Finite Group Databasebeta

← C4×#19098905 #34295439

Subgroups — C4×#19098905 #34295439

Order 20224.

888 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098905C211yesmaximal, characteristic
2C4×#14579140C211yesmaximal, characteristic
3C4×#14579120C211yesmaximal, characteristic
4#23764042C211yesmaximal, characteristic, complemented
5#23764035C211yesmaximal, characteristic, complemented
6#23763979C211yesmaximal, characteristic, complemented
7#23763972C211yesmaximal, characteristic, complemented
8#23763710C211yesmaximal, characteristic
9#23763601C211yesmaximal, characteristic
10#23763496C211yesmaximal, characteristic
11C4×#14579095C211yesmaximal, characteristic, complemented
12C4×#14579093C211yesmaximal, characteristic, complemented
13C4×#14579086C211yesmaximal, characteristic, complemented
14C4×#14579086C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C79C211yesmaximal, characteristic
16C2×#14579140C2211yescharacteristic
17C2×C4×Dic158C2211yescharacteristic
18C2×#14579120C2211yescharacteristic
19C2×#14579120C2211yescharacteristic
20#19098905C418yesdirect product factor
21C2×#14579095C2211yescharacteristic
22C2×#14579095C2211yescharacteristic
23C2×#14579093C2211yescharacteristic
24C2×#14579093C2211yescharacteristic
25C2×#14579086C2211yescharacteristic
26C2×#14579086C2211yescharacteristic
27C2×#14579086C2211yescharacteristic
28C2×#14579086C2211yescharacteristic
29#19098469C2211yescharacteristic
30#19098461C2211yescharacteristic
31#19098447—21no—
32#19098436—21no—
33#19098423C2211yescharacteristic
34C4×Dic79⋊C4—21no—
35C4×C4⋊Dic79C2211yescharacteristic
36C4×C4⋊Dic79C2211yescharacteristic
37C4×C4⋊Dic79C2211yescharacteristic
38C4×C4⋊Dic79C2211yescharacteristic
39C4×C4⋊Dic79C2211yescharacteristic
40C4×C22⋊Dic79—21no—
41C4×C22⋊Dic79—21no—
42C4×C22⋊Dic79—21no—
43#19098409—21no—
44C42×Dic79—21no—
45#19098326C2211yescharacteristic
46#19098326C2211yescharacteristic
47#19098326C2211yescharacteristic
48#19098326C2211yescharacteristic
49#19098326C2211yescharacteristic
50#19098326C2211yescharacteristic
51#19098326C2211yescharacteristic
52#19098326C2211yescharacteristic
53C22×C42×C79C2211yescharacteristic
54C2×C22⋊C8×C79C2211yescharacteristic
55C2×C22⋊C8×C79C2211yescharacteristic
56C2×C4×C8×C79C2211yescharacteristic
57C2×C4×C8×C79C2211yescharacteristic
58#336×C79C2211yescharacteristic
59#336×C79C2211yescharacteristic
60C22×Dic158C2311yescharacteristic
61#14579140—22no—
62#14579140C2×C414yes—
63C4×Dic158—22no—
64C4×Dic158—22no—
65#14579120—22no—
66#14579120—22no—
67#14579120—22no—
68#14579120C2×C414yes—
69C2×C4⋊Dic79C2311yescharacteristic
70C2×C4⋊Dic79C2311yescharacteristic
71C2×C4⋊Dic79C2311yescharacteristic
72C2×C4⋊Dic79C2311yescharacteristic
73C2×C4⋊Dic79C2311yescharacteristic
74C2×C4⋊Dic79C2311yescharacteristic
75C2×C4⋊Dic79C2311yescharacteristic
76C2×Dic79⋊C4—21no—
77C2×Dic79⋊C4—21no—
78C2×Dic79⋊C4—21no—
79C2×C22⋊Dic79—21no—
80C2×C22⋊Dic79—21no—
81C2×C22⋊Dic79—21no—
82C2×C22⋊Dic79—21no—
