Finite Group Databasebeta

← C2×#23775261 #35164648

Subgroups — C2×#23775261 #35164648

Order 20224.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D79C211yesmaximal, characteristic, complemented
2C2×#19099214C211yesmaximal, characteristic
3#23775261C2116yesmaximal, direct product factor
4C2×#19098912C211yesmaximal, characteristic, complemented
5C2×#19098893C211yesmaximal, characteristic, complemented
6C2×#19098892C211yesmaximal, characteristic, complemented
7C2×#19098846C211yesmaximal, characteristic, complemented
8C2×#19098795C211yesmaximal, characteristic, complemented
9C2×#19098792C211yesmaximal, characteristic, complemented
10C2×#19098767C211yesmaximal, characteristic, complemented
11C2×#19098703C211yesmaximal, characteristic, complemented
12C2×#19098702C211yesmaximal, characteristic, complemented
13C2×#19098648C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D79C211yesmaximal, characteristic, complemented
15C2×#103×D79C211yesmaximal, characteristic, complemented
16C22×#103×C79C211yesmaximal, characteristic, complemented
17C22×#11929624—21no—
18C22×Q8×D79C2211yescharacteristic
19C22×#11929613C2211yescharacteristic
20C22×#11929611C2211yescharacteristic
21C22×#11929611C2211yescharacteristic
22C22×C8×D79C2211yescharacteristic
23Q8×C22⋊D79—24no—
24Q8×C22⋊D79C2218yescomplemented
25#19099214—24no—
26#19099214C2218yes—
27C2×#14579160C2211yescharacteristic
28C2×#14579159—21no—
29C2×#14579159C2211yescharacteristic
30C2×#14579146—21no—
31C2×#14579144—21no—
32C2×#14579140—21no—
33C2×#14579140C2211yescharacteristic
34C2×#14579139—21no—
35C2×#14579137—21no—
36C2×#14579137C2211yescharacteristic
37C2×#14579136C2211yescharacteristic
38C2×#14579135C2211yescharacteristic
39C2×Q8×Dic79C2211yescharacteristic
40C2×#14579123C2211yescharacteristic
41C2×C4×C22⋊D79—21no—
42C2×C4×C22⋊D79C2211yescharacteristic
43C2×C4⋊C4×D79C2211yescharacteristic
44#19098912C2218yescomplemented
45#19098893C2218yescomplemented
46#19098892C2218yescomplemented
47#19098846C2218yescomplemented
48#19098795C2218yescomplemented
49#19098792C2218yescomplemented
50#19098767C2218yescomplemented
51#19098703C2218yescomplemented
52#19098702C2218yescomplemented
53#19098648C2218yescomplemented
54C8×C22⋊D79C2218yescomplemented
55C2×#14579093C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64#103×D79C2218yescomplemented
65C2×#14579083C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C23×Q8×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C22×C4⋊C4×C79C2211yescharacteristic
72C2×#103×C79C2211yescharacteristic
73C2×#103×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2218yescomplemented
77C2×#11929624—28no—
