Finite Group Databasebeta

← C2×#23774956 #35163299

Subgroups — C2×#23774956 #35163299

Order 20224.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579192C211yesmaximal, characteristic, complemented
2C22×#14579181C211yesmaximal, characteristic, complemented
3C2×#19099218C211yesmaximal, characteristic, complemented
4#23774956C2116yesmaximal, direct product factor
5C2×#19098958C211yesmaximal, characteristic, complemented
6C2×#19098807C211yesmaximal, characteristic, complemented
7C2×#19098802C211yesmaximal, characteristic, complemented
8C2×#19098773C211yesmaximal, characteristic, complemented
9C2×#19098775C211yesmaximal, characteristic, complemented
10C2×#19098725C211yesmaximal, characteristic, complemented
11C2×#19098723C211yesmaximal, characteristic, complemented
12C2×#19098706C211yesmaximal, characteristic, complemented
13C2×#19098719C211yesmaximal, characteristic, complemented
14C2×#19098661C211yesmaximal, characteristic, complemented
15C2×#19098635C211yesmaximal, characteristic, complemented
16C2×#548×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×#11929624C2211yescharacteristic
19C2×#14579192—28no—
20C2×#14579192C2218yescomplemented
21C2×#14579181—28no—
22C2×#14579181C2218yescomplemented
23C22×#11929614C2211yescharacteristic
24C22×#11929614C2211yescharacteristic
25C22×#11929614C2211yescharacteristic
26C22×#11929614C2211yescharacteristic
27C22×#11929612C2211yescharacteristic
28C22×#11929612C2211yescharacteristic
29C22×#11929611C2211yescharacteristic
30C22×#11929611C2211yescharacteristic
31C22×#11929609C2211yescharacteristic
32C22×#11929608C2211yescharacteristic
33C23×C79⋊C8C2211yescharacteristic
34#19099218—24no—
35#19099218C2218yescomplemented
36C2×#14579161C2211yescharacteristic
37C2×#14579143—21no—
38C2×#14579143—21no—
39C2×#14579140C2211yescharacteristic
40C2×#14579140C2211yescharacteristic
41C2×#14579132—21no—
42C2×C4×D316C2211yescharacteristic
43C2×C4⋊C4×D79—21no—
44#19098958C2218yescomplemented
45#19098807C2218yescomplemented
46#19098802C2218yescomplemented
47#19098775C2218yescomplemented
48#19098773C2218yescomplemented
49#19098725C2218yescomplemented
50#19098723C2218yescomplemented
51#19098719C2218yescomplemented
52#19098706C2218yescomplemented
53#19098661C2218yescomplemented
54#19098635C2218yescomplemented
55C2×#14579094C2211yescharacteristic
56C2×C4⋊(C79⋊C8)C2211yescharacteristic
57C2×#14579085C2211yescharacteristic
58C2×#14579085C2211yescharacteristic
59C2×#14579084C2211yescharacteristic
60C2×#14579084C2211yescharacteristic
61C2×#14579082C2211yescharacteristic
62C2×#14579081C2211yescharacteristic
63C2×C22⋊(C79⋊C8)C2211yescharacteristic
64C2×C22⋊(C79⋊C8)C2211yescharacteristic
65C2×#14579072C2211yescharacteristic
66C22×#41×C79C2211yescharacteristic
67C23×Q8×C79C2211yescharacteristic
68#548×C79—24no—
69#548×C79C2218yescomplemented
