Finite Group Databasebeta

← C2×#23774068 #35158137

Subgroups — C2×#23774068 #35158137

Order 20224.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099184C211yesmaximal, characteristic
2C2×#19099175C211yesmaximal, characteristic, complemented
3#23774068C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098957C211yesmaximal, characteristic, complemented
6C2×#19098918C211yesmaximal, characteristic, complemented
7C2×#19098914C211yesmaximal, characteristic, complemented
8C2×#19098821C211yesmaximal, characteristic, complemented
9C2×#19098809C211yesmaximal, characteristic
10C2×#19098804C211yesmaximal, characteristic, complemented
11C2×#19098792C211yesmaximal, characteristic
12C2×#19098671C211yesmaximal, characteristic, complemented
13C2×#19098665C211yesmaximal, characteristic, complemented
14C2×C4×Dic316C211yesmaximal, characteristic, complemented
15C2×C4×#11929613C211yesmaximal, characteristic, complemented
16C2×#405×C79C211yesmaximal, characteristic, complemented
17C22×Dic316C2211yescharacteristic
18C22×Dic316C2211yescharacteristic
19C22×#11929613C2211yescharacteristic
20C22×#11929613C2211yescharacteristic
21#19099184—24no—
22#19099184C2218yes—
23#19099175—24no—
24#19099175C2218yescomplemented
25C2×#14579161C2211yescharacteristic
26C2×#14579161C2211yescharacteristic
27C2×#14579156—21no—
28C2×#14579154—21no—
29C2×#14579154—21no—
30C2×#14579153C2211yescharacteristic
31C2×#14579151—21no—
32C2×#14579151—21no—
33C2×#14579149C2211yescharacteristic
34C2×#14579147—21no—
35C2×#14579143—21no—
36C2×#14579140C2211yescharacteristic
37C2×#14579140C2211yescharacteristic
38C2×#14579140C2211yescharacteristic
39C2×#14579139—21no—
40C2×#14579135C2211yescharacteristic
41C2×C4×Dic158C2211yescharacteristic
42C2×C4×Dic158C2211yescharacteristic
43C2×C4×Dic158C2211yescharacteristic
44C2×C4×D316C2211yescharacteristic
45#19098972C2218yescomplemented
46#19098957C2218yescomplemented
47#19098918C2218yescomplemented
48#19098914C2218yescomplemented
49#19098821C2218yescomplemented
50#19098809C2218yes—
51#19098804C2218yescomplemented
52#19098792C2218yes—
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
69C22×M16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×#117×C79C2211yescharacteristic
72#405×C79C2218yescomplemented
73C2×#97×C79C2211yescharacteristic
74C2×#97×C79C2211yescharacteristic
75C2×C4×C8×C79C2211yescharacteristic
76C2×C4×C8×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×Dic158C2311yescharacteristic
80C22×Dic158C2311yescharacteristic
81C22×D316C2311yescharacteristic
82C22×C22⋊D79—21no—
83C22×C4×D79—21no—
84C2×Dic316—24no—
85C2×Dic316—24no—
86C2×Dic316C2314yes—
87C2×Dic316C2314yes—
88C2×#11929613—24no—
89C2×#11929613—24no—
90C2×#11929613C2314yes—
91C2×#11929613C2314yes—
92#14579161—22no—
93#14579161—22no—
94#14579161C2314yes—
95#14579161C2314yes—
96#14579156—28no—
97#14579154—28no—
98#14579154—28no—
99#14579153—22no—
100#14579153C2314yes—
101#14579151—28no—
102#14579151—28no—
103#14579149—22no—
104#14579149C2314yes—
105#14579147—28no—
106#14579143—28no—
107#14579140—22no—
108#14579140—22no—
109#14579140—22no—
110#14579140C2314yes—
111#14579140C2314yes—
112#14579140C2314yes—
113#14579139—28no—
114#14579135—22no—
