Finite Group Databasebeta

← C2×#23775841 #35166801

Subgroups — C2×#23775841 #35166801

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×#19099252C211yesmaximal, characteristic, complemented
2C2×#19099214C211yesmaximal, characteristic
3#23775841C2116yesmaximal, direct product factor
4C2×#19098970C211yesmaximal, characteristic, complemented
5C2×#19098898C211yesmaximal, characteristic, complemented
6C2×#19098887C211yesmaximal, characteristic, complemented
7C2×#19098895C211yesmaximal, characteristic, complemented
8C2×#19098878C211yesmaximal, characteristic, complemented
9C2×#19098857C211yesmaximal, characteristic, complemented
10C2×#19098862C211yesmaximal, characteristic, complemented
11C2×#19098809C211yesmaximal, characteristic, complemented
12C2×#19098793C211yesmaximal, characteristic, complemented
13C2×#19098662C211yesmaximal, characteristic, complemented
14C2×#19098632C211yesmaximal, characteristic, complemented
15C2×#107×D79C211yesmaximal, characteristic, complemented
16C2×#428×C79C211yesmaximal, characteristic, complemented
17C22×#11929624—21no—
18C22×#11929613C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099252—24no—
21#19099252C2218yescomplemented
22#19099214—24no—
23#19099214C2218yes—
24C2×#14579160C2211yescharacteristic
25C2×#14579154—21no—
26C2×#14579153—21no—
27C2×#14579152C2211yescharacteristic
28C2×#14579146—21no—
29C2×#14579144—21no—
30C2×#14579143—21no—
31C2×#14579141C2211yescharacteristic
32C2×#14579140C2211yescharacteristic
33C2×#14579139—21no—
34C2×#14579136C2211yescharacteristic
35C2×#14579135C2211yescharacteristic
36C2×#14579126C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
38C2×C4×C22⋊D79C2211yescharacteristic
39C2×#14579118—21no—
40C2×C4⋊C4×D79C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098970C2218yescomplemented
43#19098898C2218yescomplemented
44#19098895C2218yescomplemented
45#19098887C2218yescomplemented
46#19098878C2218yescomplemented
47#19098862C2218yescomplemented
48#19098857C2218yescomplemented
49#19098809C2218yescomplemented
50#19098793C2218yescomplemented
51#19098662C2218yescomplemented
52#19098632C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57#107×D79C2218yescomplemented
58C2×#14579092C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579084C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579081C2211yescharacteristic
65C2×#14579081C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×#14579071C2211yescharacteristic
69C22×M16×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71C22×C4⋊C4×C79C2211yescharacteristic
72#428×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic
74C2×#107×C79C2211yescharacteristic
75C2×#106×C79C2211yescharacteristic
76C2×#106×C79C2211yescharacteristic
77C2×#11929624—28no—
78C2×#11929624—48no—
79C22×Dic158—21no—
80C22×Dic158C2311yescharacteristic
81C22×D316—21no—
82C22×D316C2311yescharacteristic
83C22×C22⋊D79—21no—
84C22×C22⋊D79D411yescharacteristic
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79—21no—
88C22×C4×D79C2311yescharacteristic
89C2×#11929613—24no—
90C2×#11929613C2314yes—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93C2×C8×D79—24no—
