Finite Group Databasebeta

← C2×#23776475 #35169285

Subgroups — C2×#23776475 #35169285

Order 20224.

1938 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×#19099286C211yesmaximal, characteristic, complemented
2#23776475C2116yesmaximal, direct product factor
3C2×#19098958C211yesmaximal, characteristic, complemented
4C2×#19098955C211yesmaximal, characteristic, complemented
5C2×#19098945C211yesmaximal, characteristic
6C2×#19098785C211yesmaximal, characteristic, complemented
7C2×#19098782C211yesmaximal, characteristic, complemented
8C2×#19098773C211yesmaximal, characteristic, complemented
9C2×#19098770C211yesmaximal, characteristic, complemented
10C2×#19098778C211yesmaximal, characteristic
11C2×#19098775C211yesmaximal, characteristic
12C2×#19098694C211yesmaximal, characteristic, complemented
13C2×#19098663C211yesmaximal, characteristic, complemented
14C2×#19098661C211yesmaximal, characteristic, complemented
15C2×C4×#11929614C211yesmaximal, characteristic, complemented
16C2×#556×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20C22×#11929614C2211yescharacteristic
21C22×#11929612C2211yescharacteristic
22C22×#11929612C2211yescharacteristic
23C22×#11929611C2211yescharacteristic
24C22×#11929611C2211yescharacteristic
25C22×#11929609C2211yescharacteristic
26#19099286—24no—
27#19099286C2218yescomplemented
28C2×#14579161C2211yescharacteristic
29C2×#14579156—21no—
30C2×#14579156—21no—
31C2×#14579149C2211yescharacteristic
32C2×#14579149C2211yescharacteristic
33C2×#14579137—21no—
34C2×C4×Dic158C2211yescharacteristic
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×D316C2211yescharacteristic
37C2×#14579119—21no—
38#19098958C2218yescomplemented
39#19098955C2218yescomplemented
40#19098945C2218yes—
41#19098785C2218yescomplemented
42#19098782C2218yescomplemented
43#19098778C2218yes—
44#19098775C2218yes—
45#19098773C2218yescomplemented
46#19098770C2218yescomplemented
47#19098694C2218yescomplemented
48#19098663C2218yescomplemented
49#19098661C2218yescomplemented
50C4×#11929614C2218yescomplemented
51C2×#14579094C2211yescharacteristic
52C2×C4⋊(C79⋊C8)C2211yescharacteristic
53C2×C4⋊(C79⋊C8)C2211yescharacteristic
54C2×C4⋊(C79⋊C8)C2211yescharacteristic
55C2×#14579085C2211yescharacteristic
56C2×#14579085C2211yescharacteristic
57C2×#14579084C2211yescharacteristic
58C2×#14579084C2211yescharacteristic
59C2×#14579082C2211yescharacteristic
60C2×#14579081C2211yescharacteristic
61C2×#14579072C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#556×C79—24no—
65#556×C79C2218yescomplemented
66C2×C4⋊Q8×C79C2211yescharacteristic
67C2×#126×C79—21no—
68C2×#126×C79—21no—
69C2×#124×C79C2211yescharacteristic
70C2×#124×C79C2211yescharacteristic
71C2×C22⋊Q8×C79—21no—
72C2×C4×Q8×C79C2211yescharacteristic
73C2×C4×Q8×C79C2211yescharacteristic
74C2×C4×Q8×C79C2211yescharacteristic
