Finite Group Databasebeta

← C2×#23774509 #35159664

Subgroups — C2×#23774509 #35159664

Order 20224.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099184C211yesmaximal, characteristic, complemented
2#23774509C2116yesmaximal, direct product factor
3C2×#19098955C211yesmaximal, characteristic, complemented
4C2×#19098945C211yesmaximal, characteristic, complemented
5C2×#19098922C211yesmaximal, characteristic, complemented
6C2×#19098913C211yesmaximal, characteristic, complemented
7C2×#19098782C211yesmaximal, characteristic, complemented
8C2×#19098770C211yesmaximal, characteristic, complemented
9C2×#19098775C211yesmaximal, characteristic, complemented
10C2×#19098765C211yesmaximal, characteristic, complemented
11C2×#19098725C211yesmaximal, characteristic, complemented
12C2×#19098708C211yesmaximal, characteristic
13C2×#19098719C211yesmaximal, characteristic, complemented
14C2×#19098702C211yesmaximal, characteristic, complemented
15C2×#19098624C211yesmaximal, characteristic, complemented
16C2×#536×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20C22×#11929612C2211yescharacteristic
21C22×#11929611C2211yescharacteristic
22C22×#11929611C2211yescharacteristic
23C22×#11929611C2211yescharacteristic
24C22×#11929609C2211yescharacteristic
25#19099184—24no—
26#19099184C2218yescomplemented
27C2×#14579161C2211yescharacteristic
28C2×#14579156—21no—
29C2×#14579149C2211yescharacteristic
30C2×#14579147—21no—
31C2×#14579143—21no—
32C2×#14579140C2211yescharacteristic
33C2×#14579139—21no—
34C2×#14579135C2211yescharacteristic
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×D316C2211yescharacteristic
37#19098955C2218yescomplemented
38#19098945C2218yescomplemented
39#19098922C2218yescomplemented
40#19098913C2218yescomplemented
41#19098782C2218yescomplemented
42#19098775C2218yescomplemented
43#19098770C2218yescomplemented
44#19098765C2218yescomplemented
45#19098725C2218yescomplemented
46#19098719C2218yescomplemented
47#19098708C2218yes—
48#19098702C2218yescomplemented
49#19098624C2218yescomplemented
50C2×C4⋊(C79⋊C8)C2211yescharacteristic
51C2×C4⋊(C79⋊C8)C2211yescharacteristic
52C2×#14579085C2211yescharacteristic
53C2×#14579085C2211yescharacteristic
54C2×#14579085C2211yescharacteristic
55C2×#14579085C2211yescharacteristic
56C2×#14579085C2211yescharacteristic
57C2×#14579085C2211yescharacteristic
58C2×#14579082C2211yescharacteristic
59C2×#14579082C2211yescharacteristic
60C2×C22⋊(C79⋊C8)C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64C22×#41×C79C2211yescharacteristic
65C23×Q8×C79C2211yescharacteristic
66#536×C79—24no—
67#536×C79C2218yescomplemented
68C2×C4⋊Q8×C79C2211yescharacteristic
69C2×C4⋊Q8×C79C2211yescharacteristic
70C2×#124×C79C2211yescharacteristic
71C2×#124×C79C2211yescharacteristic
72C2×#123×C79—21no—
73C2×#123×C79—21no—
74C2×C22⋊Q8×C79—21no—
75C2×C22⋊Q8×C79—21no—
76C2×#117×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C22×C4×D79—21no—
82C2×#11929614—42no—
83C2×#11929614—42no—
84C2×#11929614—42no—
85C2×#11929614C2314yes—
