Finite Group Databasebeta

← C2×#23775753 #35166688

Subgroups — C2×#23775753 #35166688

Order 20224.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099268C211yesmaximal, characteristic, complemented
2C2×#19099214C211yesmaximal, characteristic
3#23775753C2116yesmaximal, direct product factor
4C2×#19098960C211yesmaximal, characteristic, complemented
5C2×#19098883C211yesmaximal, characteristic, complemented
6C2×#19098881C211yesmaximal, characteristic, complemented
7C2×#19098895C211yesmaximal, characteristic, complemented
8C2×#19098893C211yesmaximal, characteristic, complemented
9C2×#19098847C211yesmaximal, characteristic, complemented
10C2×#19098852C211yesmaximal, characteristic, complemented
11C2×#19098793C211yesmaximal, characteristic, complemented
12C2×#19098792C211yesmaximal, characteristic, complemented
13C2×#19098650C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D79C211yesmaximal, characteristic, complemented
15C2×#106×D79C211yesmaximal, characteristic, complemented
16C22×#106×C79C211yesmaximal, characteristic, complemented
17C22×#11929624—21no—
18C22×#11929613C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099268—24no—
21#19099268C2218yescomplemented
22#19099214—24no—
23#19099214C2218yes—
24C2×#14579160C2211yescharacteristic
25C2×#14579160C2211yescharacteristic
26C2×#14579151—21no—
27C2×#14579146—21no—
28C2×#14579144—21no—
29C2×#14579141C2211yescharacteristic
30C2×#14579140—21no—
31C2×#14579140C2211yescharacteristic
32C2×#14579139—21no—
33C2×#14579139—21no—
34C2×#14579136C2211yescharacteristic
35C2×#14579135C2211yescharacteristic
36C2×#14579126C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
38C2×C4×C22⋊D79—21no—
39C2×C4×C22⋊D79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098960C2218yescomplemented
43#19098895C2218yescomplemented
44#19098893C2218yescomplemented
45#19098883C2218yescomplemented
46#19098881C2218yescomplemented
47#19098852C2218yescomplemented
48#19098847C2218yescomplemented
49#19098793C2218yescomplemented
50#19098792C2218yescomplemented
51#19098650C2218yescomplemented
52C8×C22⋊D79C2218yescomplemented
53C2×#14579093C2211yescharacteristic
54C2×#14579092C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58#106×D79C2218yescomplemented
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
69C23×C8×C79C2211yescharacteristic
70C22×C4⋊C4×C79C2211yescharacteristic
71C22×C4⋊C4×C79C2211yescharacteristic
72C2×#106×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×#106×C79C2211yescharacteristic
75C2×#106×C79C2211yescharacteristic
76C2×#106×C79C2218yescomplemented
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×D79—21no—
89C22×C4×D79C2311yescharacteristic
90C2×#11929613—24no—
91C2×#11929613C2314yes—
92C22×C79⋊C8C2311yescharacteristic
93C22×C79⋊C8C2311yescharacteristic
94C2×C8×D79—24no—
95C2×C8×D79C2314yes—
96#14579160—22no—
97#14579160—22no—
98#14579160C2314yes—
99#14579160C2314yes—
100#14579151—28no—
101#14579146—28no—
102#14579144—28no—
103#14579141—22no—
104#14579141C2314yes—
105#14579140—22no—
106#14579140—28no—
107#14579140C2314yes—
108#14579139—28no—
109#14579139—28no—
110#14579136—22no—
