Finite Group Databasebeta

← C2×#23774981 #35163326

Subgroups — C2×#23774981 #35163326

Order 20224.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579191C211yesmaximal, characteristic, complemented
2C22×#14579181C211yesmaximal, characteristic, complemented
3C2×#19099222C211yesmaximal, characteristic, complemented
4#23774981C2116yesmaximal, direct product factor
5C2×#19098950C211yesmaximal, characteristic, complemented
6C2×#19098814C211yesmaximal, characteristic, complemented
7C2×#19098790C211yesmaximal, characteristic, complemented
8C2×#19098785C211yesmaximal, characteristic, complemented
9C2×#19098760C211yesmaximal, characteristic, complemented
10C2×#19098725C211yesmaximal, characteristic, complemented
11C2×#19098708C211yesmaximal, characteristic, complemented
12C2×#19098706C211yesmaximal, characteristic, complemented
13C2×#19098701C211yesmaximal, characteristic, complemented
14C2×#19098668C211yesmaximal, characteristic, complemented
15C2×#19098635C211yesmaximal, characteristic, complemented
16C2×#550×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C23×Dic158C2211yescharacteristic
19C2×#14579191—28no—
20C2×#14579191C2218yescomplemented
21C2×#14579181—28no—
22C2×#14579181C2218yescomplemented
23C22×#11929614C2211yescharacteristic
24C22×#11929614C2211yescharacteristic
25C22×#11929612C2211yescharacteristic
26C22×#11929612C2211yescharacteristic
27C22×#11929612C2211yescharacteristic
28C22×#11929612C2211yescharacteristic
29C22×#11929611C2211yescharacteristic
30C22×#11929609C2211yescharacteristic
31C22×#11929609C2211yescharacteristic
32C22×#11929608C2211yescharacteristic
33C23×C79⋊C8C2211yescharacteristic
34#19099222—24no—
35#19099222C2218yescomplemented
36C2×#14579149C2211yescharacteristic
37C2×#14579147—21no—
38C2×#14579140C2211yescharacteristic
39C2×#14579139—21no—
40C2×#14579135C2211yescharacteristic
41C2×#14579133—21no—
42C2×C4×Dic158C2211yescharacteristic
43C2×(C22⋊D79)⋊C4—21no—
44#19098950C2218yescomplemented
45#19098814C2218yescomplemented
46#19098790C2218yescomplemented
47#19098785C2218yescomplemented
48#19098760C2218yescomplemented
49#19098725C2218yescomplemented
50#19098708C2218yescomplemented
51#19098706C2218yescomplemented
52#19098701C2218yescomplemented
53#19098668C2218yescomplemented
54#19098635C2218yescomplemented
55C2×#14579092C2211yescharacteristic
56C2×C4⋊(C79⋊C8)C2211yescharacteristic
57C2×#14579085C2211yescharacteristic
58C2×#14579084C2211yescharacteristic
59C2×#14579084C2211yescharacteristic
60C2×#14579082C2211yescharacteristic
61C2×#14579082C2211yescharacteristic
62C2×#14579081C2211yescharacteristic
63C2×C22⋊(C79⋊C8)C2211yescharacteristic
64C2×C22⋊(C79⋊C8)C2211yescharacteristic
65C2×#14579072C2211yescharacteristic
66C22×#41×C79C2211yescharacteristic
67C22×#41×C79C2211yescharacteristic
68#550×C79—24no—
69#550×C79C2218yescomplemented
70C2×#127×C79—21no—
71C2×#127×C79C2211yescharacteristic
72C2×#121×C79—21no—