115#14579135C2314yes—
116C4×Dic158—22no—
117C4×Dic158—22no—
118C4×Dic158—22no—
119C4×Dic158C2314yes—
120C4×Dic158C2314yes—
121C4×Dic158C2314yes—
122C4×D316—22no—
123C4×D316C2314yes—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79—21no—
126C2×C4⋊Dic79—21no—
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×C4⋊Dic79C2311yescharacteristic
130C2×C4⋊Dic79C2311yescharacteristic
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
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×C22⋊Dic79—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×(C2×D79)⋊C4—21no—
144C2×(C2×D79)⋊C4—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×C4×Dic79—21no—
147C2×C4×Dic79—21no—
148C2×C4×Dic79—21no—
149#14579095C2314yes—
150#14579095C2314yes—
151#14579093C2314yes—
152#14579093C2314yes—
153#14579086C2314yes—
154#14579086C2314yes—
155#14579086C2314yes—
156#14579086C2314yes—
157#14579086C2314yes—
158#14579086C2314yes—
159#14579083C2314yes—
160#14579083C2314yes—
161C23×C4×C79C2311yescharacteristic
162C2×M16×C79—24no—
163C2×M16×C79C2314yes—
164C22×C8×C79—24no—
165C22×C8×C79C2314yes—
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170#117×C79D414yes—
171#117×C79C2314yes—
172C2×C4⋊C4×C79D411yescharacteristic
173C2×C4⋊C4×C79D411yescharacteristic
174C2×C22⋊C4×C79D411yescharacteristic
175C2×C22⋊C4×C79D411yescharacteristic
176C2×C42×C79C2311yescharacteristic
177C2×C42×C79C2311yescharacteristic
178#97×C79C2314yes—
179#97×C79C2314yes—
180C4×C8×C79C2314yes—
181C4×C8×C79C2314yes—
182C23×D79—21no—
183C2×Dic158—21no—
184C2×Dic158—21no—
185C2×Dic158—21no—
186C2×Dic158—24no—
187C2×Dic158—22no—
188C2×Dic158—22no—
189C2×Dic158—22no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158—22no—
193C2×Dic158—82no—
194C2×Dic158C2412yes—
195C2×Dic158C2412yes—
196C2×Dic158C2412yes—
197C2×D316—21no—
198C2×D316—22no—
199C2×D316—22no—
200C2×D316C2412yes—
201C2×C22⋊D79—24no—
202C2×C22⋊D79—82no—
203C22×Dic79—21no—
204C22×Dic79—21no—
205C22×Dic79—21no—
206C22×Dic79—21no—
207C22×Dic79—21no—
208C22×Dic79—21no—
209C22×Dic79—21no—
210C2×C4×D79—24no—
211C2×C4×D79—82no—
212Dic316—28no—
213Dic316—28no—
214#11929613—28no—
215#11929613—28no—
216C4⋊Dic79—24no—
217C4⋊Dic79—24no—
218C4⋊Dic79—24no—
219C4⋊Dic79—21no—
220C4⋊Dic79—21no—
221C4⋊Dic79—21no—
222C4⋊Dic79—21no—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
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—
234Dic79⋊C4—24no—
235C22⋊Dic79—24no—
236C22⋊Dic79—24no—
237C22⋊Dic79—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4—24no—
241(C2×D79)⋊C4—24no—
242C4×Dic79—24no—
243C4×Dic79—24no—
244C4×Dic79—24no—
245C24×C79C2×D411yescharacteristic
246C22×C4×C79—22no—
247C22×C4×C79—22no—
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D412yes—
254C22×C4×C79C2412yes—
255C22×C4×C79C2411yescharacteristic
256M16×C79—28no—
257C2×C8×C79—28no—
258C2×C8×C79—22no—
259C2×C8×C79—22no—
260C2×C8×C79#4114yes—
261C2×C8×C79#4114yes—
262C2×C8×C79C2412yes—
263C2×C8×C79C2412yes—
264C2×C8×C79C2412yes—
265C2×C8×C79C2412yes—
266C4⋊C4×C79C2×D414yes—
267C4⋊C4×C79C2×D414yes—
268C22⋊C4×C79C2×D414yes—
269C22⋊C4×C79C2×D414yes—
270C42×C79C2×D412yes—
271C42×C79C2×D412yes—
272C42×C79C2412yes—
273C42×C79C2412yes—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79C22×D412yes—
