Finite Group Databasebeta

← C2×#23775887 #35166850

Subgroups — C2×#23775887 #35166850

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×#19099270C211yesmaximal, characteristic, complemented
2C2×#19099259C211yesmaximal, characteristic
3#23775887C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098899C211yesmaximal, characteristic, complemented
6C2×#19098882C211yesmaximal, characteristic, complemented
7C2×#19098905C211yesmaximal, characteristic, complemented
8C2×#19098877C211yesmaximal, characteristic, complemented
9C2×#19098871C211yesmaximal, characteristic, complemented
10C2×#19098844C211yesmaximal, characteristic, complemented
11C2×#19098809C211yesmaximal, characteristic, complemented
12C2×#19098792C211yesmaximal, characteristic, complemented
13C2×#19098665C211yesmaximal, characteristic, complemented
14C2×#19098605C211yesmaximal, characteristic, complemented
15C22×#14579095C211yesmaximal, characteristic, complemented
16C2×#435×C79C211yesmaximal, characteristic, complemented
17C22×#11929613C2211yescharacteristic
18#19099270—24no—
19#19099270C2218yescomplemented
20#19099259—24no—
21#19099259C2218yes—
22C2×#14579161C2211yescharacteristic
23C2×#14579156—21no—
24C2×#14579153C2211yescharacteristic
25C2×#14579152—21no—
26C2×#14579143—21no—
27C2×#14579140C2211yescharacteristic
28C2×#14579140C2211yescharacteristic
29C2×#14579138—21no—
30C2×#14579138—21no—
31C2×#14579135C2211yescharacteristic
32C2×#14579135C2211yescharacteristic
33C2×#14579133—21no—
34C2×C4×Dic158C2211yescharacteristic
35C2×C4×D316C2211yescharacteristic
36C2×D4×Dic79—21no—
37C2×(C22⋊D79)⋊C4—21no—
38C2×#14579120C2211yescharacteristic
39C22×C4⋊Dic79C2211yescharacteristic
40C22×C4⋊Dic79C2211yescharacteristic
41C22×C4⋊Dic79C2211yescharacteristic
42#19098972C2218yescomplemented
43#19098905C2218yescomplemented
44#19098899C2218yescomplemented
45#19098882C2218yescomplemented
46#19098877C2218yescomplemented
47#19098871C2218yescomplemented
48#19098844C2218yescomplemented
49#19098809C2218yescomplemented
50#19098792C2218yescomplemented
51#19098665C2218yescomplemented
52#19098605C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579095C2211yescharacteristic
56C2×#14579095C2211yescharacteristic
57C2×#14579095C2211yescharacteristic
58C2×#14579095C2211yescharacteristic
59C2×#14579095C2218yescomplemented
60C2×#14579093C2211yescharacteristic
61C2×#14579093C2211yescharacteristic
62C2×#14579093C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579086C2211yescharacteristic
66C2×#14579083C2211yescharacteristic
67C2×#14579083C2211yescharacteristic
68C2×#14579083C2211yescharacteristic
69C22×M16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#435×C79C2218yescomplemented
73C2×C4⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×C22⋊C8×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C22×C22⋊D79—21no—
82C23×Dic79—21no—
83C23×Dic79—21no—
84C23×Dic79—21no—
85C22×C4×D79—21no—
86C2×#11929613—24no—
87C2×#11929613C2314yes—
88#14579161—22no—
89#14579161C2314yes—
90#14579156—28no—
91#14579153—22no—
92#14579153C2314yes—
93#14579152—28no—
94#14579143—28no—
95#14579140—22no—
96#14579140—22no—
97#14579140C2314yes—
98#14579140C2314yes—