78C2×#11929624—48no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×Dic158C2311yescharacteristic
82C2×Q8×D79—22no—
83C2×Q8×D79—24no—
84C2×Q8×D79—42no—
85C2×Q8×D79C2314yes—
86C22×D316—21no—
87C22×D316C2311yescharacteristic
88C22×C22⋊D79—21no—
89C22×C22⋊D79D411yescharacteristic
90C22×C4×D79—21no—
91C22×C4×D79—21no—
92C22×C4×D79—21no—
93C22×C4×D79C2311yescharacteristic
94C2×#11929613—42no—
95C2×#11929613C2314yes—
96C2×#11929611—24no—
97C2×#11929611—42no—
98C2×#11929611C2314yes—
99C2×#11929611C2314yes—
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2311yescharacteristic
102C2×C8×D79—42no—
103C2×C8×D79C2314yes—
104#14579160—22no—
105#14579160C2314yes—
106#14579159—28no—
107#14579159—22no—
108#14579159C2314yes—
109#14579146—28no—
110#14579144—28no—
111#14579140—22no—
112#14579140—28no—
113#14579140C2314yes—
114#14579139—28no—
115#14579137—22no—
116#14579137—28no—
117#14579137C2314yes—
118#14579136—22no—
119#14579136C2314yes—
120#14579135—22no—
121#14579135C2314yes—
122Q8×Dic79—22no—
123Q8×Dic79C2314yes—
124#14579123—22no—
125#14579123C2314yes—
126C4×C22⋊D79—28no—
127C4×C22⋊D79D414yes—
128C4×C22⋊D79C2314yes—
129C2×C4⋊Dic79—21no—
130C2×C4⋊Dic79C2311yescharacteristic
131C2×C4⋊Dic79C2311yescharacteristic
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×Dic79⋊C4—21no—
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4D411yescharacteristic
139C4⋊C4×D79—22no—
140C4⋊C4×D79C2314yes—
141C2×C22⋊Dic79—21no—
142C2×C22⋊Dic79D411yescharacteristic
143C2×(C2×D79)⋊C4—21no—
144C2×(C2×D79)⋊C4—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×(C2×D79)⋊C4—21no—
147C2×(C2×D79)⋊C4D411yescharacteristic
148C2×C4×Dic79—21no—
149C2×C4×Dic79C2311yescharacteristic
150#14579093C2314yes—
151#14579092C2314yes—
152#14579092C2314yes—
153Dic79⋊C8C2314yes—
154#14579086C2314yes—
155#14579085C2314yes—
156#14579085C2314yes—
157#14579084C2314yes—
158#14579084C2314yes—
159#14579083C2314yes—
160C22⋊(C79⋊C8)C2314yes—
161(C2×D79)⋊C8C2314yes—
162C8×Dic79C2314yes—
163C22×Q8×C79—22no—
164C22×Q8×C79—21no—
165C22×Q8×C79—24no—
166C22×Q8×C79—42no—
167C22×Q8×C79C2311yescharacteristic
168C22×Q8×C79C2314yes—
169C22×Q8×C79C2311yescharacteristic
170C23×C4×C79—21no—
171C23×C4×C79—21no—
172C23×C4×C79C2311yescharacteristic
173C22×C8×C79—42no—
174C22×C8×C79C2311yescharacteristic
175C22×C8×C79C2311yescharacteristic
176C22×C8×C79C2314yes—
177C2×C4⋊C4×C79—22no—
178C2×C4⋊C4×C79—21no—
179C2×C4⋊C4×C79C2314yes—
180C2×C4⋊C4×C79C2311yescharacteristic
181C2×C4⋊C4×C79C2311yescharacteristic
182#103×C79C2314yes—
183#103×C79C2314yes—
184#103×C79C2314yes—
185#103×C79C2314yes—
186C23×D79—21no—
187C23×D79C2×D411yescharacteristic
188#11929624—432no—
189C2×Dic158—24no—
