Finite Group Databasebeta

← C2×#23775752 #35166687

Subgroups — C2×#23775752 #35166687

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×#19099271C211yesmaximal, characteristic, complemented
2C2×#19099213C211yesmaximal, characteristic
3#23775752C2116yesmaximal, direct product factor
4C2×#19098960C211yesmaximal, characteristic, complemented
5C2×#19098880C211yesmaximal, characteristic, complemented
6C2×#19098879C211yesmaximal, characteristic, complemented
7C2×#19098892C211yesmaximal, characteristic, complemented
8C2×#19098891C211yesmaximal, characteristic, complemented
9C2×#19098846C211yesmaximal, characteristic, complemented
10C2×#19098851C211yesmaximal, characteristic, complemented
11C2×#19098789C211yesmaximal, characteristic, complemented
12C2×SD16×Dic79C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D79C211yesmaximal, characteristic, complemented
14C22×#14579093C211yesmaximal, characteristic, complemented
15C2×#106×D79C211yesmaximal, characteristic, complemented
16C2×#465×C79C211yesmaximal, characteristic, complemented
17C22×#11929623—21no—
18C22×C8×D79C2211yescharacteristic
19#19099271—24no—
20#19099271C2218yescomplemented
21#19099213—24no—
22#19099213C2218yes—
23C2×#14579160C2211yescharacteristic
24C2×#14579160C2211yescharacteristic
25C2×#14579151—21no—
26C2×#14579143—21no—
27C2×#14579142—21no—
28C2×#14579141—21no—
29C2×#14579138—21no—
30C2×#14579138—21no—
31C2×#14579137C2211yescharacteristic
32C2×#14579132C2211yescharacteristic
33C2×Q8×Dic79C2211yescharacteristic
34C2×D4×Dic79C2211yescharacteristic
35C2×C4×C22⋊D79C2211yescharacteristic
36C2×(C22⋊D79)⋊C4—21no—
37C22×C4⋊Dic79C2211yescharacteristic
38C22×C4⋊Dic79C2211yescharacteristic
39C2×C4⋊C4×D79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41#19098960C2218yescomplemented
42#19098892C2218yescomplemented
43#19098891C2218yescomplemented
44#19098880C2218yescomplemented
45#19098879C2218yescomplemented
46#19098851C2218yescomplemented
47#19098846C2218yescomplemented
48#19098789C2218yescomplemented
49SD16×Dic79C2218yescomplemented
50C8×C22⋊D79C2218yescomplemented
51C2×#14579093C2211yescharacteristic
52C2×#14579093C2211yescharacteristic
53C2×#14579093C2211yescharacteristic
54C2×#14579093C2211yescharacteristic
55C2×#14579093C2218yescomplemented
56C2×#14579092C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60#106×D79C2218yescomplemented
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73#465×C79C2218yescomplemented
74C2×#106×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C2×#11929623—28no—
78C2×#11929623—48no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×C22⋊D79—21no—
82C22×C22⋊D79D411yescharacteristic
83C23×Dic79—21no—
84C23×Dic79—21no—
85C23×Dic79—21no—
86C22×C4×D79—21no—
87C22×C4×D79—21no—
88C22×C4×D79C2311yescharacteristic
89C22×C79⋊C8C2311yescharacteristic
90C22×C79⋊C8C2311yescharacteristic
91C2×C8×D79—24no—
92C2×C8×D79C2314yes—
93#14579160—22no—
94#14579160—22no—
95#14579160C2314yes—
96#14579160C2314yes—
97#14579151—28no—
98#14579143—28no—
99#14579142—28no—
100#14579141—28no—
101#14579138—28no—
102#14579138—28no—
103#14579137—22no—
104#14579137C2314yes—