94C2×C8×D79C2314yes—
95#14579160—22no—
96#14579160C2314yes—
97#14579154—28no—
98#14579153—28no—
99#14579152—22no—
100#14579152C2314yes—
101#14579146—28no—
102#14579144—28no—
103#14579143—28no—
104#14579141—22no—
105#14579141C2314yes—
106#14579140—22no—
107#14579140C2314yes—
108#14579139—28no—
109#14579136—22no—
110#14579136C2314yes—
111#14579135—22no—
112#14579135C2314yes—
113#14579126—22no—
114#14579126C2314yes—
115#14579123—22no—
116#14579123C2314yes—
117C4×C22⋊D79D414yes—
118C4×C22⋊D79C2314yes—
119#14579118—28no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4D411yescharacteristic
131C4⋊C4×D79—22no—
132C4⋊C4×D79—22no—
133C4⋊C4×D79C2314yes—
134C4⋊C4×D79C2314yes—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79D411yescharacteristic
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4D411yescharacteristic
142C2×C4×Dic79—21no—
143C2×C4×Dic79C2311yescharacteristic
144#14579095C2314yes—
145#14579094C2314yes—
146#14579094C2314yes—
147#14579094C2314yes—
148#14579092C2314yes—
149Dic79⋊C8C2314yes—
150#14579086C2314yes—
151#14579084C2314yes—
152#14579084C2314yes—
153#14579083C2314yes—
154#14579081C2314yes—
155#14579081C2314yes—
156C22⋊(C79⋊C8)C2314yes—
157(C2×D79)⋊C8C2314yes—
158#14579071C2314yes—
159C23×C4×C79—21no—
160C23×C4×C79C2311yescharacteristic
161C2×M16×C79—24no—
162C2×M16×C79C2314yes—
163C22×C8×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165#117×C79—22no—
166#117×C79C2314yes—
167C2×C4⋊C4×C79—22no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2314yes—
174C2×C22⋊C4×C79—21no—
175C2×C42×C79—21no—
176#107×C79C2314yes—
177#107×C79C2314yes—
178#106×C79C2314yes—
179#106×C79C2314yes—
180C23×D79—21no—
181C23×D79C2×D411yescharacteristic
182#11929624—432no—
183C2×Dic158—24no—
184C2×Dic158—21no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—44no—
188C2×Dic158C2412yes—
189C2×D316—24no—
190C2×D316—21no—
191C2×D316—22no—
192C2×D316—22no—
193C2×D316—44no—
194C2×D316C2412yes—
195C2×C22⋊D79—24no—
196C2×C22⋊D79—24no—
197C2×C22⋊D79—44no—
198C2×C22⋊D79C2×D414yes—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C2×C4×D79—24no—
206C2×C4×D79—24no—
207C2×C4×D79—24no—
208C2×C4×D79—22no—
209C2×C4×D79—22no—
210C2×C4×D79—44no—
211C2×C4×D79—44no—
212C2×C4×D79—44no—
213C2×C4×D79C2×D412yes—
214C2×C4×D79C2412yes—
215#11929613—28no—
216C2×C79⋊C8—22no—
217C2×C79⋊C8—22no—
218C2×C79⋊C8C2412yes—
219C2×C79⋊C8C2412yes—
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⋊C4C2×D414yes—
234C22⋊Dic79—24no—
235C22⋊Dic79C2×D414yes—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4C2×D414yes—
241C4×Dic79—24no—
242C4×Dic79C2×D412yes—
243C4×Dic79C2412yes—
244C24×C79C2×D411yescharacteristic
245C22×C4×C79—22no—
246C22×C4×C79—22no—
247C22×C4×C79—21no—
248C22×C4×C79—24no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79—44no—
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D412yes—
255C22×C4×C79C2412yes—
256C22×C4×C79C2411yescharacteristic
257M16×C79—28no—
258C2×C8×C79—22no—
259C2×C8×C79#4114yescomplemented
260C2×C8×C79C2412yes—
261C2×C8×C79C2412yes—
