Finite Group Databasebeta

← C2×#501×D79 #35157875

Subgroups — C2×#501×D79 #35157875

Order 20224.

2142 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D79C211yesmaximal, characteristic
2C2×#125×D79C211yesmaximal, characteristic
3C2×#19098973C211yesmaximal, characteristic, complemented
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098971C212yesmaximal, complemented
6C2×#19098970C212yesmaximal, complemented
7C2×#19098969C211yesmaximal, characteristic, complemented
8#501×D79C2116yesmaximal, direct product factor
9C2×#107×D79C212yesmaximal
10C2×#106×D79C212yesmaximal
11C2×#97×D79C211yesmaximal, characteristic
12C2×#501×C79C211yesmaximal, characteristic, complemented
13C22×Q8×D79—21no—
14C22×C8×D79C2212yes—
15C2×#14579161C2211yescharacteristic
16C2×#14579160—21no—
17C2×#14579160C2212yes—
18C2×#14579159—21no—
19C4⋊Q8×D79—24no—
20C4⋊Q8×D79C2218yes—
21C2×#14579153C2211yescharacteristic
22C2×#14579152C2211yescharacteristic
23C2×#14579152C2211yescharacteristic
24C2×#14579151—21no—
25C2×#14579151—21no—
26#125×D79—24no—
27#125×D79C2218yes—
28C2×C4⋊C4×D79—21no—
29C2×C4⋊C4×D79—21no—
30C2×C4⋊C4×D79—21no—
31C2×C4⋊C4×D79C2211yescharacteristic
32C2×C4⋊C4×D79C2212yes—
33C2×C4⋊C4×D79C2211yescharacteristic
34C2×C42×D79C2211yescharacteristic
35#19098973C2218yescomplemented
36#19098972C2218yescomplemented
37#19098971C22116yescomplemented
38#19098970C22116yescomplemented
39#19098969C2218yescomplemented
40C2×#14579095C2212yes—
41C2×#14579094C2212yes—
42C2×#14579094C2212yes—
43#107×D79C22116yes—
44C2×#14579093C2212yes—
45C2×#14579092C2212yes—
46C2×#14579092C2212yes—
47#106×D79C22116yes—
48C2×#14579072C2211yescharacteristic
49C2×#14579071C2212yes—
50#97×D79C2218yes—
51C2×C4⋊Q8×C79C2211yescharacteristic
52C2×#125×C79C2211yescharacteristic
53#501×C79C2218yescomplemented
54C2×#107×C79C2212yes—
55C2×#106×C79C2212yes—
56C2×#97×C79C2211yescharacteristic
57C22×Dic158—21no—
58C22×Dic158—22no—
59C2×Q8×D79—28no—
60C2×Q8×D79—48no—
61C22×C4×D79—21no—
62C22×C4×D79—21no—
63C22×C4×D79—22no—
64C22×C4×D79D411yescharacteristic
65C22×C4×D79D411yescharacteristic
66C22×C4×D79C2311yescharacteristic
67C22×C79⋊C8C2312yes—
68C2×C8×D79Q8116yescomplemented
69C2×C8×D79C2318yes—
70#14579161—22no—
71#14579161C2314yes—
72#14579160—24no—
73#14579160—28no—
74#14579160C2318yes—
75#14579159—28no—
76#14579153—22no—
77#14579153C2314yes—
78#14579152—22no—
79#14579152—22no—
80#14579152C2314yes—
81#14579152C2314yes—
82#14579151—28no—
83#14579151—28no—
84C2×C4⋊Dic79—21no—
85C2×C4⋊Dic79—21no—
86C2×C4⋊Dic79—21no—
87C2×C4⋊Dic79C2311yescharacteristic
88C2×C4⋊Dic79C2311yescharacteristic
89C2×C4⋊Dic79C2312yes—
