Finite Group Databasebeta

← C2×#23775842 #35166802

Subgroups — C2×#23775842 #35166802

Order 20224.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099253C211yesmaximal, characteristic, complemented
2C2×#19099217C211yesmaximal, characteristic
3#23775842C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098899C211yesmaximal, characteristic, complemented
6C2×#19098888C211yesmaximal, characteristic, complemented
7C2×#19098894C211yesmaximal, characteristic, complemented
8C2×#19098877C211yesmaximal, characteristic, complemented
9C2×#19098859C211yesmaximal, characteristic, complemented
10C2×#19098864C211yesmaximal, characteristic, complemented
11C2×#19098809C211yesmaximal, characteristic, complemented
12C2×#19098792C211yesmaximal, characteristic, complemented
13C2×#19098665C211yesmaximal, characteristic, complemented
14C2×#19098605C211yesmaximal, characteristic, complemented
15C22×#14579095C211yesmaximal, characteristic, complemented
16C2×#435×C79C211yesmaximal, characteristic, complemented
17C22×#11929623—21no—
18C22×#11929613C2211yescharacteristic
19#19099253—24no—
20#19099253C2218yescomplemented
21#19099217—24no—
22#19099217C2218yes—
23C2×#14579161C2211yescharacteristic
24C2×#14579154—21no—
25C2×#14579153C2211yescharacteristic
26C2×#14579151—21no—
27C2×#14579145—21no—
28C2×#14579145—21no—
29C2×#14579142—21no—
30C2×#14579141—21no—
31C2×#14579140C2211yescharacteristic
32C2×#14579140C2211yescharacteristic
33C2×#14579135C2211yescharacteristic
34C2×#14579135C2211yescharacteristic
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×D316C2211yescharacteristic
37C2×#14579120C2211yescharacteristic
38C2×#14579117—21no—
39C22×C4⋊Dic79C2211yescharacteristic
40C22×C4⋊Dic79C2211yescharacteristic
41C22×C4⋊Dic79C2211yescharacteristic
42#19098972C2218yescomplemented
43#19098899C2218yescomplemented
44#19098894C2218yescomplemented
45#19098888C2218yescomplemented
46#19098877C2218yescomplemented
47#19098864C2218yescomplemented
48#19098859C2218yescomplemented
49#19098809C2218yescomplemented
50#19098792C2218yescomplemented
51#19098665C2218yescomplemented
52#19098605C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579095C2211yescharacteristic
56C2×#14579095C2211yescharacteristic
57C2×#14579095C2211yescharacteristic
58C2×#14579095C2211yescharacteristic
59C2×#14579095C2218yescomplemented
60C2×#14579093C2211yescharacteristic
61C2×#14579093C2211yescharacteristic
62C2×#14579093C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579086C2211yescharacteristic
66C2×#14579083C2211yescharacteristic
67C2×#14579083C2211yescharacteristic
68C2×#14579083C2211yescharacteristic
69C22×M16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#435×C79C2218yescomplemented
73C2×C4⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×C22⋊C8×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C2×#11929623—28no—
78C2×#11929623—48no—
79C22×Dic158—21no—
80C22×Dic158C2311yescharacteristic
81C22×D316C2311yescharacteristic
82C22×C22⋊D79—21no—
83C22×C22⋊D79—21no—
84C23×Dic79—21no—
85C23×Dic79—21no—
86C23×Dic79—21no—
87C22×C4×D79—21no—
88C2×#11929613—24no—
89C2×#11929613C2314yes—
90#14579161—22no—
91#14579161C2314yes—
92#14579154—28no—
93#14579153—22no—
94#14579153C2314yes—
95#14579151—28no—
96#14579145—28no—
97#14579145—28no—
98#14579142—28no—
99#14579141—28no—
100#14579140—22no—
101#14579140—22no—
102#14579140C2314yes—
103#14579140C2314yes—
