Finite Group Databasebeta

← C4×C4⋊Q8×D79 #34446785

Subgroups — C4×C4⋊Q8×D79 #34446785

Order 20224.

3358 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D79C211yesmaximal, characteristic
2C2×C4×Q8×D79C212yesmaximal
3C4⋊Q8×Dic79C211yesmaximal, characteristic, complemented
4C4×#14579161C211yesmaximal, characteristic, complemented
5#23765971C214yesmaximal, complemented
6C4×#14579160C214yesmaximal, complemented
7#23765969C212yesmaximal, complemented
8C4×#14579159C212yesmaximal, complemented
9#23765967C211yesmaximal, characteristic, complemented
10#391×D79C212yesmaximal
11#389×D79C214yesmaximal
12#384×D79C211yesmaximal, characteristic
13C4×C4⋊C4×D79C214yesmaximal
14C43×D79C211yesmaximal, characteristic
15C4×C4⋊Q8×C79C211yesmaximal, characteristic, complemented
16C22×Q8×D79C2212yes—
17C2×#14579161C2211yescharacteristic
18C2×#14579160C2214yes—
19C2×#14579159C2212yes—
20C4⋊Q8×D79C4116yesdirect product factor
21C2×Q8×Dic79C2212yes—
22C2×C4×Dic158C2212yes—
23C2×C4×Dic158C2214yes—
24C2×#14579126C2212yes—
25C2×#14579126C2214yes—
26C4×Q8×D79—216no—
27C2×C4⋊C4×D79C2212yes—
28C2×C4⋊C4×D79C2214yes—
29C2×C4⋊C4×D79C2214yes—
30C2×C4⋊C4×D79C2214yes—
31C2×C42×D79C2214yes—
32C2×C42×D79C2212yes—
33C2×C42×D79C2211yescharacteristic
34C2×C42×D79C2211yescharacteristic
35C2×C42×D79C2211yescharacteristic
36C2×C42×D79C2212yes—
37#19098470C2212yes—
38#19098469C2212yes—
39#19098468C2212yes—
40#19098467C2218yes—
41#19098462C2214yes—
42#19098461C2214yes—
43#19098460C2218yes—
44#19098459C2214yes—
45#19098458C2218yes—
46#19098433C2211yescharacteristic
47#19098432C2212yes—
48#19098432C2214yes—
49C4⋊C4×Dic79C2214yes—
50C4⋊C4×Dic79C2214yes—
51C4×Dic79⋊C4C2218yes—
52C4×C4⋊Dic79C2214yes—
53#19098414C2218yes—
54#95×D79C2218yes—
55C42×Dic79C2211yescharacteristic
56C42×Dic79C2211yescharacteristic
57C42×Dic79C2211yescharacteristic
58C42×Dic79C2212yes—
59C42×Dic79C2212yes—
60C2×C4⋊Q8×C79C2211yescharacteristic
61C2×C4×Q8×C79C2212yes—
62#391×C79C2212yes—
63#389×C79C2214yes—
64#384×C79C2211yescharacteristic
65C4×C4⋊C4×C79C2214yes—
66C43×C79C2211yescharacteristic
67C22×Dic158C2314yes—
68C22×Dic158C2312yes—
69C2×Q8×D79—28no—
70C2×Q8×D79—28no—
71C2×Q8×D79C2×C4116yes—
72C22×C4×D79C2314yes—
73C22×C4×D79C2314yes—
74C22×C4×D79C2311yescharacteristic
75C22×C4×D79C2312yes—
76C22×C4×D79C2311yescharacteristic
77C22×C4×D79C2312yes—
78C22×C4×D79C2311yescharacteristic
79#14579161C2×C418yescomplemented
80#14579160C2×C4132yescomplemented