278C23×C79C22×D411yescharacteristic
279C22×D79—22no—
280C22×D79—42no—
281C22×D79—42no—
282C22×D79—42no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—24no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79C22×D412yes—
292C2×C4×C79C22×D412yes—
293C2×C4×C79C22×D412yes—
294C2×C4×C79C22×D412yes—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D411yescharacteristic
297C2×C4×C79C2×#4112yes—
298C2×C4×C79C2×#4112yes—
299C2×C4×C79C2511yescharacteristic
300C22⋊D79—84no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—42no—
309C2×Dic79—42no—
310C2×Dic79—42no—
311C2×Dic79—42no—
312C2×Dic79—42no—
313C2×Dic79—42no—
314C2×Dic79—42no—
315D316—22no—
316D316—22no—
317D316—42no—
318C4×D79—84no—
319Dic158—22no—
320Dic158—22no—
321Dic158—22no—
322Dic158—22no—
323Dic158—22no—
324Dic158—22no—
325Dic158—42no—
326Dic158—42no—
327Dic158—42no—
328Dic158—84no—
329C8×C79—22no—
330C8×C79—22no—
331C8×C79C2×#4114yes—
332C8×C79C2×#4114yes—
333C22×C79—22no—
334C22×C79—22no—
335C22×C79—22no—
336C22×C79—44no—
337C22×C79#53212yes—
338C22×C79#57712yes—
339C22×C79#57812yes—
340C22×C79C23×D411yescharacteristic
341C2×D79—42no—
342C2×D79—42no—
343C2×D79—42no—
344C2×D79—84no—
345C4×C79—22no—
346C4×C79—22no—
347C4×C79—22no—
348C4×C79—22no—
349C4×C79—22no—
350C4×C79#53212yes—
351C4×C79C22×#4111yescharacteristic
352C4×C79C22×#4111yescharacteristic
353Dic79—42no—
354Dic79—42no—
355Dic79—42no—
356Dic79—42no—
357Dic79—42no—
358Dic79—42no—
359Dic79—42no—
360C2×#3178—791nomaximal, Sylow
361C2×C79—42no—
362C2×C79#317814yescomplemented
363C2×C79C2×#53211yescharacteristic
364C2×C79C2×#57711yescharacteristic
365C2×C79C2×#57811yescharacteristic
366D79—82no—
367C2×#542—791no—
368C2×#541—791no—
369#3178—7916no—
370C2×#501—791no—
371C2×#497—791no—
372C2×#488—791no—
373C2×#487—791no—
374C2×#470—791no—
375C2×#468—791no—
376C2×#467—791no—
377C2×#465—791no—
378C2×#441—791no—
379C2×#440—791no—
380C2×C4×Q16—791no—
381C2×C4×SD16—791no—
382C2×#405D7911yescharacteristic, complemented
383C79C2×#317811yescharacteristic, complemented, Sylow
384C22×Q16—791no—
385C22×Q16—791no—
386C22×SD16—791no—
387C22×SD16—791no—
388C22×M16C2×D7911yescharacteristic
389C23×C8C2×D7911yescharacteristic
390#542—798no—
391#542—1584no—
392#541—798no—
393#541—1584no—
394C2×C4⋊Q8—791no—
395C2×C4⋊Q8—791no—
396C2×#126—1581no—
397C2×#126—1581no—
398C2×#126—1581no—
399C2×#125—791no—
400C2×#125—1581no—
401C2×#125—1581no—
402C2×#124—791no—
403C2×#124—1581no—
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—791no—
412C2×C4×Q8—791no—
413C2×C4×D4—791no—
414C2×#117C2×D7911yescharacteristic
415#501—798no—
416#497—798no—
417#488—798no—
418#487—798no—
419#470—798no—
420#468—798no—
421#467—798no—
422#465—798no—
423#441—798no—
424#440—798no—
425C4×Q16—798no—
426C4×SD16—798no—
427C2×#107—791no—
428C2×#107—791no—
429C2×#106—791no—
430C2×#106—791no—
431C2×#103—791no—
432C2×#103—791no—
433C2×#103—791no—
434C2×#103—791no—
435C2×#103—791no—
436C2×#103—791no—
437C2×#102—791no—
438C2×#102—791no—
439#405C2×D7918yescomplemented
440C2×#97C2×D7911yescharacteristic
441C2×#97C2×D7911yescharacteristic
442C2×C4×C8C2×D7911yescharacteristic
443C2×C4×C8C2×D7911yescharacteristic