99#14579138—28no—
100#14579138—28no—
101#14579135—22no—
102#14579135—22no—
103#14579135C2314yes—
104#14579135C2314yes—
105#14579133—28no—
106C4×Dic158—22no—
107C4×Dic158C2314yes—
108C4×D316—22no—
109C4×D316C2314yes—
110D4×Dic79—28no—
111(C22⋊D79)⋊C4—28no—
112#14579120—22no—
113#14579120C2314yes—
114C2×C4⋊Dic79—22no—
115C2×C4⋊Dic79—22no—
116C2×C4⋊Dic79—22no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79C2314yes—
122C2×C4⋊Dic79C2314yes—
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2314yes—
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×C4⋊Dic79C2311yescharacteristic
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×C22⋊Dic79—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143#14579095C2314yes—
144#14579095C2314yes—
145#14579095C2314yes—
146#14579095C2314yes—
147#14579095C2314yes—
148#14579095C2314yes—
149#14579093C2314yes—
150#14579093C2314yes—
151#14579093C2314yes—
152#14579086C2314yes—
153#14579086C2314yes—
154#14579086C2314yes—
155#14579083C2314yes—
156#14579083C2314yes—
157#14579083C2314yes—
158C22×D4×C79D411yescharacteristic
159C23×C4×C79C2311yescharacteristic
160C23×C4×C79C2311yescharacteristic
161C2×M16×C79—24no—
162C2×M16×C79C2314yes—
163C22×C8×C79—24no—
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2314yes—
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C4×D4×C79D414yes—
170C4×D4×C79C2314yes—
171C2×C4⋊C4×C79D411yescharacteristic
172C2×C22⋊C4×C79D411yescharacteristic
173C2×C22⋊C4×C79D411yescharacteristic
174C2×C42×C79C2311yescharacteristic
175C4⋊C8×C79C2314yes—
176C22⋊C8×C79C2314yes—
177C22⋊C8×C79C2314yes—
178#97×C79C2314yes—
179C23×D79—21no—
180C2×Dic158—21no—
181C2×Dic158—24no—
182C2×Dic158—22no—
183C2×Dic158—22no—
184C2×Dic158—82no—
185C2×Dic158C2412yes—
186C2×D316—21no—
187C2×D316—22no—
188C2×D316—22no—
189C2×D316C2412yes—
190C2×C22⋊D79—24no—
191C2×C22⋊D79—24no—
192C2×C22⋊D79—44no—
193C2×C22⋊D79—82no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—24no—
202C22×Dic79—24no—
203C22×Dic79—24no—
204C22×Dic79—82no—
205C22×Dic79—82no—
206C22×Dic79—82no—
207C2×C4×D79—24no—
208C2×C4×D79—82no—
209#11929613—28no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79—24no—
214C4⋊Dic79—24no—
215C4⋊Dic79—21no—
216C4⋊Dic79—21no—
217C4⋊Dic79—24no—
218C4⋊Dic79—24no—
219C4⋊Dic79—21no—
220C4⋊Dic79C2412yes—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225C4⋊Dic79C2412yes—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4—24no—
231C22⋊Dic79—24no—
232C22⋊Dic79—24no—
233C22⋊Dic79—24no—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4—24no—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C24×C79C2×D411yescharacteristic
240C24×C79C2×D411yescharacteristic
241C2×D4×C79—24no—
242C2×D4×C79C2×D414yes—
243C22×C4×C79—22no—
244C22×C4×C79—22no—
245C22×C4×C79—22no—
246C22×C4×C79—22no—
247C22×C4×C79C2×D411yescharacteristic
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D412yes—
252C22×C4×C79C2×D412yes—
253C22×C4×C79C2412yes—
254C22×C4×C79C2412yes—
255C22×C4×C79C2411yescharacteristic
256M16×C79—28no—
257C2×C8×C79—28no—
258C2×C8×C79—22no—
259C2×C8×C79—22no—
260C2×C8×C79—22no—
261C2×C8×C79#4114yes—
262C2×C8×C79C2412yes—
263C2×C8×C79C2412yes—
264C2×C8×C79C2412yes—