81#14579159C2×C4116yescomplemented
82Q8×Dic79—28no—
83C4×Dic158—28no—
84C4×Dic158—216no—
85#14579126—28no—
86#14579126—216no—
87C2×C4⋊Dic79C2314yes—
88C2×C4⋊Dic79C2312yes—
89C2×C4⋊Dic79C2314yes—
90C2×C4⋊Dic79C2314yes—
91C2×Dic79⋊C4C2318yes—
92C2×Dic79⋊C4C2314yes—
93C2×Dic79⋊C4C2314yes—
94C2×Dic79⋊C4C2314yes—
95C2×Dic79⋊C4C2318yes—
96C4⋊C4×D79—28no—
97C4⋊C4×D79—216no—
98C4⋊C4×D79—216no—
99C4⋊C4×D79C2×C4132yes—
100C2×C4×Dic79C2312yes—
101C2×C4×Dic79C2312yes—
102C2×C4×Dic79C2312yes—
103C2×C4×Dic79C2312yes—
104C2×C4×Dic79C2311yescharacteristic
105C2×C4×Dic79C2314yes—
106C2×C4×Dic79C2314yes—
107C2×C4×Dic79C2314yes—
108C2×C4×Dic79C2311yescharacteristic
109C2×C4×Dic79C2312yes—
110C2×C4×Dic79C2311yescharacteristic
111C2×C4×Dic79C2311yescharacteristic
112C2×C4×Dic79C2311yescharacteristic
113C2×C4×Dic79C2312yes—
114C2×C4×Dic79C2312yes—
115C2×C4×Dic79C2312yes—
116C42×D79—216no—
117C42×D79—24no—
118C42×D79—28no—
119C42×D79C2×C418yes—
120C42×D79D418yes—
121C42×D79Q8116yescomplemented
122C79⋊#95C2318yes—
123C79⋊#95C2318yes—
124C79⋊#95C2318yes—
125C22×Q8×C79C2312yes—
126C4⋊Q8×C79C2×C418yescomplemented
127C4×Q8×C79—28no—
128C2×C4⋊C4×C79C2314yes—
129C2×C4⋊C4×C79C2312yes—
130C2×C4⋊C4×C79C2314yes—
131C2×C4⋊C4×C79C2314yes—
132C2×C42×C79C2312yes—
133C2×C42×C79C2311yescharacteristic
134C2×C42×C79C2314yes—
135C2×C42×C79C2311yescharacteristic
136C2×C42×C79C2311yescharacteristic
137C2×C42×C79C2312yes—
138#95×C79C2318yes—
139C23×D79C2411yescharacteristic
140C2×Dic158—28no—
141C2×Dic158—28no—
142C2×Dic158—24no—
143C2×Dic158—24no—
144C2×Dic158C22×C418yes—
145C2×Dic158C22×C4116yes—
146Q8×D79—264no—
147C22×Dic79C2414yes—
148C22×Dic79C2414yes—
149C22×Dic79C2411yescharacteristic
150C22×Dic79C2412yes—
151C22×Dic79C2411yescharacteristic
152C22×Dic79C2412yes—
153C22×Dic79C2411yescharacteristic
154C2×C4×D79—28no—
155C2×C4×D79—28no—
156C2×C4×D79—28no—
157C2×C4×D79—24no—
158C2×C4×D79—24no—
159C2×C4×D79—24no—
160C2×C4×D79—216no—
161C2×C4×D79C22×C4116yes—
162C2×C4×D79C22×C414yes—
163C2×C4×D79C22×C418yes—
164C2×C4×D79C2×D414yes—
165C2×C4×D79C2×D414yes—
166C2×C4×D79C2×D414yes—
167C2×C4×D79C2×Q818yes—
168C2×C4×D79C2×Q818yes—
169C2×C4×D79C2×Q818yes—
170C2×C4×D79#4114yes—
171C2×C4×D79#4118yes—
172C4⋊Dic79—28no—
173C4⋊Dic79—24no—
174C4⋊Dic79—28no—
175C4⋊Dic79C22×C4116yes—
176Dic79⋊C4—28no—
177Dic79⋊C4—28no—
178Dic79⋊C4—216no—
179Dic79⋊C4—28no—
180Dic79⋊C4C22×C4132yes—
181C4×Dic79—28no—
182C4×Dic79—28no—
183C4×Dic79—24no—
