Finite Group Databasebeta

← C2×#23773698 #35156623

Subgroups — C2×#23773698 #35156623

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×#19099174C211yesmaximal, characteristic
2C2×#19099039C211yesmaximal, characteristic
3#23773698C2116yesmaximal, direct product factor
4C2×#19098903C211yesmaximal, characteristic
5C2×#19098902C211yesmaximal, characteristic
6C2×#19098871C211yesmaximal, characteristic, complemented
7C2×#19098870C211yesmaximal, characteristic, complemented
8C2×#19098770C211yesmaximal, characteristic, complemented
9C2×#19098717C211yesmaximal, characteristic
10C2×#19098717C211yesmaximal, characteristic
11C2×#19098670C211yesmaximal, characteristic, complemented
12C2×#19098667C211yesmaximal, characteristic, complemented
13C2×Q16×Dic79C211yesmaximal, characteristic, complemented
14C2×#19098655C211yesmaximal, characteristic, complemented
15C2×#19098623C211yesmaximal, characteristic
16C2×#462×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20#19099174—24no—
21#19099174C2218yes—
22C2×#14579156—21no—
23C2×#14579156—21no—
24C2×#14579153C2211yescharacteristic
25C2×#14579151—21no—
26C2×#14579151—21no—
27C2×#14579137C2211yescharacteristic
28C2×#14579137C2211yescharacteristic
29#19099039—24no—
30#19099039C2218yes—
31C2×Q8×Dic79C2211yescharacteristic
32C2×Q8×Dic79C2211yescharacteristic
33C2×Q8×Dic79C2211yescharacteristic
34C2×C4×Dic158—21no—
35C2×C4×Dic158C2211yescharacteristic
36C2×#14579126—21no—
37C2×#14579126C2211yescharacteristic
38C2×#14579119—21no—
39C2×#14579119C2211yescharacteristic
40C2×#14579118—21no—
41C2×#14579118C2211yescharacteristic
42#19098903C2218yes—
43#19098902C2218yes—
44#19098871C2218yescomplemented
45#19098870C2218yescomplemented
46#19098770C2218yescomplemented
47#19098717C2218yes—
48#19098717C2218yes—
49#19098670C2218yescomplemented
50#19098667C2218yescomplemented
51Q16×Dic79C2218yescomplemented
52#19098655C2218yescomplemented
53#19098623C2218yes—
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×C4⋊(C79⋊C8)C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×(C2×D79)⋊C8C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C22×Q16×C79C2211yescharacteristic
71C2×C4⋊Q8×C79C2211yescharacteristic
72C2×C4×Q8×C79C2211yescharacteristic
73#462×C79C2218yescomplemented
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C2×Q8×D79—24no—
80C2×Q8×D79—24no—
81C2×Q8×D79—22no—
82C2×Q8×D79C2314yes—
83C22×C4×D79—21no—
84C22×C4×D79C2311yescharacteristic
85C2×#11929614—24no—
86C2×#11929614—24no—
87C2×#11929614C2314yes—
88C2×#11929614C2314yes—
89C22×C79⋊C8C2311yescharacteristic
90C22×C79⋊C8C2311yescharacteristic
91#14579156—28no—
92#14579156—28no—
93#14579153—22no—
94#14579153C2314yes—
95#14579151—28no—
96#14579151—28no—
97#14579137—22no—
98#14579137—22no—
99#14579137C2314yes—
100#14579137C2314yes—
101Q8×Dic79—22no—
102Q8×Dic79—22no—
103Q8×Dic79—22no—
104Q8×Dic79C2314yes—
105Q8×Dic79C2314yes—
106Q8×Dic79C2314yes—
107C4×Dic158—22no—
108C4×Dic158—28no—
109C4×Dic158C2314yes—
110#14579126—28no—
111#14579126—22no—
112#14579126C2314yes—
113#14579119—22no—
114#14579119—28no—
115#14579119C2314yes—
116#14579118—28no—
117#14579118D414yes—
118#14579118C2314yes—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
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×Dic79⋊C4—21no—
131C2×Dic79⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4D411yescharacteristic
137C2×(C2×D79)⋊C4D411yescharacteristic
