Finite Group Databasebeta

← C2×#23775881 #35166844

Subgroups — C2×#23775881 #35166844

Order 20224.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099268C211yesmaximal, characteristic, complemented
2C2×#19099261C211yesmaximal, characteristic
3#23775881C2116yesmaximal, direct product factor
4C2×#19098971C211yesmaximal, characteristic, complemented
5C2×#19098898C211yesmaximal, characteristic, complemented
6C2×#19098881C211yesmaximal, characteristic, complemented
7C2×#19098906C211yesmaximal, characteristic, complemented
8C2×#19098878C211yesmaximal, characteristic, complemented
9C2×#19098869C211yesmaximal, characteristic, complemented
10C2×#19098842C211yesmaximal, characteristic, complemented
11C2×#19098810C211yesmaximal, characteristic, complemented
12C2×#19098792C211yesmaximal, characteristic, complemented
13C2×#19098662C211yesmaximal, characteristic, complemented
14C2×#19098634C211yesmaximal, characteristic, complemented
15C2×#19098604C211yesmaximal, characteristic, complemented
16C22×#107×C79C211yesmaximal, characteristic, complemented
17C22×#11929613C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19#19099268—24no—
20#19099268C2218yescomplemented
21#19099261—24no—
22#19099261C2218yes—
23C2×#14579160C2211yescharacteristic
24C2×#14579156—21no—
25C2×#14579152C2211yescharacteristic
26C2×#14579151—21no—
27C2×#14579146—21no—
28C2×#14579141C2211yescharacteristic
29C2×#14579140—21no—
30C2×#14579140C2211yescharacteristic
31C2×#14579139—21no—
32C2×#14579136C2211yescharacteristic
33C2×#14579135—21no—
34C2×#14579135C2211yescharacteristic
35C2×#14579126C2211yescharacteristic
36C2×#14579123C2211yescharacteristic
37C2×C4×C22⋊D79—21no—
38C2×C4×C22⋊D79—21no—
39C2×C4×C22⋊D79C2211yescharacteristic
40C2×#14579119C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098971C2218yescomplemented
43#19098906C2218yescomplemented
44#19098898C2218yescomplemented
45#19098881C2218yescomplemented
46#19098878C2218yescomplemented
47#19098869C2218yescomplemented
48#19098842C2218yescomplemented
49#19098810C2218yescomplemented
50#19098792C2218yescomplemented
51#19098662C2218yescomplemented
52#19098634C2218yescomplemented
53#19098604C2218yescomplemented
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
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
69C23×C8×C79C2211yescharacteristic
70C22×C4⋊C4×C79C2211yescharacteristic
71C22×C4⋊C4×C79C2211yescharacteristic
72C2×#107×C79C2211yescharacteristic
73C2×#107×C79C2211yescharacteristic
74C2×#107×C79C2211yescharacteristic
75C2×#107×C79C2211yescharacteristic
76C2×#107×C79C2218yescomplemented
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×D316—21no—
80C22×D316C2311yescharacteristic
81C22×C22⋊D79—21no—
82C22×C22⋊D79D411yescharacteristic
83C22×C4×D79—21no—
84C22×C4×D79—21no—
85C22×C4×D79C2311yescharacteristic
86C2×#11929613—24no—
87C2×#11929613C2314yes—
88C2×#11929607—24no—
89C2×#11929607C2314yes—
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92#14579160—22no—
93#14579160C2314yes—
94#14579156—28no—
95#14579152—22no—
96#14579152C2314yes—
97#14579151—28no—
98#14579146—28no—
99#14579141—22no—
100#14579141C2314yes—
101#14579140—22no—
102#14579140—28no—
103#14579140C2314yes—