265C2×C8×C79C2412yes—
266C4⋊C4×C79C2×D414yes—
267C22⋊C4×C79C2×D414yes—
268C22⋊C4×C79C2×D414yes—
269C42×C79C2×D412yes—
270C42×C79C2412yes—
271C23×C79—22no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79#13714yes—
277C23×C79C22×D412yes—
278C23×C79C22×D412yes—
279C23×C79C22×D411yescharacteristic
280C22×D79—22no—
281C22×D79—42no—
282C22×D79—42no—
283C22×D79—42no—
284D4×C79—28no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—24no—
290C2×C4×C79—24no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D412yes—
297C2×C4×C79C22×D412yes—
298C2×C4×C79C22×D412yes—
299C2×C4×C79C22×D411yescharacteristic
300C2×C4×C79C2×#4112yes—
301C2×C4×C792−1+412yes—
302C2×C4×C79C2511yescharacteristic
303C22⋊D79—48no—
304C22⋊D79—84no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—42no—
313C2×Dic79—42no—
314C2×Dic79—42no—
315C2×Dic79—42no—
316C2×Dic79—42no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79—84no—
320C2×Dic79—84no—
321C2×Dic79—84no—
322D316—22no—
323D316—22no—
324D316—42no—
325C4×D79—84no—
326Dic158—22no—
327Dic158—22no—
328Dic158—42no—
329Dic158—84no—
330C8×C79—22no—
331C8×C79—22no—
332C8×C79—22no—
333C8×C79C2×#4114yes—
334C22×C79—28no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—44no—
341C22×C79#54712yes—
342C22×C79C2×#13714yes—
343C22×C79C2×#13712yes—
344C22×C79#57612yes—
345C22×C79C23×D411yescharacteristic
346C2×D79—42no—
347C2×D79—42no—
348C2×D79—42no—
349C2×D79—84no—
350C4×C79—22no—
351C4×C79—22no—
352C4×C79—22no—
353C4×C79—22no—
354C4×C79#54712yes—
355C4×C79C22×#4111yescharacteristic
356C4×C79C2×2−1+411yescharacteristic
357Dic79—42no—
358Dic79—42no—
359Dic79—42no—
360Dic79—42no—
361Dic79—42no—
362Dic79—42no—
363Dic79—42no—
364C2×#3346—791nomaximal, Sylow
365C2×C79—24no—
366C2×C79—42no—
367C2×C79#334614yescomplemented
368C2×C79C2×#54711yescharacteristic
369C2×C79C22×#13711yescharacteristic
370C2×C79C2×#57611yescharacteristic
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×#435D7911yescharacteristic, complemented
386C2×#428—791no—
387C22×#107—791no—
388C79C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—791no—
390C22×M16C2×D7911yescharacteristic
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—1581no—
411C2×C4×D4—1581no—
412C2×C4×D4C2×D7911yescharacteristic
413C2×#117—791no—
414C22×C4⋊C4—791no—
415C22×C4⋊C4—791no—
416C22×C4⋊C4—791no—
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#435C2×D7918yescomplemented
428#428—798no—
429C2×#107—791no—
430C2×#107—791no—
431C2×#107—791no—
432C2×#107—791no—
433C2×#107—798no—
434C2×#107—791no—
435C2×#107—791no—
436C2×#106—791no—
437C2×#106—791no—
438C2×#106—791no—
439C2×C4⋊C8C2×D7911yescharacteristic
440C2×#103—791no—
441C2×#103—791no—
442C2×#103—791no—
443C2×#102—791no—
444C2×#102—791no—
445C2×#102—791no—
446C2×C22⋊C8C2×D7911yescharacteristic
447C2×C22⋊C8C2×D7911yescharacteristic
448C2×#97C2×D7911yescharacteristic
449C22×Q8—791no—
450C22×Q8—1581no—
451C22×D4—791no—
452C22×D4—1581no—
453C22×D4—1581no—
454C22×D4D31611yescharacteristic
455C23×C4—1581no—
456C23×C4—1581no—
457C23×C4—1581no—
458C23×C4—1581no—
459C23×C4C22×D7911yescharacteristic
460C23×C4C22×D7911yescharacteristic
461C2×SD16—794no—
462C2×SD16—1584no—