75C2×C4×D4×C79C2211yescharacteristic
76C2×#117×C79—21no—
77C22×Dic158C2311yescharacteristic
78C22×Dic158C2311yescharacteristic
79C22×D316C2311yescharacteristic
80C22×C4×D79—21no—
81C2×#11929614—24no—
82C2×#11929614—42no—
83C2×#11929614—42no—
84C2×#11929614—42no—
85C2×#11929614C2314yes—
86C2×#11929614C2314yes—
87C2×#11929614C2314yes—
88C2×#11929614C2314yes—
89C2×#11929612—24no—
90C2×#11929612—42no—
91C2×#11929612C2314yes—
92C2×#11929612C2314yes—
93C2×#11929611—24no—
94C2×#11929611—42no—
95C2×#11929611C2314yes—
96C2×#11929611C2314yes—
97C2×#11929609—42no—
98C2×#11929609C2314yes—
99C22×C79⋊C8C2311yescharacteristic
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2311yescharacteristic
102C22×C79⋊C8C2311yescharacteristic
103#14579161—22no—
104#14579161C2314yes—
105#14579156—28no—
106#14579156—28no—
107#14579149—22no—
108#14579149—22no—
109#14579149C2314yes—
110#14579149C2314yes—
111#14579137—28no—
112C4×Dic158—22no—
113C4×Dic158—22no—
114C4×Dic158C2314yes—
115C4×Dic158C2314yes—
116C4×D316—22no—
117C4×D316C2314yes—
118#14579119—28no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79C2311yescharacteristic
122C2×Dic79⋊C4—21no—
123C2×Dic79⋊C4—21no—
124C2×(C2×D79)⋊C4—21no—
125C2×(C2×D79)⋊C4—21no—
126C2×(C2×D79)⋊C4—21no—
127C2×(C2×D79)⋊C4—21no—
128C2×(C2×D79)⋊C4—21no—
129C2×C4×Dic79—21no—
130C2×C4×Dic79—21no—
131#14579094C2314yes—
132C4⋊(C79⋊C8)C2314yes—
133C4⋊(C79⋊C8)C2314yes—
134C4⋊(C79⋊C8)C2314yes—
135#14579085C2314yes—
136#14579085C2314yes—
137#14579084C2314yes—
138#14579084C2314yes—
139#14579082C2314yes—
140#14579081C2314yes—
141#14579072C2314yes—
142#14579072C2314yes—
143C4×C79⋊C8C2314yes—
144C22×Q8×C79D411yescharacteristic
145C22×Q8×C79C2311yescharacteristic
146C22×Q8×C79C2311yescharacteristic
147C22×D4×C79C2311yescharacteristic
148C23×C4×C79—21no—
149C4⋊Q8×C79—22no—
150C4⋊Q8×C79C2314yes—
151#126×C79—28no—
152#126×C79—28no—
153#124×C79—22no—
154#124×C79—22no—
155#124×C79C2314yes—
156#124×C79C2314yes—
157C22⋊Q8×C79—28no—
158C4×Q8×C79—22no—
159C4×Q8×C79—22no—
160C4×Q8×C79D414yes—
161C4×Q8×C79C2314yes—
162C4×Q8×C79C2314yes—
163C4×Q8×C79C2314yes—
164C4×D4×C79—22no—
165C4×D4×C79C2314yes—
166#117×C79—28no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79D411yescharacteristic
172C2×C4⋊C4×C79D411yescharacteristic
173C2×C4⋊C4×C79D411yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179C2×C22⋊C4×C79—21no—
180C2×C42×C79—21no—
181C2×C42×C79—21no—
182C2×C42×C79C2311yescharacteristic
183C2×C42×C79C2311yescharacteristic
184C2×C42×C79C2311yescharacteristic
185C23×D79—21no—
186C2×Dic158—21no—
187C2×Dic158—21no—
188C2×Dic158—22no—
189C2×Dic158—22no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158C2412yes—
193C2×Dic158C2412yes—
194C2×D316—21no—
195C2×D316—22no—
196C2×D316—22no—
197C2×D316C2412yes—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C2×C4×D79—24no—