104#14579139—28no—
105#14579136—22no—
106#14579136C2314yes—
107#14579135—22no—
108#14579135—28no—
109#14579135C2314yes—
110#14579126—22no—
111#14579126C2314yes—
112#14579123—22no—
113#14579123C2314yes—
114C4×C22⋊D79—28no—
115C4×C22⋊D79—28no—
116C4×C22⋊D79D414yes—
117C4×C22⋊D79C2314yes—
118#14579119—22no—
119#14579119C2314yes—
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⋊C4D411yescharacteristic
130C4⋊C4×D79—22no—
131C4⋊C4×D79C2314yes—
132C2×C22⋊Dic79—21no—
133C2×C22⋊Dic79D411yescharacteristic
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4D411yescharacteristic
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79C2311yescharacteristic
143#14579094C2314yes—
144#14579094C2314yes—
145#14579093C2314yes—
146#14579092C2314yes—
147#14579092C2314yes—
148Dic79⋊C8C2314yes—
149#14579086C2314yes—
150#14579084C2314yes—
151#14579084C2314yes—
152#14579083C2314yes—
153#14579081C2314yes—
154#14579081C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156(C2×D79)⋊C8C2314yes—
157#14579071C2314yes—
158C23×C4×C79—21no—
159C23×C4×C79—21no—
160C23×C4×C79C2311yescharacteristic
161C22×C8×C79—24no—
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2314yes—
164C22×C8×C79C2311yescharacteristic
165C2×C4⋊C4×C79—22no—
166C2×C4⋊C4×C79—22no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79C2314yes—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2314yes—
175#107×C79C2314yes—
176#107×C79C2314yes—
177#107×C79C2314yes—
178#107×C79C2314yes—
179C23×D79—21no—
180C23×D79C2×D411yescharacteristic
181C2×Dic158—24no—
182C2×Dic158—21no—
183C2×Dic158—22no—
184C2×Dic158—22no—
185C2×Dic158—82no—
186C2×Dic158C2412yes—
187C2×D316—24no—
188C2×D316—21no—
189C2×D316—22no—
190C2×D316—22no—
191C2×D316—82no—
192C2×D316C2412yes—
193C2×C22⋊D79—24no—
194C2×C22⋊D79—24no—
195C2×C22⋊D79—44no—
196C2×C22⋊D79C2×D414yes—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C22×Dic79C2×D411yescharacteristic
203C2×C4×D79—24no—
204C2×C4×D79—24no—
205C2×C4×D79—22no—
206C2×C4×D79—22no—
207C2×C4×D79—82no—
208C2×C4×D79—82no—
209C2×C4×D79C2×D412yes—
210C2×C4×D79C2412yes—
211#11929613—28no—
212#11929607—28no—
213C2×C79⋊C8—22no—
214C2×C79⋊C8—22no—
215C2×C79⋊C8C2412yes—
216C2×C79⋊C8C2412yes—
217C4⋊Dic79—24no—
218C4⋊Dic79—24no—
219C4⋊Dic79—21no—
220C4⋊Dic79—21no—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4C2×D414yes—
229C22⋊Dic79—24no—
230C22⋊Dic79C2×D414yes—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4C2×D414yes—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C4×Dic79C2×D412yes—
240C4×Dic79C2412yes—
241C24×C79C2×D411yescharacteristic
242C22×C4×C79—22no—
243C22×C4×C79—22no—
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—24no—
249C22×C4×C79—24no—
250C22×C4×C79—82no—
251C22×C4×C79—82no—
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D412yes—
254C22×C4×C79C2412yes—
255C22×C4×C79C2411yescharacteristic
256C2×C8×C79—28no—
257C2×C8×C79—22no—
258C2×C8×C79#4114yes—
259C2×C8×C79C2412yes—
260C2×C8×C79C2412yes—
261C4⋊C4×C79—21no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—24no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79—24no—
267C4⋊C4×C79C2412yes—
268C4⋊C4×C79C2412yes—
269C4⋊C4×C79C2412yes—
270C4⋊C4×C79C2412yes—
271C23×C79—22no—
