Finite Group Databasebeta

← C2×#23775980 #35166969

Subgroups — C2×#23775980 #35166969

Order 20224.

2082 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×#19099281C211yesmaximal, characteristic, complemented
2C2×#19099214C211yesmaximal, characteristic
3#23775980C2116yesmaximal, direct product factor
4C2×#19098967C211yesmaximal, characteristic, complemented
5C2×#19098900C211yesmaximal, characteristic, complemented
6C2×#19098898C211yesmaximal, characteristic, complemented
7C2×#19098889C211yesmaximal, characteristic, complemented
8C2×#19098887C211yesmaximal, characteristic, complemented
9C2×#19098847C211yesmaximal, characteristic, complemented
10C2×#19098842C211yesmaximal, characteristic, complemented
11C2×#19098810C211yesmaximal, characteristic, complemented
12C2×#19098809C211yesmaximal, characteristic, complemented
13C2×#19098650C211yesmaximal, characteristic, complemented
14C2×#19098639C211yesmaximal, characteristic, complemented
15C2×#19098602C211yesmaximal, characteristic, complemented
16C2×#428×C79C211yesmaximal, characteristic, complemented
17C22×#11929624—21no—
18C22×#11929613C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20#19099281—24no—
21#19099281C2218yescomplemented
22#19099214—24no—
23#19099214C2218yes—
24C2×#14579160C2211yescharacteristic
25C2×#14579160C2211yescharacteristic
26C2×#14579155—21no—
27C2×#14579154—21no—
28C2×#14579147—21no—
29C2×#14579146—21no—
30C2×#14579144—21no—
31C2×#14579141C2211yescharacteristic
32C2×#14579140C2211yescharacteristic
33C2×#14579139—21no—
34C2×#14579136C2211yescharacteristic
35C2×#14579135C2211yescharacteristic
36C2×C4×Dic158—21no—
37C2×#14579126C2211yescharacteristic
38C2×#14579123C2211yescharacteristic
39C2×C4×C22⋊D79C2211yescharacteristic
40C2×#14579119C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098967C2218yescomplemented
43#19098900C2218yescomplemented
44#19098898C2218yescomplemented
45#19098889C2218yescomplemented
46#19098887C2218yescomplemented
47#19098847C2218yescomplemented
48#19098842C2218yescomplemented
49#19098810C2218yescomplemented
50#19098809C2218yescomplemented
51#19098650C2218yescomplemented
52#19098639C2218yescomplemented
53#19098602C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
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×C8×Dic79C2211yescharacteristic
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×Dic158—21no—
81C22×Dic158C2311yescharacteristic
82C22×D316—21no—
83C22×D316C2311yescharacteristic
84C22×C22⋊D79—21no—
85C22×C22⋊D79D411yescharacteristic
86C22×C4×D79—21no—
87C22×C4×D79—21no—
88C22×C4×D79C2311yescharacteristic
89C2×#11929613—24no—
90C2×#11929613C2314yes—
91C2×#11929607—24no—
92C2×#11929607C2314yes—
93C22×C79⋊C8C2311yescharacteristic
94C22×C79⋊C8C2311yescharacteristic
95#14579160—22no—
96#14579160—22no—
97#14579160C2314yes—
98#14579160C2314yes—
99#14579155—28no—
100#14579154—28no—
101#14579147—28no—
102#14579146—28no—
103#14579144—28no—
104#14579141—22no—
105#14579141C2314yes—
106#14579140—22no—
107#14579140C2314yes—
108#14579139—28no—
109#14579136—22no—
110#14579136C2314yes—
111#14579135—22no—
112#14579135C2314yes—
113C4×Dic158—28no—
114#14579126—22no—
115#14579126C2314yes—
116#14579123—22no—
117#14579123C2314yes—
118C4×C22⋊D79D414yes—
119C4×C22⋊D79C2314yes—
120#14579119—22no—
121#14579119C2314yes—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
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×D79C2314yes—
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79D411yescharacteristic
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4D411yescharacteristic
141C2×C4×Dic79—21no—
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—
158C8×Dic79C2314yes—
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—24no—
185C2×Dic158—21no—
186C2×Dic158—22no—
187C2×Dic158—22no—
188C2×Dic158—44no—
189C2×Dic158—44no—
190C2×Dic158C2412yes—
191C2×D316—24no—
192C2×D316—21no—
193C2×D316—22no—
194C2×D316—22no—
195C2×D316—44no—
196C2×D316C2412yes—
197C2×C22⋊D79—24no—
198C2×C22⋊D79—24no—