262C4⋊C4×C79—21no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—24no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79—21no—
267C4⋊C4×C79C2412yes—
268C4⋊C4×C79C2412yes—
269C4⋊C4×C79C2412yes—
270C4⋊C4×C79C2412yes—
271C22⋊C4×C79—24no—
272C42×C79—24no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79C22×D412yes—
277C23×C79C22×D411yescharacteristic
278C22×D79—22no—
279C22×D79—22no—
280C22×D79—22no—
281C22×D79—42no—
282C22×D79—42no—
283C22×D79—42no—
284C22×D79AGL(1,ℤ/8)14yes—
285C22×D79C22×D412yes—
286C2×C4×C79—22no—
287C2×C4×C79—24no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—48no—
295C2×C4×C79—42no—
296C2×C4×C79—42no—
297C2×C4×C79—42no—
298C2×C4×C79—42no—
299C2×C4×C79C22×D412yes—
300C2×C4×C79C22×D411yescharacteristic
301C2×C4×C79C2×#4112yes—
302C2×C4×C792−1+412yes—
303C2×C4×C79C2511yescharacteristic
304C22⋊D79—28no—
305C22⋊D79—48no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—42no—
313C2×Dic79—42no—
314C2×Dic79—42no—
315C2×Dic79C22×D412yes—
316C2×Dic79C22×D412yes—
317C2×Dic79C22×D412yes—
318D316—22no—
319D316—22no—
320D316—48no—
321D316—42no—
322C4×D79—24no—
323C4×D79—22no—
324C4×D79—22no—
325C4×D79—48no—
326C4×D79—48no—
327C4×D79—48no—
328Dic158—22no—
329Dic158—22no—
330Dic158—48no—
331Dic158—42no—
332C8×C79—22no—
333C8×C79C2×#4114yescomplemented
334C79⋊C8—22no—
335C79⋊C8—22no—
336C22×C79—22no—
337C22×C79—22no—
338C22×C79—22no—
339C22×C79—44no—
340C22×C79#54712yes—
341C22×C79C2×AGL(1,ℤ/8)12yes—
342C22×C79#57812yes—
343C22×C79C23×D411yescharacteristic
344C2×D79—28no—
345C2×D79—22no—
346C2×D79—22no—
347C2×D79—42no—
348C2×D79—42no—
349C2×D79—42no—
350C2×D79—84no—
351C2×D79C2×AGL(1,ℤ/8)14yes—
352C4×C79—22no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79—42no—
356C4×C79—42no—
357C4×C79#54712yes—
358C4×C79C22×#4111yescharacteristic
359C4×C79C2×2−1+411yescharacteristic
360Dic79—22no—
361Dic79—22no—
362Dic79—22no—
363Dic79—42no—
364Dic79—42no—
365Dic79—42no—
366C2×#3343—791nomaximal, Sylow
367C2×C79—42no—
368C2×C79#334314yescomplemented
369C2×C79C2×#54711yescharacteristic
370C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
371C2×C79C2×#57811yescharacteristic
372D79—24no—
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×#435—791no—
388C2×#428D7911yescharacteristic, complemented
389C22×#107—791no—
390C79C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1581no—
392C22×SD16—791no—
393C22×M16C2×D7911yescharacteristic
394C23×C8—791no—
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×D4—791no—
414C2×#117—1581no—
415C2×#117C2×D7911yescharacteristic
416C22×C4⋊C4—791no—
417C22×C4⋊C4—791no—
418C22×C4⋊C4C2×D7911yescharacteristic
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#435—798no—
430#428C2×D7918yescomplemented
431C2×#107—791no—
432C2×#107—791no—
433C2×#107—791no—
434C2×#107—791no—
435C2×#107—798no—
436C2×#107C2×D7911yescharacteristic
437C2×#107C2×D7911yescharacteristic
438C2×#106—791no—
439C2×#106C2×D7911yescharacteristic
440C2×#106C2×D7911yescharacteristic
441C2×C4⋊C8—791no—
442C2×#103—791no—
443C2×#103—791no—
444C2×#103—791no—
445C2×#102—791no—
446C2×#102—791no—
447C2×#102—791no—
448C2×C22⋊C8—791no—
449C2×C22⋊C8—791no—
450C2×#97—791no—
451C2×#41—3168no—