190C2×Dic158—24no—
191C2×Dic158—21no—
192C2×Dic158—22no—
193C2×Dic158—22no—
194C2×Dic158—44no—
195C2×Dic158—44no—
196C2×Dic158C2412yes—
197Q8×D79—28no—
198Q8×D79—44no—
199Q8×D79—48no—
200C2×D316—24no—
201C2×D316—21no—
202C2×D316—22no—
203C2×D316—22no—
204C2×D316—44no—
205C2×D316C2412yes—
206C2×C22⋊D79—24no—
207C2×C22⋊D79—44no—
208C2×C22⋊D79SD1618yescomplemented
209C2×C22⋊D79C2×D414yes—
210C22×Dic79—21no—
211C22×Dic79—21no—
212C22×Dic79—21no—
213C22×Dic79C2×D411yescharacteristic
214C22×Dic79C2×D411yescharacteristic
215C22×Dic79C2×D411yescharacteristic
216C2×C4×D79—24no—
217C2×C4×D79—24no—
218C2×C4×D79—24no—
219C2×C4×D79—22no—
220C2×C4×D79—22no—
221C2×C4×D79—44no—
222C2×C4×D79—44no—
223C2×C4×D79—44no—
224C2×C4×D79C2×D412yes—
225C2×C4×D79C2412yes—
226#11929613—44no—
227#11929611—28no—
228#11929611—44no—
229C2×C79⋊C8—22no—
230C2×C79⋊C8—22no—
231C2×C79⋊C8C2412yes—
232C2×C79⋊C8C2412yes—
233C8×D79—44no—
234C4⋊Dic79—24no—
235C4⋊Dic79—21no—
236C4⋊Dic79—21no—
237C4⋊Dic79C2412yes—
238C4⋊Dic79C2412yes—
239Dic79⋊C4—24no—
240Dic79⋊C4—24no—
241Dic79⋊C4—24no—
242Dic79⋊C4—24no—
243Dic79⋊C4—24no—
244Dic79⋊C4—24no—
245Dic79⋊C4C2×D414yes—
246C22⋊Dic79—24no—
247C22⋊Dic79C2×D414yes—
248(C2×D79)⋊C4—24no—
249(C2×D79)⋊C4—24no—
250(C2×D79)⋊C4—24no—
251(C2×D79)⋊C4—24no—
252(C2×D79)⋊C4C2×D414yes—
253C4×Dic79—24no—
254C4×Dic79C2×D412yes—
255C4×Dic79C2412yes—
256C24×C79C2×D411yescharacteristic
257C2×Q8×C79—21no—
258C2×Q8×C79—24no—
259C2×Q8×C79—21no—
260C2×Q8×C79—22no—
261C2×Q8×C79—28no—
262C2×Q8×C79—22no—
263C2×Q8×C79—22no—
264C2×Q8×C79—44no—
265C2×Q8×C79—44no—
266C2×Q8×C79—48no—
267C2×Q8×C79#4114yescomplemented
268C2×Q8×C79C2412yes—
269C2×Q8×C79C2412yes—
270C22×C4×C79—21no—
271C22×C4×C79—22no—
272C22×C4×C79—22no—
273C22×C4×C79—21no—
274C22×C4×C79—24no—
275C22×C4×C79—21no—
276C22×C4×C79—21no—
277C22×C4×C79—24no—
278C22×C4×C79—44no—
279C22×C4×C79—44no—
280C22×C4×C79C2×D411yescharacteristic
281C22×C4×C79C2×D412yes—
282C22×C4×C79C2412yes—
283C22×C4×C79C2411yescharacteristic
284C2×C8×C79—22no—
285C2×C8×C79—22no—
286C2×C8×C79—44no—
287C2×C8×C79C2412yes—
288C2×C8×C79C2412yes—
289C4⋊C4×C79—21no—
290C4⋊C4×C79—21no—
291C4⋊C4×C79—24no—
292C4⋊C4×C79C2412yes—
293C4⋊C4×C79C2412yes—
294C23×C79—22no—
295C23×C79—22no—
296C23×C79C2×SD1614yes—
297C23×C79C22×D412yes—
298C23×C79C22×D411yescharacteristic
299C22×D79—22no—
300C22×D79—22no—
301C22×D79—22no—
302C22×D79—42no—
303C22×D79—42no—
304C22×D79—42no—
305C22×D79C2×SD1614yes—
306C22×D79C22×D412yes—
307Q8×C79—24no—
308Q8×C79—22no—
309Q8×C79—22no—
310Q8×C79—22no—
311Q8×C79—48no—
312Q8×C79—42no—
313Q8×C79C2×#4114yescomplemented
314C2×C4×C79—24no—
315C2×C4×C79—22no—
316C2×C4×C79—22no—