70C2×#124×C79—21no—
71C2×#124×C79C2211yescharacteristic
72C2×C22⋊Q8×C79—21no—
73C2×C22⋊Q8×C79C2211yescharacteristic
74C2×#121×C79—21no—
75C2×#121×C79C2211yescharacteristic
76C2×C4×Q8×C79C2211yescharacteristic
77C2×C4×D4×C79—21no—
78C2×C4×D4×C79C2211yescharacteristic
79C2×#11929624—22no—
80C2×#11929624—22no—
81C2×#11929624—24no—
82C2×#11929624—24no—
83C2×#11929624—42no—
84C2×#11929624—42no—
85C2×#11929624C2314yes—
86C2×#11929624C2314yes—
87C22×Dic158C2311yescharacteristic
88C22×Dic158C2311yescharacteristic
89C22×D316C2311yescharacteristic
90C22×C22⋊D79—21no—
91C22×C22⋊D79—21no—
92C22×C4×D79—21no—
93C22×C4×D79—21no—
94C22×C4×D79—21no—
95#14579192—232no—
96#14579181—232no—
97C2×#11929614—24no—
98C2×#11929614—24no—
99C2×#11929614—24no—
100C2×#11929614—42no—
101C2×#11929614C2314yes—
102C2×#11929614C2314yes—
103C2×#11929614C2314yes—
104C2×#11929614C2314yes—
105C2×#11929612—24no—
106C2×#11929612—42no—
107C2×#11929612C2314yes—
108C2×#11929612C2314yes—
109C2×#11929611—24no—
110C2×#11929611D418yescomplemented
111C2×#11929611C2314yes—
112C2×#11929611C2314yes—
113C2×#11929609—24no—
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#14579161—22no—
124#14579161C2314yes—
125#14579143—28no—
126#14579143—28no—
127#14579140—22no—
128#14579140—22no—
129#14579140C2314yes—
130#14579140C2314yes—
131#14579132—28no—
132C4×D316—22no—
133C4×D316C2314yes—
134C2×C4⋊Dic79—21no—
135C2×C4⋊Dic79—21no—
136C2×C4⋊Dic79C2311yescharacteristic
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C4⋊C4×D79—28no—
140C2×C22⋊Dic79—21no—
141C2×C22⋊Dic79—21no—
142C2×(C2×D79)⋊C4—21no—
143#14579094C2314yes—
144C4⋊(C79⋊C8)C2314yes—
145#14579085C2314yes—
146#14579085C2314yes—
147#14579084C2314yes—
148#14579084C2314yes—
149#14579082C2314yes—
150#14579081C2314yes—
151C22⋊(C79⋊C8)C2314yes—
152C22⋊(C79⋊C8)C2314yes—
153#14579072C2314yes—
154C2×#41×C79—22no—
155C2×#41×C79—24no—
156C2×#41×C79—42no—
157C2×#41×C79C2314yes—
158C22×Q8×C79—21no—
159C22×Q8×C79—22no—
160C22×Q8×C79—24no—
161C22×Q8×C79—42no—
162C22×Q8×C79C2311yescharacteristic
163C22×Q8×C79C2314yes—
164C22×Q8×C79C2311yescharacteristic
165C22×D4×C79—21no—
166C22×D4×C79—21no—
167C22×D4×C79D411yescharacteristic
168C22×D4×C79C2311yescharacteristic
169C23×C4×C79—21no—
170C23×C4×C79—21no—
171C23×C4×C79C2311yescharacteristic
172C23×C4×C79C2311yescharacteristic
173#124×C79—28no—
174#124×C79—22no—
175#124×C79C2314yes—
176C22⋊Q8×C79—22no—
177C22⋊Q8×C79—28no—
178C22⋊Q8×C79C2314yes—
179#121×C79—28no—
180#121×C79—22no—
181#121×C79C2314yes—
182C4×Q8×C79—22no—
183C4×Q8×C79C2314yes—
184C4×D4×C79—28no—
185C4×D4×C79D414yes—
186C4×D4×C79C2314yes—
187C2×C4⋊C4×C79—21no—
188C2×C4⋊C4×C79—21no—
189C2×C4⋊C4×C79D411yescharacteristic
190C2×C4⋊C4×C79C2311yescharacteristic
191C2×C22⋊C4×C79—21no—
192C2×C22⋊C4×C79—21no—
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—28no—