463C2×M16—24no—
464C2×M16C22×D7914yes—
465C22×C8—24no—
466C22×C8C22×D7911yescharacteristic
467C22×C8C22×D7914yes—
468C22×C8C22×D7911yescharacteristic
469C22×C8C22×D7911yescharacteristic
470C22×C8C22×D7911yescharacteristic
471C4⋊Q8—794no—
472C4⋊Q8—1582no—
473#126—1588no—
474#125—794no—
475#125—1588no—
476#125—1582no—
477#123—1588no—
478C22⋊Q8—794no—
479C22⋊Q8—794no—
480C22⋊Q8—1582no—
481C22⋊Q8—1582no—
482C22⋊Q8—1588no—
483C22⋊Q8—1588no—
484#121—794no—
485#121—794no—
486#121—1588no—
487#121—1582no—
488#121—1582no—
489C4×Q8—794no—
490C4×Q8—1582no—
491C4×D4—794no—
492C4×D4—1588no—
493C4×D4—1588no—
494C4×D4—1582no—
495C4×D4D31614yes—
496C4×D4C22×D7914yes—
497#117—794no—
498#117—1582no—
499C2×C4⋊C4—791no—
500C2×C4⋊C4—791no—
501C2×C4⋊C4—791no—
502C2×C4⋊C4—791no—
503C2×C4⋊C4—791no—
504C2×C4⋊C4—794no—
505C2×C4⋊C4—794no—
506C2×C4⋊C4—794no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—1581no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1582no—
512C2×C4⋊C4—1582no—
513C2×C4⋊C4—1582no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4—1581no—
520C2×C4⋊C4D31611yescharacteristic
521C2×C22⋊C4—1581no—
522C2×C22⋊C4—1581no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4D31611yescharacteristic
528C2×C22⋊C4D31611yescharacteristic
529C2×C42—1581no—
530C2×C42—1581no—
531C2×C42C22×D7911yescharacteristic
532#107—794no—
533#107—794no—
534#107—794no—
535#107—794no—
536#107—794no—
537#107—794no—
538#106—794no—
539#106—794no—
540#106—794no—
541C4⋊C8C22×D7914yes—
542#103—794no—
543#103—794no—
544#103—794no—
545#102—794no—
546#102—794no—
547#102—794no—
548C22⋊C8C22×D7914yes—
549C22⋊C8C22×D7914yes—
550#97C22×D7914yes—
551C24—1581no—
552C24C2×D31611yescharacteristic
553C24C2×D31611yescharacteristic
554C2×Q8—792no—
555C2×Q8—6322no—
556C2×Q8—1582no—
557C2×Q8—1582no—
558C2×Q8—1581no—
559C2×Q8—1584no—
560C2×D4—24no—
561C2×D4—3164no—
562C2×D4—792no—
563C2×D4—6322no—
564C2×D4—1584no—
565C2×D4—1584no—
566C2×D4—1582no—
567C2×D4—1582no—
568C2×D4—1581no—
569C2×D4C2×D31614yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—6322no—
575C22×C4—6322no—
576C22×C4—6322no—
577C22×C4—6322no—
578C22×C4—1581no—
579C22×C4—1581no—
580C22×C4—1581no—
581C22×C4—1581no—
582C22×C4—1581no—
583C22×C4—1581no—
584C22×C4—1581no—
585C22×C4—1584no—
586C22×C4—1584no—
587C22×C4—1584no—
588C22×C4—1584no—
589C22×C4C2×D31612yes—
590C22×C4C2×D31612yes—
591C22×C4C2×D31611yescharacteristic
592C22×C4C2×D31611yescharacteristic
593C22×C4C2×D31611yescharacteristic
594C22×C4C2×D31611yescharacteristic
595C22×C4C23×D7912yes—
596C22×C4C23×D7912yes—
597C22×C4C23×D7911yescharacteristic
598SD16—1588no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#1192962314yes—
605C2×C8C23×D7912yes—
606C2×C8C23×D7912yes—
607C2×C8C23×D7912yes—
608C2×C8C23×D7912yes—
609C4⋊C4—792no—
610C4⋊C4—792no—
611C4⋊C4—792no—
612C4⋊C4—792no—
613C4⋊C4—792no—
614C4⋊C4—792no—
615C4⋊C4—1584no—
616C4⋊C4—1584no—
617C4⋊C4—1584no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1581no—
621C4⋊C4—1581no—
622C4⋊C4—1581no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1581no—
626C4⋊C4—1581no—
627C4⋊C4—1584no—
628C4⋊C4—1581no—
629C4⋊C4—1584no—
630C4⋊C4C2×D31614yes—
631C22⋊C4—1584no—