184C4×Dic79—24no—
185C4×Dic79—24no—
186C4×Dic79—28no—
187C4×Dic79—22no—
188C4×Dic79—24no—
189C4×Dic79C22×C414yes—
190C4×Dic79C22×C418yes—
191C4×Dic79C2×D414yes—
192C4×Dic79C2×D414yes—
193C4×Dic79C2×D414yes—
194C4×Dic79C2×Q818yescomplemented
195C4×Dic79C2×Q818yescomplemented
196C4×Dic79C2×Q818yescomplemented
197C2×Q8×C79—24no—
198C2×Q8×C79—24no—
199C2×Q8×C79C22×C418yes—
200C22×C4×C79C2414yes—
201C22×C4×C79C2414yes—
202C22×C4×C79C2411yescharacteristic
203C22×C4×C79C2412yes—
204C22×C4×C79C2411yescharacteristic
205C22×C4×C79C2412yes—
206C22×C4×C79C2411yescharacteristic
207C4⋊C4×C79—28no—
208C4⋊C4×C79—24no—
209C4⋊C4×C79—28no—
210C4⋊C4×C79C22×C4116yes—
211C42×C79—28no—
212C42×C79—22no—
213C42×C79—24no—
214C42×C79C22×C414yes—
215C42×C79C2×D414yes—
216C42×C79C2×Q818yescomplemented
217C23×C79C2511yescharacteristic
218C22×D79C23×C412yes—
219C22×D79C22×D412yes—
220C22×D79C22×Q814yes—
221C22×D79C2×#4112yes—
222C22×D79C2×#4114yes—
223Q8×C79—216no—
224C2×C4×C79—24no—
225C2×C4×C79—22no—
226C2×C4×C79—22no—
227C2×C4×C79—22no—
228C2×C4×C79—24no—
229C2×C4×C79—24no—
230C2×C4×C79—28no—
231C2×C4×C79C23×C418yes—
232C2×C4×C79C23×C412yes—
233C2×C4×C79C23×C414yes—
234C2×C4×C79C22×D412yes—
235C2×C4×C79C22×D412yes—
236C2×C4×C79C22×D412yes—
237C2×C4×C79C22×Q814yes—
238C2×C4×C79C22×Q814yes—
239C2×C4×C79C22×Q814yes—
240C2×C4×C79C2×#4112yes—
241C2×C4×C79C2×#4114yes—
242C2×Dic79—24no—
243C2×Dic79—22no—
244C2×Dic79—22no—
245C2×Dic79—22no—
246C2×Dic79—24no—
247C2×Dic79—24no—
248C2×Dic79—28no—
249C2×Dic79C23×C418yes—
250C2×Dic79C23×C412yes—
251C2×Dic79C23×C414yes—
252C2×Dic79C22×D412yes—
253C2×Dic79C22×D412yes—
254C2×Dic79C22×D412yes—
255C2×Dic79C22×Q814yes—
256C2×Dic79C22×Q814yes—
257C2×Dic79C22×Q814yes—
258C2×Dic79C2×#4112yes—
259C2×Dic79C2×#4114yes—
260C4×D79—232no—
261C4×D79—28no—
262C4×D79—216no—
263C4×D79—416no—
264C4×D79C4×D4116yes—
265C4×D79C4×Q8132yescomplemented
266C4×D79C4⋊Q8116yesdirect product factor
267Dic158—216no—
268Dic158—232no—
269C22×C79C24×C411yescharacteristic
270C22×C79C23×D411yescharacteristic
271C22×C79C23×Q812yes—
272C22×C79C22×#4111yescharacteristic
273C22×C79C22×#4112yes—
274C2×D79C2×C4×D414yes—
275C2×D79C2×C4×Q818yes—
276C2×D79C2×C4⋊Q814yes—
277C2×D79#53214yes—
278C2×D79#53318yes—
279C4×C79—28no—
280C4×C79—22no—
281C4×C79—24no—
282C4×C79—44no—
283C4×C79C2×C4×D414yes—
284C4×C79C2×C4×Q818yescomplemented
285C4×C79C2×C4⋊Q814yescomplemented
286Dic79—28no—
287Dic79—22no—
288Dic79—24no—
289Dic79—44no—