111#14579136C2314yes—
112#14579135—22no—
113#14579135C2314yes—
114#14579126—22no—
115#14579126C2314yes—
116#14579123—22no—
117#14579123C2314yes—
118C4×C22⋊D79—28no—
119C4×C22⋊D79D414yes—
120C4×C22⋊D79C2314yes—
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#14579093C2314yes—
145#14579092C2314yes—
146#14579092C2314yes—
147#14579092C2314yes—
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×C79—21no—
161C23×C4×C79C2311yescharacteristic
162C22×C8×C79—24no—
163C22×C8×C79C2314yes—
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C2×C4⋊C4×C79—22no—
167C2×C4⋊C4×C79—22no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2314yes—
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C4⋊C4×C79C2314yes—
176#106×C79C2314yes—
177#106×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—82no—
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—44no—
199C2×C22⋊D79SD1618yescomplemented
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—24no—
210C2×C4×D79—22no—
211C2×C4×D79—22no—
212C2×C4×D79—44no—
213C2×C4×D79—44no—
214C2×C4×D79—82no—
215C2×C4×D79C2×D412yes—
216C2×C4×D79C2412yes—
217#11929613—28no—
218C2×C79⋊C8—22no—
219C2×C79⋊C8—22no—
220C2×C79⋊C8C2412yes—
221C2×C79⋊C8C2412yes—
222C8×D79—28no—
223C4⋊Dic79—24no—
224C4⋊Dic79—21no—
225C4⋊Dic79—21no—
226C4⋊Dic79C2412yes—
227C4⋊Dic79C2412yes—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4—24no—
234Dic79⋊C4C2×D414yes—
235C22⋊Dic79—24no—
236C22⋊Dic79C2×D414yes—
237(C2×D79)⋊C4—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4—24no—
241(C2×D79)⋊C4C2×D414yes—
242C4×Dic79—24no—
243C4×Dic79C2×D412yes—
244C4×Dic79C2412yes—
245C24×C79C2×D411yescharacteristic
246C22×C4×C79—22no—
247C22×C4×C79—22no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—24no—
251C22×C4×C79—21no—
252C22×C4×C79—21no—
253C22×C4×C79—24no—
254C22×C4×C79—44no—
255C22×C4×C79—82no—
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D412yes—
258C22×C4×C79C2412yes—
259C22×C4×C79C2411yescharacteristic
260C2×C8×C79—28no—
261C2×C8×C79—22no—
262C2×C8×C79#4114yescomplemented
263C2×C8×C79C2412yes—
264C2×C8×C79C2412yes—
265C4⋊C4×C79—21no—
266C4⋊C4×C79—21no—
267C4⋊C4×C79—21no—
268C4⋊C4×C79—24no—
269C4⋊C4×C79—24no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79C2412yes—
272C4⋊C4×C79C2412yes—
273C4⋊C4×C79C2412yes—
274C4⋊C4×C79C2412yes—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79C2×SD1614yes—
278C23×C79C22×D412yes—
279C23×C79C22×D411yescharacteristic
280C22×D79—22no—
281C22×D79—22no—
282C22×D79—22no—
283C22×D79—42no—
284C22×D79—42no—
285C22×D79—42no—
286C22×D79C2×SD1614yes—
287C22×D79C22×D412yes—
288C2×C4×C79—22no—
289C2×C4×C79—24no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—42no—
297C2×C4×C79—42no—
298C2×C4×C79—48no—
299C2×C4×C79—42no—
300C2×C4×C79—42no—
301C2×C4×C79—84no—
302C2×C4×C79C22×D412yes—
303C2×C4×C79C22×D411yescharacteristic
304C2×C4×C79C2×#4112yes—
305C2×C4×C792−1+412yes—
306C2×C4×C79C2511yescharacteristic
307C22⋊D79—48no—
308C22⋊D79C2×SD16116yescomplemented
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—42no—
315C2×Dic79—42no—
316C2×Dic79—42no—
317C2×Dic79C2×SD1614yes—
318C2×Dic79C22×D412yes—