202#11929624—44no—
203#11929624—44no—
204#11929624—48no—
205#11929624—48no—
206C2×Dic158—22no—
207C2×Dic158—22no—
208C2×Dic158—21no—
209C2×Dic158—21no—
210C2×Dic158—22no—
211C2×Dic158—22no—
212C2×Dic158C2412yes—
213C2×Dic158C2412yes—
214C2×D316—21no—
215C2×D316—22no—
216C2×D316C2×D414yes—
217C2×D316C2412yes—
218C2×C22⋊D79—24no—
219C2×C22⋊D79—24no—
220C2×C22⋊D79—44no—
221C2×C22⋊D79—44no—
222C22×Dic79—21no—
223C22×Dic79—21no—
224C22×Dic79—21no—
225C2×C4×D79—24no—
226C2×C4×D79—24no—
227C2×C4×D79—24no—
228C2×C4×D79—44no—
229C2×C4×D79—44no—
230C2×C4×D79—44no—
231#11929614—28no—
232#11929614—28no—
233#11929614—28no—
234#11929614—44no—
235#11929612—28no—
236#11929612—44no—
237#11929611—28no—
238#11929611C2×D4116yescomplemented
239#11929609—28no—
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—24no—
251C4⋊Dic79—24no—
252C4⋊Dic79—21no—
253C4⋊Dic79C2412yes—
254Dic79⋊C4—24no—
255Dic79⋊C4—24no—
256C22⋊Dic79—24no—
257C22⋊Dic79—24no—
258(C2×D79)⋊C4—24no—
259C24×C79—21no—
260C24×C79C2×D411yescharacteristic
261C24×C79C2×D411yescharacteristic
262#41×C79—28no—
263#41×C79—44no—
264#41×C79—48no—
265C2×Q8×C79—21no—
266C2×Q8×C79—24no—
267C2×Q8×C79—21no—
268C2×Q8×C79—22no—
269C2×Q8×C79—28no—
270C2×Q8×C79—22no—
271C2×Q8×C79—22no—
272C2×Q8×C79—44no—
273C2×Q8×C79—44no—
274C2×Q8×C79—48no—
275C2×Q8×C79C2×D414yes—
276C2×Q8×C79C2412yes—
277C2×Q8×C79C2412yes—
278C2×D4×C79—24no—
279C2×D4×C79—24no—
280C2×D4×C79—22no—
281C2×D4×C79—21no—
282C2×D4×C79—22no—
283C2×D4×C79—42no—
284C2×D4×C79—44no—
285C2×D4×C79—44no—
286C2×D4×C79C2×D414yes—
287C2×D4×C79C2412yes—
288C22×C4×C79—21no—
289C22×C4×C79—22no—
290C22×C4×C79—22no—
291C22×C4×C79—22no—
292C22×C4×C79—22no—
293C22×C4×C79—21no—
294C22×C4×C79—21no—
295C22×C4×C79—24no—
296C22×C4×C79—24no—
297C22×C4×C79—44no—
298C22×C4×C79—44no—
299C22×C4×C79C2×D412yes—
300C22×C4×C79C2×D412yes—
301C22×C4×C79C2×D411yescharacteristic
302C22×C4×C79C2×D411yescharacteristic
303C22×C4×C79C2×D411yescharacteristic
304C22×C4×C79C2×D411yescharacteristic
305C22×C4×C79C2412yes—
306C22×C4×C79C2412yes—
307C22×C4×C79C2411yescharacteristic
308C4⋊C4×C79—24no—
309C4⋊C4×C79—24no—
310C4⋊C4×C79—21no—
311C4⋊C4×C79C2×D414yes—
312C4⋊C4×C79C2412yes—
313C22⋊C4×C79—24no—
314C22⋊C4×C79—24no—
315C22⋊C4×C79—24no—
316C22⋊C4×C79—24no—
317C22⋊C4×C79C2×D414yes—
318C22⋊C4×C79C2×D414yes—
319C42×C79—24no—
320C42×C79C2×D412yes—
321C42×C79C2412yes—
322C23×C79—22no—
323C23×C79—22no—
324C23×C79—22no—
325C23×C79—22no—
326C23×C79—22no—
327C23×C79—22no—
328C23×C79—22no—
329C23×C79—42no—
330C23×C79—42no—
331C23×C79—42no—
332C23×C79C22×D412yes—
333C23×C79C22×D412yes—
334C23×C79C22×D411yescharacteristic
335C22×D79—24no—
336C22×D79—22no—
337C22×D79—42no—
338C22×D79—42no—
339Q8×C79—24no—
340Q8×C79—22no—
341Q8×C79—22no—
342Q8×C79—22no—
343Q8×C79—48no—
344Q8×C79—42no—
345Q8×C79C22×D414yes—
