Finite Group Databasebeta

← C2×#23773762 #35157514

Subgroups — C2×#23773762 #35157514

Order 20224.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099190C211yesmaximal, characteristic, complemented
2C2×#19099133C211yesmaximal, characteristic
3#23773762C2116yesmaximal, direct product factor
4C2×#19098932C211yesmaximal, characteristic, complemented
5C2×#19098930C211yesmaximal, characteristic, complemented
6C2×#19098921C211yesmaximal, characteristic, complemented
7C2×#19098917C211yesmaximal, characteristic, complemented
8C2×#19098916C211yesmaximal, characteristic, complemented
9C2×#19098915C211yesmaximal, characteristic, complemented
10C2×#19098912C211yesmaximal, characteristic, complemented
11C2×#19098561C211yesmaximal, characteristic
12C2×#19098570C211yesmaximal, characteristic, complemented
13C2×#19098556C211yesmaximal, characteristic
14C2×#103×D79C211yesmaximal, characteristic, complemented
15C2×#19098520C211yesmaximal, characteristic, complemented
16C2×#489×C79C211yesmaximal, characteristic, complemented
17C22×#11929623C2211yescharacteristic
18C22×Q8×D79C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20C22×C8×D79C2211yescharacteristic
21#19099190—24no—
22#19099190C2218yescomplemented
23#19099133—24no—
24#19099133C2218yes—
25C2×#14579161C2211yescharacteristic
26C2×#14579160C2211yescharacteristic
27C2×#14579159—21no—
28C2×#14579159C2211yescharacteristic
29C2×#14579153C2211yescharacteristic
30C2×#14579152C2211yescharacteristic
31C2×#14579151—21no—
32C2×#14579148C2211yescharacteristic
33C2×#14579143—21no—
34C2×#14579143—21no—
35C2×#14579139—21no—
36C2×#14579138—21no—
37C2×#14579138—21no—
38C2×#14579137—21no—
39C2×#14579119C2211yescharacteristic
40C2×#14579118C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098932C2218yescomplemented
43#19098930C2218yescomplemented
44#19098921C2218yescomplemented
45#19098917C2218yescomplemented
46#19098916C2218yescomplemented
47#19098915C2218yescomplemented
48#19098912C2218yescomplemented
49#19098570C2218yescomplemented
50#19098561C2218yes—
51#19098556C2218yes—
52C2×#14579086C2211yescharacteristic
53C2×#14579086C2211yescharacteristic
54C2×#14579086C2211yescharacteristic
55C2×#14579086C2211yescharacteristic
56C2×#14579085C2211yescharacteristic
57C2×#14579085C2211yescharacteristic
58C2×#14579084C2211yescharacteristic
59C2×#14579084C2211yescharacteristic
60C2×#14579084C2211yescharacteristic
61C2×#14579084C2211yescharacteristic
62#103×D79C2218yescomplemented
63C2×#14579082C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65#19098520C2218yescomplemented
66C2×#14579071C2211yescharacteristic
67C2×C4×C79⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C2×C4⋊Q8×C79C2211yescharacteristic
70C2×#124×C79C2211yescharacteristic
71#489×C79C2218yescomplemented
72C2×#103×C79C2211yescharacteristic