317C2×C4×C79—24no—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—22no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—48no—
324C2×C4×C79—42no—
325C2×C4×C79—42no—
326C2×C4×C79—42no—
327C2×C4×C79—48no—
328C2×C4×C79C22×D412yes—
329C2×C4×C79C22×D411yescharacteristic
330C2×C4×C79C2×#4112yes—
331C2×C4×C79H(5,𝔽2)12yes—
332C2×C4×C79C2511yescharacteristic
333C22⋊D79—48no—
334C22⋊D79C2×SD16116yescomplemented
335C2×Dic79—22no—
336C2×Dic79—22no—
337C2×Dic79—22no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—42no—
341C2×Dic79—42no—
342C2×Dic79—42no—
343C2×Dic79C2×SD1614yes—
344C2×Dic79C22×D412yes—
345C2×Dic79C22×D412yes—
346C2×Dic79C22×D412yes—
347D316—22no—
348D316—22no—
349D316—48no—
350D316—42no—
351C4×D79—24no—
352C4×D79—22no—
353C4×D79—22no—
354C4×D79—48no—
355C4×D79—48no—
356C4×D79—48no—
357Dic158—22no—
358Dic158—22no—
359Dic158—48no—
360Dic158—42no—
361Dic158—48no—
362C8×C79—22no—
363C8×C79—22no—
364C79⋊C8—22no—
365C79⋊C8—22no—
366C22×C79—22no—
367C22×C79—28no—
368C22×C79—22no—
369C22×C79#54612yes—
370C22×C79C22×SD1614yes—
371C22×C79C22×SD1612yes—
372C22×C79#57812yes—
373C22×C79C23×D411yescharacteristic
374C2×D79—22no—
375C2×D79—28no—
376C2×D79—22no—
377C2×D79—42no—
378C2×D79—42no—
379C2×D79—42no—
380C2×D79—84no—
381C2×D79C22×SD1614yes—
382C4×C79—22no—
383C4×C79—24no—
384C4×C79—42no—
385C4×C79—42no—
386C4×C79—42no—
387C4×C79#54612yes—
388C4×C79C22×#4111yescharacteristic
389C4×C79C2×H(5,𝔽2)11yescharacteristic
390Dic79—22no—
391Dic79—22no—
392Dic79—42no—
393Dic79—42no—
394Dic79—42no—
395Dic79C22×SD1614yes—
396C2×#3298—791nomaximal, Sylow
397C2×C79—24no—
398C2×C79#329814yescomplemented
399C2×C79C2×#54611yescharacteristic
400C2×C79C23×SD1611yescharacteristic
401C2×C79C2×#57811yescharacteristic
402D79—24no—
403D79—82no—
404C2×D4×Q8—791no—
405C2×#547—791no—
406#3298—7916no—
407C2×#487—791no—
408C2×#483—791no—
409C2×#483—791no—
410C2×#475—791no—
411C2×#465—791no—
412C2×#465—791no—
413C2×#461—791no—
414C2×#448—791no—
415C2×#448—791no—
416C2×C4×SD16—791no—
417C2×C8×D4—791no—
418C22×#103—791no—
419C22×#103D7911yescharacteristic, complemented
420C79C2×#329811yescharacteristic, complemented, Sylow
421C22×#41—1581no—
422C23×Q8—791no—
423C23×Q8C2×D7911yescharacteristic
424C22×SD16—791no—
425C22×SD16—791no—
426C22×SD16—791no—
427C23×C8—791no—
428C23×C8C2×D7911yescharacteristic
429D4×Q8—798no—
430D4×Q8—1584no—
431#547—798no—
432#547—1584no—
433C2×C4⋊Q8—791no—
434C2×C4⋊Q8—791no—
435C2×C4⋊Q8—1581no—
436C2×#123—1581no—
437C2×#123—1581no—
438C2×C22⋊Q8—791no—
439C2×C22⋊Q8—791no—
440C2×C22⋊Q8—1581no—
441C2×C22⋊Q8—1581no—
442C2×C22⋊Q8—1581no—
443C2×#121—791no—
444C2×#121—791no—
445C2×C4×Q8—791no—
446C2×C4×D4—791no—