199C2×C22⋊D79—44no—
200C2×C22⋊D79C2×D414yes—
201C22×Dic79—21no—
202C22×Dic79—21no—
203C22×Dic79—21no—
204C22×Dic79C2×D411yescharacteristic
205C22×Dic79C2×D411yescharacteristic
206C22×Dic79C2×D411yescharacteristic
207C2×C4×D79—24no—
208C2×C4×D79—24no—
209C2×C4×D79—22no—
210C2×C4×D79—22no—
211C2×C4×D79—44no—
212C2×C4×D79—44no—
213C2×C4×D79C2×D412yes—
214C2×C4×D79C2412yes—
215#11929613—28no—
216#11929607—28no—
217C2×C79⋊C8—22no—
218C2×C79⋊C8—22no—
219C2×C79⋊C8C2412yes—
220C2×C79⋊C8C2412yes—
221C4⋊Dic79—24no—
222C4⋊Dic79—21no—
223C4⋊Dic79—21no—
224C4⋊Dic79C2412yes—
225C4⋊Dic79C2412yes—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4—24no—
231Dic79⋊C4C2×D414yes—
232C22⋊Dic79—24no—
233C22⋊Dic79C2×D414yes—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4C2×D414yes—
240C4×Dic79—24no—
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—21no—
249C22×C4×C79—24no—
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—22no—
282C22×D79—42no—
283C22×D79—42no—
284C22×D79—42no—
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—42no—
312C2×Dic79—42no—
313C2×Dic79—42no—
314C2×Dic79AGL(1,ℤ/8)14yes—
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—
327Dic158—22no—
328Dic158—22no—
329Dic158—42no—
330Dic158—48no—
331Dic158—48no—
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—22no—
345C2×D79—22no—
346C2×D79—22no—
347C2×D79—44no—
348C2×D79—42no—
349C2×D79—42no—
350C2×D79—42no—
351C2×D79—84no—
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—42no—
363Dic79—42no—
364Dic79—42no—
365Dic79C2×AGL(1,ℤ/8)14yes—
366C2×#3353—791nomaximal, Sylow
367C2×C79—42no—
368C2×C79#335314yescomplemented
369C2×C79C2×#54711yescharacteristic
370C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
371C2×C79C2×#57811yescharacteristic
372D79—42no—
373D79—82no—
374C2×#556—791no—
375C2×#547—791no—
376#3353—7916no—
377C2×#500—791no—
378C2×#484—791no—
379C2×#484—791no—
380C2×#482—791no—
381C2×#482—791no—
382C2×#475—791no—
383C2×#474—791no—
384C2×#468—791no—
385C2×#468—791no—
386C2×C4×SD16—791no—
387C2×#436—791no—
388C2×#428—791no—
389C2×#428D7911yescharacteristic, complemented
390C79C2×#335311yescharacteristic, complemented, Sylow
391C22×#41—1581no—
392C22×SD16—791no—
393C22×M16—791no—
394C22×M16C2×D7911yescharacteristic
395#556—798no—
396#556—1584no—
397#547—798no—
398#547—1584no—
399C2×C4⋊Q8—791no—
400C2×C4⋊Q8—791no—
401C2×#126—1581no—
402C2×#126—1581no—
403C2×#124—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×Q8—1581no—
413C2×C4×D4—791no—
414C2×C4×D4—791no—
415C2×#117—791no—
416C2×#117C2×D7911yescharacteristic
417C22×C4⋊C4—791no—
418C22×C4⋊C4C2×D7911yescharacteristic
419#500—798no—
420#484—798no—
421#484—798no—
422#482—798no—
423#482—798no—
424#475—798no—
425#474—798no—
426#468—798no—
427#468—798no—
428C4×SD16—798no—
429#436—798no—
430#428—798no—
431#428C2×D7918yescomplemented
432C2×#107—791no—
433C2×#107—791no—
434C2×#107—791no—
435C2×#107—791no—
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×C4×C8—791no—
451C2×#41—3168no—
452C2×#41—1588no—
453C22×Q8—791no—
454C22×Q8—1581no—
455C22×Q8—1581no—
456C22×D4—791no—
457C22×D4—791no—
458C22×D4—1581no—
459C22×D4—1581no—
460C23×C4—21no—
461C23×C4—791no—
462C23×C4—1581no—
463C23×C4—1581no—
464C23×C4C22×D7911yescharacteristic
465C2×SD16—794no—
466C2×SD16—1584no—
467C2×M16—24no—
468C2×M16—794no—
469C2×M16—1584no—
470C2×M16C22×D7914yes—
471C22×C8—791no—
472C22×C8—791no—
473C22×C8C22×D7911yescharacteristic
474C22×C8C22×D7911yescharacteristic
475C4⋊Q8—794no—
476C4⋊Q8—794no—
477C4⋊Q8—1582no—
478C4⋊Q8—1582no—
479#126—1588no—
480#126—1588no—
481#124—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—1588no—
495C4×Q8—1582no—
496C4×D4—794no—
497C4×D4—794no—
498C4×D4—794no—
499C4×D4—1582no—
500#117—22no—
501#117—794no—
502#117—1582no—
503#117C22×D7914yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—791no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—794no—
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⋊C4C22×D7911yescharacteristic
518C2×C4⋊C4C22×D7911yescharacteristic