105#14579132—22no—
106#14579132C2314yes—
107Q8×Dic79—22no—
108Q8×Dic79C2314yes—
109D4×Dic79—22no—
110D4×Dic79C2314yes—
111C4×C22⋊D79D414yes—
112C4×C22⋊D79C2314yes—
113(C22⋊D79)⋊C4—28no—
114C2×C4⋊Dic79—22no—
115C2×C4⋊Dic79—22no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79C2314yes—
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2314yes—
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×D79—22no—
133C4⋊C4×D79C2314yes—
134C4⋊C4×D79C2314yes—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×C22⋊Dic79D411yescharacteristic
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4D411yescharacteristic
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142#14579093C2314yes—
143#14579093C2314yes—
144#14579093C2314yes—
145#14579093C2314yes—
146#14579092C2314yes—
147#14579092C2314yes—
148#14579092C2314yes—
149#14579092C2314yes—
150Dic79⋊C8C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579082C2314yes—
154#14579082C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156(C2×D79)⋊C8C2314yes—
157C8×Dic79C2314yes—
158C22×Q8×C79C2311yescharacteristic
159C22×D4×C79—21no—
160C22×D4×C79C2311yescharacteristic
161C23×C4×C79C2311yescharacteristic
162C2×SD16×C79—24no—
163C2×SD16×C79C2314yes—
164C22×C8×C79—24no—
165C22×C8×C79C2314yes—
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168C22⋊Q8×C79—22no—
169C22⋊Q8×C79C2314yes—
170#121×C79—22no—
171#121×C79C2314yes—
172C2×C4⋊C4×C79—21no—
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177#106×C79C2314yes—
178#103×C79C2314yes—
179#102×C79C2314yes—
180C23×D79C2×D411yescharacteristic
181#11929623—432no—
182C2×Dic158—24no—
183C2×Dic158—24no—
184C2×Dic158—44no—
185C2×Dic158—82no—
186C2×C22⋊D79—24no—
187C2×C22⋊D79—44no—
188C2×C22⋊D79SD1618yescomplemented
189C2×C22⋊D79C2×D414yes—
190C22×Dic79—24no—
191C22×Dic79—21no—
192C22×Dic79—21no—
193C22×Dic79—24no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—24no—
197C22×Dic79—44no—
198C22×Dic79—44no—
199C22×Dic79—82no—
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—44no—
208C2×C4×D79—82no—
209C2×C4×D79C2×D412yes—
210C2×C4×D79C2412yes—
211C2×C79⋊C8—22no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8C2412yes—
214C2×C79⋊C8C2412yes—
215C8×D79—28no—
216C4⋊Dic79—24no—
217C4⋊Dic79—21no—
218C4⋊Dic79—21no—
219C4⋊Dic79—21no—
220C4⋊Dic79—21no—
221C4⋊Dic79—24no—
222C4⋊Dic79—24no—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225C4⋊Dic79C2412yes—
226C4⋊Dic79C2412yes—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4C2×D414yes—
233C22⋊Dic79—24no—
234C22⋊Dic79—24no—
235C22⋊Dic79C2×D414yes—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4C2×D414yes—
238C4×Dic79—24no—
239C4×Dic79C2×D412yes—
240C4×Dic79C2412yes—
241C24×C79—21no—
242C24×C79C2×D411yescharacteristic
243C2×Q8×C79—21no—
244C2×Q8×C79—22no—
245C2×Q8×C79—22no—
246C2×Q8×C79C2412yes—
247C2×D4×C79—24no—
248C2×D4×C79—21no—
249C2×D4×C79—22no—
250C2×D4×C79—22no—
251C2×D4×C79—44no—
252C2×D4×C79C2412yes—
253C22×C4×C79—22no—
254C22×C4×C79—22no—
255C22×C4×C79—21no—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2×D412yes—
260C22×C4×C79C2412yes—
261C22×C4×C79C2411yescharacteristic