202C2×C4×D79—44no—
203#11929614—28no—
204#11929614—44no—
205#11929614—44no—
206#11929614—44no—
207#11929612—28no—
208#11929612—44no—
209#11929611—28no—
210#11929611—44no—
211#11929609—44no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8—22no—
214C2×C79⋊C8—22no—
215C2×C79⋊C8#4114yes—
216C2×C79⋊C8C2412yes—
217C2×C79⋊C8C2412yes—
218C2×C79⋊C8C2412yes—
219C2×C79⋊C8C2412yes—
220C4⋊Dic79—24no—
221C4⋊Dic79—24no—
222C4⋊Dic79—21no—
223C4⋊Dic79C2412yes—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231C4×Dic79—24no—
232C4×Dic79—24no—
233C24×C79—21no—
234C2×Q8×C79—21no—
235C2×Q8×C79—21no—
236C2×Q8×C79—22no—
237C2×Q8×C79—22no—
238C2×Q8×C79—22no—
239C2×Q8×C79—22no—
240C2×Q8×C79—42no—
241C2×Q8×C79C2×D414yes—
242C2×Q8×C79C2412yes—
243C2×Q8×C79C2412yes—
244C2×D4×C79—21no—
245C2×D4×C79—22no—
246C2×D4×C79—22no—
247C2×D4×C79C2412yes—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—24no—
252C22×C4×C79—44no—
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2411yescharacteristic
260C4⋊C4×C79—24no—
261C4⋊C4×C79—24no—
262C4⋊C4×C79—24no—
263C4⋊C4×C79—24no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79C2×D414yes—
266C4⋊C4×C79C2×D414yes—
267C4⋊C4×C79C2×D414yes—
268C4⋊C4×C79C2412yes—
269C22⋊C4×C79—24no—
270C22⋊C4×C79—24no—
271C22⋊C4×C79—24no—
272C22⋊C4×C79—24no—
273C22⋊C4×C79—24no—
274C42×C79—24no—
275C42×C79—24no—
276C42×C79C2×D412yes—
277C42×C79C2×D412yes—
278C42×C79C2×D412yes—
279C42×C79C2412yes—
280C42×C79C2412yes—
281C42×C79C2412yes—
282C23×C79—22no—
283C23×C79—42no—
284C23×C79—42no—
285C23×C79—42no—
286C23×C79C22×D411yescharacteristic
287C22×D79—22no—
288C22×D79—42no—
289C22×D79—42no—
290C22×D79—42no—
291Q8×C79—22no—
292Q8×C79—22no—
293Q8×C79—22no—
294Q8×C79—22no—
295Q8×C79—44no—
296Q8×C79—42no—
297Q8×C79—42no—
298D4×C79—22no—
299D4×C79—22no—
300D4×C79—42no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—48no—
311C2×C4×C79—42no—
312C2×C4×C79—42no—
313C2×C4×C79—42no—
314C2×C4×C79C22×D412yes—
315C2×C4×C79C22×D412yes—
316C2×C4×C79C22×D412yes—
317C2×C4×C79C22×D412yes—
318C2×C4×C79C22×D412yes—
319C2×C4×C79C22×D412yes—
320C2×C4×C79C22×D411yescharacteristic
321C2×C4×C79C2×#4112yes—
322C2×C4×C79H(5,𝔽2)12yes—
323C2×C4×C79C2511yescharacteristic
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—42no—
328C2×Dic79—42no—
329C2×Dic79—42no—
330D316—22no—
331D316—22no—
332D316—42no—
333C4×D79—48no—
334Dic158—22no—
335Dic158—22no—
336Dic158—22no—
337Dic158—22no—
338Dic158—42no—
339Dic158—42no—
340C79⋊C8—22no—
341C79⋊C8—22no—
342C79⋊C8—22no—
343C79⋊C8C2×#4114yes—
344C22×C79—42no—
345C22×C79—42no—
346C22×C79—42no—
347C22×C79—84no—
348C22×C79#55012yes—
349C22×C79#57512yes—
350C22×C79#57812yes—
351C22×C79C23×D411yescharacteristic
352C2×D79—42no—
353C2×D79—42no—
354C2×D79—42no—
355C2×D79—84no—
356C4×C79—22no—
357C4×C79—22no—