73C2×#121×C79—21no—
74C2×#121×C79C2211yescharacteristic
75C2×#121×C79C2211yescharacteristic
76C2×C4×Q8×C79C2211yescharacteristic
77C2×C4×D4×C79—21no—
78C2×C4×D4×C79C2211yescharacteristic
79C2×#11929624—22no—
80C2×#11929624—24no—
81C2×#11929624—42no—
82C2×#11929624C2314yes—
83C22×Dic158—22no—
84C22×Dic158—21no—
85C22×Dic158—24no—
86C22×Dic158—42no—
87C22×Dic158C2311yescharacteristic
88C22×Dic158C2314yes—
89C22×Dic158C2311yescharacteristic
90C22×D316C2311yescharacteristic
91C22×C22⋊D79—21no—
92C22×C22⋊D79—21no—
93C23×Dic79—21no—
94C22×C4×D79—21no—
95#14579191—232no—
96#14579181—232no—
97C2×#11929614—24no—
98C2×#11929614D418yescomplemented
99C2×#11929614C2314yes—
100C2×#11929614C2314yes—
101C2×#11929612—24no—
102C2×#11929612—24no—
103C2×#11929612—24no—
104C2×#11929612—42no—
105C2×#11929612C2314yes—
106C2×#11929612C2314yes—
107C2×#11929612C2314yes—
108C2×#11929612C2314yes—
109C2×#11929611—24no—
110C2×#11929611C2314yes—
111C2×#11929609—24no—
112C2×#11929609—42no—
113C2×#11929609C2314yes—
114C2×#11929609C2314yes—
115C2×#11929608—24no—
116C2×#11929608C2314yes—
117C22×C79⋊C8—24no—
118C22×C79⋊C8C2314yes—
119C22×C79⋊C8C2311yescharacteristic
120C22×C79⋊C8C2311yescharacteristic
121C22×C79⋊C8C2311yescharacteristic
122C22×C79⋊C8C2311yescharacteristic
123#14579149—22no—
124#14579149C2314yes—
125#14579147—28no—
126#14579140—22no—
127#14579140C2314yes—
128#14579139—28no—
129#14579135—22no—
130#14579135C2314yes—
131#14579133—28no—
132C4×Dic158—22no—
133C4×Dic158C2314yes—
134(C22⋊D79)⋊C4—28no—
135C2×C4⋊Dic79C2311yescharacteristic
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×C22⋊Dic79—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×C4×Dic79—21no—
143#14579092C2314yes—
144C4⋊(C79⋊C8)C2314yes—
145#14579085C2314yes—
146#14579084C2314yes—
147#14579084C2314yes—
148#14579082C2314yes—
149#14579082C2314yes—
150#14579081C2314yes—
151C22⋊(C79⋊C8)C2314yes—
152C22⋊(C79⋊C8)C2314yes—
153#14579072C2314yes—
154C2×#41×C79—22no—
155C2×#41×C79—22no—
156C2×#41×C79—24no—
157C2×#41×C79—24no—
158C2×#41×C79—42no—
159C2×#41×C79—42no—
160C2×#41×C79C2314yes—
161C2×#41×C79C2314yes—
162C22×Q8×C79C2311yescharacteristic
163C22×D4×C79—21no—
164C22×D4×C79—21no—
165C22×D4×C79—21no—
166C22×D4×C79—21no—
167C22×D4×C79—21no—
168C22×D4×C79—21no—
169C22×D4×C79D411yescharacteristic
170C22×D4×C79C2311yescharacteristic
171C22×D4×C79C2311yescharacteristic
172C23×C4×C79—21no—
173C23×C4×C79—21no—
174C23×C4×C79C2311yescharacteristic
175C23×C4×C79C2311yescharacteristic
176#127×C79—28no—
177#127×C79—22no—
178#127×C79C2314yes—
179#121×C79—22no—
180#121×C79—22no—
181#121×C79—28no—
182#121×C79—28no—
183#121×C79C2314yes—
184#121×C79C2314yes—
185C4×Q8×C79—22no—
186C4×Q8×C79C2314yes—
187C4×D4×C79—28no—
188C4×D4×C79D414yes—
189C4×D4×C79C2314yes—
190C2×C4⋊C4×C79—21no—
191C2×C4⋊C4×C79D411yescharacteristic
192C2×C4⋊C4×C79C2311yescharacteristic
193C2×C22⋊C4×C79—21no—
194C2×C22⋊C4×C79—21no—
