Finite Group Databasebeta

← C2×#23773694 #35156619

Subgroups — C2×#23773694 #35156619

Order 20224.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099173C211yesmaximal, characteristic
2C2×#19099041C211yesmaximal, characteristic
3#23773694C2116yesmaximal, direct product factor
4C2×#19098905C211yesmaximal, characteristic
5C2×#19098901C211yesmaximal, characteristic
6C2×#19098872C211yesmaximal, characteristic, complemented
7C2×#19098868C211yesmaximal, characteristic, complemented
8C2×#19098771C211yesmaximal, characteristic, complemented
9C2×#19098771C211yesmaximal, characteristic, complemented
10C2×#19098719C211yesmaximal, characteristic
11C2×#19098670C211yesmaximal, characteristic, complemented
12C2×#19098667C211yesmaximal, characteristic, complemented
13C2×Q16×Dic79C211yesmaximal, characteristic, complemented
14C2×#19098655C211yesmaximal, characteristic, complemented
15C2×#19098621C211yesmaximal, characteristic
16C2×#451×C79C211yesmaximal, characteristic
17C22×#11929614C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19#19099173—24no—
20#19099173C2218yes—
21C2×#14579159C2211yescharacteristic
22C2×#14579154—21no—
23C2×#14579154—21no—
24C2×#14579152—21no—
25C2×#14579152C2211yescharacteristic
26C2×#14579151—21no—
27C2×#14579140C2211yescharacteristic
28#19099041—24no—
29#19099041C2218yes—
30C2×Q8×Dic79—21no—
31C2×Q8×Dic79—21no—
32C2×Q8×Dic79C2211yescharacteristic
33C2×Q8×Dic79C2211yescharacteristic
34C2×Q8×Dic79C2211yescharacteristic
35C2×Q8×Dic79C2211yescharacteristic
36C2×Q8×Dic79C2211yescharacteristic
37C2×#14579126C2211yescharacteristic
38C2×#14579120—21no—
39C2×#14579120—21no—
40C2×#14579120C2211yescharacteristic
41C2×#14579120C2211yescharacteristic
42#19098905C2218yes—
43#19098901C2218yes—
44#19098872C2218yescomplemented
45#19098868C2218yescomplemented
46#19098771C2218yescomplemented
47#19098771C2218yescomplemented
48#19098719C2218yes—
49#19098670C2218yescomplemented
50#19098667C2218yescomplemented
51Q16×Dic79C2218yescomplemented
52#19098655C2218yescomplemented
53#19098621C2218yes—
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579085C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C23×Q8×C79C2211yescharacteristic
70C22×Q16×C79C2211yescharacteristic
71C22×Q16×C79C2211yescharacteristic
72C2×C22⋊Q8×C79C2211yescharacteristic
73#451×C79C2218yes—
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C22×Dic158C2311yescharacteristic
78C2×#11929614—24no—
79C2×#11929614—24no—
80C2×#11929614C2314yes—
81C2×#11929614C2314yes—
82C22×C79⋊C8C2311yescharacteristic
83C22×C79⋊C8C2311yescharacteristic
84#14579159—22no—
85#14579159C2314yes—
86#14579154—28no—
87#14579154—28no—
88#14579152—28no—
89#14579152—22no—
90#14579152C2314yes—
91#14579151—28no—
92#14579140—22no—
93#14579140C2314yes—
94Q8×Dic79—28no—
95Q8×Dic79—28no—
96Q8×Dic79—22no—
97Q8×Dic79—22no—
98Q8×Dic79—22no—
99Q8×Dic79—22no—
100Q8×Dic79—22no—
101Q8×Dic79C2314yes—
102Q8×Dic79C2314yes—
103Q8×Dic79C2314yes—
104Q8×Dic79C2314yes—
105Q8×Dic79C2314yes—
106#14579126—22no—
107#14579126C2314yes—
108#14579120—22no—
109#14579120—28no—
110#14579120—28no—
111#14579120D414yes—