104#14579135—22no—
105#14579135—22no—
106#14579135C2314yes—
107#14579135C2314yes—
108C4×Dic158—22no—
109C4×Dic158C2314yes—
110C4×D316—22no—
111C4×D316C2314yes—
112#14579120—22no—
113#14579120C2314yes—
114#14579117—28no—
115C2×C4⋊Dic79—22no—
116C2×C4⋊Dic79—22no—
117C2×C4⋊Dic79—22no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79C2314yes—
123C2×C4⋊Dic79C2314yes—
124C2×C4⋊Dic79C2314yes—
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
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×C22⋊Dic79—21no—
137C2×C22⋊Dic79—21no—
138C2×C22⋊Dic79—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144#14579095C2314yes—
145#14579095C2314yes—
146#14579095C2314yes—
147#14579095C2314yes—
148#14579095C2314yes—
149#14579095C2314yes—
150#14579093C2314yes—
151#14579093C2314yes—
152#14579093C2314yes—
153#14579086C2314yes—
154#14579086C2314yes—
155#14579086C2314yes—
156#14579083C2314yes—
157#14579083C2314yes—
158#14579083C2314yes—
159C22×D4×C79D411yescharacteristic
160C23×C4×C79C2311yescharacteristic
161C23×C4×C79C2311yescharacteristic
162C2×M16×C79—24no—
163C2×M16×C79C2314yes—
164C22×C8×C79—24no—
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2314yes—
168C22×C8×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170C4×D4×C79D414yes—
171C4×D4×C79C2314yes—
172C2×C4⋊C4×C79D411yescharacteristic
173C2×C22⋊C4×C79D411yescharacteristic
174C2×C22⋊C4×C79D411yescharacteristic
175C2×C42×C79C2311yescharacteristic
176C4⋊C8×C79C2314yes—
177C22⋊C8×C79C2314yes—
178C22⋊C8×C79C2314yes—
179#97×C79C2314yes—
180C23×D79—21no—
181#11929623—432no—
182C2×Dic158—24no—
183C2×Dic158—21no—
184C2×Dic158—22no—
185C2×Dic158—22no—
186C2×Dic158—44no—
187C2×Dic158C2412yes—
188C2×D316—21no—
189C2×D316—22no—
190C2×D316—22no—
191C2×D316C2412yes—
192C2×C22⋊D79—24no—
193C2×C22⋊D79—24no—
194C2×C22⋊D79—44no—
195C2×C22⋊D79—44no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—24no—
200C22×Dic79—24no—
201C22×Dic79—21no—
202C22×Dic79—21no—
203C22×Dic79—21no—
204C22×Dic79—21no—
205C22×Dic79—24no—
206C22×Dic79—44no—
207C22×Dic79—44no—
208C22×Dic79—44no—
209C2×C4×D79—24no—
210C2×C4×D79—44no—
211#11929613—28no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79—21no—
215C4⋊Dic79—21no—
216C4⋊Dic79—21no—
217C4⋊Dic79—24no—
218C4⋊Dic79—24no—
219C4⋊Dic79—24no—
220C4⋊Dic79—24no—
221C4⋊Dic79—21no—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225C4⋊Dic79C2412yes—
226C4⋊Dic79C2412yes—
227C4⋊Dic79C2412yes—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233C22⋊Dic79—24no—
234C22⋊Dic79—24no—
235C22⋊Dic79—24no—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4—24no—
238(C2×D79)⋊C4—24no—
239C4×Dic79—24no—
240C4×Dic79—24no—
241C24×C79C2×D411yescharacteristic
242C24×C79C2×D411yescharacteristic
243C2×D4×C79—24no—
244C2×D4×C79C2×D414yes—
245C22×C4×C79—22no—
246C22×C4×C79—22no—
247C22×C4×C79—22no—
248C22×C4×C79—22no—
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D412yes—
254C22×C4×C79C2×D412yes—
255C22×C4×C79C2412yes—
256C22×C4×C79C2412yes—
257C22×C4×C79C2411yescharacteristic
258M16×C79—28no—
259C2×C8×C79—28no—
260C2×C8×C79—22no—
261C2×C8×C79—22no—
262C2×C8×C79—22no—
263C2×C8×C79#4114yescomplemented
264C2×C8×C79C2412yes—
265C2×C8×C79C2412yes—
266C2×C8×C79C2412yes—
267C2×C8×C79C2412yes—
268C4⋊C4×C79C2×D414yes—
269C22⋊C4×C79C2×D414yes—
270C22⋊C4×C79C2×D414yes—
271C42×C79C2×D412yes—
272C42×C79C2412yes—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79AGL(1,ℤ/8)14yes—