319C2×Dic79C22×D412yes—
320C2×Dic79C22×D412yes—
321D316—22no—
322D316—22no—
323D316—48no—
324D316—42no—
325C4×D79—24no—
326C4×D79—22no—
327C4×D79—22no—
328C4×D79—48no—
329C4×D79—48no—
330C4×D79—84no—
331Dic158—22no—
332Dic158—22no—
333Dic158—42no—
334Dic158—48no—
335Dic158—84no—
336C8×C79—22no—
337C8×C79C2×#4114yescomplemented
338C79⋊C8—22no—
339C79⋊C8—22no—
340C22×C79—28no—
341C22×C79—22no—
342C22×C79—22no—
343C22×C79#54712yes—
344C22×C79C22×SD1614yes—
345C22×C79C22×SD1612yes—
346C22×C79#57712yes—
347C22×C79C23×D411yescharacteristic
348C2×D79—28no—
349C2×D79—22no—
350C2×D79—22no—
351C2×D79—42no—
352C2×D79—42no—
353C2×D79—42no—
354C2×D79—84no—
355C2×D79C22×SD1614yes—
356C4×C79—22no—
357C4×C79—42no—
358C4×C79—42no—
359C4×C79—42no—
360C4×C79—42no—
361C4×C79#54712yes—
362C4×C79C22×#4111yescharacteristic
363C4×C79C2×2−1+411yescharacteristic
364Dic79—22no—
365Dic79—22no—
366Dic79—42no—
367Dic79—42no—
368Dic79—42no—
369Dic79C22×SD1614yes—
370C2×#3335—791nomaximal, Sylow
371C2×C79—24no—
372C2×C79#333514yescomplemented
373C2×C79C2×#54711yescharacteristic
374C2×C79C23×SD1611yescharacteristic
375C2×C79C2×#57711yescharacteristic
376D79—24no—
377D79—82no—
378C2×#554—791no—
379C2×#547—791no—
380#3335—7916no—
381C2×#498—791no—
382C2×#481—791no—
383C2×#481—791no—
384C2×#483—791no—
385C2×#483—791no—
386C2×#475—791no—
387C2×#476—791no—
388C2×#465—791no—
389C2×#465—791no—
390C2×C4×SD16—791no—
391C2×C8×D4—791no—
392C22×#106—791no—
393C22×#106D7911yescharacteristic, complemented
394C79C2×#333511yescharacteristic, complemented, Sylow
395C22×#41—1581no—
396C22×SD16—791no—
397C23×C8—791no—
398C23×C8C2×D7911yescharacteristic
399#554—798no—
400#554—1584no—
401#547—798no—
402#547—1584no—
403C2×C4⋊Q8—791no—
404C2×C4⋊Q8—791no—
405C2×#125—1581no—
406C2×#123—1581no—
407C2×#123—1581no—
408C2×C22⋊Q8—791no—
409C2×C22⋊Q8—791no—
410C2×C22⋊Q8—1581no—
411C2×C22⋊Q8—1581no—
412C2×C22⋊Q8—1581no—
413C2×#121—791no—
414C2×#121—791no—
415C2×C4×Q8—791no—
416C2×C4×D4—791no—
417C2×C4×D4—791no—
418C2×C4×D4—1581no—
419C22×C4⋊C4—791no—
420C22×C4⋊C4—791no—
421C22×C4⋊C4C2×D7911yescharacteristic
422C22×C4⋊C4C2×D7911yescharacteristic
423#498—798no—
424#483—798no—
425#483—798no—
426#481—798no—
427#481—798no—
428#476—798no—
429#475—798no—
430#465—798no—
431#465—798no—
432C4×SD16—798no—
433C8×D4—798no—
434C2×#106—791no—
435C2×#106—791no—
436C2×#106—791no—
437C2×#106—791no—
438C2×#106—791no—
439C2×#106—798no—
440C2×#106C2×D7911yescharacteristic
441C2×#106C2×D7911yescharacteristic
442C2×#106C2×D7911yescharacteristic
443C2×#106C2×D7911yescharacteristic
444C2×#106C2×D7918yescomplemented
445C2×C4⋊C8—791no—
446C2×#103—791no—
447C2×#103—791no—
448C2×#103—791no—
449C2×#102—791no—
450C2×#102—791no—
451C2×#102—791no—
452C2×C22⋊C8—791no—
453C2×C22⋊C8—791no—
454C2×C4×C8—791no—
455C2×#41—3168no—
456C2×#41—1588no—
457C22×Q8—791no—
458C22×Q8—1581no—
459C22×Q8—1581no—
460C22×D4—791no—
461C22×D4—791no—
462C22×D4—1581no—
463C22×D4—1581no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—791no—
467C23×C4—1581no—
468C23×C4—1581no—
469C23×C4—1581no—
470C23×C4C22×D7911yescharacteristic
471C2×SD16—794no—
472C2×SD16—1584no—