112#14579120C2314yes—
113#14579120C2314yes—
114C2×C4⋊Dic79—21no—
115C2×C4⋊Dic79—21no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79D411yescharacteristic
121C2×C4⋊Dic79D411yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
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×C22⋊Dic79—21no—
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79D411yescharacteristic
133C2×C22⋊Dic79D411yescharacteristic
134C2×C4×Dic79—21no—
135C2×C4×Dic79—21no—
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142C2×C4×Dic79C2311yescharacteristic
143#14579095C2314yes—
144#14579094C2314yes—
145#14579093C2314yes—
146#14579092C2314yes—
147Dic79⋊C8C2314yes—
148Dic79⋊C8C2314yes—
149#14579086C2314yes—
150#14579086C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579085C2314yes—
154#14579085C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156#14579071C2314yes—
157C8×Dic79C2314yes—
158C22×Q8×C79—24no—
159C22×Q8×C79—24no—
160C22×Q8×C79—21no—
161C22×Q8×C79—22no—
162C22×Q8×C79C2314yes—
163C22×Q8×C79C2311yescharacteristic
164C22×Q8×C79C2311yescharacteristic
165C22×Q8×C79C2311yescharacteristic
166C23×C4×C79—21no—
167C23×C4×C79C2311yescharacteristic
168C2×Q16×C79—24no—
169C2×Q16×C79—24no—
170C2×Q16×C79C2314yes—
171C2×Q16×C79C2314yes—
172C22×C8×C79C2311yescharacteristic
173C22×C8×C79C2311yescharacteristic
174C22⋊Q8×C79—22no—
175C22⋊Q8×C79C2314yes—
176C2×C4⋊C4×C79—21no—
177C2×C4⋊C4×C79C2311yescharacteristic
178C2×C22⋊C4×C79—21no—
179#103×C79C2314yes—
180#103×C79C2314yes—
181C22⋊C8×C79C2314yes—
182C2×Dic158—21no—
183C2×Dic158—22no—
184C2×Dic158—22no—
185C2×Dic158C2412yes—
186C22×Dic79—21no—
187C22×Dic79—21no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79C2×D411yescharacteristic
191C22×Dic79C2×D411yescharacteristic
192C22×Dic79C2×D411yescharacteristic
193C22×Dic79C2×D411yescharacteristic
194#11929614—28no—
195#11929614—28no—
196C2×C79⋊C8—22no—
197C2×C79⋊C8—22no—
198C2×C79⋊C8C2412yes—
199C2×C79⋊C8C2412yes—
200C4⋊Dic79—24no—
201C4⋊Dic79—24no—
202C4⋊Dic79—24no—
203C4⋊Dic79—24no—
204C4⋊Dic79—24no—
205C4⋊Dic79—24no—
206C4⋊Dic79—21no—
207C4⋊Dic79—21no—
208C4⋊Dic79—21no—
209C4⋊Dic79C2×D414yes—
210C4⋊Dic79C2×D414yes—
211C4⋊Dic79C2412yes—
212C4⋊Dic79C2412yes—
213C4⋊Dic79C2412yes—
214Dic79⋊C4—24no—
215Dic79⋊C4—24no—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219C22⋊Dic79—24no—
220C22⋊Dic79—24no—
221C22⋊Dic79C2×D414yes—
222C22⋊Dic79C2×D414yes—
223C4×Dic79—24no—
224C4×Dic79—24no—
225C4×Dic79—24no—
226C4×Dic79—24no—
227C4×Dic79—24no—
228C4×Dic79—24no—
229C4×Dic79—24no—
230C4×Dic79C2×D412yes—
231C4×Dic79C2×D412yes—
232C4×Dic79C2412yes—
233C4×Dic79C2412yes—
234C24×C79C2×D411yescharacteristic
235C2×Q8×C79—216no—
236C2×Q8×C79—28no—
237C2×Q8×C79—28no—
238C2×Q8×C79—28no—
239C2×Q8×C79—24no—
240C2×Q8×C79—21no—
241C2×Q8×C79—21no—
242C2×Q8×C79—21no—
243C2×Q8×C79—22no—
244C2×Q8×C79—22no—
245C2×Q8×C79—22no—
246C2×Q8×C79—22no—
247C2×Q8×C79#4114yes—
248C2×Q8×C79#4114yes—
249C2×Q8×C79C2412yes—
250C2×Q8×C79C2412yes—
251C2×Q8×C79C2412yes—
252C22×C4×C79—28no—
253C22×C4×C79—21no—
254C22×C4×C79—21no—
255C22×C4×C79—24no—
256C22×C4×C79—22no—
257C22×C4×C79—22no—
