Finite Group Databasebeta

← C2×#23775480 #35164794

Subgroups — C2×#23775480 #35164794

Order 20224.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099274C211yesmaximal, characteristic, complemented
2C2×#19099206C211yesmaximal, characteristic
3#23775480C2116yesmaximal, direct product factor
4C2×#19098897C211yesmaximal, characteristic, complemented
5C2×#19098875C211yesmaximal, characteristic, complemented
6C2×#19098840C211yesmaximal, characteristic, complemented
7C2×#19098808C211yesmaximal, characteristic, complemented
8C2×#19098803C211yesmaximal, characteristic, complemented
9C2×#19098782C211yesmaximal, characteristic, complemented
10C2×#19098728C211yesmaximal, characteristic, complemented
11C2×#19098715C211yesmaximal, characteristic, complemented
12C2×#19098665C211yesmaximal, characteristic, complemented
13C2×#19098636C211yesmaximal, characteristic, complemented
14C2×#19098563C211yesmaximal, characteristic, complemented
15C2×#102×D79C211yesmaximal, characteristic, complemented
16C2×#489×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic
18C22×D4×D79C2211yescharacteristic
19C22×#11929614C2211yescharacteristic, complemented
20C22×#11929613C2211yescharacteristic
21C22×#11929612C2211yescharacteristic
22C22×#11929607C2211yescharacteristic, complemented
23C22×C8×D79C2211yescharacteristic
24#19099274—24no—
25#19099274C2218yescomplemented
26#19099206—24no—
27#19099206C2218yes—
28C2×#14579152—21no—
29C2×#14579143—21no—
30C2×#14579141C2211yescharacteristic
31C2×#14579141C2211yescharacteristic, complemented
32C2×#14579137—21no—
33C2×#14579137—21no—
34C2×#14579137C2211yescharacteristic
35C2×#14579134—21no—
36C2×#14579132C2211yescharacteristic
37C2×#14579131—21no—
38C2×C4×Dic158C2211yescharacteristic, complemented
39C2×C4×D316C2211yescharacteristic
40C2×C4×D316C2211yescharacteristic
41C2×#14579123—21no—
42C2×C4⋊C4×D79C2211yescharacteristic
43C2×C4⋊C4×D79C2211yescharacteristic, complemented
44C2×C22⋊C4×D79—21no—
45#19098897C2218yescomplemented
46#19098875C2218yescomplemented
47#19098840C2218yescomplemented
48#19098808C2218yescomplemented
49#19098803C2218yescomplemented
50#19098782C2218yescomplemented
51#19098728C2218yescomplemented
52#19098715C2218yescomplemented
53#19098665C2218yescomplemented
54#19098636C2218yescomplemented
55C2×#14579095C2211yescharacteristic, complemented
56C2×#14579094C2211yescharacteristic, complemented
57C2×#14579094C2211yescharacteristic, complemented
58C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
59#19098563C2218yescomplemented
60C2×#14579086C2211yescharacteristic, complemented
61C2×#14579085C2211yescharacteristic, complemented
62C2×#14579083C2211yescharacteristic
63C2×#14579082C2211yescharacteristic
64C2×#14579081C2211yescharacteristic
65C2×#14579081C2211yescharacteristic
66#102×D79C2218yescomplemented
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×(C2×D79)⋊C8C2211yescharacteristic, complemented