290Dic79C2×C4×D414yes—
291Dic79C2×C4×Q818yescomplemented
292Dic79C2×C4⋊Q814yescomplemented
293C2×C4×C4⋊Q8—791nomaximal, Sylow
294C2×C79C22×C4×D411yescharacteristic
295C2×C79C22×C4×Q812yes—
296C2×C79C22×C4⋊Q811yescharacteristic
297C2×C79C2×#53211yescharacteristic
298C2×C79C2×#53312yes—
299D79C4×C4⋊Q818yesdirect product factor
300C22×C4⋊Q8—791no—
301C22×C4×Q8—792no—
302C4×C4⋊Q8—792no—
303C4×C4⋊Q8—794no—
304C4×C4⋊Q8—791no—
305C4×C4⋊Q8—794no—
306C4×C4⋊Q8—791no—
307C4×C4⋊Q8—791no—
308C4×C4⋊Q8—792no—
309C4×C4⋊Q8D7911yescharacteristic, direct product factor
310C2×#391—792no—
311C2×#389—794no—
312C2×#384—791no—
313C2×C4×C4⋊C4—794no—
314C2×C43—791no—
315C79C2×C4×C4⋊Q811yescharacteristic, complemented, Sylow
316C23×Q8—792no—
317C2×C4⋊Q8—792no—
318C2×C4⋊Q8—7916no—
319C2×C4⋊Q8—794no—
320C2×C4⋊Q8—791no—
321C2×C4⋊Q8C2×D7911yescharacteristic
322C2×C4×Q8—792no—
323C2×C4×Q8—794no—
324C2×C4×Q8—792no—
325C2×C4×Q8—794no—
326C2×C4×Q8—792no—
327C2×C4×Q8—15816no—
328C2×C4×Q8C2×D7912yes—
329C22×C4⋊C4—794no—
330C22×C4⋊C4—792no—
331C22×C4⋊C4—794no—
332C22×C4⋊C4—794no—
333C22×C42—791no—
334C22×C42—791no—
335C22×C42—792no—
336C22×C42—794no—
337C22×C42—792no—
338C22×C42—791no—
339#391—792no—
340#391—792no—
341#391—792no—
342#391—798no—
343#391C2×D7912yes—
344#389—798no—
345#389—794no—
346#389—794no—
347#389—794no—
348#389—798no—
349#389C2×D7914yes—
350#384—794no—
351#384—792no—
352#384—791no—
353#384C2×D7911yescharacteristic
354C4×C4⋊C4—794no—
355C4×C4⋊C4—794no—
356C4×C4⋊C4—794no—
357C4×C4⋊C4—798no—
358C4×C4⋊C4—798no—
359C4×C4⋊C4C2×D7914yes—
360C2×#95—798no—
361C43—791no—
362C43—792no—
363C43—791no—
364C43—792no—
365C43—791no—
366C43C2×D7911yescharacteristic
367C22×Q8—7916no—
368C22×Q8—794no—
369C22×Q8—792no—
370C22×Q8—1588no—
371C22×Q8—1588no—
372C22×Q8C22×D7912yes—
373C23×C4—792no—
374C23×C4—791no—
375C23×C4—791no—
376C23×C4—791no—
377C23×C4—794no—
378C23×C4—792no—
379C23×C4—794no—
380C4⋊Q8—7916no—
381C4⋊Q8—7932no—
382C4⋊Q8—798no—
383C4⋊Q8C4×D7918yesdirect product factor
384C4×Q8—28no—
385C4×Q8—15816no—
386C4×Q8—1588no—
387C4×Q8—15816no—
388C4×Q8—1588no—
389C4×Q8—1588no—
390C2×C4⋊C4—798no—
391C2×C4⋊C4—794no—
392C2×C4⋊C4—7932no—
393C2×C4⋊C4—794no—
394C2×C4⋊C4—792no—
395C2×C4⋊C4—794no—
396C2×C4⋊C4—794no—
397C2×C4⋊C4—794no—
398C2×C4⋊C4—798no—
399C2×C4⋊C4—794no—
400C2×C4⋊C4—1588no—
401C2×C4⋊C4—15816no—
402C2×C4⋊C4—15816no—
403C2×C4⋊C4C22×D7912yes—
404C2×C4⋊C4C22×D7914yes—
405C2×C4⋊C4C22×D7914yes—