358C4×C79—22no—
359C4×C79—22no—
360C4×C79—22no—
361C4×C79—22no—
362C4×C79—42no—
363C4×C79—42no—
364C4×C79—42no—
365C4×C79#55012yes—
366C4×C79C22×#4111yescharacteristic
367C4×C79C2×H(5,𝔽2)11yescharacteristic
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371C2×#3402—791nomaximal, Sylow
372C2×C79—82no—
373C2×C79#340214yescomplemented
374C2×C79C2×#55011yescharacteristic
375C2×C79C2×#57511yescharacteristic
376C2×C79C2×#57811yescharacteristic
377D79—82no—
378C2×#556—791no—
379C2×#556D7911yescharacteristic, complemented
380#3402—7916no—
381C2×#497—791no—
382C2×#497—791no—
383C2×#495—791no—
384C2×#464—791no—
385C2×#464—791no—
386C2×#462—791no—
387C2×#462—791no—
388C2×#463—791no—
389C2×#463—791no—
390C2×#446—791no—
391C2×#440—791no—
392C2×#440—791no—
393C2×C4×Q16—791no—
394C79C2×#340211yescharacteristic, complemented, Sylow
395C22×Q16—791no—
396C22×Q16—791no—
397C22×Q16—791no—
398C22×Q16—791no—
399C22×SD16—791no—
400C22×SD16—791no—
401C22×SD16—791no—
402C22×SD16—791no—
403C22×D8—791no—
404#556—24no—
405#556—798no—
406#556—1584no—
407#556C2×D7918yescomplemented
408C2×C4⋊Q8—791no—
409C2×C4⋊Q8C2×D7911yescharacteristic
410C2×#126—21no—
411C2×#126—21no—
412C2×#126—1581no—
413C2×#126—1581no—
414C2×#124—791no—
415C2×#124—791no—
416C2×#124C2×D7911yescharacteristic
417C2×#124C2×D7911yescharacteristic
418C2×C22⋊Q8—21no—
419C2×C22⋊Q8—1581no—
420C2×C4×Q8—791no—
421C2×C4×Q8—791no—
422C2×C4×Q8C2×D7911yescharacteristic
423C2×C4×Q8C2×D7911yescharacteristic
424C2×C4×Q8C2×D7911yescharacteristic
425C2×C4×D4—791no—
426C2×C4×D4C2×D7911yescharacteristic
427C2×#117—21no—
428C2×#117—1581no—
429#497—798no—
430#497—798no—
431#495—798no—
432#464—798no—
433#464—798no—
434#463—798no—
435#463—798no—
436#462—798no—
437#462—798no—
438#446—798no—
439#440—798no—
440#440—798no—
441C4×Q16—798no—
442C2×#107—791no—
443C2×C4⋊C8—791no—
444C2×C4⋊C8—791no—
445C2×C4⋊C8—791no—
446C2×#103—791no—
447C2×#103—791no—
448C2×#103—791no—
449C2×#103—791no—
450C2×#102—791no—
451C2×#102—791no—
452C2×#97—791no—
453C2×#97—791no—
454C2×C4×C8—791no—
455C22×Q8—791no—
456C22×Q8—791no—
457C22×Q8C22⋊D7911yescharacteristic
458C22×Q8C22×D7911yescharacteristic
459C22×Q8C22×D7911yescharacteristic
460C22×D4—791no—
461C22×D4C22×D7911yescharacteristic
462C23×C4—21no—
463C23×C4—1581no—
464C2×Q16—3162no—
465C2×Q16—3162no—
466C2×Q16—3162no—
467C2×Q16—794no—
468C2×Q16—794no—
469C2×Q16—794no—
470C2×Q16—794no—
471C2×Q16—1584no—
472C2×SD16—3162no—
473C2×SD16—3162no—
474C2×SD16—794no—
475C2×SD16—794no—
476C2×SD16—794no—
477C2×SD16—794no—
478C2×SD16—1584no—
479C2×SD16—1584no—
480C2×D8—3162no—
481C2×D8—794no—
482C22×C8—791no—
483C22×C8—791no—
484C22×C8—791no—
485C22×C8—791no—
486C4⋊Q8—22no—
487C4⋊Q8—794no—
488C4⋊Q8—1582no—
489C4⋊Q8C22×D7914yes—
490#126—28no—
491#126—28no—
492#126—1588no—
493#126—1588no—
494#124—22no—
495#124—22no—