83C2×C4×Dic79—21no—
84C2×C4×Dic79—21no—
85C2×C4×Dic79—21no—
86C2×C4×Dic79—21no—
87C2×C4×Dic79—21no—
88C2×C4×Dic79—21no—
89C2×C4×Dic79—21no—
90C2×C4×Dic79—21no—
91#14579095—22no—
92#14579095C2×C414yescomplemented
93#14579093—22no—
94#14579093C2×C414yescomplemented
95#14579086—22no—
96#14579086—22no—
97#14579086C2×C414yescomplemented
98#14579086C2×C414yescomplemented
99C79⋊#95—21no—
100C79⋊#95—21no—
101C79⋊#95—21no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C79⋊#95—21no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C23×C4×C79D411yescharacteristic
109C23×C4×C79D411yescharacteristic
110C23×C4×C79C2311yescharacteristic
111C22×C8×C79C2311yescharacteristic
112C22×C8×C79C2311yescharacteristic
113C22×C8×C79C2311yescharacteristic
114C22×C8×C79C2311yescharacteristic
115C2×C42×C79—22no—
116C2×C42×C79—22no—
117C2×C42×C79D411yescharacteristic
118C2×C42×C79D411yescharacteristic
119C2×C42×C79C2311yescharacteristic
120C2×C42×C79C2311yescharacteristic
121C22⋊C8×C79—22no—
122C22⋊C8×C79C2×C414yes—
123C4×C8×C79—22no—
124C4×C8×C79—22no—
125C2×Dic158—21no—
126C2×Dic158—21no—
127C2×Dic158—21no—
128C2×Dic158—21no—
129C2×Dic158—21no—
130C2×Dic158C22×C412yes—
131C22×Dic79—21no—
132C22×Dic79—21no—
133C22×Dic79—21no—
134C22×Dic79—21no—
135C22×Dic79—21no—
136C22×Dic79—21no—
137C22×Dic79—21no—
138C22×Dic79—21no—
139C4⋊Dic79—21no—
140C4⋊Dic79—21no—
141C4⋊Dic79—21no—
142C4⋊Dic79—21no—
143C4⋊Dic79—21no—
144C4⋊Dic79—21no—
145C4⋊Dic79—21no—
146C4⋊Dic79—21no—
147C4⋊Dic79—21no—
148C4⋊Dic79C22×C412yes—
149C4⋊Dic79C22×C412yes—
150C4⋊Dic79C22×C412yes—
151C4⋊Dic79#4112yes—
152C4⋊Dic79#4112yes—
153Dic79⋊C4—24no—
154Dic79⋊C4—42no—
155Dic79⋊C4—42no—
156C22⋊Dic79—24no—
157C22⋊Dic79—24no—
158C22⋊Dic79—24no—
159C22⋊Dic79—42no—
160C4×Dic79—24no—
161C4×Dic79—24no—
162C4×Dic79—42no—
163C4×Dic79—42no—
164C4×Dic79—42no—
165C4×Dic79—42no—
166C4×Dic79—42no—
167C4×Dic79—42no—
168C24×C79C2×D411yescharacteristic
169C22×C4×C79—21no—
170C22×C4×C79—21no—
171C22×C4×C79—21no—
172C22×C4×C79—21no—
173C22×C4×C79—22no—
174C22×C4×C79—22no—
175C22×C4×C79—22no—
176C22×C4×C79—22no—
177C22×C4×C79—22no—
178C22×C4×C79—41no—
179C22×C4×C79C22×C412yes—
180C22×C4×C79C2×D411yescharacteristic
181C22×C4×C79C2×D411yescharacteristic
182C22×C4×C79C2×D411yescharacteristic
183C22×C4×C79C2×D411yescharacteristic
184C22×C4×C79C2×D411yescharacteristic
185C22×C4×C79#4112yes—
186C22×C4×C79C2411yescharacteristic
187C2×C8×C79—21no—
188C2×C8×C79—21no—
189C2×C8×C79—21no—
190C2×C8×C79—21no—
191C2×C8×C79—21no—
192C2×C8×C79—21no—
193C2×C8×C79—21no—
194C2×C8×C79—21no—
195C2×C8×C79—21no—
196C2×C8×C79—21no—
197C2×C8×C79C22×C412yes—
198C2×C8×C79C22×C412yes—
199C42×C79—22no—
200C42×C79—22no—
201C42×C79—21no—
202C42×C79—21no—
203C42×C79#4112yes—
204C42×C79#4112yes—
205C23×C79—21no—
206C23×C79—21no—
207C23×C79—21no—
208C23×C79—21no—
209C23×C79—21no—
210C23×C79—21no—
211C23×C79C4×D412yes—
212C23×C79C22×D411yescharacteristic
213C2×C4×C79—21no—
214C2×C4×C79—21no—
215C2×C4×C79—21no—