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79C2311yescharacteristic
145#14579095C2314yes—
146#14579094C2314yes—
147#14579093C2314yes—
148#14579092C2314yes—
149C4⋊(C79⋊C8)C2314yes—
150#14579086C2314yes—
151#14579086C2314yes—
152#14579085C2314yes—
153#14579085C2314yes—
154#14579085C2314yes—
155#14579085C2314yes—
156(C2×D79)⋊C8C2314yes—
157(C2×D79)⋊C8C2314yes—
158#14579071C2314yes—
159C8×Dic79C2314yes—
160C22×Q8×C79C2311yescharacteristic
161C22×Q8×C79C2311yescharacteristic
162C22×Q8×C79C2311yescharacteristic
163C2×Q16×C79—24no—
164C2×Q16×C79—24no—
165C2×Q16×C79C2314yes—
166C2×Q16×C79C2314yes—
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C4⋊Q8×C79—22no—
170C4⋊Q8×C79C2314yes—
171C4×Q8×C79—22no—
172C4×Q8×C79C2314yes—
173C2×C4⋊C4×C79—21no—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79—21no—
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C42×C79—21no—
178C2×C42×C79C2311yescharacteristic
179C4⋊C8×C79C2314yes—
180#103×C79C2314yes—
181#103×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183C2×Dic158—28no—
184C2×Dic158—24no—
185C2×Dic158—21no—
186C2×Dic158—22no—
187C2×Dic158#4114yes—
188C2×Dic158C2412yes—
189Q8×D79—216no—
190Q8×D79—28no—
191Q8×D79—28no—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C2×C4×D79—28no—
200C2×C4×D79—24no—
201C2×C4×D79—22no—
202C2×C4×D79—22no—
203C2×C4×D79C2×D412yes—
204C2×C4×D79C2412yes—
205#11929614—28no—
206#11929614—28no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8—22no—
209C2×C79⋊C8C2412yes—
210C2×C79⋊C8C2412yes—
211C4⋊Dic79—24no—
212C4⋊Dic79—24no—
213C4⋊Dic79—24no—
214C4⋊Dic79—21no—
215C4⋊Dic79—21no—
216C4⋊Dic79—21no—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219C4⋊Dic79C2412yes—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4C2×D414yes—
227Dic79⋊C4C2×D414yes—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4C2×D414yes—
232(C2×D79)⋊C4C2×D414yes—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79—24no—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C4×Dic79C2×D412yes—
240C4×Dic79C2412yes—
241C2×Q8×C79—21no—
242C2×Q8×C79—21no—
243C2×Q8×C79—21no—
244C2×Q8×C79—22no—
245C2×Q8×C79—22no—
246C2×Q8×C79—22no—
247C2×Q8×C79—22no—
248C2×Q8×C79—22no—
249C2×Q8×C79#4114yes—
250C2×Q8×C79C2412yes—
251C2×Q8×C79C2412yes—
252C2×Q8×C79C2412yes—
253C22×C4×C79—21no—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79—21no—
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2411yescharacteristic
260Q16×C79—28no—
261Q16×C79—28no—
262C2×C8×C79—22no—
263C2×C8×C79—22no—
264C2×C8×C79C2412yes—
265C2×C8×C79C2412yes—
266C4⋊C4×C79—24no—
267C4⋊C4×C79—24no—
268C4⋊C4×C79—24no—
269C4⋊C4×C79—21no—
270C4⋊C4×C79C2412yes—
271C42×C79—24no—
272C42×C79C2×D412yes—
273C42×C79C2412yes—
274C23×C79C22×D411yescharacteristic
275C22×D79—22no—
276C22×D79—22no—
277C22×D79—22no—
278C22×D79C22×D412yes—
279Q8×C79—24no—
280Q8×C79—22no—
281Q8×C79—22no—
282Q8×C79—22no—
283Q8×C79—22no—
284Q8×C79—22no—
285Q8×C79—42no—
286Q8×C79—42no—
287Q8×C79C2×#4114yes—
288C2×C4×C79—24no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—42no—
296C2×C4×C79—42no—
297C2×C4×C79—42no—
298C2×C4×C79C22×D412yes—
299C2×C4×C79C22×D412yes—
300C2×C4×C79C22×D411yescharacteristic
301C2×C4×C79C2×#4112yes—
302C2×C4×C79C2×#4112yes—
303C2×C4×C79C2511yescharacteristic
304C2×Dic79—24no—
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×Dic79C22×D412yes—
316C2×Dic79C22×D412yes—
317C2×Dic79C22×D412yes—
318C4×D79—216no—
319C4×D79—24no—
320C4×D79—22no—