90C2×Dic79⋊C4—21no—
91C2×Dic79⋊C4—21no—
92C2×Dic79⋊C4—21no—
93C2×Dic79⋊C4—21no—
94C2×Dic79⋊C4—22no—
95C2×Dic79⋊C4—21no—
96C2×Dic79⋊C4—21no—
97C2×Dic79⋊C4—22no—
98C4⋊C4×D79—28no—
99C4⋊C4×D79—28no—
100C4⋊C4×D79—28no—
101C4⋊C4×D79—22no—
102C4⋊C4×D79—22no—
103C4⋊C4×D79—24no—
104C4⋊C4×D79C2314yes—
105C4⋊C4×D79C2314yes—
106C4⋊C4×D79C2318yes—
107C2×C4×Dic79D411yescharacteristic
108C2×C4×Dic79D411yescharacteristic
109C2×C4×Dic79C2311yescharacteristic
110C42×D79D414yes—
111C42×D79C2314yes—
112#14579095C2318yes—
113#14579094C2318yes—
114#14579094C2318yes—
115#14579093C2318yes—
116#14579092C2318yes—
117#14579092C2318yes—
118#14579072C2314yes—
119#14579071C2318yes—
120C22×Q8×C79—21no—
121C22×C8×C79C2312yes—
122C4⋊Q8×C79—22no—
123C4⋊Q8×C79C2314yes—
124#125×C79—22no—
125#125×C79C2314yes—
126C2×C4⋊C4×C79—21no—
127C2×C4⋊C4×C79—21no—
128C2×C4⋊C4×C79—21no—
129C2×C4⋊C4×C79C2311yescharacteristic
130C2×C4⋊C4×C79C2312yes—
131C2×C4⋊C4×C79C2311yescharacteristic
132C2×C42×C79C2311yescharacteristic
133#107×C79C2318yes—
134#106×C79C2318yes—
135#97×C79C2314yes—
136C23×D79C2×D411yescharacteristic
137C2×Dic158—28no—
138C2×Dic158—24no—
139C2×Dic158—44no—
140C2×Dic158—48no—
141Q8×D79—432no—
142C22×Dic79—22no—
143C22×Dic79—21no—
144C22×Dic79—21no—
145C22×Dic79C2×D411yescharacteristic
146C22×Dic79C2×D411yescharacteristic
147C22×Dic79C2×D411yescharacteristic
148C2×C4×D79—24no—
149C2×C4×D79—24no—
150C2×C4×D79—28no—
151C2×C4×D79—24no—
152C2×C4×D79—24no—
153C2×C4×D79—48no—
154C2×C4×D79—44no—
155C2×C4×D79—44no—
156C2×C4×D79C2×D414yes—
157C2×C4×D79C2×D414yes—
158C2×C4×D79C2×D412yes—
159C2×C4×D79C2×Q818yes—
160C2×C4×D79C2412yes—
161C2×C79⋊C8C2×Q818yescomplemented
162C2×C79⋊C8C2414yes—
163C8×D79C2×Q8132yescomplemented
164C4⋊Dic79—24no—
165C4⋊Dic79—24no—
166C4⋊Dic79—24no—
167C4⋊Dic79—21no—
168C4⋊Dic79—21no—
169C4⋊Dic79—22no—
170C4⋊Dic79C2412yes—
171C4⋊Dic79C2414yes—
172C4⋊Dic79C2412yes—
173Dic79⋊C4—24no—
174Dic79⋊C4—24no—
175Dic79⋊C4—28no—
176Dic79⋊C4—24no—
177Dic79⋊C4—24no—
178Dic79⋊C4—28no—
179Dic79⋊C4—24no—
180Dic79⋊C4—24no—
181C4×Dic79C2×D412yes—
182C4×Dic79C2×D414yes—
183C4×Dic79C2×D414yes—
184C4×Dic79C2412yes—
185C2×Q8×C79—24no—
186C2×Q8×C79—44no—
187C22×C4×C79—22no—
188C22×C4×C79—21no—
189C22×C4×C79—21no—
190C22×C4×C79C2×D411yescharacteristic
191C22×C4×C79C2×D411yescharacteristic
192C22×C4×C79C2411yescharacteristic
193C2×C8×C79C2×Q818yescomplemented
194C2×C8×C79C2414yes—
195C4⋊C4×C79—24no—
196C4⋊C4×C79—24no—
197C4⋊C4×C79—24no—
198C4⋊C4×C79—21no—
199C4⋊C4×C79—21no—
200C4⋊C4×C79—22no—
201C4⋊C4×C79C2412yes—
202C4⋊C4×C79C2414yes—
203C4⋊C4×C79C2412yes—
204C42×C79C2×D412yes—
205C42×C79C2412yes—