519C2×C4⋊C4C22×D7914yes—
520C2×C4⋊C4C22×D7911yescharacteristic
521C2×C4⋊C4C22×D7911yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—791no—
524C2×C22⋊C4—791no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4—1581no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4—1581no—
531C2×C42—21no—
532C2×C42—791no—
533C2×C42—1581no—
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—
553C4×C8—794no—
554C24—791no—
555C24—1581no—
556C24D4×D7911yescharacteristic
557#41—31632no—
558C2×Q8—3164no—
559C2×Q8—3164no—
560C2×Q8—792no—
561C2×Q8—1584no—
562C2×Q8—1584no—
563C2×Q8—1582no—
564C2×Q8—1582no—
565C2×Q8—1581no—
566C2×D4—3164no—
567C2×D4—3164no—
568C2×D4—794no—
569C2×D4—792no—
570C2×D4—1584no—
571C2×D4—1584no—
572C2×D4—1584no—
573C2×D4—1582no—
574C2×D4—1582no—
575C2×D4—1581no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—3164no—
585C22×C4—3164no—
586C22×C4—791no—
587C22×C4—791no—
588C22×C4—791no—
589C22×C4—792no—
590C22×C4—792no—
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—
604M16—1588no—
605C2×C8—22no—
606C2×C8—792no—
607C2×C8—792no—
608C2×C8—1582no—
609C2×C8—1582no—
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—1581no—
628C4⋊C4—1581no—
629C4⋊C4C23×D7912yes—
630C4⋊C4C23×D7912yes—
631C4⋊C4C23×D7912yes—
632C4⋊C4C23×D7912yes—
633C22⋊C4—24no—
634C22⋊C4—794no—
635C22⋊C4—794no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C22⋊C4—1584no—
639C22⋊C4—1584no—
640C22⋊C4—1584no—
641C22⋊C4—1584no—
642C42—24no—
643C42—792no—
644C42—792no—
645C42—1584no—
646C42—1584no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—3162no—
651C23—3162no—
652C23—3162no—
653C23—792no—
654C23—1582no—
655C23—1582no—
656C23—1582no—
657C23—1582no—
658C23C2×D4×D7912yes—
659C23C2×D4×D7911yescharacteristic
660Q8—3168no—
661Q8—3168no—
662Q8—3162no—
663Q8—1582no—
664Q8—1582no—
665D4—3168no—
666D4—3168no—
667D4—3162no—
668D4—1588no—
669D4—1582no—
670D4—1582no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—48no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—3168no—
685C2×C4—3168no—
686C2×C4—3162no—
687C2×C4—3162no—
688C2×C4—3162no—
689C2×C4—794no—
690C2×C4—792no—
691C2×C4—792no—
692C2×C4—792no—
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—3164no—
715C22—3162no—
716C22—3162no—
717C22—3162no—
718C22—6324no—
719C22—1582no—
720C22—1582no—
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—794no—
735C4—1582no—
736C4—1582no—
737C4#1909921412yes—
738C4C22×#1192962411yescharacteristic
739C4C2×#1457920911yescharacteristic
740C2—42no—
741C2—3162no—
742C2—6322no—
743C2#2377598014yesdirect 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×#3353
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×#19099281C2semidirect
3. #23775980C2direct (N × H)
4. C2×#19098967C2semidirect
5. C2×#19098900C2semidirect
6. C2×#19098898C2semidirect
7. C2×#19098889C2semidirect
8. C2×#19098887C2semidirect
9. C2×#19098847C2semidirect
10. C2×#19098842C2semidirect
11. C2×#19098810C2semidirect
12. C2×#19098809C2semidirect
13. C2×#19098650C2semidirect
14. C2×#19098639C2semidirect
15. C2×#19098602C2semidirect
16. C2×#428×C79C2semidirect
21. #19099281C22semidirect
42. #19098967C22semidirect
43. #19098900C22semidirect
44. #19098898C22semidirect
45. #19098889C22semidirect
46. #19098887C22semidirect
47. #19098847C22semidirect
48. #19098842C22semidirect
49. #19098810C22semidirect
50. #19098809C22semidirect
51. #19098650C22semidirect
52. #19098639C22semidirect
53. #19098602C22semidirect
72. #428×C79C22semidirect
259. C2×C8×C79#41semidirect
333. C8×C79C2×#41semidirect
368. C2×C79#3353semidirect
389. C2×#428D79semidirect
390. C79C2×#3353semidirect
431. #428C2×D79semidirect
610. C2×C8#11929624semidirect
709. C8C2×#11929624semidirect
743. C2#23775980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992812
C2×#190992142
#237759802
C2×#190989672
C2×#190989002
C2×#190988982
C2×#190988892
C2×#190988872
C2×#190988472
C2×#190988422
C2×#190988102
C2×#190988092
C2×#190986502
C2×#190986392
C2×#190986022
C2×#428×C792
C2×#335379