195C2×C22⋊C4×C79D411yescharacteristic
196C2×C22⋊C4×C79D411yescharacteristic
197C2×C42×C79—21no—
198C2×C42×C79C2311yescharacteristic
199C23×D79—21no—
200#11929624—28no—
201#11929624—44no—
202#11929624—48no—
203C2×Dic158—28no—
204C2×Dic158—21no—
205C2×Dic158—22no—
206C2×Dic158—24no—
207C2×Dic158—21no—
208C2×Dic158—22no—
209C2×Dic158—22no—
210C2×Dic158—44no—
211C2×Dic158—48no—
212C2×Dic158—44no—
213C2×Dic158C2×D414yes—
214C2×Dic158C2412yes—
215C2×Dic158C2412yes—
216C2×D316—21no—
217C2×D316—22no—
218C2×D316—22no—
219C2×D316C2412yes—
220C2×C22⋊D79—24no—
221C2×C22⋊D79—24no—
222C2×C22⋊D79—44no—
223C2×C22⋊D79—44no—
224C22×Dic79—21no—
225C22×Dic79—21no—
226C22×Dic79—24no—
227C22×Dic79—21no—
228C22×Dic79—44no—
229C2×C4×D79—24no—
230C2×C4×D79—44no—
231#11929614—28no—
232#11929614C2×D4116yescomplemented
233#11929612—28no—
234#11929612—28no—
235#11929612—28no—
236#11929612—44no—
237#11929611—28no—
238#11929609—28no—
239#11929609—44no—
240#11929608—28no—
241C2×C79⋊C8—28no—
242C2×C79⋊C8—22no—
243C2×C79⋊C8—22no—
244C2×C79⋊C8—22no—
245C2×C79⋊C8C2×D414yes—
246C2×C79⋊C8C2412yes—
247C2×C79⋊C8C2412yes—
248C2×C79⋊C8C2412yes—
249C2×C79⋊C8C2412yes—
250C4⋊Dic79—21no—
251C4⋊Dic79C2412yes—
252Dic79⋊C4—24no—
253Dic79⋊C4—24no—
254C22⋊Dic79—24no—
255(C2×D79)⋊C4—24no—
256(C2×D79)⋊C4—24no—
257(C2×D79)⋊C4—24no—
258C4×Dic79—24no—
259C24×C79—21no—
260C24×C79—21no—
261C24×C79C2×D411yescharacteristic
262C24×C79C2×D411yescharacteristic
263#41×C79—28no—
264#41×C79—28no—
265#41×C79—44no—
266#41×C79—44no—
267#41×C79—48no—
268#41×C79—48no—
269C2×Q8×C79—21no—
270C2×Q8×C79—22no—
271C2×Q8×C79C2×D414yes—
272C2×Q8×C79C2412yes—
273C2×D4×C79—24no—
274C2×D4×C79—24no—
275C2×D4×C79—24no—
276C2×D4×C79—24no—
277C2×D4×C79—22no—
278C2×D4×C79—22no—
279C2×D4×C79—24no—
280C2×D4×C79—21no—
281C2×D4×C79—21no—
282C2×D4×C79—24no—
283C2×D4×C79—22no—
284C2×D4×C79—22no—
285C2×D4×C79—42no—
286C2×D4×C79—44no—
287C2×D4×C79—44no—
288C2×D4×C79—44no—
289C2×D4×C79—82no—
290C2×D4×C79—82no—
291C2×D4×C79—82no—
292C2×D4×C79C2×D414yes—
293C2×D4×C79C2412yes—
294C2×D4×C79C2412yes—
295C22×C4×C79—21no—
296C22×C4×C79—22no—
297C22×C4×C79—22no—
298C22×C4×C79—22no—
299C22×C4×C79—22no—
300C22×C4×C79—21no—
301C22×C4×C79—24no—
302C22×C4×C79—24no—
303C22×C4×C79—44no—
304C22×C4×C79—44no—
305C22×C4×C79C2×D411yescharacteristic
306C22×C4×C79C2×D412yes—
307C22×C4×C79C2×D412yes—
308C22×C4×C79C2×D411yescharacteristic
309C22×C4×C79C2×D411yescharacteristic
310C22×C4×C79C2×D411yescharacteristic
311C22×C4×C79C2412yes—
312C22×C4×C79C2412yes—
313C22×C4×C79C2411yescharacteristic
314C4⋊C4×C79—24no—
315C4⋊C4×C79—21no—
316C4⋊C4×C79C2×D414yes—
317C4⋊C4×C79C2412yes—
318C22⋊C4×C79—24no—
319C22⋊C4×C79—24no—
320C22⋊C4×C79C2×D414yes—
321C22⋊C4×C79C2×D414yes—
322C42×C79—24no—
323C42×C79C2×D412yes—
324C42×C79C2412yes—
325C23×C79—22no—
326C23×C79—22no—
327C23×C79—22no—
328C23×C79—22no—
329C23×C79—22no—
330C23×C79—22no—
331C23×C79—22no—
332C23×C79—22no—
333C23×C79—42no—