86C2×#11929614C2314yes—
87C2×#11929614C2314yes—
88C2×#11929612—42no—
89C2×#11929612C2314yes—
90C2×#11929611—42no—
91C2×#11929611—42no—
92C2×#11929611—42no—
93C2×#11929611C2314yes—
94C2×#11929611C2314yes—
95C2×#11929611C2314yes—
96C2×#11929609—42no—
97C2×#11929609C2314yes—
98C22×C79⋊C8C2311yescharacteristic
99C22×C79⋊C8C2311yescharacteristic
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2311yescharacteristic
102#14579161—22no—
103#14579161C2314yes—
104#14579156—28no—
105#14579149—22no—
106#14579149C2314yes—
107#14579147—28no—
108#14579143—28no—
109#14579140—22no—
110#14579140C2314yes—
111#14579139—28no—
112#14579135—22no—
113#14579135C2314yes—
114C4×Dic158—22no—
115C4×Dic158C2314yes—
116C4×D316—22no—
117C4×D316C2314yes—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79C2311yescharacteristic
120C2×C4⋊Dic79C2311yescharacteristic
121C2×Dic79⋊C4—21no—
122C2×Dic79⋊C4—21no—
123C2×C22⋊Dic79—21no—
124C2×(C2×D79)⋊C4—21no—
125C2×(C2×D79)⋊C4—21no—
126C2×(C2×D79)⋊C4—21no—
127C2×(C2×D79)⋊C4—21no—
128C2×C4×Dic79—21no—
129C4⋊(C79⋊C8)C2314yes—
130C4⋊(C79⋊C8)C2314yes—
131#14579085C2314yes—
132#14579085C2314yes—
133#14579085C2314yes—
134#14579085C2314yes—
135#14579085C2314yes—
136#14579085C2314yes—
137#14579082C2314yes—
138#14579082C2314yes—
139C22⋊(C79⋊C8)C2314yes—
140C22⋊(C79⋊C8)C2314yes—
141#14579072C2314yes—
142C4×C79⋊C8C2314yes—
143C2×#41×C79—22no—
144C2×#41×C79—42no—
145C2×#41×C79—42no—
146C2×#41×C79C2314yes—
147C22×Q8×C79—21no—
148C22×Q8×C79—22no—
149C22×Q8×C79—42no—
150C22×Q8×C79—42no—
151C22×Q8×C79C2311yescharacteristic
152C22×Q8×C79C2311yescharacteristic
153C22×Q8×C79C2311yescharacteristic
154C22×Q8×C79C2314yes—
155C22×D4×C79—21no—
156C22×D4×C79C2311yescharacteristic
157C23×C4×C79—21no—
158C23×C4×C79—21no—
159C23×C4×C79C2311yescharacteristic
160C4⋊Q8×C79—22no—
161C4⋊Q8×C79—22no—
162C4⋊Q8×C79C2314yes—
163C4⋊Q8×C79C2314yes—
164#124×C79—22no—
165#124×C79—22no—
166#124×C79C2314yes—
167#124×C79C2314yes—
168#123×C79—28no—
169#123×C79—28no—
170C22⋊Q8×C79—28no—
171C22⋊Q8×C79—28no—
172#117×C79D414yes—
173#117×C79C2314yes—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79—21no—
176C2×C4⋊C4×C79—21no—
177C2×C4⋊C4×C79—21no—
178C2×C4⋊C4×C79D411yescharacteristic
179C2×C4⋊C4×C79D411yescharacteristic
180C2×C22⋊C4×C79—21no—
181C2×C22⋊C4×C79—21no—
182C2×C22⋊C4×C79—21no—
183C2×C22⋊C4×C79—21no—
184C2×C22⋊C4×C79D411yescharacteristic
185C2×C22⋊C4×C79D411yescharacteristic
186C2×C42×C79C2311yescharacteristic
187C2×C42×C79C2311yescharacteristic
188C23×D79—21no—
189C2×Dic158—21no—
190C2×Dic158—24no—
191C2×Dic158—22no—
192C2×Dic158—22no—
193C2×Dic158—82no—
194C2×Dic158C2412yes—
195C2×D316—21no—
196C2×D316—22no—
197C2×D316—22no—
198C2×D316C2412yes—
199C2×C22⋊D79—24no—
200C2×C22⋊D79—82no—
201C22×Dic79—21no—
202C22×Dic79—21no—
203C22×Dic79—21no—
204C2×C4×D79—24no—
205C2×C4×D79—82no—
206#11929614—44no—
207#11929614—44no—
208#11929614—44no—
209#11929612—44no—
210#11929611—44no—
211#11929611—44no—
212#11929611—44no—
213#11929609—44no—