69C2×C4⋊Q8×C79C2211yescharacteristic, complemented
70C2×#124×C79C2211yescharacteristic
71#489×C79C2218yescomplemented
72C2×#103×C79C2211yescharacteristic, complemented
73C2×#103×C79C2211yescharacteristic, complemented
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic, complemented
77C24×D79—21no—
78C2×#11929625—22no—
79C2×#11929625—24no—
80C2×#11929625—42no—
81C2×#11929625C2314yes—
82C22×Dic158C2311yescharacteristic
83C22×D316—21no—
84C22×D316D411yescharacteristic
85C22×D316C2311yescharacteristic
86C22×C22⋊D79—21no—
87C22×C22⋊D79—21no—
88C2×D4×D79—24no—
89C2×D4×D79—22no—
90C2×D4×D79—42no—
91C2×D4×D79C2314yes—
92C22×C4×D79—21no—
93C22×C4×D79—21no—
94C22×C4×D79—21no—
95C22×C4×D79—21no—
96C22×C4×D79C2311yescharacteristic
97C22×C4×D79C2311yescharacteristic
98C2×#11929614—42no—
99C2×#11929614C2314yescomplemented
100C2×#11929613—24no—
101C2×#11929613C2314yes—
102C2×#11929612—42no—
103C2×#11929612C2314yes—
104C2×#11929607—42no—
105C2×#11929607C2314yescomplemented
106C22×C79⋊C8C2311yescharacteristic
107C22×C79⋊C8C2311yescharacteristic
108C2×C8×D79—42no—
109C2×C8×D79C2314yes—
110#14579152—28no—
111#14579143—28no—
112#14579141—22no—
113#14579141—22no—
114#14579141C2314yes—
115#14579141C2314yescomplemented
116#14579137—22no—
117#14579137—28no—
118#14579137—28no—
119#14579137C2314yes—
120#14579134—28no—
121#14579132—22no—
122#14579132C2314yes—
123#14579131—28no—
124C4×Dic158—22no—
125C4×Dic158C2314yescomplemented
126C4×D316—22no—
127C4×D316D414yes—
128C4×D316C2314yes—
129C4×D316C2314yes—
130#14579123—28no—
131C2×C4⋊Dic79—21no—
132C2×C4⋊Dic79—21no—
133C2×C4⋊Dic79D411yescharacteristic
134C2×C4⋊Dic79C2311yescharacteristic
135C2×C4⋊Dic79C2311yescharacteristic
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C2×Dic79⋊C4—21no—
140C4⋊C4×D79—22no—
141C4⋊C4×D79—22no—
142C4⋊C4×D79C2314yes—
143C4⋊C4×D79C2314yescomplemented
144C2×C22⋊Dic79—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×(C2×D79)⋊C4—21no—
147C2×(C2×D79)⋊C4—21no—
148C2×(C2×D79)⋊C4—21no—
149C2×(C2×D79)⋊C4D411yescharacteristic
150C2×(C2×D79)⋊C4D411yescharacteristic
151C22⋊C4×D79—28no—
152C2×C4×Dic79—21no—
153#14579095C2314yescomplemented
154#14579094C2314yescomplemented
155#14579094C2314yescomplemented
156C4⋊(C79⋊C8)C2314yescomplemented
157#14579086C2314yescomplemented
158#14579085C2314yescomplemented
159#14579083C2314yes—
160#14579082C2314yes—
161#14579081C2314yes—
162#14579081C2314yes—
163(C2×D79)⋊C8C2314yes—
164(C2×D79)⋊C8C2314yescomplemented
165C22×Q8×C79—21no—
166C22×Q8×C79C2311yescharacteristic
167C22×D4×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170C4⋊Q8×C79—22no—
171C4⋊Q8×C79C2314yescomplemented
172#124×C79—22no—
173#124×C79C2314yes—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179C2×C42×C79C2311yescharacteristic
180#103×C79C2314yescomplemented
181#103×C79C2314yescomplemented
182#102×C79C2314yes—
183#102×C79C2314yes—
184#97×C79C2314yescomplemented
185C23×D79—21no—
186C23×D79—24no—
187C23×D79—44no—