73C2×#103×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C2×#11929623—22no—
78C2×#11929623—24no—
79C2×#11929623—24no—
80C2×#11929623C2314yes—
81C22×Dic158—21no—
82C22×Dic158—21no—
83C22×Dic158C2311yescharacteristic
84C22×Dic158C2311yescharacteristic
85C2×Q8×D79—22no—
86C2×Q8×D79—24no—
87C2×Q8×D79—24no—
88C2×Q8×D79C2314yes—
89C22×C22⋊D79—21no—
90C23×Dic79—21no—
91C22×C4×D79—21no—
92C22×C4×D79—21no—
93C22×C4×D79C2311yescharacteristic
94C2×#11929607—24no—
95C2×#11929607C2314yes—
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2311yescharacteristic
98C2×C8×D79—24no—
99C2×C8×D79C2314yes—
100#14579161—22no—
101#14579161C2314yes—
102#14579160—22no—
103#14579160C2314yes—
104#14579159—28no—
105#14579159—22no—
106#14579159C2314yes—
107#14579153—22no—
108#14579153C2314yes—
109#14579152—22no—
110#14579152C2314yes—
111#14579151—28no—
112#14579148—22no—
113#14579148C2314yes—
114#14579143—28no—
115#14579143—28no—
116#14579139—28no—
117#14579138—28no—
118#14579138—28no—
119#14579137—28no—
120#14579119—22no—
121#14579119C2314yes—
122#14579118D414yes—
123#14579118C2314yes—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79—21no—
126C2×C4⋊Dic79—21no—
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×Dic79⋊C4—21no—
136C2×Dic79⋊C4D411yescharacteristic
137C2×Dic79⋊C4D411yescharacteristic
138C4⋊C4×D79—22no—
139C4⋊C4×D79C2314yes—
140C2×C22⋊Dic79—21no—
141C2×C22⋊Dic79—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×(C2×D79)⋊C4D411yescharacteristic
144C2×(C2×D79)⋊C4D411yescharacteristic
145C2×C4×Dic79—21no—
146C2×C4×Dic79C2311yescharacteristic
147#14579086C2314yes—
148#14579086C2314yes—
149#14579086C2314yes—
150#14579086C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579084C2314yes—
154#14579084C2314yes—
155#14579084C2314yes—
156#14579084C2314yes—
157#14579082C2314yes—
158#14579082C2314yes—
159#14579071C2314yes—
160C4×C79⋊C8C2314yes—
161C8×Dic79C2314yes—
162C22×Q8×C79—21no—
163C22×Q8×C79C2311yescharacteristic
164C22×D4×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C4⋊Q8×C79—22no—
168C4⋊Q8×C79C2314yes—
169#124×C79—22no—
170#124×C79C2314yes—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C42×C79C2311yescharacteristic
177#103×C79C2314yes—
178#103×C79C2314yes—
179#102×C79C2314yes—
180#102×C79C2314yes—
181#97×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183#11929623—28no—
184#11929623—28no—
185#11929623—48no—
186C2×Dic158—24no—
187C2×Dic158—24no—
188C2×Dic158—21no—
189C2×Dic158—21no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158—22no—
193C2×Dic158—22no—
194C2×Dic158—44no—
195C2×Dic158—82no—
196C2×Dic158C2412yes—
197C2×Dic158C2412yes—
198Q8×D79—28no—
199Q8×D79—28no—
200Q8×D79—48no—
201C2×C22⋊D79—24no—
202C2×C22⋊D79—44no—
203C22×Dic79—24no—
204C22×Dic79—21no—
205C22×Dic79—21no—
206C22×Dic79—21no—
207C22×Dic79—21no—
208C22×Dic79—44no—