262SD16×C79—28no—
263C2×C8×C79—28no—
264C2×C8×C79—22no—
265C2×C8×C79#4114yescomplemented
266C2×C8×C79C2412yes—
267C2×C8×C79C2412yes—
268C4⋊C4×C79—24no—
269C4⋊C4×C79—21no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79C2412yes—
272C4⋊C4×C79C2412yes—
273C22⋊C4×C79—24no—
274C22⋊C4×C79—24no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79—42no—
279C23×C79—42no—
280C23×C79—42no—
281C23×C79C2×SD1614yes—
282C23×C79C22×D412yes—
283C23×C79C22×D411yescharacteristic
284C22×D79—22no—
285C22×D79—22no—
286C22×D79C2×SD1614yes—
287C22×D79C22×D412yes—
288Q8×C79—22no—
289Q8×C79—22no—
290Q8×C79—42no—
291D4×C79—22no—
292D4×C79—22no—
293D4×C79—48no—
294D4×C79—42no—
295C2×C4×C79—22no—
296C2×C4×C79—24no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—42no—
303C2×C4×C79—42no—
304C2×C4×C79—42no—
305C2×C4×C79C22×D412yes—
306C2×C4×C79C22×D411yescharacteristic
307C2×C4×C79C2×#4112yes—
308C2×C4×C792−1+412yes—
309C2×C4×C79C2511yescharacteristic
310C22⋊D79—48no—
311C22⋊D79C2×SD16116yescomplemented
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—48no—
321C2×Dic79—42no—
322C2×Dic79—42no—
323C2×Dic79—48no—
324C2×Dic79—84no—
325C2×Dic79C2×SD1614yes—
326C2×Dic79C22×D412yes—
327C2×Dic79C22×D412yes—
328C2×Dic79C22×D412yes—
329C4×D79—24no—
330C4×D79—22no—
331C4×D79—22no—
332C4×D79—48no—
333C4×D79—84no—
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—42no—
344C22×C79—42no—
345C22×C79—42no—
346C22×C79—84no—
347C22×C79#54712yes—
348C22×C79C22×SD1614yes—
349C22×C79C22×SD1612yes—
350C22×C79#57712yes—
351C22×C79C23×D411yescharacteristic
352C2×D79—28no—
353C2×D79—22no—
354C2×D79—22no—
355C2×D79C22×SD1614yes—
356C4×C79—22no—
357C4×C79—42no—
358C4×C79—42no—
359C4×C79—42no—
360C4×C79#54712yes—
361C4×C79C22×#4111yescharacteristic
362C4×C79C2×2−1+411yescharacteristic
363Dic79—22no—
364Dic79—22no—
365Dic79—42no—
366Dic79—42no—
367Dic79—42no—
368Dic79—42no—
369Dic79C22×SD1614yes—
370C2×#3335—791nomaximal, Sylow
371C2×C79—24no—
372C2×C79—82no—
373C2×C79#333514yescomplemented
374C2×C79C2×#54711yescharacteristic
375C2×C79C23×SD1611yescharacteristic
376C2×C79C2×#57711yescharacteristic
377D79—24no—
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×#465D7911yescharacteristic, complemented
390C2×C4×SD16—791no—
391C2×C8×D4—791no—
392C22×#106—791no—
393C22×#106—791no—
394C79C2×#333511yescharacteristic, complemented, Sylow
395C22×#41—1581no—
396C22×SD16C2×D7911yescharacteristic
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—1581no—
410C2×C22⋊Q8—1581no—
411C2×C22⋊Q8—1581no—
412C2×C22⋊Q8C2×D7911yescharacteristic
413C2×#121—791no—
414C2×#121C2×D7911yescharacteristic
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⋊C4—791no—
422C22×C4⋊C4—791no—
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#465C2×D7918yescomplemented
432C4×SD16—798no—
433C8×D4—798no—
434C2×#106—791no—
435C2×#106—798no—
436C2×#106—791no—
437C2×#106—791no—
438C2×#106—791no—
439C2×#106—791no—
440C2×#106—791no—
441C2×#106—791no—
442C2×#106—791no—
443C2×#106—798no—
444C2×#106C2×D7911yescharacteristic
445C2×C4⋊C8—791no—
446C2×#103—791no—
447C2×#103—791no—
448C2×#103C2×D7911yescharacteristic