321C4×D79—22no—
322Dic158—216no—
323Dic158—24no—
324Dic158—22no—
325Dic158C2×#4114yes—
326C8×C79—22no—
327C8×C79—22no—
328C79⋊C8—22no—
329C79⋊C8—22no—
330C22×C79#52512yes—
331C22×C79#57812yes—
332C22×C79#57812yes—
333C22×C79C23×D411yescharacteristic
334C2×D79—22no—
335C2×D79—22no—
336C2×D79—22no—
337C2×D79—44no—
338C4×C79—24no—
339C4×C79—22no—
340C4×C79—22no—
341C4×C79—42no—
342C4×C79—42no—
343C4×C79—42no—
344C4×C79#52512yes—
345C4×C79C22×#4111yescharacteristic
346C4×C79C22×#4111yescharacteristic
347Dic79—22no—
348Dic79—24no—
349Dic79—22no—
350Dic79—22no—
351Dic79—42no—
352Dic79—42no—
353Dic79—42no—
354C2×#3127—791nomaximal, Sylow
355C2×C79#312714yescomplemented
356C2×C79C2×#52511yescharacteristic
357C2×C79C2×#57811yescharacteristic
358C2×C79C2×#57811yescharacteristic
359D79—42no—
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×#462D7911yescharacteristic, complemented
369C2×#451—791no—
370C2×#451—791no—
371C2×#441—791no—
372C2×#441—791no—
373C2×C4×Q16—791no—
374C2×C4×Q16—791no—
375C2×#433—791no—
376C79C2×#312711yescharacteristic, complemented, Sylow
377C23×Q8—791no—
378C22×Q16—791no—
379C22×Q16—791no—
380C22×Q16C2×D7911yescharacteristic
381C22×Q16C2×D7911yescharacteristic
382#541—798no—
383#541—1584no—
384C2×C4⋊Q8C2×D7911yescharacteristic
385C2×#126—1581no—
386C2×#126—1581no—
387C2×#125—791no—
388C2×#125—1581no—
389C2×#125—1581no—
390C2×C22⋊Q8—791no—
391C2×C22⋊Q8—791no—
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—1581no—
400C2×C4×Q8—1581no—
401C2×C4×Q8C2×D7911yescharacteristic
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#462C2×D7918yescomplemented
412#451—798no—
413#451—798no—
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⋊C8C2×D7911yescharacteristic
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⋊C8—791no—
435C2×#97—791no—
436C2×C4×C8—791no—
437C22×Q8—794no—
438C22×Q8—791no—
439C22×Q8—1581no—
440C22×Q8—1582no—
441C22×Q8—1584no—
442C22×Q8—1584no—
443C22×Q8C22×D7911yescharacteristic
444C22×Q8C22×D7911yescharacteristic
445C22×Q8C22×D7911yescharacteristic
446C23×C4—791no—
447C23×C4—1581no—
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—22no—
461C4⋊Q8C22×D7914yes—
462#126—1588no—
463#126—1588no—
464#125—794no—
465#125—1588no—
466#125—1588no—
467#125—1582no—
468C22⋊Q8—794no—
469C22⋊Q8—794no—
470C22⋊Q8—1582no—
471C22⋊Q8—1582no—
472C4×Q8—22no—
473C4×Q8—794no—
474C4×Q8—794no—
475C4×Q8—794no—
476C4×Q8—794no—
477C4×Q8—794no—
478C4×Q8—1588no—
479C4×Q8—1582no—
480C4×Q8—1582no—
481C4×Q8—1582no—
482C4×Q8—1582no—
483C4×Q8—1588no—
484C4×Q8—1582no—
485C4×Q8C22×D7914yes—
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—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—791no—
496C2×C4⋊C4—791no—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—791no—
499C2×C4⋊C4—791no—
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—791no—
511C2×C22⋊C4—791no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C22⋊C4—1581no—
515C2×C42—21no—
516C2×C42—791no—
517C2×C42—1581no—
518C2×C42—1581no—
519C2×C42—1581no—
520C2×C42—1581no—
521C2×C42—1581no—
522C2×C42—1581no—
523C2×C42C22×D7911yescharacteristic
524#107—794no—
525#107—794no—
526#106—794no—
527#106—794no—
528C4⋊C8—794no—
529C4⋊C8C22×D7914yes—
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⋊C8—794no—
540#97—794no—
541C4×C8—794no—
542C24—791no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—794no—
552C2×Q8—792no—
553C2×Q8—1584no—
554C2×Q8—1588no—