209C22×Dic79C2×D411yescharacteristic
210C22×Dic79C2×D411yescharacteristic
211C22×Dic79C2×D411yescharacteristic
212C2×C4×D79—24no—
213C2×C4×D79—24no—
214C2×C4×D79—44no—
215C2×C4×D79—82no—
216C2×C4×D79C2×D412yes—
217C2×C4×D79#4114yes—
218C2×C4×D79#4114yes—
219C2×C4×D79C2412yes—
220#11929607—28no—
221C2×C79⋊C8—22no—
222C2×C79⋊C8—22no—
223C2×C79⋊C8C2412yes—
224C2×C79⋊C8C2412yes—
225C8×D79—28no—
226C4⋊Dic79—24no—
227C4⋊Dic79—21no—
228C4⋊Dic79—24no—
229C4⋊Dic79—24no—
230C4⋊Dic79—21no—
231C4⋊Dic79C2412yes—
232C4⋊Dic79C2412yes—
233Dic79⋊C4—24no—
234Dic79⋊C4—24no—
235Dic79⋊C4—24no—
236Dic79⋊C4—24no—
237Dic79⋊C4—24no—
238Dic79⋊C4—24no—
239Dic79⋊C4—24no—
240Dic79⋊C4C2×D414yes—
241Dic79⋊C4C2×D414yes—
242C22⋊Dic79—24no—
243C22⋊Dic79—24no—
244(C2×D79)⋊C4—24no—
245(C2×D79)⋊C4C2×D414yes—
246(C2×D79)⋊C4C2×D414yes—
247C4×Dic79—24no—
248C4×Dic79C2×D412yes—
249C4×Dic79C2412yes—
250C24×C79—21no—
251C2×Q8×C79—21no—
252C2×Q8×C79—24no—
253C2×Q8×C79—22no—
254C2×Q8×C79—22no—
255C2×Q8×C79—82no—
256C2×Q8×C79C2412yes—
257C2×D4×C79—21no—
258C2×D4×C79—22no—
259C2×D4×C79—22no—
260C2×D4×C79C2412yes—
261C22×C4×C79—21no—
262C22×C4×C79—21no—
263C22×C4×C79—21no—
264C22×C4×C79C2×D411yescharacteristic
265C22×C4×C79C2×D411yescharacteristic
266C22×C4×C79C2411yescharacteristic
267C2×C8×C79—22no—
268C2×C8×C79—22no—
269C2×C8×C79C2412yes—
270C2×C8×C79C2412yes—
271C4⋊C4×C79—24no—
272C4⋊C4×C79—21no—
273C4⋊C4×C79—21no—
274C4⋊C4×C79C2412yes—
275C4⋊C4×C79C2412yes—
276C22⋊C4×C79—24no—
277C22⋊C4×C79—24no—
278C42×C79C2×D412yes—
279C42×C79C2412yes—
280C23×C79—22no—
281C23×C79—42no—
282C23×C79—42no—
283C23×C79—42no—
284C23×C79C22×D411yescharacteristic
285C22×D79—22no—
286C22×D79—22no—
287C22×D79#12414yes—
288C22×D79C22×D412yes—
289Q8×C79—22no—
290Q8×C79—22no—
291Q8×C79—42no—
292Q8×C79—84no—
293D4×C79—22no—
294D4×C79—22no—
295D4×C79—42no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—42no—
302C2×C4×C79—42no—
303C2×C4×C79—42no—
304C2×C4×C79C22×D412yes—
305C2×C4×C79C22×D412yes—
306C2×C4×C79C22×D411yescharacteristic
307C2×C4×C79C2×#4112yes—
308C2×C4×C79C2×#4112yes—
309C2×C4×C79C2511yescharacteristic
310C22⋊D79—48no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—42no—
321C2×Dic79—48no—
322C2×Dic79#12414yes—
323C2×Dic79C22×D412yes—
324C2×Dic79C22×D412yes—
325C2×Dic79C22×D412yes—
326C4×D79—48no—
327C4×D79—84no—
328C4×D79#12418yes—
329C4×D79C2×#4114yes—
330C4×D79C2×#4114yes—
331Dic158—22no—
332Dic158—22no—
333Dic158—22no—
334Dic158—22no—
335Dic158—42no—
336Dic158—42no—
337Dic158—48no—
338Dic158—84no—
339C8×C79—22no—
340C8×C79—22no—
341C79⋊C8—22no—
342C79⋊C8—22no—
343C22×C79—42no—
344C22×C79—42no—
345C22×C79—42no—
346C22×C79—84no—
347C22×C79C2×#12412yes—
348C22×C79#57712yes—
349C22×C79#57812yes—
350C22×C79C23×D411yescharacteristic
351C2×D79—28no—
352C2×D79—22no—
353C2×D79—22no—
354C2×D79C2×#12414yes—
355C4×C79—22no—