452C2×#41—1588no—
453C22×Q8—791no—
454C22×Q8—1581no—
455C22×D4—791no—
456C22×D4—791no—
457C22×D4—1581no—
458C22×D4—1581no—
459C23×C4—21no—
460C23×C4—791no—
461C23×C4—1581no—
462C23×C4—1581no—
463C23×C4—1581no—
464C23×C4C22×D7911yescharacteristic
465C2×SD16—794no—
466C2×SD16—1584no—
467C2×M16—24no—
468C2×M16C22×D7914yes—
469C22×C8—791no—
470C22×C8—791no—
471C22×C8—794no—
472C22×C8—1584no—
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—1588no—
487C22⋊Q8—1582no—
488C22⋊Q8—1582no—
489#121—794no—
490#121—794no—
491#121—1582no—
492#121—1582no—
493C4×Q8—794no—
494C4×Q8—1582no—
495C4×D4—794no—
496C4×D4—794no—
497C4×D4—794no—
498C4×D4—1582no—
499#117—22no—
500#117—1588no—
501#117C22×D7914yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—791no—
505C2×C4⋊C4—791no—
506C2×C4⋊C4—791no—
507C2×C4⋊C4—794no—
508C2×C4⋊C4—794no—
509C2×C4⋊C4—1582no—
510C2×C4⋊C4—1582no—
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×C4⋊C4C22×D7911yescharacteristic
522C2×C4⋊C4C22×D7914yes—
523C2×C4⋊C4C22×D7911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—791no—
526C2×C22⋊C4—791no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4—1581no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4—1581no—
531C2×C22⋊C4—1581no—
532C2×C42—21no—
533C2×C42—791no—
534C2×C42—1581no—
535#107—794no—
536#107—794no—
537#107—794no—
538#107—794no—
539#107C22×D7914yes—
540#107C22×D7914yes—
541#106—794no—
542#106C22×D7914yes—
543#106C22×D7914yes—
544C4⋊C8—794no—
545#103—794no—
546#103—794no—
547#103—794no—
548#102—794no—
549#102—794no—
550#102—794no—
551C22⋊C8—794no—
552C22⋊C8—794no—
553#97—794no—
554C24—791no—
555C24—1581no—
556C24D4×D7911yescharacteristic
557#41—31632no—
558C2×Q8—3164no—
559C2×Q8—792no—
560C2×Q8—1584no—
561C2×Q8—1582no—
562C2×Q8—1582no—
563C2×Q8—1581no—
564C2×D4—3164no—
565C2×D4—3164no—
566C2×D4—794no—
567C2×D4—792no—
568C2×D4—1584no—
569C2×D4—1584no—
570C2×D4—1584no—
571C2×D4—1582no—
572C2×D4—1582no—
573C2×D4—1581no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—44no—
582C22×C4—3164no—
583C22×C4—3164no—
584C22×C4—3164no—
585C22×C4—791no—
586C22×C4—791no—
587C22×C4—791no—
588C22×C4—792no—
589C22×C4—792no—
590C22×C4—1584no—
591C22×C4—1584no—
592C22×C4—1584no—
593C22×C4—1581no—
594C22×C4—1581no—
595C22×C4—1581no—
596C22×C4—1582no—
597C22×C4—1582no—
598C22×C4D4×D7912yes—
599C22×C4D4×D7911yescharacteristic
600C22×C4C23×D7912yes—
601C22×C4C23×D7911yescharacteristic
602SD16—1588no—
603M16—28no—
604C2×C8—22no—
605C2×C8—792no—
606C2×C8—792no—
607C2×C8—1582no—
608C2×C8—1582no—
609C2×C8—1588no—
610C2×C8#1192962414yescomplemented
611C2×C8C23×D7912yes—
612C2×C8C23×D7912yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—794no—
619C4⋊C4—792no—
620C4⋊C4—792no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1584no—
626C4⋊C4—1584no—
627C4⋊C4—1584no—
628C4⋊C4—1584no—
629C4⋊C4—1581no—
630C4⋊C4—1581no—
631C4⋊C4C23×D7912yes—
632C4⋊C4C23×D7912yes—
633C4⋊C4C23×D7912yes—
634C4⋊C4C23×D7912yes—
635C22⋊C4—24no—
636C22⋊C4—794no—
637C22⋊C4—794no—
638C22⋊C4—1584no—
639C22⋊C4—1584no—
640C22⋊C4—1584no—
641C22⋊C4—1584no—
642C22⋊C4—1584no—
643C42—24no—
644C42—792no—