449C2×#102—791no—
450C2×#102—791no—
451C2×#102C2×D7911yescharacteristic
452C2×C22⋊C8—791no—
453C2×C22⋊C8—791no—
454C2×C4×C8—791no—
455C2×#41—3168no—
456C2×#41—1588no—
457C22×Q8—1581no—
458C22×Q8—1581no—
459C22×Q8C22×D7911yescharacteristic
460C22×D4—21no—
461C22×D4—791no—
462C22×D4—1581no—
463C22×D4C22×D7911yescharacteristic
464C23×C4—791no—
465C23×C4—1581no—
466C23×C4—1581no—
467C23×C4—1581no—
468C23×C4—1581no—
469C23×C4—1581no—
470C23×C4C22×D7911yescharacteristic
471C2×SD16—24no—
472C2×SD16C22×D7914yes—
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—22no—
489C22⋊Q8—794no—
490C22⋊Q8—1588no—
491C22⋊Q8—1588no—
492C22⋊Q8—1588no—
493C22⋊Q8—1582no—
494C22⋊Q8C22×D7914yes—
495#121—22no—
496#121—794no—
497#121—1582no—
498#121C22×D7914yes—
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—791no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—791no—
512C2×C4⋊C4—794no—
513C2×C4⋊C4—794no—
514C2×C4⋊C4—794no—
515C2×C4⋊C4—794no—
516C2×C4⋊C4—1582no—
517C2×C4⋊C4—1582no—
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⋊C4—1581no—
525C2×C4⋊C4—1581no—
526C2×C4⋊C4—1582no—
527C2×C4⋊C4—1582no—
528C2×C4⋊C4C22×D7911yescharacteristic
529C2×C4⋊C4C22×D7911yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—791no—
533C2×C22⋊C4—791no—
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#106—794no—
545#106—794no—
546#106—794no—
547#106C22×D7914yes—
548C4⋊C8—794no—
549#103—794no—
550#103—794no—
551#103C22×D7914yes—
552#102—794no—
553#102—794no—
554#102C22×D7914yes—
555C22⋊C8—794no—
556C22⋊C8—794no—
557C4×C8—794no—
558C24—21no—
559C24—791no—
560C24D4×D7911yescharacteristic
561#41—31632no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—3164no—
566C2×Q8—6322no—
567C2×Q8—1584no—
568C2×Q8—1584no—
569C2×Q8C23×D7912yes—
570C2×D4—24no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—44no—
575C2×D4—3164no—
576C2×D4—798no—
577C2×D4—794no—
578C2×D4—1584no—
579C2×D4C23×D7912yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—3164no—
586C22×C4—3164no—
587C22×C4—3164no—
588C22×C4—791no—
589C22×C4—791no—
590C22×C4—791no—
591C22×C4—792no—
592C22×C4—792no—
593C22×C4—6322no—
594C22×C4—6322no—
595C22×C4—1584no—
596C22×C4—1584no—
597C22×C4—1584no—
598C22×C4—1584no—
599C22×C4—1581no—
600C22×C4—1581no—
601C22×C4—1581no—
602C22×C4—1581no—
603C22×C4—1584no—
604C22×C4—1582no—
605C22×C4—1582no—
606C22×C4D4×D7912yes—
607C22×C4D4×D7911yescharacteristic
608C22×C4C23×D7912yes—
609C22×C4C23×D7911yescharacteristic
610SD16—28no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—792no—
614C2×C8—792no—
615C2×C8—1582no—
616C2×C8—1582no—
617C2×C8—1588no—
618C2×C8#1192962314yescomplemented
619C2×C8C23×D7912yes—
620C2×C8C23×D7912yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—794no—
625C4⋊C4—792no—
626C4⋊C4—792no—
627C4⋊C4—792no—
628C4⋊C4—792no—
629C4⋊C4—1584no—
630C4⋊C4—1584no—
631C4⋊C4—1584no—
632C4⋊C4—1584no—
633C4⋊C4—1584no—
634C4⋊C4—1584no—
635C4⋊C4—1581no—
636C4⋊C4—1581no—
637C4⋊C4—1581no—
638C4⋊C4—1584no—
639C4⋊C4—1584no—
640C4⋊C4—1581no—
641C4⋊C4C23×D7912yes—
642C4⋊C4C23×D7912yes—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—794no—
646C22⋊C4—794no—