272C23×C79—22no—
273C23×C79#13714yes—
274C23×C79C22×D412yes—
275C23×C79C22×D411yescharacteristic
276C22×D79—22no—
277C22×D79—22no—
278C22×D79—22no—
279C22×D79—22no—
280C22×D79—42no—
281C22×D79—42no—
282C22×D79—42no—
283C22×D79C22×D412yes—
284C2×C4×C79—22no—
285C2×C4×C79—24no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—42no—
293C2×C4×C79—42no—
294C2×C4×C79—42no—
295C2×C4×C79—42no—
296C2×C4×C79—84no—
297C2×C4×C79—84no—
298C2×C4×C79C22×D412yes—
299C2×C4×C79C22×D411yescharacteristic
300C2×C4×C79C2×#4112yes—
301C2×C4×C792−1+412yes—
302C2×C4×C79C2511yescharacteristic
303C22⋊D79—28no—
304C22⋊D79—48no—
305C2×Dic79—22no—
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×Dic79C22×D412yes—
315C2×Dic79C22×D412yes—
316C2×Dic79C22×D412yes—
317D316—22no—
318D316—22no—
319D316—42no—
320D316—84no—
321C4×D79—24no—
322C4×D79—22no—
323C4×D79—22no—
324C4×D79—84no—
325C4×D79—84no—
326Dic158—22no—
327Dic158—22no—
328Dic158—42no—
329Dic158—84no—
330C8×C79—22no—
331C8×C79C2×#4114yes—
332C79⋊C8—22no—
333C79⋊C8—22no—
334C22×C79—28no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79#54712yes—
338C22×C79C2×#13714yes—
339C22×C79C2×#13712yes—
340C22×C79#57612yes—
341C22×C79C23×D411yescharacteristic
342C2×D79—22no—
343C2×D79—22no—
344C2×D79—22no—
345C2×D79—44no—
346C2×D79—42no—
347C2×D79—42no—
348C2×D79—42no—
349C2×D79—84no—
350C4×C79—22no—
351C4×C79—42no—
352C4×C79—42no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79#54712yes—
356C4×C79C22×#4111yescharacteristic
357C4×C79C2×2−1+411yescharacteristic
358Dic79—22no—
359Dic79—22no—
360Dic79—22no—
361Dic79—42no—
362Dic79—42no—
363Dic79—42no—
364C2×#3346—791nomaximal, Sylow
365C2×C79—24no—
366C2×C79#334614yescomplemented
367C2×C79C2×#54711yescharacteristic
368C2×C79C22×#13711yescharacteristic
369C2×C79C2×#57611yescharacteristic
370D79—42no—
371D79—82no—
372C2×#554—791no—
373C2×#553—791no—
374#3346—7916no—
375C2×#501—791no—
376C2×#484—791no—
377C2×#481—791no—
378C2×#485—791no—
379C2×#480—791no—
380C2×#479—791no—
381C2×#474—791no—
382C2×#468—791no—
383C2×#465—791no—
384C2×#440—791no—
385C2×#435—791no—
386C2×#428—791no—
387C22×#107D7911yescharacteristic, complemented
388C79C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—791no—
390C22×M16—791no—
391C23×C8C2×D7911yescharacteristic
392#554—798no—
393#554—1584no—
394#553—798no—
395#553—1584no—
396C2×C4⋊Q8—791no—
397C2×#126—1581no—
398C2×#125—791no—
399C2×#125—1581no—
400C2×#123—1581no—
401C2×C22⋊Q8—791no—
402C2×C22⋊Q8—791no—
403C2×C22⋊Q8—1581no—
404C2×C22⋊Q8—1581no—
405C2×#121—791no—
406C2×#121—791no—
407C2×#121—1581no—
408C2×C4×Q8—791no—
409C2×C4×D4—791no—
410C2×C4×D4—791no—
411C2×C4×D4—1581no—
412C2×C4×D4—1581no—
413C2×#117—791no—
414C22×C4⋊C4—791no—
415C22×C4⋊C4C2×D7911yescharacteristic
416C22×C4⋊C4C2×D7911yescharacteristic
417#501—798no—
418#485—798no—
419#484—798no—
420#481—798no—
421#480—798no—
422#479—798no—
423#474—798no—
424#468—798no—
425#465—798no—
426#440—798no—
427#435—798no—
428#428—798no—
429C2×#107—791no—
430C2×#107—791no—
431C2×#107C2×D7911yescharacteristic
432C2×#107C2×D7911yescharacteristic
433C2×#107C2×D7911yescharacteristic
434C2×#107C2×D7911yescharacteristic
435C2×#107C2×D7918yescomplemented