555C2×Q8—1588no—
556C2×Q8—15816no—
557C2×Q8—1588no—
558C2×Q8—1582no—
559C2×Q8—1581no—
560C2×Q8#1192962314yes—
561C2×Q8C23×D7912yes—
562C2×Q8C23×D7912yes—
563C2×Q8C23×D7912yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—791no—
569C22×C4—791no—
570C22×C4—791no—
571C22×C4—792no—
572C22×C4—792no—
573C22×C4—1584no—
574C22×C4—1588no—
575C22×C4—1581no—
576C22×C4—1581no—
577C22×C4—1581no—
578C22×C4—1581no—
579C22×C4—1582no—
580C22×C4—1582no—
581C22×C4D4×D7911yescharacteristic
582C22×C4D4×D7911yescharacteristic
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—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—794no—
601C4⋊C4—794no—
602C4⋊C4—792no—
603C4⋊C4—792no—
604C4⋊C4—792no—
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—794no—
619C22⋊C4—794no—
620C22⋊C4—1584no—
621C22⋊C4—1584no—
622C22⋊C4—1584no—
623C42—24no—
624C42—792no—
625C42—792no—
626C42—1584no—
627C42—1584no—
628C42—1584no—
629C42—1584no—
630C42—1584no—
631C42—1584no—
632C42D4×D7912yes—
633C42C23×D7912yes—
634C23—792no—
635C23—1582no—
636C23—1582no—
637C23—1582no—
638C23C2×D4×D7911yescharacteristic
639Q8—24no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—42no—
647Q8—794no—
648Q8—15816no—
649Q8—1584no—
650Q8—1582no—
651Q8C2×#1192962314yes—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—3162no—
663C2×C4—3162no—
664C2×C4—3162no—
665C2×C4—792no—
666C2×C4—792no—
667C2×C4—792no—
668C2×C4—15816no—
669C2×C4—1582no—
670C2×C4—1582no—
671C2×C4—1582no—
672C2×C4—1582no—
673C2×C4—1584no—
674C2×C4—1582no—
675C2×C4—1582no—
676C2×C4—1582no—
677C2×C4—1584no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4C2×D4×D7912yes—
681C2×C4C2×D4×D7912yes—
682C2×C4C2×D4×D7911yescharacteristic
683C2×C4#41×D7912yes—
684C2×C4C2×#1192962312yes—
685C2×C4C24×D7911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1582no—
689C8—1582no—
690C22—3164no—
691C22—1582no—
692C22—1582no—
693C22—1582no—
694C22#1909907312yes—
695C22#1909937612yes—
696C22#1909937912yes—
697C22C22×D4×D7911yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—3162no—
705C4—3162no—
706C4—3162no—
707C4—1582no—
708C4—1582no—
709C4—1582no—
710C4—1584no—
711C4#1909907312yes—
712C4C2×#41×D7911yescharacteristic
713C4C22×#1192962311yescharacteristic
714C2—3162no—
715C2#2377369814yesdirect product factor
716C2C2×#1909907311yescharacteristic
717C2C2×#1909937611yescharacteristic
718C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#462×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenterC2×#462D79
hypocenterC79C2×#3127
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #23773698C2direct (N × H)
6. C2×#19098871C2semidirect
7. C2×#19098870C2semidirect
8. C2×#19098770C2semidirect
11. C2×#19098670C2semidirect
12. C2×#19098667C2semidirect
13. C2×Q16×Dic79C2semidirect
14. C2×#19098655C2semidirect
16. C2×#462×C79C2semidirect
44. #19098871C22semidirect
45. #19098870C22semidirect
46. #19098770C22semidirect
49. #19098670C22semidirect
50. #19098667C22semidirect
51. Q16×Dic79C22semidirect
52. #19098655C22semidirect
73. #462×C79C22semidirect
355. C2×C79#3127semidirect
368. C2×#462D79semidirect
376. C79C2×#3127semidirect
411. #462C2×D79semidirect
715. C2#23773698direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991742
C2×#190990392
#237736982
C2×#190989032
C2×#190989022
C2×#190988712
C2×#190988702
C2×#190987702
C2×#190987172
C2×#190986702
C2×#190986672
C2×Q16×Dic792
C2×#190986552
C2×#190986232
C2×#462×C792
C2×#312779