Finite Group Databasebeta

← C2×#23776141 #35167993

Subgroups — C2×#23776141 #35167993

Order 20224.

1842 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic158C211yesmaximal, characteristic, complemented
2C2×#19099285C211yesmaximal, characteristic
3#23776141C2116yesmaximal, direct product factor
4C2×#19098924C211yesmaximal, characteristic
5C2×#19098923C211yesmaximal, characteristic
6C2×#19098912C211yesmaximal, characteristic, complemented
7C2×#19098848C211yesmaximal, characteristic, complemented
8C2×#19098847C211yesmaximal, characteristic, complemented
9C2×#19098852C211yesmaximal, characteristic
10C2×#19098787C211yesmaximal, characteristic
11C2×#19098785C211yesmaximal, characteristic
12C2×#19098771C211yesmaximal, characteristic, complemented
13C2×#19098691C211yesmaximal, characteristic, complemented
14C2×#19098667C211yesmaximal, characteristic, complemented
15C2×#19098648C211yesmaximal, characteristic
16C2×#441×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929611C2211yescharacteristic
19Q8×Dic158—24no—
20Q8×Dic158C2218yescomplemented
21#19099285—24no—
22#19099285C2218yes—
23C2×#14579161—21no—
24C2×#14579161C2211yescharacteristic
25C2×#14579160—21no—
26C2×#14579160—21no—
27C2×#14579160C2211yescharacteristic
28C2×#14579160C2211yescharacteristic
29C2×#14579159C2211yescharacteristic
30C2×#14579156—21no—
31C2×#14579155—21no—
32C2×#14579150C2211yescharacteristic
33C2×#14579149C2211yescharacteristic
34C2×#14579139—21no—
35C2×Q8×Dic79C2211yescharacteristic
36C2×Q8×Dic79C2211yescharacteristic
37C2×C4×Dic158—21no—
38C2×C4×Dic158C2211yescharacteristic
39C2×#14579126C2211yescharacteristic
40C2×#14579123C2211yescharacteristic
41C2×#14579118—21no—
42#19098924C2218yes—
43#19098923C2218yes—
44#19098912C2218yescomplemented
45#19098852C2218yes—
46#19098848C2218yescomplemented
47#19098847C2218yescomplemented
48#19098787C2218yes—
49#19098785C2218yes—
50#19098771C2218yescomplemented
51#19098691C2218yescomplemented
52#19098667C2218yescomplemented
53#19098648C2218yes—
54C2×#14579092C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56C2×C4⋊(C79⋊C8)C2211yescharacteristic
57C2×Dic79⋊C8C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64C2×#14579083C2211yescharacteristic
65C2×#14579083C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71C2×C4×Q8×C79C2211yescharacteristic
72#441×C79C2218yescomplemented
73C2×#106×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158—21no—
80C22×Dic158D411yescharacteristic
81C22×Dic158C2311yescharacteristic
82C22×D316C2311yescharacteristic
83C22×C4×D79—21no—
84C2×#11929614—24no—
85C2×#11929614C2314yes—
86C2×#11929611—24no—
87C2×#11929611C2314yes—
88C22×C79⋊C8C2311yescharacteristic
89C22×C79⋊C8C2311yescharacteristic
90#14579161—22no—
91#14579161—28no—
92#14579161C2314yes—
93#14579160—28no—
94#14579160—28no—
95#14579160—22no—
96#14579160—22no—
97#14579160C2314yes—
98#14579160C2314yes—
99#14579159—22no—
100#14579159C2314yes—
101#14579156—28no—
102#14579155—28no—
103#14579150—22no—
104#14579150C2314yes—
105#14579149—22no—
106#14579149C2314yes—
107#14579139—28no—
108Q8×Dic79—22no—
109Q8×Dic79—22no—
110Q8×Dic79C2314yes—
111Q8×Dic79C2314yes—
112C4×Dic158—28no—
113C4×Dic158D414yes—
114C4×Dic158C2314yes—
115#14579126—22no—
116#14579126C2314yes—
117#14579123—22no—
118#14579123C2314yes—
119#14579118—28no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79D411yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142C2×C4×Dic79C2311yescharacteristic
143#14579092C2314yes—
144#14579092C2314yes—
145C4⋊(C79⋊C8)C2314yes—
146Dic79⋊C8C2314yes—
147Dic79⋊C8C2314yes—
148#14579086C2314yes—
149#14579086C2314yes—
150#14579085C2314yes—
151#14579085C2314yes—
152#14579084C2314yes—
153#14579083C2314yes—
154#14579083C2314yes—
155#14579081C2314yes—
156#14579071C2314yes—
157C8×Dic79C2314yes—
158C22×Q8×C79C2311yescharacteristic