632C22⋊C4—1584no—
633C22⋊C4—1584no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4C2×D31614yes—
638C22⋊C4C2×D31614yes—
639C42—1584no—
640C42—1584no—
641C42C2×D31612yes—
642C42C23×D7912yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—3162no—
649C23—3162no—
650C23—3162no—
651C23—1582no—
652C23#1457919414yes—
653C23C22×D31612yes—
654C23C22×D31612yes—
655C23C22×D31611yescharacteristic
656Q8—3162no—
657Q8—6324no—
658Q8—1582no—
659Q8—1582no—
660D4—28no—
661D4—3168no—
662D4—3162no—
663D4—6324no—
664D4—1582no—
665D4—1582no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—3162no—
677C2×C4—3162no—
678C2×C4—3162no—
679C2×C4—3162no—
680C2×C4—3162no—
681C2×C4—3162no—
682C2×C4—3162no—
683C2×C4—6324no—
684C2×C4—6324no—
685C2×C4—6324no—
686C2×C4—6324no—
687C2×C4—1582no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4C22×D31612yes—
695C2×C4C22×D31612yes—
696C2×C4C22×D31612yes—
697C2×C4C22×D31612yes—
698C2×C4C22×D31611yescharacteristic
699C2×C4C2×#1192962312yes—
700C2×C4#1457920812yes—
701C2×C4C24×D7911yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#1192962314yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—3162no—
714C22—3162no—
715C22—3162no—
716C22—6324no—
717C22#1909921712yes—
718C22C2×#1457919414yes—
719C22C2×#1457919412yes—
720C22#1909936812yes—
721C22C23×D31611yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—3162no—
727C4—3162no—
728C4—3162no—
729C4—3162no—
730C4—3162no—
731C4—3162no—
732C4—3162no—
733C4#1909921712yes—
734C4C22×#1192962311yescharacteristic
735C4C2×#1457920811yescharacteristic
736C2—24no—
737C2—42no—
738C2—6322no—
739C2#2377588714yesdirect product factor
740C2C2×#1909921711yescharacteristic
741C2C22×#1457919411yescharacteristic
742C2C2×#1909936811yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#435×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099259C2
hypercenterC2×#435D79
hypocenterC79C2×#3346
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#19099270C2semidirect
3. #23775887C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098899C2semidirect
6. C2×#19098882C2semidirect
7. C2×#19098905C2semidirect
8. C2×#19098877C2semidirect
9. C2×#19098871C2semidirect
10. C2×#19098844C2semidirect
11. C2×#19098809C2semidirect
12. C2×#19098792C2semidirect
13. C2×#19098665C2semidirect
14. C2×#19098605C2semidirect
15. C22×#14579095C2semidirect
16. C2×#435×C79C2semidirect
19. #19099270C22semidirect
42. #19098972C22semidirect
43. #19098905C22semidirect
44. #19098899C22semidirect
45. #19098882C22semidirect
46. #19098877C22semidirect
47. #19098871C22semidirect
48. #19098844C22semidirect
49. #19098809C22semidirect
50. #19098792C22semidirect
51. #19098665C22semidirect
52. #19098605C22semidirect
59. C2×#14579095C22semidirect
72. #435×C79C22semidirect
367. C2×C79#3346semidirect
385. C2×#435D79semidirect
388. C79C2×#3346semidirect
427. #435C2×D79semidirect
739. C2#23775887direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992702
C2×#190992592
#237758872
C2×#190989722
C2×#190988992
C2×#190988822
C2×#190989052
C2×#190988772
C2×#190988712
C2×#190988442
C2×#190988092
C2×#190987922
C2×#190986652
C2×#190986052
C22×#145790952
C2×#435×C792
C2×#334679