258C22×C4×C79—21no—
259C22×C4×C79—21no—
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D412yes—
262C22×C4×C79C2412yes—
263C22×C4×C79C2411yescharacteristic
264Q16×C79—28no—
265Q16×C79—28no—
266C2×C8×C79—22no—
267C2×C8×C79—22no—
268C2×C8×C79C2412yes—
269C2×C8×C79C2412yes—
270C4⋊C4×C79—24no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79C2412yes—
273C22⋊C4×C79—24no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79C22×D412yes—
278C23×C79C22×D411yescharacteristic
279Q8×C79—216no—
280Q8×C79—24no—
281Q8×C79—24no—
282Q8×C79—22no—
283Q8×C79—22no—
284Q8×C79—22no—
285Q8×C79—22no—
286Q8×C79—42no—
287Q8×C79C2×#4114yes—
288Q8×C79C2×#4114yes—
289C2×C4×C79—216no—
290C2×C4×C79—24no—
291C2×C4×C79—24no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—24no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—42no—
301C2×C4×C79—42no—
302C2×C4×C79C22×D412yes—
303C2×C4×C79C22×D411yescharacteristic
304C2×C4×C79C2×#4112yes—
305C2×C4×C79C2×#4112yes—
306C2×C4×C79C2511yescharacteristic
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—42no—
316C2×Dic79—42no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79C22×D412yes—
320C2×Dic79C22×D412yes—
321C2×Dic79C22×D412yes—
322C2×Dic79C22×D412yes—
323Dic158—22no—
324Dic158—22no—
325Dic158—42no—
326C8×C79—22no—
327C8×C79—22no—
328C79⋊C8—22no—
329C79⋊C8—22no—
330C22×C79—22no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—44no—
334C22×C79#52512yes—
335C22×C79#57812yes—
336C22×C79#57812yes—
337C22×C79C23×D411yescharacteristic
338C4×C79—24no—
339C4×C79—24no—
340C4×C79—22no—
341C4×C79—42no—
342C4×C79—42no—
343C4×C79#52512yes—
344C4×C79C22×#4111yescharacteristic
345C4×C79C22×#4111yescharacteristic
346Dic79—22no—
347Dic79—22no—
348Dic79—22no—
349Dic79—22no—
350Dic79—42no—
351Dic79—42no—
352Dic79—42no—
353Dic79—42no—
354C2×#3127—791nomaximal, Sylow
355C2×C79—42no—
356C2×C79#312714yescomplemented
357C2×C79C2×#52511yescharacteristic
358C2×C79C2×#57811yescharacteristic
359C2×C79C2×#57811yescharacteristic
360C2×#541—791no—
361C2×#519—791no—
362#3127—7916no—
363C2×#485—791no—
364C2×#485—791no—
365C2×#479—791no—
366C2×#479—791no—
367C2×#462—791no—
368C2×#462—791no—
369C2×#451—791no—
370C2×#451D7911yescharacteristic
371C2×#441—791no—
372C2×#441—791no—
373C2×C4×Q16—791no—
374C2×C4×Q16—791no—
375C2×#433—791no—
376C79C2×#312711yescharacteristic, complemented, Sylow
377C23×Q8C2×D7911yescharacteristic
378C22×Q16—791no—
379C22×Q16—791no—
380C22×Q16C2×D7911yescharacteristic
381C22×Q16C2×D7911yescharacteristic
382#541—798no—
383#541—1584no—
384C2×C4⋊Q8—791no—
385C2×#126—1581no—
386C2×#126—1581no—
387C2×#125—791no—
388C2×#125—1581no—
389C2×#125—1581no—
390C2×C22⋊Q8—791no—
391C2×C22⋊Q8C2×D7911yescharacteristic
392#519—798no—
393#519—1584no—
394C2×C4×Q8—791no—
395C2×C4×Q8—791no—
396C2×C4×Q8—791no—
397C2×C4×Q8—791no—
398C2×C4×Q8—791no—
399C2×C4×Q8—791no—
400C2×C4×Q8—1581no—
401C2×C4×Q8—1581no—
402C2×#117—791no—
403C2×#117—791no—
404C2×#117—1581no—
405C2×#117—1581no—
406#485—798no—
407#485—798no—
408#479—798no—
409#479—798no—
410#462—798no—
411#462—798no—
412#451—798no—
413#451C2×D7918yes—
414#441—798no—