436C2×#106—791no—
437C2×#106—791no—
438C2×#106—791no—
439C2×C4⋊C8—791no—
440C2×#103—791no—
441C2×#103—791no—
442C2×#103—791no—
443C2×#102—791no—
444C2×#102—791no—
445C2×#102—791no—
446C2×C22⋊C8—791no—
447C2×C22⋊C8—791no—
448C2×#97—791no—
449C22×Q8—791no—
450C22×Q8—1581no—
451C22×D4—791no—
452C22×D4—791no—
453C22×D4—1581no—
454C22×D4—1581no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—791no—
458C23×C4—1581no—
459C23×C4—1581no—
460C23×C4C22×D7911yescharacteristic
461C2×SD16—794no—
462C2×SD16—1584no—
463C2×M16—794no—
464C2×M16—1584no—
465C22×C8—24no—
466C22×C8—791no—
467C22×C8—791no—
468C22×C8C22×D7911yescharacteristic
469C22×C8C22×D7914yes—
470C22×C8C22×D7911yescharacteristic
471C4⋊Q8—794no—
472C4⋊Q8—1582no—
473#126—1588no—
474#125—794no—
475#125—1582no—
476#125—1588no—
477#123—1588no—
478C22⋊Q8—794no—
479C22⋊Q8—794no—
480C22⋊Q8—1588no—
481C22⋊Q8—1588no—
482C22⋊Q8—1582no—
483C22⋊Q8—1582no—
484#121—794no—
485#121—794no—
486#121—1582no—
487#121—1588no—
488#121—1582no—
489C4×Q8—794no—
490C4×Q8—1582no—
491C4×D4—794no—
492C4×D4—794no—
493C4×D4—794no—
494C4×D4—1582no—
495C4×D4—1588no—
496C4×D4—1588no—
497#117—794no—
498#117—1582no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—791no—
504C2×C4⋊C4—791no—
505C2×C4⋊C4—791no—
506C2×C4⋊C4—794no—
507C2×C4⋊C4—1582no—
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⋊C4C22×D7911yescharacteristic
516C2×C4⋊C4C22×D7911yescharacteristic
517C2×C4⋊C4C22×D7911yescharacteristic
518C2×C4⋊C4C22×D7911yescharacteristic
519C2×C4⋊C4C22×D7914yes—
520C2×C4⋊C4C22×D7914yes—
521C2×C22⋊C4—791no—
522C2×C22⋊C4—791no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4—1581no—
529C2×C42—791no—
530C2×C42—1581no—
531C2×C42—1581no—
532#107—794no—
533#107—794no—
534#107C22×D7914yes—
535#107C22×D7914yes—
536#107C22×D7914yes—
537#107C22×D7914yes—
538#106—794no—
539#106—794no—
540#106—794no—
541C4⋊C8—794no—
542#103—794no—
543#103—794no—
544#103—794no—
545#102—794no—
546#102—794no—
547#102—794no—
548C22⋊C8—794no—
549C22⋊C8—794no—
550#97—794no—
551C24—791no—
552C24—1581no—
553C24D4×D7911yescharacteristic
554C2×Q8—792no—
555C2×Q8—6322no—
556C2×Q8—1584no—
557C2×Q8—1582no—
558C2×Q8—1582no—
559C2×Q8—1581no—
560C2×D4—3164no—
561C2×D4—794no—
562C2×D4—792no—
563C2×D4—6322no—
564C2×D4—1584no—
565C2×D4—1584no—
566C2×D4—1584no—
567C2×D4—1582no—
568C2×D4—1582no—
569C2×D4—1581no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—791no—
581C22×C4—791no—
582C22×C4—791no—
583C22×C4—792no—
584C22×C4—792no—
585C22×C4—6322no—
586C22×C4—6322no—
587C22×C4—1584no—
588C22×C4—1584no—
589C22×C4—1581no—
590C22×C4—1581no—
591C22×C4—1581no—
592C22×C4—1582no—
593C22×C4—1582no—
594C22×C4D4×D7912yes—
595C22×C4D4×D7911yescharacteristic
596C22×C4C23×D7912yes—
597C22×C4C23×D7911yescharacteristic
598SD16—1588no—
599M16—1588no—
600C2×C8—22no—
601C2×C8—28no—
602C2×C8—792no—
603C2×C8—792no—
604C2×C8—1582no—
605C2×C8—1582no—
606C2×C8#1192962414yes—
607C2×C8C23×D7912yes—
608C2×C8C23×D7912yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—794no—
616C4⋊C4—792no—
617C4⋊C4—792no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1584no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1581no—
626C4⋊C4—1581no—
627C4⋊C4C23×D7912yes—