188C23×D79—44no—
189C23×D79—82no—
190C23×D79C2×D411yescharacteristic
191C23×D79C2×D411yescharacteristic
192#11929625—28no—
193#11929625—44no—
194#11929625—48no—
195C2×Dic158—21no—
196C2×Dic158—22no—
197C2×Dic158—22no—
198C2×Dic158C2412yes—
199C2×D316—24no—
200C2×D316—24no—
201C2×D316—21no—
202C2×D316—22no—
203C2×D316—44no—
204C2×D316C2×D414yes—
205C2×D316#4114yes—
206C2×D316C2412yes—
207C2×C22⋊D79—24no—
208C2×C22⋊D79—24no—
209C2×C22⋊D79—44no—
210C2×C22⋊D79—82no—
211D4×D79—28no—
212D4×D79—44no—
213D4×D79—48no—
214C22×Dic79—21no—
215C22×Dic79—21no—
216C22×Dic79—21no—
217C22×Dic79C2×D411yescharacteristic
218C22×Dic79C2×D411yescharacteristic
219C2×C4×D79—24no—
220C2×C4×D79—24no—
221C2×C4×D79—24no—
222C2×C4×D79—24no—
223C2×C4×D79—22no—
224C2×C4×D79—22no—
225C2×C4×D79—22no—
226C2×C4×D79—22no—
227C2×C4×D79—44no—
228C2×C4×D79—82no—
229C2×C4×D79—82no—
230C2×C4×D79—82no—
231C2×C4×D79C2×D412yes—
232C2×C4×D79C2×D412yes—
233C2×C4×D79C2412yes—
234C2×C4×D79C2412yes—
235#11929614—44no—
236#11929613—28no—
237#11929612—44no—
238#11929607—44no—
239C2×C79⋊C8—22no—
240C2×C79⋊C8—22no—
241C2×C79⋊C8C2412yes—
242C2×C79⋊C8C2412yes—
243C8×D79—44no—
244C4⋊Dic79—24no—
245C4⋊Dic79—24no—
246C4⋊Dic79—21no—
247C4⋊Dic79—21no—
248C4⋊Dic79C2×D414yes—
249C4⋊Dic79C2412yes—
250C4⋊Dic79C2412yes—
251Dic79⋊C4—24no—
252Dic79⋊C4—24no—
253Dic79⋊C4—24no—
254Dic79⋊C4—24no—
255C22⋊Dic79—24no—
256(C2×D79)⋊C4—24no—
257(C2×D79)⋊C4—24no—
258(C2×D79)⋊C4—24no—
259(C2×D79)⋊C4—24no—
260(C2×D79)⋊C4C2×D414yes—
261(C2×D79)⋊C4C2×D414yes—
262C4×Dic79—24no—
263C24×C79—21no—
264C2×Q8×C79—21no—
265C2×Q8×C79—24no—
266C2×Q8×C79—22no—
267C2×Q8×C79—22no—
268C2×Q8×C79—82no—
269C2×Q8×C79C2412yes—
270C2×D4×C79—21no—
271C2×D4×C79—22no—
272C2×D4×C79—22no—
273C2×D4×C79C2412yes—
274C22×C4×C79—21no—
275C22×C4×C79—21no—
276C22×C4×C79—21no—
277C22×C4×C79C2×D411yescharacteristic
278C22×C4×C79C2×D411yescharacteristic
279C22×C4×C79C2411yescharacteristic
280C2×C8×C79—22no—
281C2×C8×C79—22no—
282C2×C8×C79C2412yes—
283C2×C8×C79C2412yes—
284C4⋊C4×C79—24no—
285C4⋊C4×C79—21no—
286C4⋊C4×C79—21no—
287C4⋊C4×C79C2412yes—
288C4⋊C4×C79C2412yes—
289C22⋊C4×C79—24no—
290C22⋊C4×C79—24no—
291C42×C79C2×D412yes—
292C42×C79C2412yes—
293C23×C79—22no—
294C23×C79—42no—
295C23×C79—42no—
296C23×C79—42no—
297C23×C79C22×D411yescharacteristic
298C22×D79—22no—
299C22×D79—22no—
300C22×D79—22no—
301C22×D79—24no—
302C22×D79—22no—
303C22×D79—22no—
304C22×D79—22no—
305C22×D79—48no—
306C22×D79—42no—
307C22×D79—42no—
308C22×D79—48no—
309C22×D79—84no—
310C22×D79—816no—
311C22×D79#13714yes—
312C22×D79C22×D412yes—
313C22×D79C22×D412yes—
314Q8×C79—22no—
315Q8×C79—22no—
316Q8×C79—42no—
317Q8×C79—84no—
318D4×C79—22no—
319D4×C79—22no—
320D4×C79—42no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—22no—
324C2×C4×C79—22no—
325C2×C4×C79—22no—
326C2×C4×C79—42no—
327C2×C4×C79—42no—
328C2×C4×C79—42no—
329C2×C4×C79C22×D412yes—
330C2×C4×C79C22×D412yes—
331C2×C4×C79C22×D411yescharacteristic