214C2×C79⋊C8—22no—
215C2×C79⋊C8—22no—
216C2×C79⋊C8—22no—
217C2×C79⋊C8—22no—
218C2×C79⋊C8C2412yes—
219C2×C79⋊C8C2412yes—
220C2×C79⋊C8C2412yes—
221C2×C79⋊C8C2412yes—
222C4⋊Dic79—24no—
223C4⋊Dic79—21no—
224C4⋊Dic79—21no—
225C4⋊Dic79C2412yes—
226C4⋊Dic79C2412yes—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229C22⋊Dic79—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234C4×Dic79—24no—
235C24×C79—21no—
236C24×C79C2×D411yescharacteristic
237#41×C79—44no—
238#41×C79—44no—
239#41×C79—48no—
240C2×Q8×C79—24no—
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—22no—
250C2×Q8×C79—44no—
251C2×Q8×C79—44no—
252C2×Q8×C79—44no—
253C2×Q8×C79—48no—
254C2×Q8×C79C2412yes—
255C2×Q8×C79C2412yes—
256C2×Q8×C79C2412yes—
257C2×D4×C79—24no—
258C2×D4×C79—21no—
259C2×D4×C79—22no—
260C2×D4×C79—22no—
261C2×D4×C79—44no—
262C2×D4×C79C2412yes—
263C22×C4×C79—22no—
264C22×C4×C79—22no—
265C22×C4×C79—21no—
266C22×C4×C79—21no—
267C22×C4×C79—21no—
268C22×C4×C79—24no—
269C22×C4×C79—24no—
270C22×C4×C79—44no—
271C22×C4×C79—44no—
272C22×C4×C79C2×D411yescharacteristic
273C22×C4×C79C2×D411yescharacteristic
274C22×C4×C79C2×D411yescharacteristic
275C22×C4×C79C2×D411yescharacteristic
276C22×C4×C79C2×D411yescharacteristic
277C22×C4×C79C2×D412yes—
278C22×C4×C79C2412yes—
279C22×C4×C79C2411yescharacteristic
280C4⋊C4×C79—24no—
281C4⋊C4×C79—24no—
282C4⋊C4×C79—24no—
283C4⋊C4×C79—24no—
284C4⋊C4×C79C2×D414yes—
285C4⋊C4×C79C2×D414yes—
286C22⋊C4×C79—24no—
287C22⋊C4×C79—24no—
288C22⋊C4×C79—24no—
289C22⋊C4×C79—24no—
290C22⋊C4×C79C2×D414yes—
291C22⋊C4×C79C2×D414yes—
292C42×C79C2×D412yes—
293C42×C79C2×D412yes—
294C42×C79C2412yes—
295C42×C79C2412yes—
296C23×C79—22no—
297C23×C79—22no—
298C23×C79—22no—
299C23×C79—22no—
300C23×C79—42no—
301C23×C79—42no—
302C23×C79—42no—
303C23×C79C22×D412yes—
304C23×C79C22×D411yescharacteristic
305C22×D79—22no—
306C22×D79—42no—
307C22×D79—42no—
308C22×D79—42no—
309Q8×C79—22no—
310Q8×C79—22no—
311Q8×C79—22no—
312Q8×C79—22no—
313Q8×C79—22no—
314Q8×C79—22no—
315Q8×C79—48no—
316Q8×C79—42no—
317Q8×C79—42no—
318Q8×C79—42no—
319D4×C79—22no—
320D4×C79—22no—
321D4×C79—48no—
322D4×C79—42no—
323C2×C4×C79—22no—
324C2×C4×C79—22no—
325C2×C4×C79—22no—
326C2×C4×C79—22no—
327C2×C4×C79—22no—
328C2×C4×C79—24no—
329C2×C4×C79—22no—
330C2×C4×C79—22no—
331C2×C4×C79—22no—
332C2×C4×C79—22no—
333C2×C4×C79—22no—
334C2×C4×C79—48no—
335C2×C4×C79—48no—
336C2×C4×C79—42no—
337C2×C4×C79—42no—
338C2×C4×C79—42no—
339C2×C4×C79C22×D412yes—
340C2×C4×C79C22×D412yes—
341C2×C4×C79C22×D412yes—
342C2×C4×C79C22×D412yes—
343C2×C4×C79C22×D412yes—
344C2×C4×C79C22×D411yescharacteristic
345C2×C4×C79H(5,𝔽2)12yes—
346C2×C4×C79H(5,𝔽2)12yes—
347C2×C4×C79C2511yescharacteristic
348C22⋊D79—84no—
349C2×Dic79—22no—
350C2×Dic79—22no—
351C2×Dic79—22no—
352C2×Dic79—42no—
353C2×Dic79—42no—
354C2×Dic79—42no—
355D316—22no—
356D316—22no—
357D316—42no—
358C4×D79—84no—
359Dic158—22no—
360Dic158—22no—
361Dic158—42no—
362Dic158—84no—
363C79⋊C8—22no—
364C79⋊C8—22no—
365C79⋊C8—22no—
366C79⋊C8—22no—
367C22×C79—22no—