356C4×C79—22no—
357C4×C79—42no—
358C4×C79—42no—
359C4×C79—42no—
360C4×C79C2×#12412yes—
361C4×C79C22×#4111yescharacteristic
362C4×C79C22×#4111yescharacteristic
363Dic79—22no—
364Dic79—22no—
365Dic79—42no—
366Dic79—42no—
367Dic79—42no—
368Dic79—42no—
369Dic79C2×#12414yes—
370C2×#3137—791nomaximal, Sylow
371C2×C79—82no—
372C2×C79#313714yescomplemented
373C2×C79C22×#12411yescharacteristic
374C2×C79C2×#57711yescharacteristic
375C2×C79C2×#57811yescharacteristic
376D79—24no—
377C2×#544—791no—
378C2×#536—791no—
379#3137—7916no—
380C2×#491—791no—
381C2×#491—791no—
382C2×#489—791no—
383C2×#489D7911yescharacteristic, complemented
384C2×#488—791no—
385C2×#488—791no—
386C2×#487—791no—
387C2×#487—791no—
388C2×#417—791no—
389C2×#419—791no—
390C2×#416—791no—
391C22×#103—791no—
392C2×#405—791no—
393C79C2×#313711yescharacteristic, complemented, Sylow
394C22×#41—791no—
395C23×Q8—791no—
396C22×M16—791no—
397C23×C8—791no—
398#544—798no—
399#544—1584no—
400#536—798no—
401#536—1584no—
402C2×C4⋊Q8—791no—
403C2×C4⋊Q8—791no—
404C2×C4⋊Q8—791no—
405C2×C4⋊Q8—1581no—
406C2×C4⋊Q8C2×D7911yescharacteristic
407C2×#125—791no—
408C2×#125—791no—
409C2×#125—1581no—
410C2×#124—791no—
411C2×#124C2×D7911yescharacteristic
412C2×#123—1581no—
413C2×#123—1581no—
414C2×C22⋊Q8—1581no—
415C2×C22⋊Q8—1581no—
416C2×C22⋊Q8—1581no—
417C2×C22⋊Q8—1581no—
418C2×#117—791no—
419C2×#117—791no—
420C22×C4⋊C4—791no—
421#491—798no—
422#491—798no—
423#489—798no—
424#489C2×D7918yescomplemented
425#488—798no—
426#488—798no—
427#487—798no—
428#487—798no—
429#419—798no—
430#417—798no—
431#416—798no—
432C2×#103—791no—
433C2×#103—791no—
434C2×#103—791no—
435C2×#103—791no—
436C2×#103—791no—
437C2×#103—791no—
438C2×#103—791no—
439C2×#103—791no—
440C2×#103—791no—
441C2×#103—791no—
442C2×#103—798no—
443C2×#103C2×D7911yescharacteristic
444C2×#103C2×D7911yescharacteristic
445C2×#102—791no—
446C2×#102—791no—
447C2×#102C2×D7911yescharacteristic
448C2×#102C2×D7911yescharacteristic
449#405—798no—
450C2×#97—791no—
451C2×#97C2×D7911yescharacteristic
452C2×C4×C8—791no—
453C2×C4×C8—791no—
454C2×#41—794no—
455C2×#41—1584no—
456C2×#41—1584no—
457C2×#41—1582no—
458C22×Q8—21no—
459C22×Q8—794no—
460C22×Q8—791no—
461C22×Q8—791no—
462C22×Q8—1581no—
463C22×Q8—1581no—
464C22×Q8—1584no—
465C22×Q8—1584no—
466C22×Q8—1582no—
467C22×Q8C22×D7911yescharacteristic
468C22×D4—1581no—
469C22×D4C22×D7911yescharacteristic
470C23×C4—791no—
471C23×C4—1581no—
472C23×C4—1581no—
473C23×C4—1581no—
474C2×M16—794no—
475C2×M16—1584no—
476C22×C8—791no—
477C22×C8—791no—
478C22×C8—794no—
479C22×C8—1584no—
480C22×C8C22×D7911yescharacteristic
481C22×C8C22×D7911yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—794no—
484C4⋊Q8—794no—
485C4⋊Q8—794no—
486C4⋊Q8—1582no—
487C4⋊Q8—1582no—
488C4⋊Q8—1588no—
489C4⋊Q8—1582no—
490C4⋊Q8C22×D7914yes—
491#125—794no—
492#125—794no—