447C2×C4×D4—791no—
448C2×C4×D4—1581no—
449C22×C4⋊C4—791no—
450C22×C4⋊C4C2×D7911yescharacteristic
451#487—798no—
452#483—798no—
453#483—798no—
454#475—798no—
455#465—798no—
456#465—798no—
457#461—798no—
458#448—798no—
459#448—798no—
460C4×SD16—798no—
461C8×D4—798no—
462C2×#106—791no—
463C2×#106—791no—
464C2×#106—791no—
465C2×C4⋊C8—791no—
466C2×#103—791no—
467C2×#103—791no—
468C2×#103—791no—
469C2×#103—791no—
470C2×#103—791no—
471C2×#103—798no—
472C2×#103C2×D7911yescharacteristic
473C2×#103C2×D7911yescharacteristic
474C2×#103C2×D7911yescharacteristic
475C2×#103C2×D7911yescharacteristic
476C2×#103C2×D7918yescomplemented
477C2×#102—791no—
478C2×C22⋊C8—791no—
479C2×C22⋊C8—791no—
480C2×C4×C8—791no—
481C2×#41—3168no—
482C2×#41—1588no—
483C22×Q8—21no—
484C22×Q8—22no—
485C22×Q8—24no—
486C22×Q8—42no—
487C22×Q8—3162no—
488C22×Q8—794no—
489C22×Q8—791no—
490C22×Q8—1581no—
491C22×Q8—1581no—
492C22×Q8—1584no—
493C22×Q8—1582no—
494C22×Q8C22×D7911yescharacteristic
495C22×Q8C22×D7914yes—
496C22×Q8C22×D7911yescharacteristic
497C22×D4—791no—
498C22×D4—791no—
499C22×D4—1581no—
500C22×D4—1581no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—791no—
504C23×C4—1581no—
505C23×C4—1581no—
506C23×C4—1581no—
507C23×C4C22×D7911yescharacteristic
508C2×SD16—3162no—
509C2×SD16—3162no—
510C2×SD16—794no—
511C2×SD16—794no—
512C2×SD16—794no—
513C2×SD16—1584no—
514C22×C8—42no—
515C22×C8—3162no—
516C22×C8—794no—
517C22×C8—791no—
518C22×C8—791no—
519C22×C8C22×D7911yescharacteristic
520C22×C8C22×D7911yescharacteristic
521C22×C8C22×D7914yes—
522C4⋊Q8—794no—
523C4⋊Q8—794no—
524C4⋊Q8—1582no—
525C4⋊Q8—1582no—
526C4⋊Q8—1588no—
527#123—1588no—
528#123—1588no—
529C22⋊Q8—794no—
530C22⋊Q8—794no—
531C22⋊Q8—1588no—
532C22⋊Q8—1588no—
533C22⋊Q8—1588no—
534C22⋊Q8—1582no—
535C22⋊Q8—1582no—
536#121—794no—
537#121—794no—
538#121—1582no—
539#121—1582no—
540C4×Q8—794no—
541C4×Q8—1582no—
542C4×D4—794no—
543C4×D4—794no—
544C4×D4—794no—
545C4×D4—1582no—
546C4×D4—1588no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—791no—
550C2×C4⋊C4—791no—
551C2×C4⋊C4—791no—
552C2×C4⋊C4—794no—
553C2×C4⋊C4—1582no—
554C2×C4⋊C4—1581no—
555C2×C4⋊C4—1581no—
556C2×C4⋊C4—1581no—
557C2×C4⋊C4—1581no—
558C2×C4⋊C4—1581no—
559C2×C4⋊C4—1581no—
560C2×C4⋊C4—1581no—
561C2×C4⋊C4C22×D7911yescharacteristic
562C2×C4⋊C4C22×D7911yescharacteristic
563C2×C4⋊C4C22×D7914yes—
564C2×C22⋊C4—791no—
565C2×C22⋊C4—791no—
566C2×C22⋊C4—1581no—
567C2×C22⋊C4—1581no—
568C2×C22⋊C4—1581no—
569C2×C22⋊C4—1581no—
570C2×C22⋊C4—1581no—
571C2×C42—791no—
572C2×C42—1581no—
573#106—794no—
574#106—794no—
575#106—794no—
576C4⋊C8—794no—
577#103—794no—
578#103—794no—
579#103—794no—
580#103—794no—
581#103—794no—