368C22×C79—22no—
369C22×C79—22no—
370C22×C79—44no—
371C22×C79—42no—
372C22×C79—42no—
373C22×C79—42no—
374C22×C79—84no—
375C22×C79#53512yes—
376C22×C79#57712yes—
377C22×C79#57812yes—
378C22×C79C23×D411yescharacteristic
379C2×D79—42no—
380C2×D79—42no—
381C2×D79—42no—
382C2×D79—84no—
383C4×C79—22no—
384C4×C79—22no—
385C4×C79—22no—
386C4×C79—22no—
387C4×C79—22no—
388C4×C79—42no—
389C4×C79—42no—
390C4×C79—42no—
391C4×C79#53512yes—
392C4×C79C2×H(5,𝔽2)11yescharacteristic
393C4×C79C2×H(5,𝔽2)11yescharacteristic
394Dic79—42no—
395Dic79—42no—
396Dic79—42no—
397C2×#3225—791nomaximal, Sylow
398C2×C79—42no—
399C2×C79—82no—
400C2×C79#322514yescomplemented
401C2×C79C2×#53511yescharacteristic
402C2×C79C2×#57711yescharacteristic
403C2×C79C2×#57811yescharacteristic
404D79—82no—
405C2×#542—791no—
406C2×#536D7911yescharacteristic, complemented
407#3225—7916no—
408C2×#497—791no—
409C2×#495—791no—
410C2×#489—791no—
411C2×#487—791no—
412C2×#464—791no—
413C2×#462—791no—
414C2×#463—791no—
415C2×#461—791no—
416C2×#452—791no—
417C2×#449—791no—
418C2×#451—791no—
419C2×#448—791no—
420C2×#433—791no—
421C79C2×#322511yescharacteristic, complemented, Sylow
422C22×#41C2×D7911yescharacteristic
423C23×Q8C2×D7911yescharacteristic
424C22×Q16—791no—
425C22×Q16—791no—
426C22×Q16—791no—
427C22×SD16—791no—
428C22×SD16—791no—
429C22×SD16—791no—
430C22×SD16—791no—
431C22×D8—791no—
432#542—798no—
433#542—1584no—
434#536—24no—
435#536C2×D7918yescomplemented
436C2×C4⋊Q8—791no—
437C2×C4⋊Q8C2×D7911yescharacteristic
438C2×C4⋊Q8C2×D7911yescharacteristic
439C2×#126—1581no—
440C2×#124—791no—
441C2×#124—1581no—
442C2×#124C2×D7911yescharacteristic
443C2×#124C2×D7911yescharacteristic
444C2×#123—21no—
445C2×#123—21no—
446C2×#123—1581no—
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—21no—
449C2×C22⋊Q8—791no—
450C2×C22⋊Q8—1581no—
451C2×#121—791no—
452C2×C4×Q8—791no—
453C2×C4×D4—791no—
454C2×#117C2×D7911yescharacteristic
455#497—798no—
456#495—798no—
457#489—798no—
458#487—798no—
459#464—798no—
460#463—798no—
461#462—798no—
462#461—798no—
463#452—798no—
464#451—798no—
465#449—798no—
466#448—798no—
467#433—798no—
468C2×C4⋊C8—791no—
469C2×C4⋊C8—791no—
470C2×#103—791no—
471C2×#103—791no—
472C2×#103—791no—
473C2×#103—791no—
474C2×#103—791no—
475C2×#103—791no—
476C2×#102—791no—
477C2×#102—791no—
478C2×C22⋊C8—791no—
479C2×C22⋊C8—791no—
480C2×#97—791no—
481C2×C4×C8—791no—
482C2×#41—22no—
483C2×#41—42no—
484C2×#41—42no—
485C2×#41C22×D7914yes—
486C22×Q8—21no—
487C22×Q8—22no—
488C22×Q8—42no—
489C22×Q8—42no—
490C22×Q8—791no—
491C22×Q8—1581no—
492C22×Q8C22×D7911yescharacteristic
493C22×Q8C22×D7911yescharacteristic
494C22×Q8C22×D7911yescharacteristic
495C22×Q8C22×D7914yes—
496C22×D4—21no—
497C22×D4—791no—
498C22×D4—1581no—
499C22×D4C22×D7911yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—1581no—
503C23×C4C22×D7911yescharacteristic
504C2×Q16—3162no—
505C2×Q16—3162no—
506C2×Q16—3162no—
507C2×Q16—794no—
508C2×Q16—794no—
509C2×Q16—794no—
510C2×SD16—3162no—
511C2×SD16—3162no—
512C2×SD16—3162no—