216C2×C4×C79—21no—
217C2×C4×C79—21no—
218C2×C4×C79—21no—
219C2×C4×C79—22no—
220C2×C4×C79—22no—
221C2×C4×C79—22no—
222C2×C4×C79—22no—
223C2×C4×C79—21no—
224C2×C4×C79—21no—
225C2×C4×C79—21no—
226C2×C4×C79—44no—
227C2×C4×C79—44no—
228C2×C4×C79C4×D412yes—
229C2×C4×C79#12312yes—
230C2×C4×C79#12312yes—
231C2×C4×C79#13512yes—
232C2×C4×C79#13512yes—
233C2×C4×C79#13712yes—
234C2×C4×C79C23×C411yescharacteristic
235C2×C4×C79C2×#4111yescharacteristic
236C2×C4×C79C2×#4111yescharacteristic
237C2×C4×C79C2×#4111yescharacteristic
238C2×C4×C79C2×#4111yescharacteristic
239C2×C4×C79C2×#4111yescharacteristic
240C2×Dic79—22no—
241C2×Dic79—22no—
242C2×Dic79—22no—
243C2×Dic79—22no—
244C2×Dic79—22no—
245C2×Dic79—22no—
246C2×Dic79—41no—
247C2×Dic79—41no—
248C2×Dic79—41no—
249C2×Dic79—41no—
250C2×Dic79—41no—
251C2×Dic79—41no—
252C2×Dic79—41no—
253C2×Dic79—41no—
254C2×Dic79—41no—
255C2×Dic79—41no—
256C2×Dic79—41no—
257C2×Dic79—41no—
258C2×Dic79—41no—
259C2×Dic79—41no—
260C2×Dic79—41no—
261C2×Dic79—41no—
262C2×Dic79—41no—
263C2×Dic79—41no—
264Dic158—22no—
265Dic158—22no—
266Dic158—41no—
267Dic158—41no—
268C8×C79—22no—
269C8×C79—22no—
270C8×C79—41no—
271C8×C79—41no—
272C22×C79—22no—
273C22×C79—22no—
274C22×C79—22no—
275C22×C79—41no—
276C22×C79—41no—
277C22×C79—41no—
278C22×C79—41no—
279C22×C79C2×C4×D411yescharacteristic
280C22×C79C2×#12311yescharacteristic
281C22×C79#52511yescharacteristic
282C22×C79C2×#13511yescharacteristic
283C22×C79C2×#13511yescharacteristic
284C22×C79C2×#13711yescharacteristic
285C22×C79#57511yescharacteristic
286C4×C79—22no—
287C4×C79—22no—
288C4×C79—22no—
289C4×C79—41no—
290C4×C79#48514yescomplemented
291C4×C79C4×#4111yescharacteristic
292C4×C79C4×#4111yescharacteristic
293C4×C79#52911yescharacteristic
294C4×C79#52911yescharacteristic
295Dic79—42no—
296Dic79—42no—
297Dic79—42no—
298Dic79—42no—
299Dic79—42no—
300Dic79—42no—
301Dic79—81no—
302Dic79—81no—
303C4×#485—791nomaximal, Sylow
304C2×C79—42no—
305C2×C79C4×#12311yescharacteristic
306C2×C79C4×#13511yescharacteristic
307C2×C79C4×#13711yescharacteristic
308C2×C79C2×#48511yescharacteristic
309C2×C79#309111yescharacteristic
310C2×C79#310211yescharacteristic
311C2×C79#310711yescharacteristic
312C2×#485—791no—
313C4×C22⋊Q8—791no—
314C4×#117—791no—
315#1928—791no—
316#1927—791no—
317#1919—791no—
318#1918—791no—
319#1873—791no—
320#1854—791no—
321#1825—791no—
322C4×#107—791no—
323C4×#106—791no—
324C4×#103—791no—
325C4×#103—791no—
326C4×C22⋊C8D7911yescharacteristic
327C79C4×#48511yescharacteristic, complemented, Sylow
328C2×C22⋊Q8—791no—
329C2×C4×Q8—791no—
330C2×#117—791no—
331C2×#117—791no—
332C22×C42C2×D7911yescharacteristic
333#485—798no—
334C2×#107—791no—
335C2×#107—791no—
336C2×#106—791no—
337C2×#106—791no—
338C2×#103—791no—
339C2×#103—791no—
340C2×#103—791no—
341C2×#103—791no—
342C2×C22⋊C8C2×D7911yescharacteristic
343C2×C22⋊C8C2×D7911yescharacteristic
344C2×C4×C8C2×D7911yescharacteristic
345C2×C4×C8C2×D7911yescharacteristic
346#391—791no—
347#389—791no—