444C22×Q8—791no—
445C22×Q8—791no—
446C22×Q8—791no—
447C22×Q8—1581no—
448C22×D4—791no—
449C22×D4—1581no—
450C23×C4—1581no—
451C23×C4C22×D7911yescharacteristic
452C2×Q16—794no—
453C2×Q16—794no—
454C2×Q16—1584no—
455C2×Q16—1584no—
456C2×SD16—794no—
457C2×SD16—794no—
458C2×SD16—1584no—
459C2×SD16—1584no—
460C2×M16—24no—
461C2×M16C22×D7914yes—
462C22×C8—24no—
463C22×C8C22×D7911yescharacteristic
464C22×C8C22×D7914yes—
465C22×C8C22×D7911yescharacteristic
466C22×C8C22×D7911yescharacteristic
467C22×C8C22×D7911yescharacteristic
468C4⋊Q8—794no—
469C4⋊Q8—794no—
470C4⋊Q8—1582no—
471C4⋊Q8—1582no—
472#126—1588no—
473#126—1588no—
474#126—1588no—
475#125—794no—
476#125—1588no—
477#125—1588no—
478#125—1582no—
479#124—794no—
480#124—1588no—
481#124—1582no—
482#123—1588no—
483C22⋊Q8—794no—
484C22⋊Q8—794no—
485C22⋊Q8—794no—
486C22⋊Q8—1582no—
487C22⋊Q8—1582no—
488C22⋊Q8—1582no—
489C22⋊Q8—1588no—
490#121—794no—
491#121—1582no—
492C4×Q8—794no—
493C4×Q8—794no—
494C4×Q8—794no—
495C4×Q8—1582no—
496C4×Q8—1582no—
497C4×Q8—1582no—
498C4×D4—794no—
499C4×D4—1582no—
500#117D31614yes—
501#117C22×D7914yes—
502C2×C4⋊C4—791no—
503C2×C4⋊C4—791no—
504C2×C4⋊C4—791no—
505C2×C4⋊C4—791no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4—1581no—
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⋊C4D31611yescharacteristic
518C2×C4⋊C4D31611yescharacteristic
519C2×C22⋊C4—1581no—
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×C42C22×D7911yescharacteristic
532C2×C42C22×D7911yescharacteristic
533#107—794no—
534#107—794no—
535#106—794no—
536#106—794no—
537#103—794no—
538#103—794no—
539#103—794no—
540#103—794no—
541#103—794no—
542#103—794no—
543#102—794no—
544#102—794no—
545#97C22×D7914yes—
546#97C22×D7914yes—
547C4×C8C22×D7914yes—
548C4×C8C22×D7914yes—
549C24—1581no—
550C24C2×D31611yescharacteristic
551C2×Q8—792no—
552C2×Q8—792no—
553C2×Q8—792no—
554C2×Q8—6322no—
555C2×Q8—1582no—
556C2×Q8—1582no—
557C2×Q8—1582no—
558C2×Q8—1582no—
559C2×Q8—1582no—
560C2×Q8—1582no—
561C2×Q8—1581no—
562C2×Q8—1581no—
563C2×Q8—1581no—
564C2×Q8—1584no—
565C2×D4—792no—
566C2×D4—6322no—
567C2×D4—1584no—
568C2×D4—1582no—
569C2×D4—1582no—
570C2×D4—1581no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—6322no—
574C22×C4—1581no—
575C22×C4—1581no—
576C22×C4—1581no—
577C22×C4—1581no—
578C22×C4—1581no—
579C22×C4—1581no—
580C22×C4—1581no—
581C22×C4—1584no—
582C22×C4C2×D31612yes—
583C22×C4C2×D31611yescharacteristic
584C22×C4C2×D31611yescharacteristic
585C22×C4C2×D31611yescharacteristic
586C22×C4C2×D31611yescharacteristic
587C22×C4C2×D31611yescharacteristic
588C22×C4C23×D7912yes—
589C22×C4C23×D7911yescharacteristic
590Q16—1588no—
591Q16—1588no—
592SD16—1588no—
593SD16—1588no—
594M16—28no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—28no—
598C2×C8#1192962414yes—
599C2×C8#1192962414yes—
600C2×C8C23×D7912yes—
601C2×C8C23×D7912yes—
602C2×C8C23×D7912yes—
603C2×C8C23×D7912yes—
604C4⋊C4—792no—
605C4⋊C4—792no—
606C4⋊C4—792no—
607C4⋊C4—792no—
608C4⋊C4—1584no—
609C4⋊C4—1584no—
610C4⋊C4—1584no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C4⋊C4—1584no—
616C4⋊C4—1581no—
617C4⋊C4—1581no—
618C4⋊C4—1581no—
619C4⋊C4—1581no—
620C4⋊C4—1584no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4C2×D31614yes—