406C2×C4⋊C4C22×D7914yes—
407C2×C42—791no—
408C2×C42—791no—
409C2×C42—791no—
410C2×C42—792no—
411C2×C42—792no—
412C2×C42—792no—
413C2×C42—791no—
414C2×C42—792no—
415C2×C42—798no—
416C2×C42—798no—
417C2×C42—7916no—
418C2×C42—794no—
419C2×C42—794no—
420C2×C42—792no—
421C2×C42—792no—
422C2×C42—792no—
423C2×C42—792no—
424C2×C42—791no—
425C2×C42—794no—
426C2×C42—15816no—
427C2×C42—1588no—
428C2×C42—1584no—
429C2×C42C22×D7912yes—
430C2×C42C22×D7911yescharacteristic
431C2×C42C22×D7914yes—
432C2×C42C22×D7911yescharacteristic
433C2×C42C22×D7911yescharacteristic
434C2×C42C22×D7912yes—
435#95—798no—
436#95—798no—
437#95—798no—
438#95C22×D7918yes—
439C24—791no—
440C2×Q8—24no—
441C2×Q8—24no—
442C2×Q8—7916no—
443C2×Q8—798no—
444C2×Q8—1588no—
445C2×Q8—1588no—
446C2×Q8—15864no—
447C2×Q8—1584no—
448C2×Q8—1584no—
449C2×Q8C2×C4×D7918yes—
450C22×C4—791no—
451C22×C4—792no—
452C22×C4—791no—
453C22×C4—798no—
454C22×C4—798no—
455C22×C4—798no—
456C22×C4—794no—
457C22×C4—798no—
458C22×C4—794no—
459C22×C4—794no—
460C22×C4—794no—
461C22×C4—792no—
462C22×C4—794no—
463C22×C4—791no—
464C22×C4—798no—
465C22×C4—7916no—
466C22×C4—794no—
467C22×C4—794no—
468C22×C4—1588no—
469C22×C4—15816no—
470C22×C4—1588no—
471C22×C4—1584no—
472C22×C4—1584no—
473C22×C4—1584no—
474C22×C4—1588no—
475C22×C4C23×D7914yes—
476C22×C4C23×D7912yes—
477C22×C4C23×D7914yes—
478C22×C4C23×D7911yescharacteristic
479C22×C4C23×D7912yes—
480C22×C4C23×D7911yescharacteristic
481C22×C4C23×D7911yescharacteristic
482C4⋊C4—28no—
483C4⋊C4—28no—
484C4⋊C4—24no—
485C4⋊C4—7932no—
486C4⋊C4—7916no—
487C4⋊C4—15816no—
488C4⋊C4—1588no—
489C4⋊C4—1588no—
490C4⋊C4—1588no—
491C4⋊C4—1588no—
492C4⋊C4—1588no—
493C4⋊C4—1584no—
494C4⋊C4C2×C4×D79116yes—
495C42—22no—
496C42—24no—
497C42—28no—
498C42—798no—
499C42—798no—
500C42—798no—
501C42—794no—
502C42—798no—
503C42—794no—
504C42—794no—
505C42—794no—
506C42—1584no—
507C42—1584no—
508C42—1584no—
509C42—1588no—
510C42—1588no—
511C42—1582no—
512C42—1584no—
513C42—1588no—
514C42C2×C4×D7914yes—
515C42D4×D7914yes—
516C42Q8×D7918yescomplemented
517C23—792no—
518C23—792no—
519C23—794no—
520C23—792no—
521C23—794no—
522C23C24×D7911yescharacteristic
523Q8—216no—
524Q8—15832no—
525Q8—15816no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—28no—
533C2×C4—31616no—
534C2×C4—794no—
535C2×C4—792no—
536C2×C4—792no—
537C2×C4—792no—
538C2×C4—794no—
539C2×C4—794no—
540C2×C4—794no—
541C2×C4—792no—
542C2×C4—7916no—
543C2×C4—7932no—
544C2×C4—7916no—