279C23×C79C22×D412yes—
280C23×C79C22×D412yes—
281C23×C79C22×D411yescharacteristic
282C22×D79—22no—
283C22×D79—42no—
284C22×D79—42no—
285C22×D79—42no—
286D4×C79—28no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—24no—
292C2×C4×C79—24no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79C22×D412yes—
298C2×C4×C79C22×D412yes—
299C2×C4×C79C22×D412yes—
300C2×C4×C79C22×D412yes—
301C2×C4×C79C22×D411yescharacteristic
302C2×C4×C79C2×#4112yes—
303C2×C4×C792−1+412yes—
304C2×C4×C79C2511yescharacteristic
305C22⋊D79—48no—
306C22⋊D79—48no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—48no—
315C2×Dic79—42no—
316C2×Dic79—42no—
317C2×Dic79—48no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—42no—
321C2×Dic79—42no—
322C2×Dic79—48no—
323C2×Dic79—42no—
324D316—22no—
325D316—22no—
326D316—42no—
327C4×D79—48no—
328Dic158—22no—
329Dic158—22no—
330Dic158—48no—
331Dic158—42no—
332C8×C79—22no—
333C8×C79—22no—
334C8×C79—22no—
335C8×C79C2×#4114yescomplemented
336C22×C79—28no—
337C22×C79—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—22no—
342C22×C79—44no—
343C22×C79#54712yes—
344C22×C79C2×AGL(1,ℤ/8)14yes—
345C22×C79C2×AGL(1,ℤ/8)12yes—
346C22×C79#57812yes—
347C22×C79C23×D411yescharacteristic
348C2×D79—42no—
349C2×D79—42no—
350C2×D79—42no—
351C2×D79—84no—
352C4×C79—22no—
353C4×C79—22no—
354C4×C79—22no—
355C4×C79—22no—
356C4×C79#54712yes—
357C4×C79C22×#4111yescharacteristic
358C4×C79C2×2−1+411yescharacteristic
359Dic79—42no—
360Dic79—42no—
361Dic79—42no—
362Dic79—42no—
363Dic79—42no—
364Dic79—42no—
365Dic79—42no—
366C2×#3343—791nomaximal, Sylow
367C2×C79—24no—
368C2×C79—42no—
369C2×C79#334314yescomplemented
370C2×C79C2×#54711yescharacteristic
371C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
372C2×C79C2×#57811yescharacteristic
373D79—82no—
374C2×#552—791no—
375C2×#547—791no—
376#3343—7916no—
377C2×#501—791no—
378C2×#484—791no—
379C2×#482—791no—
380C2×#483—791no—
381C2×#480—791no—
382C2×#477—791no—
383C2×#478—791no—
384C2×#468—791no—
385C2×#465—791no—
386C2×#440—791no—
387C2×#435D7911yescharacteristic, complemented
388C2×#428—791no—
389C22×#107—791no—
390C79C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1581no—
392C22×SD16—791no—
393C22×M16C2×D7911yescharacteristic
394C23×C8C2×D7911yescharacteristic
395#552—798no—
396#552—1584no—
397#547—798no—
398#547—1584no—
399C2×C4⋊Q8—791no—
400C2×#126—1581no—
401C2×#125—791no—
402C2×#125—1581no—
403C2×#123—1581no—
404C2×#123—1581no—
405C2×#123—1581no—
406C2×C22⋊Q8—791no—
407C2×C22⋊Q8—791no—
408C2×C22⋊Q8—1581no—
409C2×#121—791no—
410C2×#121—791no—
411C2×C4×Q8—791no—
412C2×C4×D4—791no—
413C2×C4×D4C2×D7911yescharacteristic
414C2×#117—791no—
415C2×#117—1581no—
416C22×C4⋊C4—791no—
417C22×C4⋊C4—791no—
418C22×C4⋊C4—791no—
419#501—798no—
420#484—798no—
421#483—798no—
422#482—798no—
423#480—798no—
424#478—798no—
425#477—798no—
426#468—798no—
427#465—798no—
428#440—798no—
429#435C2×D7918yescomplemented
430#428—798no—
431C2×#107—791no—
432C2×#107—791no—
433C2×#107—791no—
434C2×#107—791no—
435C2×#107—798no—
436C2×#107—791no—
437C2×#107—791no—
438C2×#106—791no—
439C2×#106—791no—
440C2×#106—791no—
441C2×C4⋊C8C2×D7911yescharacteristic
442C2×#103—791no—
443C2×#103—791no—
444C2×#103—791no—
445C2×#102—791no—
446C2×#102—791no—
447C2×#102—791no—
448C2×C22⋊C8C2×D7911yescharacteristic
449C2×C22⋊C8C2×D7911yescharacteristic
450C2×#97C2×D7911yescharacteristic