582#103C22×D7914yes—
583#103C22×D7914yes—
584#103C22×D7914yes—
585#103C22×D7914yes—
586#102—794no—
587C22⋊C8—794no—
588C22⋊C8—794no—
589C4×C8—794no—
590C24—791no—
591C24—1581no—
592C24D4×D7911yescharacteristic
593#41—31632no—
594C2×Q8—22no—
595C2×Q8—21no—
596C2×Q8—24no—
597C2×Q8—21no—
598C2×Q8—28no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×Q8—48no—
604C2×Q8—3164no—
605C2×Q8—3164no—
606C2×Q8—3168no—
607C2×Q8—3164no—
608C2×Q8—792no—
609C2×Q8—1584no—
610C2×Q8—1584no—
611C2×Q8—1588no—
612C2×Q8—1582no—
613C2×Q8—1582no—
614C2×Q8—1581no—
615C2×Q8#1192962414yescomplemented
616C2×Q8C23×D7912yes—
617C2×Q8C23×D7912yes—
618C2×D4—3164no—
619C2×D4—3164no—
620C2×D4—798no—
621C2×D4—794no—
622C2×D4—792no—
623C2×D4—1584no—
624C2×D4—1584no—
625C2×D4—1582no—
626C2×D4—1582no—
627C2×D4—1581no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—3164no—
639C22×C4—3164no—
640C22×C4—3164no—
641C22×C4—791no—
642C22×C4—791no—
643C22×C4—791no—
644C22×C4—792no—
645C22×C4—792no—
646C22×C4—1584no—
647C22×C4—1584no—
648C22×C4—1584no—
649C22×C4—1581no—
650C22×C4—1581no—
651C22×C4—1581no—
652C22×C4—1582no—
653C22×C4—1582no—
654C22×C4D4×D7912yes—
655C22×C4D4×D7911yescharacteristic
656C22×C4C23×D7912yes—
657C22×C4C23×D7911yescharacteristic
658SD16—3164no—
659SD16—3164no—
660SD16—1588no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—3164no—
665C2×C8—792no—
666C2×C8—792no—
667C2×C8—1582no—
668C2×C8—1582no—
669C2×C8C23×D7912yes—
670C2×C8C23×D7912yes—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—24no—
674C4⋊C4—794no—
675C4⋊C4—792no—
676C4⋊C4—792no—
677C4⋊C4—1584no—
678C4⋊C4—1584no—
679C4⋊C4—1584no—
680C4⋊C4—1584no—
681C4⋊C4—1584no—
682C4⋊C4—1584no—
683C4⋊C4—1584no—
684C4⋊C4—1581no—
685C4⋊C4—1581no—
686C4⋊C4C23×D7912yes—
687C4⋊C4C23×D7912yes—
688C22⋊C4—794no—
689C22⋊C4—794no—
690C22⋊C4—1584no—
691C22⋊C4—1584no—
692C22⋊C4—1584no—
693C22⋊C4—1584no—
694C22⋊C4—1584no—
695C42—792no—
696C42—792no—
697C42—1584no—
698C23—22no—
699C23—22no—
700C23—3162no—
701C23—3162no—
702C23—3162no—
703C23—794no—
704C23—792no—
705C23—1582no—
706C23—1582no—
707C23—1582no—
708C23SD16×D7914yes—
709C23C2×D4×D7912yes—
710C23C2×D4×D7911yescharacteristic
711Q8—22no—
712Q8—24no—
713Q8—22no—
714Q8—22no—
715Q8—48no—
716Q8—42no—
717Q8—3168no—
718Q8—3168no—
719Q8—3162no—
720Q8—1582no—
721Q8—1582no—
722Q8C2×#1192962414yescomplemented
723D4—3168no—
724D4—3168no—
725D4—3162no—
726D4—7916no—
727D4—1582no—
728D4—1582no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—48no—
743C2×C4—3168no—
744C2×C4—3168no—
745C2×C4—3168no—
746C2×C4—3162no—
747C2×C4—3162no—
748C2×C4—3162no—
749C2×C4—794no—
750C2×C4—792no—
751C2×C4—792no—
752C2×C4—792no—
753C2×C4—1582no—