346D4×C79—22no—
347D4×C79—22no—
348D4×C79—44no—
349D4×C79—48no—
350D4×C79—48no—
351D4×C79—42no—
352C2×C4×C79—22no—
353C2×C4×C79—22no—
354C2×C4×C79—24no—
355C2×C4×C79—22no—
356C2×C4×C79—22no—
357C2×C4×C79—22no—
358C2×C4×C79—24no—
359C2×C4×C79—24no—
360C2×C4×C79—22no—
361C2×C4×C79—22no—
362C2×C4×C79—22no—
363C2×C4×C79—22no—
364C2×C4×C79—22no—
365C2×C4×C79—22no—
366C2×C4×C79—48no—
367C2×C4×C79—48no—
368C2×C4×C79—42no—
369C2×C4×C79—42no—
370C2×C4×C79C22×D412yes—
371C2×C4×C79C22×D412yes—
372C2×C4×C79C22×D412yes—
373C2×C4×C79C22×D412yes—
374C2×C4×C79C22×D412yes—
375C2×C4×C79C22×D411yescharacteristic
376C2×C4×C79H(5,𝔽2)12yes—
377C2×C4×C79C2511yescharacteristic
378C22⋊D79—48no—
379C22⋊D79—48no—
380C2×Dic79—22no—
381C2×Dic79—22no—
382C2×Dic79—22no—
383C2×Dic79—42no—
384C2×Dic79—42no—
385C2×Dic79—42no—
386D316—24no—
387D316—22no—
388D316C22×D414yes—
389C4×D79—48no—
390C4×D79—48no—
391C4×D79—48no—
392Dic158—22no—
393Dic158—22no—
394Dic158—22no—
395Dic158—22no—
396Dic158—42no—
397Dic158—42no—
398C79⋊C8—22no—
399C79⋊C8—22no—
400C79⋊C8—22no—
401C79⋊C8C22×D414yes—
402C22×C79—22no—
403C22×C79—22no—
404C22×C79—22no—
405C22×C79—22no—
406C22×C79—22no—
407C22×C79—22no—
408C22×C79—44no—
409C22×C79—44no—
410C22×C79—42no—
411C22×C79—42no—
412C22×C79—42no—
413C22×C79—84no—
414C22×C79D4212yes—
415C22×C79#57512yes—
416C22×C79#57812yes—
417C22×C79C23×D411yescharacteristic
418C2×D79—24no—
419C2×D79—48no—
420C2×D79—42no—
421C2×D79—42no—
422C4×C79—22no—
423C4×C79—22no—
424C4×C79—24no—
425C4×C79—22no—
426C4×C79—22no—
427C4×C79—42no—
428C4×C79—42no—
429C4×C79D4212yes—
430C4×C79C23×D411yescharacteristic
431C4×C79C2×H(5,𝔽2)11yescharacteristic
432Dic79—42no—
433Dic79—42no—
434Dic79—42no—
435C2×#3269—791nomaximal, Sylow
436C2×C79—42no—
437C2×C79—42no—
438C2×C79—82no—
439C2×C79#326914yescomplemented
440C2×C79C2×D4211yescharacteristic
441C2×C79C2×#57511yescharacteristic
442C2×C79C2×#57811yescharacteristic
443D79—44no—
444C22×#137—791no—
445C22×#135—791no—
446C2×#548D7911yescharacteristic, complemented
447C2×#547—791no—
448#3269—7916no—
449C2×#497—791no—
450C2×#468—791no—
451C2×#467—791no—
452C2×#462—791no—
453C2×#463—791no—
454C2×#452—791no—
455C2×#452—791no—
456C2×#449—791no—
457C2×#451—791no—
458C2×#440—791no—
459C2×#435—791no—
460C79C2×#326911yescharacteristic, complemented, Sylow
461C22×#41—791no—
462C22×#41—791no—
463C22×#41C2×D7911yescharacteristic
464C23×Q8C2×D7911yescharacteristic
465C2×#137—798no—
466C2×#137—1588no—
467C2×#135—798no—
468C2×#135—1588no—
469C22×Q16—791no—
470C22×Q16—791no—
471C22×Q16—791no—
472C22×Q16—791no—
473C22×SD16—791no—
474C22×SD16—791no—
475C22×SD16—791no—
476C22×SD16—791no—
477C22×D8—791no—
478C22×M16—791no—
479C23×C8—791no—
480#548—24no—
481#548C2×D7918yescomplemented
482#547—798no—
483#547—1584no—
484C2×C4⋊Q8—791no—
485C2×#124—21no—