493#125—1582no—
494#125—1588no—
495#125—1582no—
496#124—22no—
497#124—794no—
498#124—1582no—
499#124C22×D7914yes—
500#123—1588no—
501#123—1588no—
502C22⋊Q8—1588no—
503C22⋊Q8—1588no—
504C22⋊Q8—1588no—
505C22⋊Q8—1588no—
506#117—794no—
507#117—794no—
508#117—794no—
509#117—1582no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—791no—
512C2×C4⋊C4—791no—
513C2×C4⋊C4—791no—
514C2×C4⋊C4—791no—
515C2×C4⋊C4—794no—
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⋊C4—1581no—
525C2×C4⋊C4—1581no—
526C2×C4⋊C4—1581no—
527C2×C4⋊C4C22×D7911yescharacteristic
528C2×C4⋊C4C22×D7911yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—791no—
532C2×C22⋊C4—791no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4—1581no—
535C2×C22⋊C4—1581no—
536C2×C42—791no—
537C2×C42—1581no—
538C2×C42C22×D7911yescharacteristic
539#103—794no—
540#103—794no—
541#103—794no—
542#103—794no—
543#103—794no—
544#103—794no—
545#103—794no—
546#103—794no—
547#103—794no—
548#103—794no—
549#103C22×D7914yes—
550#103C22×D7914yes—
551#102—794no—
552#102—794no—
553#102C22×D7914yes—
554#102C22×D7914yes—
555#97—794no—
556#97C22×D7914yes—
557C4×C8—794no—
558C4×C8—794no—
559C24—21no—
560C24—791no—
561#41—3168no—
562#41—1588no—
563#41—1588no—
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—3164no—
570C2×Q8—3168no—
571C2×Q8—792no—
572C2×Q8—792no—
573C2×Q8—6322no—
574C2×Q8—1584no—
575C2×Q8—1584no—
576C2×Q8—1588no—
577C2×Q8—1588no—
578C2×Q8—1582no—
579C2×Q8—1582no—
580C2×Q8—1582no—
581C2×Q8—1582no—
582C2×Q8—1581no—
583C2×Q8—1581no—
584C2×Q8C23×D7912yes—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—3164no—
589C2×D4—1584no—
590C2×D4C23×D7912yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—3164no—
595C22×C4—3164no—
596C22×C4—791no—
597C22×C4—794no—
598C22×C4—794no—
599C22×C4—792no—
600C22×C4—792no—
601C22×C4—791no—
602C22×C4—791no—
603C22×C4—6322no—
604C22×C4—1584no—
605C22×C4—1584no—
606C22×C4—1584no—
607C22×C4—1581no—
608C22×C4—1581no—
609C22×C4—1581no—
610C22×C4—1581no—
611C22×C4D4×D7911yescharacteristic
612C22×C4D4×D7911yescharacteristic
613C22×C4C23×D7911yescharacteristic
614M16—1588no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—792no—
618C2×C8—792no—
619C2×C8—1588no—
620C2×C8—1582no—
621C2×C8—1582no—
622C2×C8C23×D7912yes—
623C2×C8C23×D7912yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—794no—
628C4⋊C4—794no—
629C4⋊C4—792no—
630C4⋊C4—792no—
631C4⋊C4—1584no—
632C4⋊C4—1584no—
633C4⋊C4—1584no—
634C4⋊C4—1584no—
635C4⋊C4—1584no—
636C4⋊C4—1584no—
637C4⋊C4—1584no—
638C4⋊C4—1584no—
639C4⋊C4—1581no—
640C4⋊C4—1581no—
641C4⋊C4—1584no—
642C4⋊C4—1584no—
643C4⋊C4C23×D7912yes—
644C4⋊C4C23×D7912yes—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—794no—
648C22⋊C4—794no—
649C22⋊C4—1584no—
650C22⋊C4—1584no—
651C22⋊C4—1584no—
652C42—792no—
653C42—792no—
654C42—1584no—
655C42D4×D7912yes—