628C4⋊C4C23×D7912yes—
629C4⋊C4C23×D7912yes—
630C4⋊C4C23×D7912yes—
631C22⋊C4—794no—
632C22⋊C4—794no—
633C22⋊C4—1584no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C22⋊C4—1584no—
639C42—792no—
640C42—792no—
641C42—1584no—
642C42—1584no—
643C23—22no—
644C23—22no—
645C23—3162no—
646C23—3162no—
647C23—3162no—
648C23—792no—
649C23—1582no—
650C23—1582no—
651C23—1582no—
652C23—1582no—
653C23#1457919314yes—
654C23C2×D4×D7912yes—
655C23C2×D4×D7911yescharacteristic
656Q8—3162no—
657Q8—6324no—
658Q8—1582no—
659Q8—1582no—
660D4—3168no—
661D4—3162no—
662D4—6324no—
663D4—1588no—
664D4—1582no—
665D4—1582no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4—3162no—
681C2×C4—3162no—
682C2×C4—3162no—
683C2×C4—792no—
684C2×C4—792no—
685C2×C4—792no—
686C2×C4—6324no—
687C2×C4—6324no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1584no—
696C2×C4—1582no—
697C2×C4C2×D4×D7912yes—
698C2×C4C2×D4×D7911yescharacteristic
699C2×C4C2×#1192962412yes—
700C2×C4#1457920912yes—
701C2×C4C24×D7911yescharacteristic
702C8—22no—
703C8—1582no—
704C8—1582no—
705C8C2×#1192962414yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—3164no—
710C22—3162no—
711C22—3162no—
712C22—3162no—
713C22—6324no—
714C22—1582no—
715C22—1582no—
716C22—1582no—
717C22#1909921412yes—
718C22C2×#1457919314yes—
719C22C2×#1457919312yes—
720C22#1909936412yes—
721C22C22×D4×D7911yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—3162no—
728C4—3162no—
729C4—3162no—
730C4—1582no—
731C4—1582no—
732C4—1582no—
733C4#1909921412yes—
734C4C22×#1192962411yescharacteristic
735C4C2×#1457920911yescharacteristic
736C2—24no—
737C2—3162no—
738C2—6322no—
739C2#2377588114yesdirect product factor
740C2C2×#1909921411yescharacteristic
741C2C22×#1457919311yescharacteristic
742C2C2×#1909936411yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC22×#107×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099261C2
hypercenterC22×#107D79
hypocenterC79C2×#3346
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#19099268C2semidirect
3. #23775881C2direct (N × H)
4. C2×#19098971C2semidirect
5. C2×#19098898C2semidirect
6. C2×#19098881C2semidirect
7. C2×#19098906C2semidirect
8. C2×#19098878C2semidirect
9. C2×#19098869C2semidirect
10. C2×#19098842C2semidirect
11. C2×#19098810C2semidirect
12. C2×#19098792C2semidirect
13. C2×#19098662C2semidirect
14. C2×#19098634C2semidirect
15. C2×#19098604C2semidirect
16. C22×#107×C79C2semidirect
20. #19099268C22semidirect
42. #19098971C22semidirect
43. #19098906C22semidirect
44. #19098898C22semidirect
45. #19098881C22semidirect
46. #19098878C22semidirect
47. #19098869C22semidirect
48. #19098842C22semidirect
49. #19098810C22semidirect
50. #19098792C22semidirect
51. #19098662C22semidirect
52. #19098634C22semidirect
53. #19098604C22semidirect
76. C2×#107×C79C22semidirect
366. C2×C79#3346semidirect
387. C22×#107D79semidirect
388. C79C2×#3346semidirect
435. C2×#107C2×D79semidirect
739. C2#23775881direct (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×#190992612
#237758812
C2×#190989712
C2×#190988982
C2×#190988812
C2×#190989062
C2×#190988782
C2×#190988692
C2×#190988422
C2×#190988102
C2×#190987922
C2×#190986622
C2×#190986342
C2×#190986042
C22×#107×C792
C2×#334679