486C2×#124C2×D7911yescharacteristic
487C2×#123—1581no—
488C2×#123—1581no—
489C2×C22⋊Q8—21no—
490C2×C22⋊Q8—791no—
491C2×C22⋊Q8—791no—
492C2×C22⋊Q8C2×D7911yescharacteristic
493C2×#121—21no—
494C2×#121—1581no—
495C2×#121C2×D7911yescharacteristic
496C2×C4×Q8C2×D7911yescharacteristic
497C2×C4×D4—21no—
498C2×C4×D4—791no—
499C2×C4×D4C2×D7911yescharacteristic
500C22×C4⋊C4—1581no—
501#497—798no—
502#468—798no—
503#467—798no—
504#463—798no—
505#462—798no—
506#452—798no—
507#452—798no—
508#451—798no—
509#449—798no—
510#440—798no—
511#435—798no—
512C2×#107—791no—
513C2×C4⋊C8—791no—
514C2×#103—791no—
515C2×#103—791no—
516C2×#103—791no—
517C2×#103—791no—
518C2×#102—791no—
519C2×#102—791no—
520C2×C22⋊C8—791no—
521C2×C22⋊C8—791no—
522C2×#97—791no—
523C2×#41—22no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—3162no—
527C2×#41—3162no—
528C2×#41—794no—
529C2×#41—794no—
530C2×#41—1584no—
531C2×#41—1584no—
532C2×#41—1582no—
533C2×#41—1582no—
534C2×#41C22×D7914yes—
535C22×Q8—21no—
536C22×Q8—22no—
537C22×Q8—24no—
538C22×Q8—42no—
539C22×Q8—791no—
540C22×Q8—791no—
541C22×Q8C22×D7911yescharacteristic
542C22×Q8C22×D7914yes—
543C22×Q8C22×D7911yescharacteristic
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—791no—
547C22×D4—1581no—
548C22×D4—1581no—
549C22×D4C22⋊D7911yescharacteristic
550C22×D4C22×D7911yescharacteristic
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—1581no—
554C23×C4—1581no—
555C23×C4—1581no—
556C23×C4C22×D7911yescharacteristic
557C23×C4C22×D7911yescharacteristic
558#137—15832no—
559#135—15832no—
560C2×Q16—3162no—
561C2×Q16—794no—
562C2×Q16—794no—
563C2×Q16—794no—
564C2×Q16—794no—
565C2×Q16—1584no—
566C2×Q16—1584no—
567C2×Q16—1584no—
568C2×SD16—3162no—
569C2×SD16—794no—
570C2×SD16—798no—
571C2×SD16—794no—
572C2×SD16—794no—
573C2×SD16—794no—
574C2×SD16—1584no—
575C2×SD16—1584no—
576C2×D8—794no—
577C2×D8—1584no—
578C2×M16—794no—
579C2×M16—1584no—
580C22×C8—791no—
581C22×C8—791no—
582C22×C8—794no—
583C22×C8—791no—
584C22×C8—791no—
585C22×C8—1584no—
586C4⋊Q8—794no—
587C4⋊Q8—1582no—
588#124—28no—
589#124—22no—
590#124C22×D7914yes—
591#123—1588no—
592#123—1588no—
593C22⋊Q8—22no—
594C22⋊Q8—28no—
595C22⋊Q8—794no—
596C22⋊Q8—794no—
597C22⋊Q8—1582no—
598C22⋊Q8—1582no—
599C22⋊Q8C22×D7914yes—
600#121—28no—
601#121—22no—
602#121—1588no—
603#121C22×D7914yes—
604C4×Q8—22no—
605C4×Q8C22×D7914yes—
606C4×D4—28no—
607C4×D4—794no—
608C4×D4—1582no—
609C4×D4C22⋊D7914yes—
610C4×D4C22×D7914yes—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—791no—
614C2×C4⋊C4—1581no—
615C2×C4⋊C4—1581no—
616C2×C4⋊C4—1581no—
617C2×C4⋊C4—1581no—
618C2×C4⋊C4—1588no—
619C2×C4⋊C4C22⋊D7911yescharacteristic
620C2×C4⋊C4C22×D7911yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—1581no—
626C2×C22⋊C4—1581no—
627C2×C22⋊C4—1581no—
628C2×C22⋊C4C22⋊D7911yescharacteristic