332C2×C4×C79C2×#4112yes—
333C2×C4×C79H(5,𝔽2)12yes—
334C2×C4×C79C2511yescharacteristic
335C22⋊D79—48no—
336C22⋊D79—84no—
337C2×Dic79—22no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—22no—
341C2×Dic79—22no—
342C2×Dic79—42no—
343C2×Dic79—42no—
344C2×Dic79—42no—
345C2×Dic79C22×D412yes—
346C2×Dic79C22×D412yes—
347D316—28no—
348D316—24no—
349D316—22no—
350D316—48no—
351D316C2×#4114yes—
352C4×D79—24no—
353C4×D79—24no—
354C4×D79—22no—
355C4×D79—22no—
356C4×D79—22no—
357C4×D79—22no—
358C4×D79—48no—
359C4×D79—84no—
360C4×D79—84no—
361C4×D79—84no—
362Dic158—22no—
363Dic158—22no—
364Dic158—42no—
365C8×C79—22no—
366C8×C79—22no—
367C79⋊C8—22no—
368C79⋊C8—22no—
369C22×C79—42no—
370C22×C79—42no—
371C22×C79—42no—
372C22×C79—84no—
373C22×C79#54612yes—
374C22×C79C2×#13712yes—
375C22×C79#57612yes—
376C22×C79C23×D411yescharacteristic
377C2×D79—22no—
378C2×D79—28no—
379C2×D79—22no—
380C2×D79—24no—
381C2×D79—22no—
382C2×D79—22no—
383C2×D79—22no—
384C2×D79—44no—
385C2×D79—48no—
386C2×D79—42no—
387C2×D79—42no—
388C2×D79—816no—
389C2×D79C2×#13714yes—
390C4×C79—22no—
391C4×C79—22no—
392C4×C79—42no—
393C4×C79—42no—
394C4×C79—42no—
395C4×C79#54612yes—
396C4×C79C22×#4111yescharacteristic
397C4×C79C2×H(5,𝔽2)11yescharacteristic
398Dic79—22no—
399Dic79—22no—
400Dic79—42no—
401Dic79—42no—
402Dic79—42no—
403C2×#3314—791nomaximal, Sylow
404C2×C79—82no—
405C2×C79#331414yescomplemented
406C2×C79C2×#54611yescharacteristic
407C2×C79C22×#13711yescharacteristic
408C2×C79C2×#57611yescharacteristic
409D79—24no—
410D79—42no—
411D79—44no—
412C2×#554—791no—
413C2×#546—791no—
414#3314—7916no—
415C2×#489D7911yescharacteristic, complemented
416C2×#484—791no—
417C2×#480—791no—
418C2×#474—791no—
419C2×#468—791no—
420C2×#467—791no—
421C2×#464—791no—
422C2×#452—791no—
423C2×#450—791no—
424C2×#440—791no—
425C2×#435—791no—
426C2×#417—791no—
427C22×#102—791no—
428C79C2×#331411yescharacteristic, complemented, Sylow
429C22×#41—791no—
430C23×D4—791no—
431C22×Q16—791no—
432C22×SD16—791no—
433C22×SD16—791no—
434C22×M16—791no—
435C23×C8—791no—
436#554—798no—
437#554—1584no—
438#546—798no—
439#546—1584no—
440C2×C4⋊Q8C2×D7911yescharacteristic, complemented
441C2×#125—1581no—
442C2×#124C2×D7911yescharacteristic
443C2×#123—1581no—
444C2×C22⋊Q8—791no—
445C2×C22⋊Q8—791no—
446C2×C22⋊Q8—791no—
447C2×C22⋊Q8—1581no—
448C2×C22⋊Q8—1581no—
449C2×#121—791no—
450C2×#121—1581no—
451C2×#120—1581no—
452C2×C4×Q8—791no—
453C2×C4×D4—791no—
454C2×C4×D4—791no—
455C2×C4×D4—1581no—
456C22×C4⋊C4—791no—
457C22×C4⋊C4—791no—
458C22×C22⋊C4—1581no—
459#489C2×D7918yescomplemented
460#484—798no—
461#480—798no—
462#474—798no—
463#468—798no—
464#467—798no—
465#464—798no—
466#452—798no—
467#450—798no—
468#440—798no—
469#435—798no—
470C2×#107—791no—
471C2×#107—791no—
472C2×#107—791no—
473C2×C4⋊C8—791no—
474#417—798no—
475C2×#103—791no—
476C2×#103—791no—
477C2×#103C2×D7911yescharacteristic, complemented