545C2×C4—798no—
546C2×C4—792no—
547C2×C4—794no—
548C2×C4—15832no—
549C2×C4—1588no—
550C2×C4—15816no—
551C2×C4—1584no—
552C2×C4—1588no—
553C2×C4—1584no—
554C2×C4—1582no—
555C2×C4—1582no—
556C2×C4—1582no—
557C2×C4—1584no—
558C2×C4C22×C4×D7918yes—
559C2×C4C22×C4×D7912yes—
560C2×C4C22×C4×D7914yes—
561C2×C4C2×D4×D7912yes—
562C2×C4C2×D4×D7912yes—
563C2×C4C2×D4×D7912yes—
564C2×C4C2×Q8×D7914yes—
565C2×C4C2×Q8×D7914yes—
566C2×C4C2×Q8×D7914yes—
567C2×C4#41×D7912yes—
568C2×C4#41×D7914yes—
569C22—794no—
570C22—798no—
571C22—794no—
572C22—794no—
573C22—798no—
574C22C23×C4×D7911yescharacteristic
575C22C22×D4×D7911yescharacteristic
576C22C22×Q8×D7912yes—
577C22C2×#41×D7911yescharacteristic
578C22C2×#41×D7912yes—
579C4—28no—
580C4—22no—
581C4—24no—
582C4—44no—
583C4—3164no—
584C4—794no—
585C4—798no—
586C4—794no—
587C4—1588no—
588C4—1582no—
589C4—1584no—
590C4C4×D4×D7914yes—
591C4C4×Q8×D7918yescomplemented
592C4C4⋊Q8×D7914yesdirect product factor
593C2—798no—
594C2C2×C4×D4×D7911yescharacteristic
595C2C2×C4×Q8×D7912yes—
596C2C2×C4⋊Q8×D7911yescharacteristic
597C2#532×D7911yescharacteristic
598C2#533×D7912yes—
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC4×C4⋊Q8×C79C2
socle, cosocleC23×C79C25
prime radicalC23×D79C24
hypercenterC4×C4⋊Q8D79
hypocenterC79C2×C4×C4⋊Q8
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C4⋊Q8×Dic79C2semidirect
4. C4×#14579161C2semidirect
5. #23765971C2semidirect
6. C4×#14579160C2semidirect
7. #23765969C2semidirect
8. C4×#14579159C2semidirect
9. #23765967C2semidirect
15. C4×C4⋊Q8×C79C2semidirect
20. C4⋊Q8×D79C4direct (N × H)
79. #14579161C2×C4semidirect
80. #14579160C2×C4semidirect
81. #14579159C2×C4semidirect
121. C42×D79Q8semidirect
126. C4⋊Q8×C79C2×C4semidirect
194. C4×Dic79C2×Q8semidirect
195. C4×Dic79C2×Q8semidirect
196. C4×Dic79C2×Q8semidirect
216. C42×C79C2×Q8semidirect
265. C4×D79C4×Q8semidirect
266. C4×D79C4⋊Q8direct (N × H)
284. C4×C79C2×C4×Q8semidirect
285. C4×C79C2×C4⋊Q8semidirect
291. Dic79C2×C4×Q8semidirect
292. Dic79C2×C4⋊Q8semidirect
299. D79C4×C4⋊Q8direct (N × H)
309. C4×C4⋊Q8D79direct (N × H)
315. C79C2×C4×C4⋊Q8semidirect
383. C4⋊Q8C4×D79direct (N × H)
516. C42Q8×D79semidirect
591. C4C4×Q8×D79semidirect
592. C4C4⋊Q8×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×C4×Q8×D792
C4⋊Q8×Dic792
C4×#145791612
#237659712
C4×#145791602
#237659692
C4×#145791592
#237659672
#391×D792
#389×D792
#384×D792
C4×C4⋊C4×D792
C43×D792
C4×C4⋊Q8×C792
C2×C4×C4⋊Q879