1582no—
469#117—794no—
470#117—1582no—
471#117D31614yes—
472#117C22×D7914yes—
473C2×C4⋊C4—791no—
474C2×C4⋊C4—791no—
475C2×C4⋊C4—794no—
476C2×C4⋊C4—791no—
477C2×C4⋊C4—791no—
478C2×C4⋊C4—791no—
479C2×C4⋊C4—791no—
480C2×C4⋊C4—1581no—
481C2×C4⋊C4—1582no—
482C2×C4⋊C4—1581no—
483C2×C4⋊C4—1581no—
484C2×C4⋊C4—1581no—
485C2×C4⋊C4—1581no—
486C2×C4⋊C4—1581no—
487C2×C4⋊C4—1581no—
488C2×C4⋊C4—1581no—
489C2×C4⋊C4—1581no—
490C2×C4⋊C4—1581no—
491C2×C4⋊C4D31611yescharacteristic
492C2×C4⋊C4D31611yescharacteristic
493C2×C22⋊C4—1581no—
494C2×C22⋊C4—1581no—
495C2×C22⋊C4—1581no—
496C2×C22⋊C4—1581no—
497C2×C22⋊C4—1581no—
498C2×C22⋊C4—1581no—
499C2×C22⋊C4D31611yescharacteristic
500C2×C22⋊C4D31611yescharacteristic
501C2×C42—1581no—
502C2×C42—1581no—
503C2×C42C22×D7911yescharacteristic
504C2×C42C22×D7911yescharacteristic
505#107—794no—
506#107—794no—
507#106—794no—
508#106—794no—
509#106—794no—
510#106—794no—
511#106—794no—
512#106—794no—
513C4⋊C8C22×D7914yes—
514C4⋊C8C22×D7914yes—
515#103—794no—
516#103—794no—
517#103—794no—
518#103—794no—
519#102—794no—
520#102—794no—
521#102—794no—
522#102—794no—
523C22⋊C8C22×D7914yes—
524C22⋊C8C22×D7914yes—
525#97C22×D7914yes—
526C4×C8C22×D7914yes—
527C24—1581no—
528C24C2×D31611yescharacteristic
529C2×Q8—792no—
530C2×Q8—6322no—
531C2×Q8—6322no—
532C2×Q8—6322no—
533C2×Q8—1582no—
534C2×Q8—1582no—
535C2×Q8—1581no—
536C2×Q8—1584no—
537C2×Q8—1584no—
538C2×Q8—1584no—
539C2×D4—792no—
540C2×D4—6322no—
541C2×D4—1584no—
542C2×D4—1582no—
543C2×D4—1582no—
544C2×D4—1581no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—6322no—
548C22×C4—6322no—
549C22×C4—1581no—
550C22×C4—1581no—
551C22×C4—1581no—
552C22×C4—1581no—
553C22×C4—1581no—
554C22×C4—1581no—
555C22×C4—1581no—
556C22×C4—1584no—
557C22×C4—1584no—
558C22×C4C2×D31612yes—
559C22×C4C2×D31611yescharacteristic
560C22×C4C2×D31611yescharacteristic
561C22×C4C2×D31611yescharacteristic
562C22×C4C2×D31611yescharacteristic
563C22×C4C2×D31611yescharacteristic
564C22×C4C23×D7912yes—
565C22×C4C23×D7911yescharacteristic
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8C23×D7912yes—
571C2×C8C23×D7912yes—
572C2×C8C23×D7912yes—
573C2×C8C23×D7912yes—
574C4⋊C4—792no—
575C4⋊C4—792no—
576C4⋊C4—792no—
577C4⋊C4—792no—
578C4⋊C4—792no—
579C4⋊C4—792no—
580C4⋊C4—1584no—
581C4⋊C4—1584no—
582C4⋊C4—1584no—
583C4⋊C4—1584no—
584C4⋊C4—1584no—
585C4⋊C4—1584no—
586C4⋊C4—1584no—
587C4⋊C4—1581no—
588C4⋊C4—1581no—
589C4⋊C4—1581no—
590C4⋊C4—1581no—
591C4⋊C4—1581no—
592C4⋊C4—1581no—
593C4⋊C4—1584no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4C2×D31614yes—
597C4⋊C4C2×D31614yes—
598C22⋊C4—1584no—
599C22⋊C4—1584no—
600C22⋊C4—1584no—
601C22⋊C4—1584no—
602C22⋊C4—1584no—
603C22⋊C4—1584no—
604C22⋊C4C2×D31614yes—
605C22⋊C4C2×D31614yes—
606C42—1584no—
607C42—1584no—
608C42C2×D31612yes—
609C42C2×D31612yes—
610C42C23×D7912yes—