513C2×SD16—3162no—
514C2×SD16—794no—
515C2×SD16—794no—
516C2×SD16—794no—
517C2×SD16—794no—
518C2×D8—3162no—
519C2×D8—794no—
520C22×C8—791no—
521C22×C8—791no—
522C22×C8—791no—
523C22×C8—791no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—794no—
527C4⋊Q8—1582no—
528C4⋊Q8C22×D7914yes—
529C4⋊Q8C22×D7914yes—
530#126—1588no—
531#124—22no—
532#124—22no—
533#124—794no—
534#124—1588no—
535#124—1582no—
536#124C22×D7914yes—
537#124C22×D7914yes—
538#123—28no—
539#123—28no—
540#123—1588no—
541C22⋊Q8—28no—
542C22⋊Q8—28no—
543C22⋊Q8—794no—
544C22⋊Q8—1582no—
545C22⋊Q8—1588no—
546#121—794no—
547#121—1582no—
548C4×Q8—794no—
549C4×Q8—1582no—
550C4×D4—794no—
551C4×D4—1582no—
552#117C22⋊D7914yes—
553#117C22×D7914yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—791no—
559C2×C4⋊C4—791no—
560C2×C4⋊C4—1581no—
561C2×C4⋊C4—1581no—
562C2×C4⋊C4—1581no—
563C2×C4⋊C4C22⋊D7911yescharacteristic
564C2×C4⋊C4C22⋊D7911yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—1581no—
570C2×C22⋊C4—1581no—
571C2×C22⋊C4—1581no—
572C2×C22⋊C4—1581no—
573C2×C22⋊C4—1581no—
574C2×C22⋊C4C22⋊D7911yescharacteristic
575C2×C22⋊C4C22⋊D7911yescharacteristic
576C2×C42—1581no—
577C2×C42C22×D7911yescharacteristic
578C2×C42C22×D7911yescharacteristic
579C4⋊C8—794no—
580C4⋊C8—794no—
581#103—794no—
582#103—794no—
583#103—794no—
584#103—794no—
585#103—794no—
586#103—794no—
587#102—794no—
588#102—794no—
589C22⋊C8—794no—
590C22⋊C8—794no—
591#97—794no—
592C4×C8—794no—
593C24—21no—
594C24—1581no—
595C24C2×C22⋊D7911yescharacteristic
596#41—44no—
597#41—44no—
598#41—48no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—48no—
613C2×Q8—792no—
614C2×Q8—6322no—
615C2×Q8—1582no—
616C2×Q8—1582no—
617C2×Q8—1581no—
618C2×Q8—1584no—
619C2×Q8C23×D7912yes—
620C2×Q8C23×D7912yes—
621C2×Q8C23×D7912yes—
622C2×D4—24no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—44no—
627C2×D4—792no—
628C2×D4—6322no—
629C2×D4—1584no—
630C2×D4—1582no—
631C2×D4—1582no—
632C2×D4—1581no—
633C2×D4C23×D7912yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—6322no—
644C22×C4—1581no—
645C22×C4—1581no—
646C22×C4—1581no—
647C22×C4—1584no—
648C22×C4C2×C22⋊D7912yes—
649C22×C4C2×C22⋊D7911yescharacteristic
650C22×C4C2×C22⋊D7911yescharacteristic
651C22×C4C2×C22⋊D7911yescharacteristic
652C22×C4C2×C22⋊D7911yescharacteristic
653C22×C4C2×C22⋊D7911yescharacteristic
654C22×C4C23×D7912yes—
655C22×C4C23×D7911yescharacteristic
656Q16—3164no—
657Q16—3164no—
658Q16—3164no—
659SD16—3164no—
660SD16—3164no—
661SD16—3164no—
662SD16—3164no—
663D8—3164no—
664C2×C8—792no—
665C2×C8—792no—
666C2×C8—792no—
667C2×C8—792no—
668C2×C8—1582no—
669C2×C8—1582no—
670C2×C8—1582no—
671C2×C8—1582no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—792no—
677C4⋊C4—792no—
678C4⋊C4—1584no—
679C4⋊C4—1584no—
680C4⋊C4—1581no—
681C4⋊C4—1581no—
682C4⋊C4—1584no—
683C4⋊C4C2×C22⋊D7914yes—
684C4⋊C4C2×C22⋊D7914yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—1584no—
690C22⋊C4—1584no—
691C22⋊C4—1584no—
692C22⋊C4—1584no—
693C22⋊C4—1584no—