206C23×C79C22×D411yescharacteristic
207C22×D79C4⋊Q814yes—
208C22×D79AGL(1,ℤ/8)14yes—
209C22×D79#13714yes—
210C22×D79C22×D412yes—
211Q8×C79—48no—
212C2×C4×C79—22no—
213C2×C4×C79—22no—
214C2×C4×C79—22no—
215C2×C4×C79—22no—
216C2×C4×C79—24no—
217C2×C4×C79—44no—
218C2×C4×C79—42no—
219C2×C4×C79—42no—
220C2×C4×C79C22×D412yes—
221C2×C4×C79C22×D412yes—
222C2×C4×C79C22×D411yescharacteristic
223C2×C4×C79C22×Q814yes—
224C2×C4×C79C2511yescharacteristic
225C2×Dic79—22no—
226C2×Dic79—22no—
227C2×Dic79—22no—
228C2×Dic79—22no—
229C2×Dic79—24no—
230C2×Dic79—42no—
231C2×Dic79—44no—
232C2×Dic79—42no—
233C2×Dic79C4⋊Q814yes—
234C2×Dic79C22×D412yes—
235C2×Dic79C22×D412yes—
236C2×Dic79C22×D412yes—
237C4×D79—28no—
238C4×D79—28no—
239C4×D79—48no—
240C4×D79—416no—
241C4×D79—48no—
242C4×D79C4⋊Q818yes—
243C4×D79C22×Q818yes—
244Dic158—416no—
245Dic158—48no—
246C8×C79C22×Q818yescomplemented
247C79⋊C8C22×Q818yescomplemented
248C22×C79C2×C4⋊Q812yes—
249C22×C79C2×AGL(1,ℤ/8)12yes—
250C22×C79C2×#13712yes—
251C22×C79C23×D411yescharacteristic
252C2×D79#501116yesdirect product factor
253C2×D79C2×C4⋊Q814yes—
254C2×D79C2×AGL(1,ℤ/8)14yes—
255C2×D79C2×#13714yes—
256C4×C79—22no—
257C4×C79—22no—
258C4×C79—44no—
259C4×C79—42no—
260C4×C79—42no—
261C4×C79C2×C4⋊Q812yes—
262C4×C79C23×Q812yes—
263Dic79—22no—
264Dic79—22no—
265Dic79—44no—
266Dic79—42no—
267Dic79—42no—
268Dic79C2×C4⋊Q814yes—
269C22×#501—791nomaximal, Sylow
270C2×C79C2×#50114yescomplemented
271C2×C79C22×C4⋊Q811yescharacteristic
272C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
273C2×C79C22×#13711yescharacteristic
274D79C2×#50118yesdirect product factor
275C22×C4⋊Q8—791no—
276C22×#125—791no—
277C2×#501—7916no—
278C2×#501—792no—
279C2×#501—792no—
280C2×#501—791no—
281C2×#501—791no—
282C2×#501—791no—
283C2×#501D7911yescharacteristic, direct product factor
284C22×#107—792no—
285C22×#106—792no—
286C22×#97—791no—
287C79C22×#50111yescharacteristic, complemented, Sylow
288C23×Q8—1581no—
289C23×C8—792no—
290C2×C4⋊Q8—798no—
291C2×C4⋊Q8—792no—
292C2×C4⋊Q8—791no—
293C2×C4⋊Q8—1581no—
294C2×C4⋊Q8—1584no—
295C2×C4⋊Q8—1581no—
296C2×C4⋊Q8C2×D7911yescharacteristic
297C2×#125—798no—
298C2×#125—791no—
299C2×#125—791no—
300C2×#125—791no—
301C2×#125—1581no—
302C2×#125—1581no—
303C2×#125—1584no—
304C2×#125C2×D7911yescharacteristic
305C22×C4⋊C4—791no—
306C22×C4⋊C4—792no—
307C22×C4⋊C4—791no—
308C22×C4⋊C4—1581no—
309C22×C4⋊C4—1581no—
310C22×C4⋊C4—1581no—
311C22×C42—791no—
312#501—798no—
313#501—798no—
314#501—7916no—
315#501—7916no—
316#501—798no—
317#501C2×D7918yesdirect product factor
318C2×#107—792no—
319C2×#107—792no—
320C2×#107—792no—
321C2×#107—7916no—
322C2×#107C2×D7912yes—