348#387—1581no—
349#385—1581no—
350#380—791no—
351C4×C4⋊C4—791no—
352C4×C4⋊C4—791no—
353C4×C4⋊C4—791no—
354C4×C4⋊C4—791no—
355C4×C4⋊C4—791no—
356C4×C4⋊C4—1581no—
357C4×C22⋊C4—1581no—
358C4×C22⋊C4—1581no—
359C4×C22⋊C4—1581no—
360#376—1581no—
361C43—1581no—
362#340—791no—
363#340—791no—
364#340—791no—
365#340—791no—
366#340—791no—
367#340—791no—
368#340—791no—
369#340—791no—
370#336C2×D7911yescharacteristic
371#336C2×D7911yescharacteristic
372C22×Q8—791no—
373C23×C4D31611yescharacteristic
374C23×C4D31611yescharacteristic
375C23×C4C22×D7911yescharacteristic
376C22×C8C22×D7911yescharacteristic
377C22×C8C22×D7911yescharacteristic
378C22×C8C22×D7911yescharacteristic
379C22×C8C22×D7911yescharacteristic
380C22⋊Q8—794no—
381C22⋊Q8—1582no—
382C4×Q8—1582no—
383C4×Q8—1582no—
384#117—794no—
385#117—1582no—
386#117—1582no—
387#117—1582no—
388C2×C4⋊C4—791no—
389C2×C4⋊C4—791no—
390C2×C4⋊C4—791no—
391C2×C4⋊C4—791no—
392C2×C4⋊C4—791no—
393C2×C4⋊C4—791no—
394C2×C4⋊C4—791no—
395C2×C4⋊C4—1581no—
396C2×C4⋊C4—1581no—
397C2×C4⋊C4—1581no—
398C2×C22⋊C4—1581no—
399C2×C22⋊C4—1581no—
400C2×C22⋊C4—1581no—
401C2×C22⋊C4—1581no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—1581no—
405C2×C42—1581no—
406C2×C42—1581no—
407C2×C42—1581no—
408C2×C42—1581no—
409C2×C42—1581no—
410C2×C42—1581no—
411C2×C42—1581no—
412C2×C42D31611yescharacteristic
413C2×C42D31611yescharacteristic
414C2×C42C22×D7911yescharacteristic
415C2×C42C22×D7911yescharacteristic
416#107—794no—
417#107—1582no—
418#106—794no—
419#106—1582no—
420#103—794no—
421#103—794no—
422#103—1582no—
423#103—1582no—
424C22⋊C8—22no—
425C22⋊C8C4×D7914yes—
426C4×C8—22no—
427C4×C8—22no—
428#95—1581no—
429#95—1581no—
430#95—1581no—
431#95—1581no—
432#95—1581no—
433#95—1581no—
434#95—1581no—
435#95—1581no—
436#95—1581no—
437C24C2×D31611yescharacteristic
438C2×Q8—792no—
439C2×Q8—1581no—
440C2×Q8—1581no—
441C2×Q8—1581no—
442C2×Q8—1581no—
443C2×Q8—1581no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—41no—
454C22×C4—1581no—
455C22×C4—1581no—
456C22×C4—1581no—
457C22×C4—1581no—
458C22×C4—1581no—
459C22×C4—1581no—
460C22×C4—1581no—
461C22×C4—1581no—
462C22×C4C2×C4×D7912yes—
463C22×C4C2×D31611yescharacteristic
464C22×C4C2×D31611yescharacteristic
465C22×C4C2×D31611yescharacteristic
466C22×C4C2×D31611yescharacteristic
467C22×C4C2×D31611yescharacteristic
468C22×C4#1192962412yes—
469C22×C4C23×D7911yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8C2×C4×D7912yes—
481C2×C8C2×C4×D7912yes—
482C4⋊C4—3162no—
483C4⋊C4—3162no—
484C4⋊C4—792no—
485C4⋊C4—792no—
486C4⋊C4—792no—
487C4⋊C4—792no—
488C4⋊C4—792no—
489C4⋊C4—1581no—
490C4⋊C4—1581no—
491C4⋊C4—1581no—
492C4⋊C4—1581no—
493C4⋊C4—1581no—
494C4⋊C4—1581no—
495C4⋊C4—1581no—
496C4⋊C4—1581no—
497C4⋊C4—1581no—
498C4⋊C4—1584no—
499C22⋊C4—3162no—
500C22⋊C4—1584no—
501C22⋊C4—1584no—
502C22⋊C4—1584no—
503C42—21no—
504C42—21no—
505C42—22no—
506C42—22no—
507C42—3162no—
508C42—3162no—
509C42—3162no—
510C42—3162no—
511C42—3162no—
512C42—3162no—