629C2×C22⋊C4C22⋊D7911yescharacteristic
630C2×C42—21no—
631C2×C42C22×D7911yescharacteristic
632#107—794no—
633C4⋊C8—794no—
634#103—794no—
635#103—794no—
636#103—794no—
637#103—794no—
638#102—794no—
639#102—794no—
640C22⋊C8—794no—
641C22⋊C8—794no—
642#97—794no—
643C24—21no—
644C24—1581no—
645C24C2×C22⋊D7911yescharacteristic
646C24C2×C22⋊D7911yescharacteristic
647#41—28no—
648#41—44no—
649#41—48no—
650#41—3168no—
651#41—3168no—
652#41—3164no—
653#41—3164no—
654#41—1588no—
655#41—1588no—
656C2×Q8—22no—
657C2×Q8—21no—
658C2×Q8—24no—
659C2×Q8—21no—
660C2×Q8—28no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—48no—
666C2×Q8—792no—
667C2×Q8—792no—
668C2×Q8—1582no—
669C2×Q8—1582no—
670C2×Q8—1582no—
671C2×Q8—1582no—
672C2×Q8—1581no—
673C2×Q8—1581no—
674C2×Q8D4×D7914yes—
675C2×Q8C23×D7912yes—
676C2×Q8C23×D7912yes—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—3164no—
686C2×D4—3164no—
687C2×D4—792no—
688C2×D4—794no—
689C2×D4—1584no—
690C2×D4—1584no—
691C2×D4—1582no—
692C2×D4—1581no—
693C2×D4C2×C22⋊D7914yes—
694C2×D4C23×D7912yes—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—24no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—24no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—3164no—
707C22×C4—3164no—
708C22×C4—3164no—
709C22×C4—1581no—
710C22×C4—1581no—
711C22×C4—1581no—
712C22×C4—1584no—
713C22×C4—1584no—
714C22×C4—1584no—
715C22×C4C2×C22⋊D7912yes—
716C22×C4C2×C22⋊D7912yes—
717C22×C4C2×C22⋊D7911yescharacteristic
718C22×C4C2×C22⋊D7911yescharacteristic
719C22×C4C2×C22⋊D7911yescharacteristic
720C22×C4C2×C22⋊D7911yescharacteristic
721C22×C4C23×D7912yes—
722C22×C4C23×D7912yes—
723C22×C4C23×D7911yescharacteristic
724Q16—3164no—
725Q16—1588no—
726Q16—1588no—
727Q16—1588no—
728SD16—3164no—
729SD16—7916no—
730SD16—1588no—
731SD16—1588no—
732D8—1588no—
733M16—1588no—
734C2×C8—792no—
735C2×C8—794no—
736C2×C8—792no—
737C2×C8—792no—
738C2×C8—792no—
739C2×C8—1588no—
740C2×C8—1582no—
741C2×C8—1582no—
742C2×C8—1582no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—21no—
746C4⋊C4—792no—
747C4⋊C4—1584no—
748C4⋊C4—1584no—
749C4⋊C4—1581no—
750C4⋊C4—1584no—
751C4⋊C4—1584no—
752C4⋊C4C2×C22⋊D7914yes—
753C4⋊C4C23×D7912yes—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—1584no—
759C22⋊C4—1584no—
760C22⋊C4—1584no—
761C22⋊C4C2×C22⋊D7914yes—
762C22⋊C4C2×C22⋊D7914yes—
763C42—24no—
764C42C2×C22⋊D7912yes—
765C42C23×D7912yes—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—3162no—
777C23—3162no—
778C23—1584no—
779C23—1582no—
780C23C22×C22⋊D7912yes—
781C23C22×C22⋊D7912yes—
782C23C22×C22⋊D7911yescharacteristic
783Q8—22no—
784Q8—24no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—42no—
789Q8—3162no—
790Q8—3162no—
791Q8—1582no—
792Q8—1582no—
793Q8—1582no—
794Q8—1582no—
795Q8C2×D4×D7914yes—
796D4—22no—
797D4—22no—
798D4—44no—
799D4—48no—
800D4—48no—
801D4—42no—