451C2×#41—3168no—
452C2×#41—1588no—
453C22×Q8—791no—
454C22×Q8—1581no—
455C22×D4—791no—
456C22×D4—1581no—
457C22×D4—1581no—
458C22×D4D31611yescharacteristic
459C23×C4—1581no—
460C23×C4—1581no—
461C23×C4—1581no—
462C23×C4—1581no—
463C23×C4C22×D7911yescharacteristic
464C23×C4C22×D7911yescharacteristic
465C2×SD16—794no—
466C2×SD16—1584no—
467C2×M16—24no—
468C2×M16C22×D7914yes—
469C22×C8—24no—
470C22×C8C22×D7911yescharacteristic
471C22×C8C22×D7914yes—
472C22×C8C22×D7911yescharacteristic
473C22×C8C22×D7911yescharacteristic
474C22×C8C22×D7911yescharacteristic
475C4⋊Q8—794no—
476C4⋊Q8—1582no—
477#126—1588no—
478#125—794no—
479#125—1588no—
480#125—1582no—
481#123—1588no—
482#123—1588no—
483#123—1588no—
484C22⋊Q8—794no—
485C22⋊Q8—794no—
486C22⋊Q8—1582no—
487C22⋊Q8—1582no—
488C22⋊Q8—1588no—
489#121—794no—
490#121—794no—
491#121—1582no—
492#121—1582no—
493C4×Q8—794no—
494C4×Q8—1582no—
495C4×D4—794no—
496C4×D4—1582no—
497C4×D4D31614yes—
498C4×D4C22×D7914yes—
499#117—794no—
500#117—1582no—
501#117—1588no—
502C2×C4⋊C4—791no—
503C2×C4⋊C4—791no—
504C2×C4⋊C4—791no—
505C2×C4⋊C4—791no—
506C2×C4⋊C4—791no—
507C2×C4⋊C4—794no—
508C2×C4⋊C4—794no—
509C2×C4⋊C4—794no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4—1581no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1582no—
515C2×C4⋊C4—1582no—
516C2×C4⋊C4—1582no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4—1581no—
520C2×C4⋊C4—1581no—
521C2×C4⋊C4—1581no—
522C2×C4⋊C4—1581no—
523C2×C4⋊C4D31611yescharacteristic
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4—1581no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4D31611yescharacteristic
531C2×C22⋊C4D31611yescharacteristic
532C2×C42—1581no—
533C2×C42—1581no—
534C2×C42C22×D7911yescharacteristic
535#107—794no—
536#107—794no—
537#107—794no—
538#107—794no—
539#107—794no—
540#107—794no—
541#106—794no—
542#106—794no—
543#106—794no—
544C4⋊C8C22×D7914yes—
545#103—794no—
546#103—794no—
547#103—794no—
548#102—794no—
549#102—794no—
550#102—794no—
551C22⋊C8C22×D7914yes—
552C22⋊C8C22×D7914yes—
553#97C22×D7914yes—
554C24—1581no—
555C24C2×D31611yescharacteristic
556C24C2×D31611yescharacteristic
557#41—31632no—
558C2×Q8—3164no—
559C2×Q8—792no—
560C2×Q8—1582no—
561C2×Q8—1582no—
562C2×Q8—1581no—
563C2×Q8—1584no—
564C2×D4—24no—
565C2×D4—3164no—
566C2×D4—3164no—
567C2×D4—792no—
568C2×D4—1584no—
569C2×D4—1584no—
570C2×D4—1582no—
571C2×D4—1582no—
572C2×D4—1581no—
573C2×D4C2×D31614yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—3164no—
579C22×C4—3164no—
580C22×C4—3164no—
581C22×C4—3164no—
582C22×C4—1584no—
583C22×C4—1584no—
584C22×C4—1584no—
585C22×C4—1581no—
586C22×C4—1581no—
587C22×C4—1581no—
588C22×C4—1581no—
589C22×C4—1581no—
590C22×C4—1581no—
591C22×C4—1581no—
592C22×C4—1584no—
593C22×C4C2×D31612yes—
594C22×C4C2×D31612yes—
595C22×C4C2×D31611yescharacteristic
596C22×C4C2×D31611yescharacteristic
597C22×C4C2×D31611yescharacteristic
598C22×C4C2×D31611yescharacteristic
599C22×C4C23×D7912yes—
600C22×C4C23×D7912yes—
601C22×C4C23×D7911yescharacteristic
602SD16—1588no—
603M16—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—28no—
608C2×C8#1192962314yescomplemented
609C2×C8C23×D7912yes—
610C2×C8C23×D7912yes—
611C2×C8C23×D7912yes—
612C2×C8C23×D7912yes—
613C4⋊C4—792no—
614C4⋊C4—792no—
615C4⋊C4—792no—
616C4⋊C4—792no—
617C4⋊C4—792no—
618C4⋊C4—792no—
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⋊C4—1584no—