334C23×C79—42no—
335C23×C79—42no—
336C23×C79—42no—
337C23×C79—42no—
338C23×C79—42no—
339C23×C79C22×D412yes—
340C23×C79C22×D412yes—
341C23×C79C22×D411yescharacteristic
342C22×D79—22no—
343C22×D79—42no—
344C22×D79—42no—
345C22×D79—42no—
346Q8×C79—24no—
347Q8×C79—22no—
348Q8×C79C22×D414yes—
349D4×C79—22no—
350D4×C79—22no—
351D4×C79—22no—
352D4×C79—22no—
353D4×C79—44no—
354D4×C79—48no—
355D4×C79—48no—
356D4×C79—48no—
357D4×C79—42no—
358D4×C79—42no—
359D4×C79—84no—
360D4×C79—84no—
361D4×C79—84no—
362C2×C4×C79—22no—
363C2×C4×C79—22no—
364C2×C4×C79—24no—
365C2×C4×C79—22no—
366C2×C4×C79—22no—
367C2×C4×C79—22no—
368C2×C4×C79—24no—
369C2×C4×C79—24no—
370C2×C4×C79—22no—
371C2×C4×C79—22no—
372C2×C4×C79—22no—
373C2×C4×C79—22no—
374C2×C4×C79—22no—
375C2×C4×C79—48no—
376C2×C4×C79—48no—
377C2×C4×C79—42no—
378C2×C4×C79C22×D412yes—
379C2×C4×C79C22×D412yes—
380C2×C4×C79C22×D412yes—
381C2×C4×C79C22×D412yes—
382C2×C4×C79C22×D412yes—
383C2×C4×C79C22×D411yescharacteristic
384C2×C4×C79H(5,𝔽2)12yes—
385C2×C4×C79C2511yescharacteristic
386C22⋊D79—48no—
387C22⋊D79—48no—
388C2×Dic79—24no—
389C2×Dic79—22no—
390C2×Dic79—22no—
391C2×Dic79—22no—
392C2×Dic79—48no—
393C2×Dic79—42no—
394C2×Dic79—42no—
395D316—22no—
396D316—22no—
397D316—42no—
398C4×D79—48no—
399Dic158—24no—
400Dic158—22no—
401Dic158—22no—
402Dic158—22no—
403Dic158—48no—
404Dic158—42no—
405Dic158C22×D414yes—
406C79⋊C8—22no—
407C79⋊C8—22no—
408C79⋊C8—22no—
409C79⋊C8C22×D414yes—
410C22×C79—22no—
411C22×C79—22no—
412C22×C79—22no—
413C22×C79—22no—
414C22×C79—22no—
415C22×C79—22no—
416C22×C79—44no—
417C22×C79—44no—
418C22×C79—42no—
419C22×C79—42no—
420C22×C79—42no—
421C22×C79—42no—
422C22×C79—42no—
423C22×C79—42no—
424C22×C79—84no—
425C22×C79—84no—
426C22×C79D4212yes—
427C22×C79#57512yes—
428C22×C79#57712yes—
429C22×C79C23×D411yescharacteristic
430C2×D79—42no—
431C2×D79—42no—
432C2×D79—42no—
433C2×D79—84no—
434C4×C79—22no—
435C4×C79—22no—
436C4×C79—24no—
437C4×C79—22no—
438C4×C79—22no—
439C4×C79—42no—
440C4×C79D4212yes—
441C4×C79C23×D411yescharacteristic
442C4×C79C2×H(5,𝔽2)11yescharacteristic
443Dic79—24no—
444Dic79—42no—
445Dic79—42no—
446C2×#3271—791nomaximal, Sylow
447C2×C79—42no—
448C2×C79—42no—
449C2×C79—82no—
450C2×C79—82no—
451C2×C79#327114yescomplemented
452C2×C79C2×D4211yescharacteristic
453C2×C79C2×#57511yescharacteristic
454C2×C79C2×#57711yescharacteristic
455D79—82no—
456C22×#137—791no—
457C22×#135—791no—
458C2×#550D7911yescharacteristic, complemented
459C2×#548—791no—
460#3271—7916no—
461C2×#496—791no—
462C2×#469—791no—
463C2×#465—791no—
464C2×#464—791no—
465C2×#460—791no—
466C2×#452—791no—
467C2×#449—791no—
468C2×#449—791no—
469C2×#448—791no—
470C2×#441—791no—
471C2×#435—791no—
472C79C2×#327111yescharacteristic, complemented, Sylow
473C22×#41—791no—
474C22×#41C2×D7911yescharacteristic
475C22×#41C2×D7911yescharacteristic
476C23×Q8—791no—
477C2×#137—798no—
478C2×#137—1588no—
479C2×#135—798no—