647C22⋊C4—1584no—
648C22⋊C4—1584no—
649C22⋊C4—1584no—
650C42—792no—
651C42—792no—
652C42—1584no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—794no—
660C23—792no—
661C23—1582no—
662C23—1582no—
663C23SD16×D7914yes—
664C23C2×D4×D7912yes—
665C23C2×D4×D7911yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—3168no—
670Q8—6324no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—3168no—
676D4—7916no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—3168no—
688C2×C4—3162no—
689C2×C4—3162no—
690C2×C4—3168no—
691C2×C4—3162no—
692C2×C4—3162no—
693C2×C4—3168no—
694C2×C4—794no—
695C2×C4—792no—
696C2×C4—792no—
697C2×C4—792no—
698C2×C4—6324no—
699C2×C4—6324no—
700C2×C4—1582no—
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×#1192962312yes—
712C2×C4#1457920812yes—
713C2×C4C24×D7911yescharacteristic
714C8—22no—
715C8—1582no—
716C8—1582no—
717C8C2×#1192962314yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—794no—
726C22—1588no—
727C22—1582no—
728C22—1582no—
729C22#1909921312yes—
730C22C2×SD16×D7914yes—
731C22C2×SD16×D7912yes—
732C22#1909937012yes—
733C22C22×D4×D7911yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—3162no—
739C4—3162no—
740C4—3162no—
741C4—3162no—
742C4—794no—
743C4—1582no—
744C4—1582no—
745C4#1909921312yes—
746C4C22×#1192962311yescharacteristic
747C4C2×#1457920811yescharacteristic
748C2—24no—
749C2—82no—
750C2—1584no—
751C2#2377575214yesdirect product factor
752C2C2×#1909921311yescharacteristic
753C2C22×SD16×D7911yescharacteristic
754C2C2×#1909937011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#465×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099213C2
hypercenterC2×#465D79
hypocenterC79C2×#3335
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#19099271C2semidirect
3. #23775752C2direct (N × H)
4. C2×#19098960C2semidirect
5. C2×#19098880C2semidirect
6. C2×#19098879C2semidirect
7. C2×#19098892C2semidirect
8. C2×#19098891C2semidirect
9. C2×#19098846C2semidirect
10. C2×#19098851C2semidirect
11. C2×#19098789C2semidirect
12. C2×SD16×Dic79C2semidirect
13. C2×C8×C22⋊D79C2semidirect
14. C22×#14579093C2semidirect
15. C2×#106×D79C2semidirect
16. C2×#465×C79C2semidirect
20. #19099271C22semidirect
41. #19098960C22semidirect
42. #19098892C22semidirect
43. #19098891C22semidirect
44. #19098880C22semidirect
45. #19098879C22semidirect
46. #19098851C22semidirect
47. #19098846C22semidirect
48. #19098789C22semidirect
49. SD16×Dic79C22semidirect
50. C8×C22⋊D79C22semidirect
55. C2×#14579093C22semidirect
60. #106×D79C22semidirect
73. #465×C79C22semidirect
188. C2×C22⋊D79SD16semidirect
265. C2×C8×C79#41semidirect
311. C22⋊D79C2×SD16semidirect
337. C8×C79C2×#41semidirect
373. C2×C79#3335semidirect
389. C2×#465D79semidirect
394. C79C2×#3335semidirect
431. #465C2×D79semidirect
618. C2×C8#11929623semidirect
717. C8C2×#11929623semidirect
751. C2#23775752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992712
C2×#190992132
#237757522
C2×#190989602
C2×#190988802
C2×#190988792
C2×#190988922
C2×#190988912
C2×#190988462
C2×#190988512
C2×#190987892
C2×SD16×Dic792
C2×C8×C22⋊D792
C22×#145790932
C2×#106×D792
C2×#465×C792
C2×#333579