630C4⋊C4—1581no—
631C4⋊C4—1584no—
632C4⋊C4—1581no—
633C4⋊C4—1584no—
634C4⋊C4C2×D31614yes—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C22⋊C4—1584no—
639C22⋊C4—1584no—
640C22⋊C4—1584no—
641C22⋊C4C2×D31614yes—
642C22⋊C4C2×D31614yes—
643C42—1584no—
644C42—1584no—
645C42C2×D31612yes—
646C42C23×D7912yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—3162no—
653C23—3162no—
654C23—3162no—
655C23—1582no—
656C23#1457918914yes—
657C23C22×D31612yes—
658C23C22×D31612yes—
659C23C22×D31611yescharacteristic
660Q8—3168no—
661Q8—3162no—
662Q8—1582no—
663Q8—1582no—
664D4—28no—
665D4—3168no—
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—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—3168no—
681C2×C4—3168no—
682C2×C4—3162no—
683C2×C4—3162no—
684C2×C4—3162no—
685C2×C4—3162no—
686C2×C4—3168no—
687C2×C4—3168no—
688C2×C4—3162no—
689C2×C4—3162no—
690C2×C4—3162no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4C22×D31612yes—
699C2×C4C22×D31612yes—
700C2×C4C22×D31612yes—
701C2×C4C22×D31612yes—
702C2×C4C22×D31611yescharacteristic
703C2×C4C2×#1192962312yes—
704C2×C4#1457920812yes—
705C2×C4C24×D7911yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#1192962314yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—3162no—
718C22—3162no—
719C22—3162no—
720C22—6324no—
721C22#1909921712yes—
722C22C2×#1457918914yes—
723C22C2×#1457918912yes—
724C22#1909938012yes—
725C22C23×D31611yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—3162no—
731C4—3162no—
732C4—3162no—
733C4—3162no—
734C4—3162no—
735C4—3162no—
736C4—3162no—
737C4#1909921712yes—
738C4C22×#1192962311yescharacteristic
739C4C2×#1457920811yescharacteristic
740C2—24no—
741C2—42no—
742C2—6322no—
743C2#2377584214yesdirect product factor
744C2C2×#1909921711yescharacteristic
745C2C22×#1457918911yescharacteristic
746C2C2×#1909938011yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#435×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099217C2
hypercenterC2×#435D79
hypocenterC79C2×#3343
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#19099253C2semidirect
3. #23775842C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098899C2semidirect
6. C2×#19098888C2semidirect
7. C2×#19098894C2semidirect
8. C2×#19098877C2semidirect
9. C2×#19098859C2semidirect
10. C2×#19098864C2semidirect
11. C2×#19098809C2semidirect
12. C2×#19098792C2semidirect
13. C2×#19098665C2semidirect
14. C2×#19098605C2semidirect
15. C22×#14579095C2semidirect
16. C2×#435×C79C2semidirect
20. #19099253C22semidirect
42. #19098972C22semidirect
43. #19098899C22semidirect
44. #19098894C22semidirect
45. #19098888C22semidirect
46. #19098877C22semidirect
47. #19098864C22semidirect
48. #19098859C22semidirect
49. #19098809C22semidirect
50. #19098792C22semidirect
51. #19098665C22semidirect
52. #19098605C22semidirect
59. C2×#14579095C22semidirect
72. #435×C79C22semidirect
263. C2×C8×C79#41semidirect
335. C8×C79C2×#41semidirect
369. C2×C79#3343semidirect
387. C2×#435D79semidirect
390. C79C2×#3343semidirect
429. #435C2×D79semidirect
608. C2×C8#11929623semidirect
709. C8C2×#11929623semidirect
743. C2#23775842direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992532
C2×#190992172
#237758422
C2×#190989722
C2×#190988992
C2×#190988882
C2×#190988942
C2×#190988772
C2×#190988592
C2×#190988642
C2×#190988092
C2×#190987922
C2×#190986652
C2×#190986052
C22×#145790952
C2×#435×C792
C2×#334379