480C2×#135—1588no—
481C22×Q16—791no—
482C22×Q16—791no—
483C22×SD16—791no—
484C22×SD16—791no—
485C22×SD16—791no—
486C22×SD16—791no—
487C22×SD16—791no—
488C22×D8—791no—
489C22×D8—791no—
490C22×M16—791no—
491C23×C8—791no—
492#550—24no—
493#550C2×D7918yescomplemented
494#548—798no—
495#548—1584no—
496C2×#127—21no—
497C2×#127C2×D7911yescharacteristic
498C2×#124—791no—
499C2×#124—1581no—
500C2×C22⋊Q8—791no—
501C2×C22⋊Q8—1581no—
502C2×#121—21no—
503C2×#121—21no—
504C2×#121—791no—
505C2×#121—1581no—
506C2×#121C2×D7911yescharacteristic
507C2×#121C2×D7911yescharacteristic
508C2×C4×Q8—791no—
509C2×C4×Q8C2×D7911yescharacteristic
510C2×C4×D4—21no—
511C2×C4×D4—1581no—
512C2×C4×D4C2×D7911yescharacteristic
513#496—798no—
514#469—798no—
515#465—798no—
516#464—798no—
517#460—798no—
518#452—798no—
519#449—798no—
520#449—798no—
521#448—798no—
522#441—798no—
523#435—798no—
524C2×#106—791no—
525C2×C4⋊C8—791no—
526C2×#103—791no—
527C2×#103—791no—
528C2×#103—791no—
529C2×#102—791no—
530C2×#102—791no—
531C2×#102—791no—
532C2×C22⋊C8—791no—
533C2×C22⋊C8—791no—
534C2×#97—791no—
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—24no—
538C2×#41—24no—
539C2×#41—42no—
540C2×#41—42no—
541C2×#41—3162no—
542C2×#41—794no—
543C2×#41—1584no—
544C2×#41—1582no—
545C2×#41C22×D7914yes—
546C2×#41C22×D7914yes—
547C22×Q8—3162no—
548C22×Q8—794no—
549C22×Q8—791no—
550C22×Q8—791no—
551C22×Q8—1584no—
552C22×Q8—1581no—
553C22×Q8—1582no—
554C22×Q8C22×D7911yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—791no—
562C22×D4—1581no—
563C22×D4—1581no—
564C22×D4C22⋊D7911yescharacteristic
565C22×D4C22×D7911yescharacteristic
566C22×D4C22×D7911yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—1581no—
570C23×C4—1581no—
571C23×C4C22×D7911yescharacteristic
572C23×C4C22×D7911yescharacteristic
573#137—15832no—
574#135—15832no—
575C2×Q16—798no—
576C2×Q16—794no—
577C2×Q16—794no—
578C2×Q16—1584no—
579C2×SD16—3162no—
580C2×SD16—794no—
581C2×SD16—794no—
582C2×SD16—794no—
583C2×SD16—794no—
584C2×SD16—794no—
585C2×SD16—1584no—
586C2×SD16—1584no—
587C2×SD16—1584no—
588C2×SD16—1584no—
589C2×D8—3162no—
590C2×D8—794no—
591C2×D8—794no—
592C2×D8—1584no—
593C2×M16—794no—
594C2×M16—1584no—
595C22×C8—791no—
596C22×C8—791no—
597C22×C8—794no—
598C22×C8—791no—
599C22×C8—791no—
600C22×C8—1584no—
601#127—28no—
602#127—22no—
603#127C22×D7914yes—
604#124—794no—
605#124—1588no—
606#124—1582no—
607C22⋊Q8—794no—
608C22⋊Q8—1582no—
609C22⋊Q8—1588no—
610#121—22no—
611#121—22no—
612#121—28no—
613#121—28no—
614#121—794no—
615#121—1588no—
616#121—1582no—
617#121C22×D7914yes—
618#121C22×D7914yes—
619C4×Q8—22no—
620C4×Q8—794no—
621C4×Q8—1582no—
622C4×Q8C22×D7914yes—
623C4×D4—28no—
624C4×D4—1588no—
625C4×D4C22⋊D7914yes—
626C4×D4C22×D7914yes—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—791no—
629C2×C4⋊C4—1581no—
630C2×C4⋊C4—1581no—
631C2×C4⋊C4C22⋊D7911yescharacteristic
632C2×C4⋊C4C22×D7911yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—1581no—