415#441—798no—
416C4×Q16—798no—
417C4×Q16—798no—
418#433—798no—
419C2×#107—791no—
420C2×#107—791no—
421C2×#106—791no—
422C2×#106—791no—
423C2×C4⋊C8—791no—
424C2×C4⋊C8—791no—
425C2×#103—791no—
426C2×#103—791no—
427C2×#103—791no—
428C2×#103—791no—
429C2×#103—791no—
430C2×#103—791no—
431C2×#103C2×D7911yescharacteristic
432C2×#103C2×D7911yescharacteristic
433C2×C22⋊C8—791no—
434C2×C22⋊C8C2×D7911yescharacteristic
435C2×#97—791no—
436C2×C4×C8—791no—
437C22×Q8—24no—
438C22×Q8—24no—
439C22×Q8—21no—
440C22×Q8—22no—
441C22×Q8—791no—
442C22×Q8C22×D7911yescharacteristic
443C22×Q8C22×D7914yes—
444C22×Q8C22×D7911yescharacteristic
445C22×Q8C22×D7911yescharacteristic
446C23×C4—21no—
447C23×C4C22×D7911yescharacteristic
448C2×Q16—24no—
449C2×Q16—24no—
450C2×Q16—794no—
451C2×Q16—794no—
452C2×Q16—1584no—
453C2×Q16—1584no—
454C2×Q16C22×D7914yes—
455C2×Q16C22×D7914yes—
456C22×C8—791no—
457C22×C8—791no—
458C22×C8C22×D7911yescharacteristic
459C22×C8C22×D7911yescharacteristic
460C4⋊Q8—794no—
461C4⋊Q8—1582no—
462#126—1588no—
463#126—1588no—
464#125—794no—
465#125—1582no—
466#125—1588no—
467#125—1588no—
468C22⋊Q8—22no—
469C22⋊Q8—794no—
470C22⋊Q8—1582no—
471C22⋊Q8C22×D7914yes—
472C4×Q8—794no—
473C4×Q8—794no—
474C4×Q8—794no—
475C4×Q8—794no—
476C4×Q8—794no—
477C4×Q8—794no—
478C4×Q8—1582no—
479C4×Q8—1582no—
480C4×Q8—1582no—
481C4×Q8—1582no—
482C4×Q8—1582no—
483C4×Q8—1582no—
484C4×Q8—1588no—
485C4×Q8—1588no—
486#117—794no—
487#117—794no—
488#117—794no—
489#117—1588no—
490#117—1588no—
491#117—1582no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—791no—
494C2×C4⋊C4—791no—
495C2×C4⋊C4—791no—
496C2×C4⋊C4—791no—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4—1581no—
509C2×C4⋊C4C22×D7911yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—791no—
512C2×C22⋊C4—791no—
513C2×C22⋊C4—1581no—
514C2×C22⋊C4—1581no—
515C2×C42—791no—
516C2×C42—791no—
517C2×C42—1581no—
518C2×C42—1581no—
519C2×C42—1581no—
520C2×C42—1581no—
521C2×C42—1581no—
522C2×C42—1581no—
523C2×C42—1581no—
524#107—794no—
525#107—794no—
526#106—794no—
527#106—794no—
528C4⋊C8—794no—
529C4⋊C8—794no—
530#103—794no—
531#103—794no—
532#103—794no—
533#103—794no—
534#103—794no—
535#103—794no—
536#103C22×D7914yes—
537#103C22×D7914yes—
538C22⋊C8—794no—
539C22⋊C8C22×D7914yes—
540#97—794no—
541C4×C8—794no—
542C24D4×D7911yescharacteristic
543C2×Q8—216no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—28no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—24no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—792no—
556C2×Q8—1582no—
557C2×Q8—1582no—
558C2×Q8—1581no—
559C2×Q8#1192962314yes—
560C2×Q8#1192962314yes—
561C2×Q8C23×D7912yes—
562C2×Q8C23×D7912yes—
563C2×Q8C23×D7912yes—
564C22×C4—28no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—791no—
573C22×C4—791no—
574C22×C4—791no—
575C22×C4—791no—
576C22×C4—1581no—
577C22×C4—1581no—
578C22×C4—1581no—
579C22×C4—1581no—
580C22×C4D4×D7912yes—
581C22×C4D4×D7911yescharacteristic
582C22×C4C23×D7912yes—
583C22×C4C23×D7911yescharacteristic
584Q16—28no—
585Q16—28no—
586Q16—1588no—
587Q16—1588no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—792no—