513C42—1584no—
514C42—1584no—
515C42#1192962312yes—
516C42#1192962312yes—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23C4×D31612yes—
524C23C22×D31611yescharacteristic
525Q8—3161no—
526Q8—3161no—
527Q8—1582no—
528Q8—1582no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—3161no—
545C2×C4—3161no—
546C2×C4—3161no—
547C2×C4—3161no—
548C2×C4—3161no—
549C2×C4—3161no—
550C2×C4—3161no—
551C2×C4—3161no—
552C2×C4—3161no—
553C2×C4—3161no—
554C2×C4—3161no—
555C2×C4—3161no—
556C2×C4—3161no—
557C2×C4—3161no—
558C2×C4—3161no—
559C2×C4—3161no—
560C2×C4—3161no—
561C2×C4—3161no—
562C2×C4—1582no—
563C2×C4—1582no—
564C2×C4—1582no—
565C2×C4—1582no—
566C2×C4—1582no—
567C2×C4—1582no—
568C2×C4C4×D31612yes—
569C2×C4#1457914512yes—
570C2×C4#1457914512yes—
571C2×C4#1457918312yes—
572C2×C4#1457918312yes—
573C2×C4#1457919412yes—
574C2×C4C22×C4×D7911yescharacteristic
575C2×C4#41×D7911yescharacteristic
576C2×C4#41×D7911yescharacteristic
577C2×C4C2×#1192962311yescharacteristic
578C2×C4C2×#1192962311yescharacteristic
579C2×C4C2×#1192962411yescharacteristic
580C8—22no—
581C8—22no—
582C8—41no—
583C8—41no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C2×C4×D31611yescharacteristic
592C22C2×#1457914511yescharacteristic
593C22#1909907511yescharacteristic
594C22C2×#1457918311yescharacteristic
595C22C2×#1457918311yescharacteristic
596C22C2×#1457919411yescharacteristic
597C22#1909936311yescharacteristic
598C4—22no—
599C4—22no—
600C4—22no—
601C4—41no—
602C4—3162no—
603C4—3162no—
604C4—3162no—
605C4—3162no—
606C4—3162no—
607C4—3162no—
608C4—6321no—
609C4—6321no—
610C4#1909890514yesdirect product factor
611C4C4×#1192962311yescharacteristic
612C4C4×#1192962311yescharacteristic
613C4#1909909311yescharacteristic
614C4#1909909311yescharacteristic
615C2—42no—
616C2C4×#1457914511yescharacteristic
617C2C4×#1457918311yescharacteristic
618C2C4×#1457919411yescharacteristic
619C2C2×#1909890511yescharacteristic
620C2#2377331511yescharacteristic
621C2#2377342011yescharacteristic
622C2#2377347211yescharacteristic
subgroupG/H
centerC22×C4C2×D316
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC4×C22⋊C8×C79C2
socleC23×C79C22×D4
prime radicalC24×C79C2×D4
cosocleC22×C4×C79C24
hypercenterC4×C22⋊C8D79
hypocenterC79C4×#485
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #23764042C2semidirect
5. #23764035C2semidirect
6. #23763979C2semidirect
7. #23763972C2semidirect
11. C4×#14579095C2semidirect
12. C4×#14579093C2semidirect
13. C4×#14579086C2semidirect
14. C4×#14579086C2semidirect
20. #19098905C4direct (N × H)
92. #14579095C2×C4semidirect
94. #14579093C2×C4semidirect
97. #14579086C2×C4semidirect
98. #14579086C2×C4semidirect
290. C4×C79#485semidirect
327. C79C4×#485semidirect
610. C4#19098905direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190989052
C4×#145791402
C4×#145791202
#237640422
#237640352
#237639792
#237639722
#237637102
#237636012
#237634962
C4×#145790952
C4×#145790932
C4×#145790862
C4×C22⋊C8×C792
C4×#48579