496#124—794no—
497#124—794no—
498#124—1582no—
499#124—1582no—
500#124C22×D7914yes—
501#124C22×D7914yes—
502C22⋊Q8—28no—
503C22⋊Q8—1588no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—794no—
507C4×Q8—794no—
508C4×Q8—1582no—
509C4×Q8—1582no—
510C4×Q8C22⋊D7914yes—
511C4×Q8C22×D7914yes—
512C4×Q8C22×D7914yes—
513C4×Q8C22×D7914yes—
514C4×D4—22no—
515C4×D4—794no—
516C4×D4—1582no—
517C4×D4C22×D7914yes—
518#117—28no—
519#117—1588no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—791no—
525C2×C4⋊C4—1581no—
526C2×C4⋊C4—1581no—
527C2×C4⋊C4—1581no—
528C2×C4⋊C4—1581no—
529C2×C4⋊C4C22⋊D7911yescharacteristic
530C2×C4⋊C4C22⋊D7911yescharacteristic
531C2×C4⋊C4C22⋊D7911yescharacteristic
532C2×C4⋊C4C22×D7911yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—1581no—
539C2×C22⋊C4—1581no—
540C2×C22⋊C4—1581no—
541C2×C22⋊C4—1581no—
542C2×C22⋊C4—1581no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—1581no—
546C2×C42—1581no—
547C2×C42C22×D7911yescharacteristic
548C2×C42C22×D7911yescharacteristic
549C2×C42C22×D7911yescharacteristic
550#107—794no—
551C4⋊C8—794no—
552C4⋊C8—794no—
553C4⋊C8—794no—
554#103—794no—
555#103—794no—
556#103—794no—
557#103—794no—
558#102—794no—
559#102—794no—
560#97—794no—
561#97—794no—
562C4×C8—794no—
563C24—21no—
564C24—1581no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—42no—
572C2×Q8—792no—
573C2×Q8—792no—
574C2×Q8—1582no—
575C2×Q8—1582no—
576C2×Q8—1582no—
577C2×Q8—1582no—
578C2×Q8—1581no—
579C2×Q8—1581no—
580C2×Q8C2×C22⋊D7914yes—
581C2×Q8C23×D7912yes—
582C2×Q8C23×D7912yes—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—792no—
587C2×D4—1582no—
588C2×D4—1582no—
589C2×D4—1581no—
590C2×D4C23×D7912yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—3164no—
597C22×C4—1581no—
598C22×C4—1581no—
599C22×C4—1581no—
600C22×C4—1584no—
601C22×C4C2×C22⋊D7911yescharacteristic
602C22×C4C2×C22⋊D7911yescharacteristic
603C22×C4C2×C22⋊D7911yescharacteristic
604C22×C4C2×C22⋊D7911yescharacteristic
605C22×C4C2×C22⋊D7911yescharacteristic
606C22×C4C2×C22⋊D7911yescharacteristic
607C22×C4C23×D7911yescharacteristic
608Q16—3164no—
609Q16—3164no—
610Q16—3164no—
611Q16—1588no—
612SD16—3164no—
613SD16—3164no—
614SD16—1588no—
615SD16—1588no—
616D8—3164no—
617C2×C8—794no—
618C2×C8—792no—
619C2×C8—792no—
620C2×C8—792no—
621C2×C8—792no—
622C2×C8—1582no—
623C2×C8—1582no—
624C2×C8—1582no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—21no—
630C4⋊C4—792no—
631C4⋊C4—1584no—
632C4⋊C4—1584no—
633C4⋊C4—1581no—
634C4⋊C4—1584no—
635C4⋊C4—1584no—
636C4⋊C4C2×C22⋊D7914yes—
637C4⋊C4C2×C22⋊D7914yes—
638C4⋊C4C2×C22⋊D7914yes—
639C4⋊C4C23×D7912yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—1584no—
646C22⋊C4—1584no—
647C22⋊C4—1584no—
648C22⋊C4—1584no—
649C22⋊C4—1584no—
650C42—24no—
651C42—24no—
652C42—1584no—
653C42—1584no—
654C42C2×C22⋊D7912yes—