694C22⋊C4C2×C22⋊D7914yes—
695C22⋊C4C2×C22⋊D7914yes—
696C42—1584no—
697C42C2×C22⋊D7912yes—
698C42C2×C22⋊D7912yes—
699C42C23×D7912yes—
700C42C23×D7912yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—3162no—
709C23—3162no—
710C23—3162no—
711C23—1582no—
712C23C22×C22⋊D7912yes—
713C23C22×C22⋊D7911yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—48no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—3162no—
725Q8—6324no—
726Q8—1582no—
727Q8—1582no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—3162no—
733D4—6324no—
734D4—1582no—
735D4—1582no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—3162no—
753C2×C4—3162no—
754C2×C4—3162no—
755C2×C4—6324no—
756C2×C4—1582no—
757C2×C4—1582no—
758C2×C4—1582no—
759C2×C4C22×C22⋊D7912yes—
760C2×C4C22×C22⋊D7912yes—
761C2×C4C22×C22⋊D7912yes—
762C2×C4C22×C22⋊D7912yes—
763C2×C4C22×C22⋊D7912yes—
764C2×C4C22×C22⋊D7911yescharacteristic
765C2×C4#1457920612yes—
766C2×C4#1457920612yes—
767C2×C4C24×D7911yescharacteristic
768C8—1582no—
769C8—1582no—
770C8—1582no—
771C8—1582no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—3162no—
781C22—3162no—
782C22—3162no—
783C22—6324no—
784C22#1909913012yes—
785C22#1909937112yes—
786C22#1909937812yes—
787C22C23×C22⋊D7911yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—3162no—
797C4—3162no—
798C4—3162no—
799C4#1909913012yes—
800C4C2×#1457920611yescharacteristic
801C4C2×#1457920611yescharacteristic
802C2—42no—
803C2—82no—
804C2—6322no—
805C2#2377450914yesdirect product factor
806C2C2×#1909913011yescharacteristic
807C2C2×#1909937111yescharacteristic
808C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#536×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098708C2
hypercenterC2×#536D79
hypocenterC79C2×#3225
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#19099184C2semidirect
2. #23774509C2direct (N × H)
3. C2×#19098955C2semidirect
4. C2×#19098945C2semidirect
5. C2×#19098922C2semidirect
6. C2×#19098913C2semidirect
7. C2×#19098782C2semidirect
8. C2×#19098770C2semidirect
9. C2×#19098775C2semidirect
10. C2×#19098765C2semidirect
11. C2×#19098725C2semidirect
13. C2×#19098719C2semidirect
14. C2×#19098702C2semidirect
15. C2×#19098624C2semidirect
16. C2×#536×C79C2semidirect
26. #19099184C22semidirect
37. #19098955C22semidirect
38. #19098945C22semidirect
39. #19098922C22semidirect
40. #19098913C22semidirect
41. #19098782C22semidirect
42. #19098775C22semidirect
43. #19098770C22semidirect
44. #19098765C22semidirect
45. #19098725C22semidirect
46. #19098719C22semidirect
48. #19098702C22semidirect
49. #19098624C22semidirect
67. #536×C79C22semidirect
400. C2×C79#3225semidirect
406. C2×#536D79semidirect
421. C79C2×#3225semidirect
435. #536C2×D79semidirect
805. C2#23774509direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991842
#237745092
C2×#190989552
C2×#190989452
C2×#190989222
C2×#190989132
C2×#190987822
C2×#190987702
C2×#190987752
C2×#190987652
C2×#190987252
C2×#190987082
C2×#190987192
C2×#190987022
C2×#190986242
C2×#536×C792
C2×#322579