323C2×#106—792no—
324C2×#106—792no—
325C2×#106—792no—
326C2×#106—7916no—
327C2×#106C2×D7912yes—
328C2×#97—792no—
329C2×#97—791no—
330C2×#97—798no—
331C2×#97C2×D7911yescharacteristic
332C22×Q8—21no—
333C22×Q8—3168no—
334C22×Q8—1582no—
335C22×Q8—1588no—
336C22×Q8—1581no—
337C23×C4—791no—
338C23×C4—791no—
339C23×C4—791no—
340C23×C4—1581no—
341C23×C4—1581no—
342C23×C4—1582no—
343C22×C8—792no—
344C22×C8—7916no—
345C22×C8—798no—
346C22×C8C22×D7912yes—
347C4⋊Q8—22no—
348C4⋊Q8—798no—
349C4⋊Q8—794no—
350C4⋊Q8—1588no—
351C4⋊Q8—1584no—
352C4⋊Q8—1588no—
353C4⋊Q8—1582no—
354C4⋊Q8C22×D7914yes—
355#125—22no—
356#125—794no—
357#125—794no—
358#125—794no—
359#125—1588no—
360#125—1588no—
361#125—1582no—
362#125—1582no—
363#125—1582no—
364#125C22×D7914yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—791no—
369C2×C4⋊C4—791no—
370C2×C4⋊C4—792no—
371C2×C4⋊C4—794no—
372C2×C4⋊C4—794no—
373C2×C4⋊C4—798no—
374C2×C4⋊C4—1582no—
375C2×C4⋊C4—1582no—
376C2×C4⋊C4—1584no—
377C2×C4⋊C4—1588no—
378C2×C4⋊C4—1588no—
379C2×C4⋊C4—1588no—
380C2×C4⋊C4—1581no—
381C2×C4⋊C4—1581no—
382C2×C4⋊C4—1582no—
383C2×C4⋊C4—1581no—
384C2×C4⋊C4—1581no—
385C2×C4⋊C4—1581no—
386C2×C4⋊C4—1581no—
387C2×C4⋊C4—1582no—
388C2×C4⋊C4—1581no—
389C2×C4⋊C4—1581no—
390C2×C4⋊C4—1581no—
391C2×C4⋊C4C22×D7911yescharacteristic
392C2×C4⋊C4C22×D7911yescharacteristic
393C2×C4⋊C4C22×D7912yes—
394C2×C42—791no—
395C2×C42—791no—
396C2×C42—791no—
397C2×C42—794no—
398C2×C42—794no—
399C2×C42C22×D7911yescharacteristic
400#107—798no—
401#107—798no—
402#107—798no—
403#107C22×D7918yes—
404#106—798no—
405#106—798no—
406#106—798no—
407#106C22×D7918yes—
408#97—798no—
409#97—794no—
410#97C22×D7914yes—
411C24—791no—
412C2×Q8—24no—
413C2×Q8—44no—
414C2×Q8—3164no—
415C2×Q8—3168no—
416C2×Q8—31632no—
417C2×Q8—1588no—
418C2×Q8—1584no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—3164no—
423C22×C4—3164no—
424C22×C4—3168no—
425C22×C4—791no—
426C22×C4—798no—
427C22×C4—792no—
428C22×C4—792no—
429C22×C4—791no—
430C22×C4—791no—
431C22×C4—794no—
432C22×C4—794no—
433C22×C4—1584no—
434C22×C4—1584no—
435C22×C4—1588no—
436C22×C4—1584no—
437C22×C4—1584no—
438C22×C4—1581no—
439C22×C4—1581no—
440C22×C4—1582no—
441C22×C4D4×D7911yescharacteristic
442C22×C4D4×D7911yescharacteristic
443C22×C4C23×D7911yescharacteristic
444C2×C8—798no—
445C2×C8—794no—
446C2×C8—7932no—
447C2×C8Q8×D7918yescomplemented
448C2×C8C23×D7914yes—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—792no—
456C4⋊C4—794no—
457C4⋊C4—792no—
458C4⋊C4—1584no—
459C4⋊C4—1584no—
460C4⋊C4—1588no—
461C4⋊C4—1584no—
462C4⋊C4—1584no—
463C4⋊C4—1588no—
464C4⋊C4—1584no—
465C4⋊C4—1584no—
466C4⋊C4—1584no—