478C2×#103C2×D7911yescharacteristic, complemented
479C2×#102—791no—
480C2×#102—791no—
481C2×#102—791no—
482C2×#102—791no—
483C2×#102—798no—
484C2×#102C2×D7911yescharacteristic
485C2×#102C2×D7911yescharacteristic
486C2×C22⋊C8—791no—
487C2×C22⋊C8—791no—
488C2×#97C2×D7911yescharacteristic, complemented
489C25—1581no—
490C2×#41—3162no—
491C2×#41—794no—
492C2×#41—1584no—
493C2×#41—1582no—
494C22×Q8—21no—
495C22×Q8—791no—
496C22×Q8C22×D7911yescharacteristic
497C22×D4—3162no—
498C22×D4—794no—
499C22×D4—791no—
500C22×D4—791no—
501C22×D4—1581no—
502C22×D4—1582no—
503C22×D4—1581no—
504C22×D4—1584no—
505C22×D4—1581no—
506C22×D4C22×D7911yescharacteristic
507C23×C4—791no—
508C23×C4—791no—
509C23×C4—1581no—
510C23×C4—1581no—
511C23×C4—1581no—
512C23×C4—1581no—
513C2×Q16—3162no—
514C2×Q16—794no—
515C2×SD16—3162no—
516C2×SD16—794no—
517C2×SD16—794no—
518C2×SD16—1584no—
519C2×M16—3162no—
520C2×M16—794no—
521C22×C8—3162no—
522C22×C8—794no—
523C22×C8—791no—
524C22×C8—791no—
525C22×C8C22×D7911yescharacteristic
526C22×C8C22×D7911yescharacteristic
527C4⋊Q8—22no—
528C4⋊Q8C22×D7914yescomplemented
529#125—1588no—
530#124—22no—
531#124C22×D7914yes—
532#123—1588no—
533C22⋊Q8—794no—
534C22⋊Q8—794no—
535C22⋊Q8—794no—
536C22⋊Q8—1588no—
537C22⋊Q8—1588no—
538C22⋊Q8—1582no—
539C22⋊Q8—1582no—
540C22⋊Q8—1582no—
541#121—794no—
542#121—1588no—
543#121—1582no—
544#120—1588no—
545C4×Q8—794no—
546C4×Q8—1582no—
547C4×D4—794no—
548C4×D4—794no—
549C4×D4—794no—
550C4×D4—1588no—
551C4×D4—1582no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—791no—
554C2×C4⋊C4—791no—
555C2×C4⋊C4—791no—
556C2×C4⋊C4—794no—
557C2×C4⋊C4—794no—
558C2×C4⋊C4—1582no—
559C2×C4⋊C4—1582no—
560C2×C4⋊C4—1581no—
561C2×C4⋊C4—1581no—
562C2×C4⋊C4—1581no—
563C2×C4⋊C4—1581no—
564C2×C4⋊C4—1581no—
565C2×C4⋊C4—1581no—
566C2×C4⋊C4C22×D7911yescharacteristic
567C2×C4⋊C4C22×D7911yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—791no—
571C2×C22⋊C4—791no—
572C2×C22⋊C4—1588no—
573C2×C22⋊C4—1581no—
574C2×C22⋊C4—1581no—
575C2×C22⋊C4—1581no—
576C2×C22⋊C4—1581no—
577C2×C22⋊C4—1581no—
578C2×C42—1581no—
579C2×C42C22×D7911yescharacteristic
580#107—794no—
581#107—794no—
582#107—794no—
583C4⋊C8—794no—
584#103—794no—
585#103—794no—
586#103C22×D7914yescomplemented
587#103C22×D7914yescomplemented
588#102—794no—
589#102—794no—
590#102—794no—
591#102—794no—
592#102C22×D7914yes—
593#102C22×D7914yes—
594C22⋊C8—794no—
595C22⋊C8—794no—
596#97C22×D7914yescomplemented
597C24—21no—
598C24—3164no—
599C24—3164no—
600C24—791no—
601C24—791no—
602C24—6322no—
603C24—1584no—
604C24—1581no—
605#41—3164no—
606#41—3168no—
607#41—1588no—
608C2×Q8—21no—
609C2×Q8—24no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—82no—
613C2×Q8—792no—
614C2×Q8—1582no—
615C2×Q8—1582no—
616C2×Q8—1581no—
617C2×Q8C23×D7912yes—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—21no—
621C2×D4—3164no—
622C2×D4—3164no—
623C2×D4—3168no—
624C2×D4—3164no—
625C2×D4—794no—
626C2×D4—792no—
627C2×D4—794no—