802D4—3168no—
803D4—3168no—
804D4—794no—
805D4—1582no—
806D4—1584no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—48no—
822C2×C4—48no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—3168no—
826C2×C4—3168no—
827C2×C4—3168no—
828C2×C4—3162no—
829C2×C4—3162no—
830C2×C4—3162no—
831C2×C4—1582no—
832C2×C4—1582no—
833C2×C4—1582no—
834C2×C4C2×D4×D7912yes—
835C2×C4C22×C22⋊D7912yes—
836C2×C4C22×C22⋊D7912yes—
837C2×C4C22×C22⋊D7912yes—
838C2×C4C22×C22⋊D7912yes—
839C2×C4C22×C22⋊D7911yescharacteristic
840C2×C4#1457920612yes—
841C2×C4C24×D7911yescharacteristic
842C8—794no—
843C8—1582no—
844C8—1582no—
845C8—1582no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—44no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—84no—
858C22—3162no—
859C22—3162no—
860C22—3168no—
861C22—1584no—
862C22D4×C22⋊D7912yes—
863C22#1909936112yes—
864C22#1909937812yes—
865C22C23×C22⋊D7911yescharacteristic
866C4—22no—
867C4—22no—
868C4—24no—
869C4—22no—
870C4—22no—
871C4—42no—
872C4—42no—
873C4—3162no—
874C4—3162no—
875C4—3162no—
876C4D4×C22⋊D7912yes—
877C4C22×D4×D7911yescharacteristic
878C4C2×#1457920611yescharacteristic
879C2—42no—
880C2—42no—
881C2—82no—
882C2—3164no—
883C2#2377495614yesdirect product factor
884C2C2×D4×C22⋊D7911yescharacteristic
885C2C2×#1909936111yescharacteristic
886C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#548×C79C2
socleC23×C79C22×D4
hypercenterC2×#548D79
hypocenterC79C2×#3269
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14579192C2semidirect
2. C22×#14579181C2semidirect
3. C2×#19099218C2semidirect
4. #23774956C2direct (N × H)
5. C2×#19098958C2semidirect
6. C2×#19098807C2semidirect
7. C2×#19098802C2semidirect
8. C2×#19098773C2semidirect
9. C2×#19098775C2semidirect
10. C2×#19098725C2semidirect
11. C2×#19098723C2semidirect
12. C2×#19098706C2semidirect
13. C2×#19098719C2semidirect
14. C2×#19098661C2semidirect
15. C2×#19098635C2semidirect
16. C2×#548×C79C2semidirect
20. C2×#14579192C22semidirect
22. C2×#14579181C22semidirect
35. #19099218C22semidirect
44. #19098958C22semidirect
45. #19098807C22semidirect
46. #19098802C22semidirect
47. #19098775C22semidirect
48. #19098773C22semidirect
49. #19098725C22semidirect
50. #19098723C22semidirect
51. #19098719C22semidirect
52. #19098706C22semidirect
53. #19098661C22semidirect
54. #19098635C22semidirect
69. #548×C79C22semidirect
110. C2×#11929611D4semidirect
238. #11929611C2×D4semidirect
439. C2×C79#3269semidirect
446. C2×#548D79semidirect
460. C79C2×#3269semidirect
481. #548C2×D79semidirect
883. C2#23774956direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791922
C22×#145791812
C2×#190992182
#237749562
C2×#190989582
C2×#190988072
C2×#190988022
C2×#190987732
C2×#190987752
C2×#190987252
C2×#190987232
C2×#190987062
C2×#190987192
C2×#190986612
C2×#190986352
C2×#548×C792
C2×#326979