611C42C23×D7912yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—3162no—
616C23—3162no—
617C23—3162no—
618C23—1582no—
619C23C22×D31612yes—
620C23C22×D31611yescharacteristic
621Q8—3162no—
622Q8—6324no—
623Q8—6324no—
624Q8—6324no—
625Q8—1582no—
626Q8—1582no—
627D4—3162no—
628D4—6324no—
629D4—1582no—
630D4—1582no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—3162no—
640C2×C4—3162no—
641C2×C4—3162no—
642C2×C4—3162no—
643C2×C4—3162no—
644C2×C4—3162no—
645C2×C4—3162no—
646C2×C4—6324no—
647C2×C4—6324no—
648C2×C4—1582no—
649C2×C4—1582no—
650C2×C4—1582no—
651C2×C4—1582no—
652C2×C4—1582no—
653C2×C4—1582no—
654C2×C4—1582no—
655C2×C4C22×D31612yes—
656C2×C4C22×D31612yes—
657C2×C4C22×D31612yes—
658C2×C4C22×D31612yes—
659C2×C4C22×D31612yes—
660C2×C4C22×D31611yescharacteristic
661C2×C4#1457920812yes—
662C2×C4#1457920812yes—
663C2×C4C24×D7911yescharacteristic
664C8—22no—
665C8—22no—
666C8—22no—
667C8—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—3162no—
673C22—3162no—
674C22—3162no—
675C22—6324no—
676C22#1909913912yes—
677C22#1909937512yes—
678C22#1909937512yes—
679C22C23×D31611yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—3162no—
686C4—3162no—
687C4—3162no—
688C4—3162no—
689C4—3162no—
690C4—3162no—
691C4—3162no—
692C4#1909913912yes—
693C4C2×#1457920811yescharacteristic
694C4C2×#1457920811yescharacteristic
695C2—42no—
696C2—6322no—
697C2#2377470014yesdirect product factor
698C2C2×#1909913911yescharacteristic
699C2C2×#1909937511yescharacteristic
700C2C2×#1909937511yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#433×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
hypercenterC2×#433D79
hypocenterC79C2×#3244
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
1. C2×#19099191C2semidirect
3. #23774700C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098961C2semidirect
6. C2×#19098923C2semidirect
7. C2×#19098918C2semidirect
9. C2×#19098905C2semidirect
11. C2×#19098894C2semidirect
12. C2×#19098871C2semidirect
13. C2×#19098849C2semidirect
14. C2×#19098864C2semidirect
15. C2×#19098854C2semidirect
16. C2×#433×C79C2semidirect
18. #19099191C22semidirect
41. #19098972C22semidirect
42. #19098961C22semidirect
43. #19098923C22semidirect
44. #19098918C22semidirect
45. #19098905C22semidirect
46. #19098894C22semidirect
49. #19098871C22semidirect
50. #19098864C22semidirect
51. #19098854C22semidirect
52. #19098849C22semidirect
70. #433×C79C22semidirect
346. C2×C79#3244semidirect
366. C2×#433D79semidirect
367. C79C2×#3244semidirect
405. #433C2×D79semidirect
697. C2#23774700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991912
C2×#190991842
#237747002
C2×#190989722
C2×#190989612
C2×#190989232
C2×#190989182
C2×#190988822
C2×#190989052
C2×#190988882
C2×#190988942
C2×#190988712
C2×#190988492
C2×#190988642
C2×#190988542
C2×#433×C792
C2×#324479