628C2×D4—6322no—
629C2×D4—1584no—
630C2×D4—1584no—
631C2×D4—1584no—
632C2×D4—1588no—
633C2×D4—1584no—
634C2×D4—1582no—
635C2×D4—1581no—
636C2×D4C23×D7912yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—3164no—
641C22×C4—791no—
642C22×C4—791no—
643C22×C4—792no—
644C22×C4—792no—
645C22×C4—792no—
646C22×C4—792no—
647C22×C4—6322no—
648C22×C4—6322no—
649C22×C4—6322no—
650C22×C4—1584no—
651C22×C4—1584no—
652C22×C4—1584no—
653C22×C4—1581no—
654C22×C4—1581no—
655C22×C4—1581no—
656C22×C4—1584no—
657C22×C4—1582no—
658C22×C4—1582no—
659C22×C4—1582no—
660C22×C4—1582no—
661C22×C4D4×D7911yescharacteristic
662C22×C4D4×D7911yescharacteristic
663C22×C4C23×D7911yescharacteristic
664Q16—3164no—
665SD16—3164no—
666SD16—1588no—
667M16—3164no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—3164no—
671C2×C8—792no—
672C2×C8—792no—
673C2×C8—1582no—
674C2×C8—1582no—
675C2×C8C23×D7912yes—
676C2×C8C23×D7912yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—794no—
681C4⋊C4—792no—
682C4⋊C4—792no—
683C4⋊C4—1584no—
684C4⋊C4—1584no—
685C4⋊C4—1584no—
686C4⋊C4—1584no—
687C4⋊C4—1584no—
688C4⋊C4—1584no—
689C4⋊C4—1581no—
690C4⋊C4—1581no—
691C4⋊C4C23×D7912yes—
692C4⋊C4C23×D7912yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—794no—
696C22⋊C4—794no—
697C22⋊C4—1584no—
698C22⋊C4—1584no—
699C22⋊C4—1584no—
700C22⋊C4—1584no—
701C22⋊C4—1584no—
702C42—1584no—
703C42D4×D7912yes—
704C42C23×D7912yes—
705C23—22no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—3168no—
710C23—3168no—
711C23—3162no—
712C23—3162no—
713C23—794no—
714C23—792no—
715C23—792no—
716C23—6324no—
717C23—63216no—
718C23—1584no—
719C23—1582no—
720C23—1582no—
721C23—1582no—
722C23—1582no—
723C23—1582no—
724C23—1582no—
725C23C2×D4×D7911yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—84no—
730Q8—3162no—
731Q8—1582no—
732Q8—1582no—
733D4—22no—
734D4—22no—
735D4—42no—
736D4—3168no—
737D4—3168no—
738D4—794no—
739D4—6324no—
740D4—1588no—
741D4—1582no—
742D4—1584no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—3168no—
752C2×C4—3162no—
753C2×C4—3162no—
754C2×C4—3162no—
755C2×C4—792no—
756C2×C4—792no—
757C2×C4—6324no—
758C2×C4—6324no—
759C2×C4—6324no—
760C2×C4—1582no—
761C2×C4—1582no—
762C2×C4—1582no—
763C2×C4—1582no—
764C2×C4—1582no—
765C2×C4—1582no—
766C2×C4—1582no—
767C2×C4—1584no—
768C2×C4—1584no—
769C2×C4—1582no—
770C2×C4—1582no—
771C2×C4C2×D4×D7912yes—
772C2×C4C2×D4×D7912yes—
773C2×C4C2×D4×D7911yescharacteristic
774C2×C4#41×D7912yes—
775C2×C4#1457920712yes—
776C2×C4C24×D7911yescharacteristic
777C8—22no—
778C8—22no—
779C8—1582no—
780C8—1582no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—3162no—
786C22—3162no—
787C22—3168no—
788C22—3164no—
789C22—794no—
790C22—63216no—
791C22—1584no—
792C22—1582no—
793C22—1582no—
794C22—1582no—
795C22—1582no—
796C22—1582no—
797C22—1588no—
798C22#1909920612yes—
799C22#137×D7912yes—
800C22#1909936712yes—
801C22C22×D4×D7911yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—3162no—