655C42C2×C22⋊D7912yes—
656C42C2×C22⋊D7912yes—
657C42C23×D7912yes—
658C42C23×D7912yes—
659C42C23×D7912yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—3162no—
665C23—3162no—
666C23—3162no—
667C23—1582no—
668C23C22×C22⋊D7911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—44no—
674Q8—42no—
675Q8—42no—
676Q8—3162no—
677Q8—3162no—
678Q8—1582no—
679Q8—1582no—
680Q8—1582no—
681Q8—1582no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—3162no—
686D4—1582no—
687D4—1582no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—3168no—
702C2×C4—3162no—
703C2×C4—3162no—
704C2×C4—3162no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4C22×C22⋊D7912yes—
709C2×C4C22×C22⋊D7912yes—
710C2×C4C22×C22⋊D7912yes—
711C2×C4C22×C22⋊D7912yes—
712C2×C4C22×C22⋊D7912yes—
713C2×C4C22×C22⋊D7912yes—
714C2×C4C22×C22⋊D7911yescharacteristic
715C2×C4#41×D7912yes—
716C2×C4#1457920712yes—
717C2×C4C24×D7911yescharacteristic
718C8—794no—
719C8—1582no—
720C8—1582no—
721C8—1582no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—3162no—
727C22—3162no—
728C22—3162no—
729C22—6324no—
730C22#1909923212yes—
731C22#1909936112yes—
732C22#1909937812yes—
733C22C23×C22⋊D7911yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—3162no—
744C4—3162no—
745C4—3162no—
746C4#1909923212yes—
747C4C2×#41×D7911yescharacteristic
748C4C2×#1457920711yescharacteristic
749C2—82no—
750C2—6322no—
751C2#2377647514yesdirect product factor
752C2C2×#1909923211yescharacteristic
753C2C2×#1909936111yescharacteristic
754C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#556×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929609C22
hypercenterC2×#556D79
hypocenterC79C2×#3402
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#19099286C2semidirect
2. #23776475C2direct (N × H)
3. C2×#19098958C2semidirect
4. C2×#19098955C2semidirect
6. C2×#19098785C2semidirect
7. C2×#19098782C2semidirect
8. C2×#19098773C2semidirect
9. C2×#19098770C2semidirect
12. C2×#19098694C2semidirect
13. C2×#19098663C2semidirect
14. C2×#19098661C2semidirect
15. C2×C4×#11929614C2semidirect
16. C2×#556×C79C2semidirect
27. #19099286C22semidirect
38. #19098958C22semidirect
39. #19098955C22semidirect
41. #19098785C22semidirect
42. #19098782C22semidirect
45. #19098773C22semidirect
46. #19098770C22semidirect
47. #19098694C22semidirect
48. #19098663C22semidirect
49. #19098661C22semidirect
50. C4×#11929614C22semidirect
65. #556×C79C22semidirect
373. C2×C79#3402semidirect
379. C2×#556D79semidirect
394. C79C2×#3402semidirect
407. #556C2×D79semidirect
751. C2#23776475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992862
#237764752
C2×#190989582
C2×#190989552
C2×#190989452
C2×#190987852
C2×#190987822
C2×#190987732
C2×#190987702
C2×#190987782
C2×#190987752
C2×#190986942
C2×#190986632
C2×#190986612
C2×C4×#119296142
C2×#556×C792
C2×#340279