473C22×C8—24no—
474C22×C8—791no—
475C22×C8—791no—
476C22×C8—794no—
477C22×C8—1584no—
478C22×C8C22×D7911yescharacteristic
479C22×C8C22×D7914yes—
480C22×C8C22×D7911yescharacteristic
481C4⋊Q8—794no—
482C4⋊Q8—794no—
483C4⋊Q8—1582no—
484C4⋊Q8—1582no—
485#125—1588no—
486#123—1588no—
487#123—1588no—
488C22⋊Q8—794no—
489C22⋊Q8—794no—
490C22⋊Q8—1588no—
491C22⋊Q8—1588no—
492C22⋊Q8—1588no—
493C22⋊Q8—1582no—
494C22⋊Q8—1582no—
495#121—794no—
496#121—794no—
497#121—1582no—
498#121—1582no—
499C4×Q8—794no—
500C4×Q8—1582no—
501C4×D4—794no—
502C4×D4—794no—
503C4×D4—794no—
504C4×D4—1582no—
505C4×D4—1588no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—791no—
512C2×C4⋊C4—791no—
513C2×C4⋊C4—794no—
514C2×C4⋊C4—794no—
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⋊C4—1581no—
524C2×C4⋊C4C22×D7911yescharacteristic
525C2×C4⋊C4C22×D7911yescharacteristic
526C2×C4⋊C4C22×D7911yescharacteristic
527C2×C4⋊C4C22×D7911yescharacteristic
528C2×C4⋊C4C22×D7914yes—
529C2×C4⋊C4C22×D7914yes—
530C2×C22⋊C4—791no—
531C2×C22⋊C4—791no—
532C2×C22⋊C4—1581no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4—1581no—
535C2×C22⋊C4—1581no—
536C2×C22⋊C4—1581no—
537C2×C42—791no—
538C2×C42—1581no—
539#106—794no—
540#106—794no—
541#106—794no—
542#106—794no—
543#106—794no—
544#106C22×D7914yes—
545#106C22×D7914yes—
546#106C22×D7914yes—
547#106C22×D7914yes—
548C4⋊C8—794no—
549#103—794no—
550#103—794no—
551#103—794no—
552#102—794no—
553#102—794no—
554#102—794no—
555C22⋊C8—794no—
556C22⋊C8—794no—
557C4×C8—794no—
558C24—791no—
559C24—1581no—
560C24D4×D7911yescharacteristic
561#41—31632no—
562C2×Q8—3164no—
563C2×Q8—792no—
564C2×Q8—6322no—
565C2×Q8—1584no—
566C2×Q8—1584no—
567C2×Q8—1582no—
568C2×Q8—1582no—
569C2×Q8—1581no—
570C2×D4—3164no—
571C2×D4—3164no—
572C2×D4—798no—
573C2×D4—794no—
574C2×D4—792no—
575C2×D4—1584no—
576C2×D4—1584no—
577C2×D4—1582no—
578C2×D4—1582no—
579C2×D4—1581no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—82no—
590C22×C4—3164no—
591C22×C4—3164no—
592C22×C4—791no—
593C22×C4—791no—
594C22×C4—791no—
595C22×C4—792no—
596C22×C4—792no—
597C22×C4—6322no—
598C22×C4—1584no—
599C22×C4—1584no—
600C22×C4—1584no—
601C22×C4—1581no—
602C22×C4—1581no—
603C22×C4—1581no—
604C22×C4—1582no—
605C22×C4—1582no—
606C22×C4D4×D7912yes—
607C22×C4D4×D7911yescharacteristic
608C22×C4C23×D7912yes—
609C22×C4C23×D7911yescharacteristic
610SD16—1588no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—792no—
614C2×C8—792no—
615C2×C8—1582no—
616C2×C8—1582no—
617C2×C8—1588no—
618C2×C8#1192962414yescomplemented
619C2×C8C23×D7912yes—
620C2×C8C23×D7912yes—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—794no—
628C4⋊C4—792no—
629C4⋊C4—792no—
630C4⋊C4—1584no—
631C4⋊C4—1584no—
632C4⋊C4—1584no—
633C4⋊C4—1584no—
634C4⋊C4—1584no—
635C4⋊C4—1584no—
636C4⋊C4—1584no—
637C4⋊C4—1581no—
638C4⋊C4—1581no—
639C4⋊C4C23×D7912yes—
640C4⋊C4C23×D7912yes—
641C4⋊C4C23×D7912yes—
642C4⋊C4C23×D7912yes—
643C22⋊C4—794no—
644C22⋊C4—794no—
645C22⋊C4—1584no—
646C22⋊C4—1584no—
647C22⋊C4—1584no—
648C22⋊C4—1584no—
649C22⋊C4—1584no—
650C42—792no—
651C42—792no—
652C42—1584no—
653C23—22no—
654C23—22no—
655C23—3162no—
656C23—3162no—
657C23—3162no—