808C4—3162no—
809C4—3162no—
810C4—1582no—
811C4—1582no—
812C4#1909920612yes—
813C4C2×#41×D7911yescharacteristic
814C4C2×#1457920711yescharacteristic
815C2—82no—
816C2—3164no—
817C2—3162no—
818C2—1584no—
819C2#2377548014yesdirect product factor
820C2C2×#1909920611yescharacteristic
821C2C2×#137×D7911yescharacteristic
822C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#489×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099206C2
hypercenterC2×#489D79
hypocenterC79C2×#3314
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#19099274C2semidirect
3. #23775480C2direct (N × H)
4. C2×#19098897C2semidirect
5. C2×#19098875C2semidirect
6. C2×#19098840C2semidirect
7. C2×#19098808C2semidirect
8. C2×#19098803C2semidirect
9. C2×#19098782C2semidirect
10. C2×#19098728C2semidirect
11. C2×#19098715C2semidirect
12. C2×#19098665C2semidirect
13. C2×#19098636C2semidirect
14. C2×#19098563C2semidirect
15. C2×#102×D79C2semidirect
16. C2×#489×C79C2semidirect
19. C22×#11929614C22semidirect
22. C22×#11929607C22semidirect
25. #19099274C22semidirect
31. C2×#14579141C22semidirect
38. C2×C4×Dic158C22semidirect
43. C2×C4⋊C4×D79C22semidirect
45. #19098897C22semidirect
46. #19098875C22semidirect
47. #19098840C22semidirect
48. #19098808C22semidirect
49. #19098803C22semidirect
50. #19098782C22semidirect
51. #19098728C22semidirect
52. #19098715C22semidirect
53. #19098665C22semidirect
54. #19098636C22semidirect
55. C2×#14579095C22semidirect
56. C2×#14579094C22semidirect
57. C2×#14579094C22semidirect
58. C2×C4⋊(C79⋊C8)C22semidirect
59. #19098563C22semidirect
60. C2×#14579086C22semidirect
61. C2×#14579085C22semidirect
66. #102×D79C22semidirect
68. C2×(C2×D79)⋊C8C22semidirect
69. C2×C4⋊Q8×C79C22semidirect
71. #489×C79C22semidirect
72. C2×#103×C79C22semidirect
73. C2×#103×C79C22semidirect
76. C2×#97×C79C22semidirect
99. C2×#11929614C23semidirect
105. C2×#11929607C23semidirect
115. #14579141C23semidirect
125. C4×Dic158C23semidirect
143. C4⋊C4×D79C23semidirect
153. #14579095C23semidirect
154. #14579094C23semidirect
155. #14579094C23semidirect
156. C4⋊(C79⋊C8)C23semidirect
157. #14579086C23semidirect
158. #14579085C23semidirect
164. (C2×D79)⋊C8C23semidirect
171. C4⋊Q8×C79C23semidirect
180. #103×C79C23semidirect
181. #103×C79C23semidirect
184. #97×C79C23semidirect
405. C2×C79#3314semidirect
415. C2×#489D79semidirect
428. C79C2×#3314semidirect
440. C2×C4⋊Q8C2×D79semidirect
459. #489C2×D79semidirect
477. C2×#103C2×D79semidirect
478. C2×#103C2×D79semidirect
488. C2×#97C2×D79semidirect
528. C4⋊Q8C22×D79semidirect
586. #103C22×D79semidirect
587. #103C22×D79semidirect
596. #97C22×D79semidirect
819. C2#23775480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992742
C2×#190992062
#237754802
C2×#190988972
C2×#190988752
C2×#190988402
C2×#190988082
C2×#190988032
C2×#190987822
C2×#190987282
C2×#190987152
C2×#190986652
C2×#190986362
C2×#190985632
C2×#102×D792
C2×#489×C792
C2×#331479