636C2×C22⋊C4—1581no—
637C2×C22⋊C4—1581no—
638C2×C22⋊C4—1581no—
639C2×C22⋊C4C22⋊D7911yescharacteristic
640C2×C22⋊C4C22⋊D7911yescharacteristic
641C2×C42—21no—
642C2×C42—1581no—
643C2×C42C22×D7911yescharacteristic
644#106—794no—
645C4⋊C8—794no—
646#103—794no—
647#103—794no—
648#103—794no—
649#102—794no—
650#102—794no—
651#102—794no—
652C22⋊C8—794no—
653C22⋊C8—794no—
654#97—794no—
655C24—21no—
656C24—21no—
657C24—1581no—
658C24C2×C22⋊D7911yescharacteristic
659C24C2×C22⋊D7911yescharacteristic
660#41—28no—
661#41—28no—
662#41—44no—
663#41—44no—
664#41—48no—
665#41—48no—
666#41—3168no—
667#41—3164no—
668#41—1588no—
669C2×Q8—22no—
670C2×Q8—21no—
671C2×Q8—3168no—
672C2×Q8—3164no—
673C2×Q8—3164no—
674C2×Q8—792no—
675C2×Q8—792no—
676C2×Q8—794no—
677C2×Q8—1588no—
678C2×Q8—1582no—
679C2×Q8—1582no—
680C2×Q8—1582no—
681C2×Q8—1581no—
682C2×Q8—1584no—
683C2×Q8—1581no—
684C2×Q8D4×D7914yes—
685C2×Q8C23×D7912yes—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—24no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—24no—
698C2×D4—42no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—82no—
703C2×D4—82no—
704C2×D4—82no—
705C2×D4—3164no—
706C2×D4—3164no—
707C2×D4—792no—
708C2×D4—1584no—
709C2×D4—1584no—
710C2×D4—1582no—
711C2×D4—1582no—
712C2×D4—1581no—
713C2×D4C2×C22⋊D7914yes—
714C2×D4C23×D7912yes—
715C2×D4C23×D7912yes—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—3164no—
727C22×C4—3164no—
728C22×C4—1584no—
729C22×C4—1581no—
730C22×C4—1581no—
731C22×C4—1584no—
732C22×C4—1581no—
733C22×C4C2×C22⋊D7912yes—
734C22×C4C2×C22⋊D7912yes—
735C22×C4C2×C22⋊D7911yescharacteristic
736C22×C4C2×C22⋊D7911yescharacteristic
737C22×C4C2×C22⋊D7911yescharacteristic
738C22×C4C2×C22⋊D7911yescharacteristic
739C22×C4C23×D7912yes—
740C22×C4C23×D7912yes—
741C22×C4C23×D7911yescharacteristic
742Q16—7916no—
743Q16—1588no—
744SD16—3164no—
745SD16—1588no—
746SD16—1588no—
747SD16—1588no—
748SD16—1588no—
749D8—3164no—
750D8—1588no—
751M16—1588no—
752C2×C8—792no—
753C2×C8—794no—
754C2×C8—792no—
755C2×C8—792no—
756C2×C8—792no—
757C2×C8—1588no—
758C2×C8—1582no—
759C2×C8—1582no—
760C2×C8—1582no—
761C4⋊C4—24no—
762C4⋊C4—21no—
763C4⋊C4—792no—
764C4⋊C4—1584no—
765C4⋊C4—1584no—
766C4⋊C4—1581no—
767C4⋊C4C2×C22⋊D7914yes—
768C4⋊C4C23×D7912yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—1584no—
772C22⋊C4—1584no—
773C22⋊C4—1584no—
774C22⋊C4—1584no—
775C22⋊C4C2×C22⋊D7914yes—
776C22⋊C4C2×C22⋊D7914yes—
777C42—24no—
778C42—1584no—
779C42C2×C22⋊D7912yes—
780C42C23×D7912yes—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—3162no—
796C23—3162no—
797C23—3162no—
798C23—1582no—
799C23C22×C22⋊D7912yes—
800C23C22×C22⋊D7912yes—
801C23C22×C22⋊D7911yescharacteristic
802Q8—22no—
803Q8—24no—
804Q8—3168no—
805Q8—3162no—
806Q8—794no—
807Q8—1582no—
808Q8—1582no—
809Q8—1582no—
810Q8—1584no—
811Q8C2×D4×D7914yes—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—44no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—42no—