591C2×C8—792no—
592C2×C8—1582no—
593C2×C8—1582no—
594C2×C8C23×D7912yes—
595C2×C8C23×D7912yes—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—794no—
599C4⋊C4—794no—
600C4⋊C4—792no—
601C4⋊C4—792no—
602C4⋊C4—792no—
603C4⋊C4—1584no—
604C4⋊C4—1584no—
605C4⋊C4—1584no—
606C4⋊C4—1584no—
607C4⋊C4—1584no—
608C4⋊C4—1584no—
609C4⋊C4—1584no—
610C4⋊C4—1584no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1581no—
615C4⋊C4—1581no—
616C4⋊C4—1581no—
617C4⋊C4C23×D7912yes—
618C22⋊C4—24no—
619C22⋊C4—794no—
620C22⋊C4—794no—
621C22⋊C4—1584no—
622C22⋊C4—1584no—
623C42—792no—
624C42—792no—
625C42—792no—
626C42—792no—
627C42—1584no—
628C42—1584no—
629C42—1584no—
630C42—1584no—
631C42—1584no—
632C42—1584no—
633C42—1584no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23C2×D4×D7912yes—
638C23C2×D4×D7911yescharacteristic
639Q8—216no—
640Q8—24no—
641Q8—24no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8—42no—
647Q8—3162no—
648Q8—1582no—
649Q8—1582no—
650Q8C2×#1192962314yes—
651Q8C2×#1192962314yes—
652C2×C4—216no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—3162no—
666C2×C4—3162no—
667C2×C4—3162no—
668C2×C4—3162no—
669C2×C4—792no—
670C2×C4—792no—
671C2×C4—792no—
672C2×C4—792no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1582no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4—1582no—
681C2×C4C2×D4×D7912yes—
682C2×C4C2×D4×D7911yescharacteristic
683C2×C4C2×#1192962312yes—
684C2×C4C2×#1192962312yes—
685C2×C4C24×D7911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1582no—
689C8—1582no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—44no—
694C22#1909906912yes—
695C22#1909937612yes—
696C22#1909937912yes—
697C22C22×D4×D7911yescharacteristic
698C4—24no—
699C4—24no—
700C4—22no—
701C4—42no—
702C4—42no—
703C4—3162no—
704C4—3162no—
705C4—3162no—
706C4—3162no—
707C4—1582no—
708C4—1582no—
709C4—1582no—
710C4—1582no—
711C4#1909906912yes—
712C4C22×#1192962311yescharacteristic
713C4C22×#1192962311yescharacteristic
714C2—42no—
715C2#2377369414yesdirect product factor
716C2C2×#1909906911yescharacteristic
717C2C2×#1909937611yescharacteristic
718C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#451×C79C2
socleC23×C79C22×D4
prime radicalC24×C79C2×D4
hypercenterC2×#451D79
hypocenterC79C2×#3127
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #23773694C2direct (N × H)
6. C2×#19098872C2semidirect
7. C2×#19098868C2semidirect
8. C2×#19098771C2semidirect
9. C2×#19098771C2semidirect
11. C2×#19098670C2semidirect
12. C2×#19098667C2semidirect
13. C2×Q16×Dic79C2semidirect
14. C2×#19098655C2semidirect
44. #19098872C22semidirect
45. #19098868C22semidirect
46. #19098771C22semidirect
47. #19098771C22semidirect
49. #19098670C22semidirect
50. #19098667C22semidirect
51. Q16×Dic79C22semidirect
52. #19098655C22semidirect
356. C2×C79#3127semidirect
376. C79C2×#3127semidirect
715. C2#23773694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991732
C2×#190990412
#237736942
C2×#190989052
C2×#190989012
C2×#190988722
C2×#190988682
C2×#190987712
C2×#190987192
C2×#190986702
C2×#190986672
C2×Q16×Dic792
C2×#190986552
C2×#190986212
C2×#451×C792
C2×#312779