658C23—794no—
659C23—792no—
660C23—1582no—
661C23—1582no—
662C23—1582no—
663C23SD16×D7914yes—
664C23C2×D4×D7912yes—
665C23C2×D4×D7911yescharacteristic
666Q8—3168no—
667Q8—3162no—
668Q8—6324no—
669Q8—1582no—
670Q8—1582no—
671D4—3168no—
672D4—3168no—
673D4—3162no—
674D4—7916no—
675D4—1582no—
676D4—1582no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—3168no—
692C2×C4—3168no—
693C2×C4—3162no—
694C2×C4—3162no—
695C2×C4—3162no—
696C2×C4—794no—
697C2×C4—792no—
698C2×C4—792no—
699C2×C4—792no—
700C2×C4—6324no—
701C2×C4—1582no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1584no—
708C2×C4—1582no—
709C2×C4C2×D4×D7912yes—
710C2×C4C2×D4×D7911yescharacteristic
711C2×C4C2×#1192962412yes—
712C2×C4#1457920912yes—
713C2×C4C24×D7911yescharacteristic
714C8—22no—
715C8—1582no—
716C8—1582no—
717C8C2×#1192962414yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—3162no—
722C22—3162no—
723C22—3162no—
724C22—794no—
725C22—6324no—
726C22—1588no—
727C22—1582no—
728C22—1582no—
729C22#1909921412yes—
730C22C2×SD16×D7914yes—
731C22C2×SD16×D7912yes—
732C22#1909936912yes—
733C22C22×D4×D7911yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—3162no—
740C4—3162no—
741C4—3162no—
742C4—794no—
743C4—1582no—
744C4—1582no—
745C4#1909921412yes—
746C4C22×#1192962411yescharacteristic
747C4C2×#1457920911yescharacteristic
748C2—24no—
749C2—6322no—
750C2—1584no—
751C2#2377575314yesdirect product factor
752C2C2×#1909921411yescharacteristic
753C2C22×SD16×D7911yescharacteristic
754C2C2×#1909936911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC22×#106×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099214C2
hypercenterC22×#106D79
hypocenterC79C2×#3335
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#19099268C2semidirect
3. #23775753C2direct (N × H)
4. C2×#19098960C2semidirect
5. C2×#19098883C2semidirect
6. C2×#19098881C2semidirect
7. C2×#19098895C2semidirect
8. C2×#19098893C2semidirect
9. C2×#19098847C2semidirect
10. C2×#19098852C2semidirect
11. C2×#19098793C2semidirect
12. C2×#19098792C2semidirect
13. C2×#19098650C2semidirect
14. C2×C8×C22⋊D79C2semidirect
15. C2×#106×D79C2semidirect
16. C22×#106×C79C2semidirect
21. #19099268C22semidirect
42. #19098960C22semidirect
43. #19098895C22semidirect
44. #19098893C22semidirect
45. #19098883C22semidirect
46. #19098881C22semidirect
47. #19098852C22semidirect
48. #19098847C22semidirect
49. #19098793C22semidirect
50. #19098792C22semidirect
51. #19098650C22semidirect
52. C8×C22⋊D79C22semidirect
58. #106×D79C22semidirect
76. C2×#106×C79C22semidirect
199. C2×C22⋊D79SD16semidirect
262. C2×C8×C79#41semidirect
308. C22⋊D79C2×SD16semidirect
337. C8×C79C2×#41semidirect
372. C2×C79#3335semidirect
393. C22×#106D79semidirect
394. C79C2×#3335semidirect
444. C2×#106C2×D79semidirect
618. C2×C8#11929624semidirect
717. C8C2×#11929624semidirect
751. C2#23775753direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992682
C2×#190992142
#237757532
C2×#190989602
C2×#190988832
C2×#190988812
C2×#190988952
C2×#190988932
C2×#190988472
C2×#190988522
C2×#190987932
C2×#190987922
C2×#190986502
C2×C8×C22⋊D792
C2×#106×D792
C22×#106×C792
C2×#333579