821D4—42no—
822D4—84no—
823D4—84no—
824D4—84no—
825D4—3168no—
826D4—3168no—
827D4—3162no—
828D4—1582no—
829D4—1582no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—48no—
844C2×C4—48no—
845C2×C4—42no—
846C2×C4—3168no—
847C2×C4—3162no—
848C2×C4—3162no—
849C2×C4—3168no—
850C2×C4—1582no—
851C2×C4—1582no—
852C2×C4—1584no—
853C2×C4—1582no—
854C2×C4C2×D4×D7912yes—
855C2×C4C22×C22⋊D7912yes—
856C2×C4C22×C22⋊D7912yes—
857C2×C4C22×C22⋊D7912yes—
858C2×C4C22×C22⋊D7912yes—
859C2×C4C22×C22⋊D7911yescharacteristic
860C2×C4#1457920612yes—
861C2×C4C24×D7911yescharacteristic
862C8—794no—
863C8—1582no—
864C8—1582no—
865C8—1582no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—44no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—84no—
881C22—84no—
882C22—3162no—
883C22—3162no—
884C22—3162no—
885C22—6324no—
886C22D4×C22⋊D7912yes—
887C22#1909936112yes—
888C22#1909937412yes—
889C22C23×C22⋊D7911yescharacteristic
890C4—22no—
891C4—22no—
892C4—24no—
893C4—22no—
894C4—22no—
895C4—42no—
896C4—3162no—
897C4—3162no—
898C4—1584no—
899C4D4×C22⋊D7912yes—
900C4C22×D4×D7911yescharacteristic
901C4C2×#1457920611yescharacteristic
902C2—42no—
903C2—42no—
904C2—82no—
905C2—82no—
906C2—6322no—
907C2#2377498114yesdirect product factor
908C2C2×D4×C22⋊D7911yescharacteristic
909C2C2×#1909936111yescharacteristic
910C2C2×#1909937411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#550×C79C2
socleC23×C79C22×D4
hypercenterC2×#550D79
hypocenterC79C2×#3271
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#14579191C2semidirect
2. C22×#14579181C2semidirect
3. C2×#19099222C2semidirect
4. #23774981C2direct (N × H)
5. C2×#19098950C2semidirect
6. C2×#19098814C2semidirect
7. C2×#19098790C2semidirect
8. C2×#19098785C2semidirect
9. C2×#19098760C2semidirect
10. C2×#19098725C2semidirect
11. C2×#19098708C2semidirect
12. C2×#19098706C2semidirect
13. C2×#19098701C2semidirect
14. C2×#19098668C2semidirect
15. C2×#19098635C2semidirect
16. C2×#550×C79C2semidirect
20. C2×#14579191C22semidirect
22. C2×#14579181C22semidirect
35. #19099222C22semidirect
44. #19098950C22semidirect
45. #19098814C22semidirect
46. #19098790C22semidirect
47. #19098785C22semidirect
48. #19098760C22semidirect
49. #19098725C22semidirect
50. #19098708C22semidirect
51. #19098706C22semidirect
52. #19098701C22semidirect
53. #19098668C22semidirect
54. #19098635C22semidirect
69. #550×C79C22semidirect
98. C2×#11929614D4semidirect
232. #11929614C2×D4semidirect
451. C2×C79#3271semidirect
458. C2×#550D79semidirect
472. C79C2×#3271semidirect
493. #550C2×D79semidirect
907. C2#23774981direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791912
C22×#145791812
C2×#190992222
#237749812
C2×#190989502
C2×#190988142
C2×#190987902
C2×#190987852
C2×#190987602
C2×#190987252
C2×#190987082
C2×#190987062
C2×#190987012
C2×#190986682
C2×#190986352
C2×#550×C792
C2×#327179