624C4⋊C4C2×D31614yes—
625C22⋊C4—1584no—
626C22⋊C4—1584no—
627C22⋊C4—1584no—
628C22⋊C4—1584no—
629C22⋊C4—1584no—
630C22⋊C4—1584no—
631C22⋊C4—1584no—
632C22⋊C4C2×D31614yes—
633C22⋊C4C2×D31614yes—
634C42—1584no—
635C42—1584no—
636C42—1584no—
637C42C2×D31612yes—
638C42C2×D31612yes—
639C42C23×D7912yes—
640C42C23×D7912yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—3162no—
645C23—3162no—
646C23—3162no—
647C23—1582no—
648C23C22×D31612yes—
649C23C22×D31611yescharacteristic
650Q8—3162no—
651Q8—3162no—
652Q8—3162no—
653Q8—6324no—
654Q8—1582no—
655Q8—1582no—
656Q8—1582no—
657Q8—1582no—
658Q8—1582no—
659Q8—1582no—
660D4—3162no—
661D4—6324no—
662D4—1582no—
663D4—1582no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—3162no—
673C2×C4—3162no—
674C2×C4—3162no—
675C2×C4—3162no—
676C2×C4—3162no—
677C2×C4—3162no—
678C2×C4—3162no—
679C2×C4—6324no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1582no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4C22×D31612yes—
688C2×C4C22×D31612yes—
689C2×C4C22×D31612yes—
690C2×C4C22×D31612yes—
691C2×C4C22×D31612yes—
692C2×C4C22×D31611yescharacteristic
693C2×C4C2×#1192962412yes—
694C2×C4C2×#1192962412yes—
695C2×C4C24×D7911yescharacteristic
696C8—22no—
697C8—22no—
698C8C2×#1192962414yes—
699C8C2×#1192962414yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—3162no—
705C22—3162no—
706C22—3162no—
707C22—6324no—
708C22#1909911312yes—
709C22#1909937512yes—
710C22#1909938012yes—
711C22C23×D31611yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—3162no—
718C4—3162no—
719C4—3162no—
720C4—3162no—
721C4—3162no—
722C4—3162no—
723C4—3162no—
724C4#1909911312yes—
725C4C22×#1192962411yescharacteristic
726C4C22×#1192962411yescharacteristic
727C2—42no—
728C2—6322no—
729C2#2377406814yesdirect product factor
730C2C2×#1909911311yescharacteristic
731C2C2×#1909937511yescharacteristic
732C2C2×#1909938011yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#405×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
hypercenterC2×#405D79
hypocenterC79C2×#3178
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×#19099175C2semidirect
3. #23774068C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098957C2semidirect
6. C2×#19098918C2semidirect
7. C2×#19098914C2semidirect
8. C2×#19098821C2semidirect
10. C2×#19098804C2semidirect
12. C2×#19098671C2semidirect
13. C2×#19098665C2semidirect
14. C2×C4×Dic316C2semidirect
15. C2×C4×#11929613C2semidirect
16. C2×#405×C79C2semidirect
24. #19099175C22semidirect
45. #19098972C22semidirect
46. #19098957C22semidirect
47. #19098918C22semidirect
48. #19098914C22semidirect
49. #19098821C22semidirect
51. #19098804C22semidirect
53. #19098671C22semidirect
54. #19098665C22semidirect
55. C4×Dic316C22semidirect
56. C4×#11929613C22semidirect
72. #405×C79C22semidirect
362. C2×C79#3178semidirect
382. C2×#405D79semidirect
383. C79C2×#3178semidirect
439. #405C2×D79semidirect
729. C2#23774068direct (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×#190991752
#237740682
C2×#190989722
C2×#190989572
C2×#190989182
C2×#190989142
C2×#190988212
C2×#190988092
C2×#190988042
C2×#190987922
C2×#190986712
C2×#190986652
C2×C4×Dic3162
C2×C4×#119296132
C2×#405×C792
C2×#317879