645C42—792no—
646C42—1584no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—3162no—
651C23—3162no—
652C23—3162no—
653C23—794no—
654C23—792no—
655C23—1582no—
656C23—1582no—
657C23—1582no—
658C23C2×D4×D7912yes—
659C23C2×D4×D7911yescharacteristic
660Q8—3168no—
661Q8—3162no—
662Q8—1582no—
663Q8—1582no—
664D4—3168no—
665D4—3168no—
666D4—3162no—
667D4—1588no—
668D4—1582no—
669D4—1582no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—48no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—3168no—
684C2×C4—3168no—
685C2×C4—3168no—
686C2×C4—3162no—
687C2×C4—3162no—
688C2×C4—3162no—
689C2×C4—792no—
690C2×C4—792no—
691C2×C4—792no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4—1584no—
700C2×C4—1582no—
701C2×C4C2×D4×D7912yes—
702C2×C4C2×D4×D7911yescharacteristic
703C2×C4C2×#1192962412yes—
704C2×C4#1457920912yes—
705C2×C4C24×D7911yescharacteristic
706C8—22no—
707C8—1582no—
708C8—1582no—
709C8C2×#1192962414yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—3162no—
715C22—3162no—
716C22—3162no—
717C22—794no—
718C22—6324no—
719C22—1582no—
720C22—1588no—
721C22—1582no—
722C22#1909921412yes—
723C22AGL(1,ℤ/8)×D7912yes—
724C22#1909937912yes—
725C22C22×D4×D7911yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—3162no—
732C4—3162no—
733C4—3162no—
734C4—1582no—
735C4—1582no—
736C4—1582no—
737C4#1909921412yes—
738C4C22×#1192962411yescharacteristic
739C4C2×#1457920911yescharacteristic
740C2—42no—
741C2—6322no—
742C2—1584no—
743C2#2377584114yesdirect product factor
744C2C2×#1909921411yescharacteristic
745C2C2×AGL(1,ℤ/8)×D7911yescharacteristic
746C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#428×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099214C2
hypercenterC2×#428D79
hypocenterC79C2×#3343
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#19099252C2semidirect
3. #23775841C2direct (N × H)
4. C2×#19098970C2semidirect
5. C2×#19098898C2semidirect
6. C2×#19098887C2semidirect
7. C2×#19098895C2semidirect
8. C2×#19098878C2semidirect
9. C2×#19098857C2semidirect
10. C2×#19098862C2semidirect
11. C2×#19098809C2semidirect
12. C2×#19098793C2semidirect
13. C2×#19098662C2semidirect
14. C2×#19098632C2semidirect
15. C2×#107×D79C2semidirect
16. C2×#428×C79C2semidirect
21. #19099252C22semidirect
42. #19098970C22semidirect
43. #19098898C22semidirect
44. #19098895C22semidirect
45. #19098887C22semidirect
46. #19098878C22semidirect
47. #19098862C22semidirect
48. #19098857C22semidirect
49. #19098809C22semidirect
50. #19098793C22semidirect
51. #19098662C22semidirect
52. #19098632C22semidirect
57. #107×D79C22semidirect
72. #428×C79C22semidirect
259. C2×C8×C79#41semidirect
333. C8×C79C2×#41semidirect
368. C2×C79#3343semidirect
388. C2×#428D79semidirect
390. C79C2×#3343semidirect
430. #428C2×D79semidirect
610. C2×C8#11929624semidirect
709. C8C2×#11929624semidirect
743. C2#23775841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992522
C2×#190992142
#237758412
C2×#190989702
C2×#190988982
C2×#190988872
C2×#190988952
C2×#190988782
C2×#190988572
C2×#190988622
C2×#190988092
C2×#190987932
C2×#190986622
C2×#190986322
C2×#107×D792
C2×#428×C792
C2×#334379