754C2×C4—1582no—
755C2×C4—1582no—
756C2×C4—1582no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4—1584no—
760C2×C4—1582no—
761C2×C4C2×D4×D7912yes—
762C2×C4C2×D4×D7911yescharacteristic
763C2×C4C2×#1192962412yes—
764C2×C4#1457920612yes—
765C2×C4C24×D7911yescharacteristic
766C8—22no—
767C8—22no—
768C8—1582no—
769C8—1582no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—3162no—
774C22—3162no—
775C22—3162no—
776C22—794no—
777C22—6324no—
778C22—1588no—
779C22—1582no—
780C22—1582no—
781C22#1909920312yes—
782C22C2×SD16×D7914yes—
783C22C2×SD16×D7912yes—
784C22#1909937612yes—
785C22C22×D4×D7911yescharacteristic
786C4—22no—
787C4—24no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—3162no—
792C4—3162no—
793C4—3162no—
794C4—794no—
795C4—1582no—
796C4—1582no—
797C4#1909920312yes—
798C4C22×#1192962411yescharacteristic
799C4C2×#1457920611yescharacteristic
800C2—24no—
801C2—6322no—
802C2—1584no—
803C2#2377526114yesdirect product factor
804C2C2×#1909920311yescharacteristic
805C2C22×SD16×D7911yescharacteristic
806C2C2×#1909937611yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC22×#103×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099214C2
hypercenterC22×#103D79
hypocenterC79C2×#3298
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D79C2semidirect
3. #23775261C2direct (N × H)
4. C2×#19098912C2semidirect
5. C2×#19098893C2semidirect
6. C2×#19098892C2semidirect
7. C2×#19098846C2semidirect
8. C2×#19098795C2semidirect
9. C2×#19098792C2semidirect
10. C2×#19098767C2semidirect
11. C2×#19098703C2semidirect
12. C2×#19098702C2semidirect
13. C2×#19098648C2semidirect
14. C2×C8×C22⋊D79C2semidirect
15. C2×#103×D79C2semidirect
16. C22×#103×C79C2semidirect
24. Q8×C22⋊D79C22semidirect
44. #19098912C22semidirect
45. #19098893C22semidirect
46. #19098892C22semidirect
47. #19098846C22semidirect
48. #19098795C22semidirect
49. #19098792C22semidirect
50. #19098767C22semidirect
51. #19098703C22semidirect
52. #19098702C22semidirect
53. #19098648C22semidirect
54. C8×C22⋊D79C22semidirect
64. #103×D79C22semidirect
76. C2×#103×C79C22semidirect
208. C2×C22⋊D79SD16semidirect
267. C2×Q8×C79#41semidirect
313. Q8×C79C2×#41semidirect
334. C22⋊D79C2×SD16semidirect
398. C2×C79#3298semidirect
419. C22×#103D79semidirect
420. C79C2×#3298semidirect
476. C2×#103C2×D79semidirect
615. C2×Q8#11929624semidirect
722. Q8C2×#11929624semidirect
803. C2#23775261direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D792
C2×#190992142
#237752612
C2×#190989122
C2×#190988932
C2×#190988922
C2×#190988462
C2×#190987952
C2×#190987922
C2×#190987672
C2×#190987032
C2×#190987022
C2×#190986482
C2×C8×C22⋊D792
C2×#103×D792
C22×#103×C792
C2×#329879