656C42C23×D7912yes—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—794no—
662C23—792no—
663C23—1582no—
664C23—1582no—
665C23C2×D4×D7911yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—84no—
670Q8—3168no—
671Q8—3162no—
672Q8—3162no—
673Q8—6324no—
674Q8—1582no—
675Q8—1582no—
676Q8—1582no—
677Q8—1582no—
678D4—22no—
679D4—22no—
680D4—42no—
681D4—3168no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—3168no—
691C2×C4—3162no—
692C2×C4—3162no—
693C2×C4—3162no—
694C2×C4—3162no—
695C2×C4—3168no—
696C2×C4—794no—
697C2×C4—792no—
698C2×C4—798no—
699C2×C4—794no—
700C2×C4—794no—
701C2×C4—792no—
702C2×C4—792no—
703C2×C4—6324no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4—1582no—
709C2×C4—1582no—
710C2×C4C2×D4×D7912yes—
711C2×C4C2×D4×D7912yes—
712C2×C4C2×D4×D7911yescharacteristic
713C2×C4#41×D7912yes—
714C2×C4#41×D7912yes—
715C2×C4C24×D7911yescharacteristic
716C8—22no—
717C8—22no—
718C8—1582no—
719C8—1582no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—794no—
725C22—1588no—
726C22—1582no—
727C22—1582no—
728C22#124×D7912yes—
729C22#1909937312yes—
730C22#1909937912yes—
731C22C22×D4×D7911yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—3162no—
738C4—3162no—
739C4—3162no—
740C4—3162no—
741C4—794no—
742C4—1582no—
743C4—1582no—
744C4#124×D7912yes—
745C4C2×#41×D7911yescharacteristic
746C4C2×#41×D7911yescharacteristic
747C2—82no—
748C2—1584no—
749C2#2377376214yesdirect product factor
750C2C2×#124×D7911yescharacteristic
751C2C2×#1909937311yescharacteristic
752C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#489×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929623C22
hypercenterC2×#489D79
hypocenterC79C2×#3137
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#19099190C2semidirect
3. #23773762C2direct (N × H)
4. C2×#19098932C2semidirect
5. C2×#19098930C2semidirect
6. C2×#19098921C2semidirect
7. C2×#19098917C2semidirect
8. C2×#19098916C2semidirect
9. C2×#19098915C2semidirect
10. C2×#19098912C2semidirect
12. C2×#19098570C2semidirect
14. C2×#103×D79C2semidirect
15. C2×#19098520C2semidirect
16. C2×#489×C79C2semidirect
22. #19099190C22semidirect
42. #19098932C22semidirect
43. #19098930C22semidirect
44. #19098921C22semidirect
45. #19098917C22semidirect
46. #19098916C22semidirect
47. #19098915C22semidirect
48. #19098912C22semidirect
49. #19098570C22semidirect
62. #103×D79C22semidirect
65. #19098520C22semidirect
71. #489×C79C22semidirect
372. C2×C79#3137semidirect
383. C2×#489D79semidirect
393. C79C2×#3137semidirect
424. #489C2×D79semidirect
749. C2#23773762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991902
C2×#190991332
#237737622
C2×#190989322
C2×#190989302
C2×#190989212
C2×#190989172
C2×#190989162
C2×#190989152
C2×#190989122
C2×#190985612
C2×#190985702
C2×#190985562
C2×#103×D792
C2×#190985202
C2×#489×C792
C2×#313779