467C4⋊C4—1584no—
468C4⋊C4—1581no—
469C4⋊C4—1581no—
470C4⋊C4—1582no—
471C4⋊C4—1584no—
472C4⋊C4C23×D7912yes—
473C4⋊C4C23×D7914yes—
474C4⋊C4C23×D7912yes—
475C42—792no—
476C42—794no—
477C42—794no—
478C42—792no—
479C42D4×D7912yes—
480C42C23×D7912yes—
481C23—794no—
482C23—794no—
483C23—794no—
484C23—792no—
485C23C2×D4×D7911yescharacteristic
486Q8—48no—
487Q8—3168no—
488Q8—31616no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—31616no—
498C2×C4—3168no—
499C2×C4—3168no—
500C2×C4—3164no—
501C2×C4—3162no—
502C2×C4—3162no—
503C2×C4—794no—
504C2×C4—792no—
505C2×C4—798no—
506C2×C4—798no—
507C2×C4—792no—
508C2×C4—792no—
509C2×C4—1588no—
510C2×C4—1588no—
511C2×C4—1582no—
512C2×C4—1582no—
513C2×C4—1584no—
514C2×C4—1582no—
515C2×C4—1582no—
516C2×C4C2×D4×D7912yes—
517C2×C4C2×D4×D7912yes—
518C2×C4C2×D4×D7911yescharacteristic
519C2×C4C2×Q8×D7914yes—
520C2×C4C24×D7911yescharacteristic
521C8—798no—
522C8C2×Q8×D7918yescomplemented
523C22—794no—
524C22—794no—
525C22—794no—
526C22—7916no—
527C22C4⋊Q8×D7912yes—
528C22AGL(1,ℤ/8)×D7912yes—
529C22#137×D7912yes—
530C22C22×D4×D7911yescharacteristic
531C4—22no—
532C4—22no—
533C4—44no—
534C4—42no—
535C4—42no—
536C4—3164no—
537C4—3162no—
538C4—3162no—
539C4—794no—
540C4—1582no—
541C4—1582no—
542C4C4⋊Q8×D7912yes—
543C4C22×Q8×D7912yes—
544C2—798no—
545C2#501×D7914yesdirect product factor
546C2C2×C4⋊Q8×D7911yescharacteristic
547C2C2×AGL(1,ℤ/8)×D7911yescharacteristic
548C2C2×#137×D7911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#501×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenterC2×#501D79
hypocenterC79C22×#501
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. C2×#19098973C2semidirect
4. C2×#19098972C2semidirect
5. C2×#19098971C2semidirect
6. C2×#19098970C2semidirect
7. C2×#19098969C2semidirect
8. #501×D79C2direct (N × H)
12. C2×#501×C79C2semidirect
35. #19098973C22semidirect
36. #19098972C22semidirect
37. #19098971C22semidirect
38. #19098970C22semidirect
39. #19098969C22semidirect
53. #501×C79C22semidirect
68. C2×C8×D79Q8semidirect
161. C2×C79⋊C8C2×Q8semidirect
163. C8×D79C2×Q8semidirect
193. C2×C8×C79C2×Q8semidirect
246. C8×C79C22×Q8semidirect
247. C79⋊C8C22×Q8semidirect
252. C2×D79#501direct (N × H)
270. C2×C79C2×#501semidirect
274. D79C2×#501direct (N × H)
283. C2×#501D79direct (N × H)
287. C79C22×#501semidirect
317. #501C2×D79direct (N × H)
447. C2×C8Q8×D79semidirect
522. C8C2×Q8×D79semidirect
545. C2#501×D79direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D792
C2×#125×D792
C2×#190989732
C2×#190989722
C2×#190989712
C2×#190989702
C2×#190989692
#501×D792
C2×#107×D792
C2×#106×D792
C2×#97×D792
C2×#501×C792
C22×#50179