159C22×Q8×C79C2311yescharacteristic
160C2×Q16×C79—24no—
161C2×Q16×C79C2314yes—
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164C4×Q8×C79—22no—
165C4×Q8×C79—22no—
166C4×Q8×C79C2314yes—
167C4×Q8×C79C2314yes—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C42×C79—21no—
173C2×C42×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#106×C79C2314yes—
176#103×C79C2314yes—
177#103×C79C2314yes—
178#97×C79C2314yes—
179C23×D79—21no—
180C2×Dic158—24no—
181C2×Dic158—24no—
182C2×Dic158—24no—
183C2×Dic158—21no—
184C2×Dic158—24no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—82no—
188C2×Dic158—82no—
189C2×Dic158—82no—
190C2×Dic158C2×D414yes—
191C2×Dic158C2412yes—
192C2×D316—21no—
193C2×D316—22no—
194C2×D316—22no—
195C2×D316C2412yes—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C22×Dic79C2×D411yescharacteristic
203C2×C4×D79—24no—
204C2×C4×D79—44no—
205#11929614—28no—
206#11929611—28no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8—22no—
209C2×C79⋊C8C2412yes—
210C2×C79⋊C8C2412yes—
211C4⋊Dic79—24no—
212C4⋊Dic79—24no—
213C4⋊Dic79—24no—
214C4⋊Dic79—21no—
215C4⋊Dic79—21no—
216C4⋊Dic79C2×D414yes—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4C2×D414yes—
225Dic79⋊C4C2×D414yes—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231C4×Dic79—24no—
232C4×Dic79—24no—
233C4×Dic79—24no—
234C4×Dic79C2×D412yes—
235C4×Dic79C2×D412yes—
236C4×Dic79C2412yes—
237C4×Dic79C2412yes—
238C2×Q8×C79—21no—
239C2×Q8×C79—21no—
240C2×Q8×C79—22no—
241C2×Q8×C79—22no—
242C2×Q8×C79—22no—
243C2×Q8×C79#4114yes—
244C2×Q8×C79C2412yes—
245C2×Q8×C79C2412yes—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2411yescharacteristic
253Q16×C79—28no—
254C2×C8×C79—22no—
255C2×C8×C79—22no—
256C2×C8×C79C2412yes—
257C2×C8×C79C2412yes—
258C4⋊C4×C79—24no—
259C4⋊C4×C79—24no—
260C4⋊C4×C79—21no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79C2412yes—
263C4⋊C4×C79C2412yes—
264C42×C79—24no—
265C42×C79—24no—
266C42×C79C2×D412yes—
267C42×C79C2412yes—
268C23×C79C22×D411yescharacteristic
269C22×D79—22no—
270C22×D79—42no—
271C22×D79—42no—
272C22×D79—42no—
273Q8×C79—24no—
274Q8×C79—22no—
275Q8×C79—22no—
276Q8×C79—22no—
277Q8×C79—42no—
278Q8×C79C2×#4114yes—
279C2×C4×C79—24no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—42no—
287C2×C4×C79—42no—
288C2×C4×C79—42no—
289C2×C4×C79C22×D412yes—
290C2×C4×C79C22×D412yes—
291C2×C4×C79C22×D411yescharacteristic
292C2×C4×C79C2×#4112yes—
293C2×C4×C792−1+412yes—
294C2×C4×C79C2511yescharacteristic
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—42no—
302C2×Dic79—42no—
303C2×Dic79—42no—
304C2×Dic79#13714yes—
305C2×Dic79C22×D412yes—
306C2×Dic79C22×D412yes—
307C2×Dic79C22×D412yes—
308C2×Dic79C22×D412yes—
309D316—22no—
310D316—22no—
311D316—42no—
312C4×D79—48no—
313Dic158—28no—
314Dic158—22no—
315Dic158—22no—
316Dic158—42no—
317Dic158—84no—
318Dic158—84no—
319Dic158—84no—
320C8×C79—22no—
321C8×C79—22no—
322C79⋊C8—22no—
323C79⋊C8—22no—
324C22×C79#54812yes—
325C22×C79C2×#13712yes—
326C22×C79#57712yes—
327C22×C79C23×D411yescharacteristic
328C2×D79—42no—
329C2×D79—42no—
330C2×D79—42no—
331C2×D79—84no—
332C4×C79—24no—
333C4×C79—22no—
334C4×C79—22no—
335C4×C79—42no—
336C4×C79—42no—
337C4×C79—42no—
338C4×C79#54812yes—
339C4×C79C22×#4111yescharacteristic
340C4×C79C2×2−1+411yescharacteristic
341Dic79—22no—
342Dic79—22no—
343Dic79—22no—
344Dic79—42no—
345Dic79—42no—
346Dic79—42no—
347Dic79C2×#13714yes—
348C2×#3369—791nomaximal, Sylow
349C2×C79#336914yescomplemented
350C2×C79C2×#54811yescharacteristic
351C2×C79C22×#13711yescharacteristic
352C2×C79C2×#57711yescharacteristic
353D79—82no—
354C2×Q82—791no—
355C2×#556—791no—
356#3369—7916no—
357C2×#489—791no—
358C2×#489—791no—
359C2×#487—791no—
360C2×#475—791no—
361C2×#475—791no—
362C2×#476—791no—
363C2×#464—791no—
364C2×#464—791no—
365C2×#462—791no—
366C2×#446—791no—
367C2×#441—791no—
368C2×#441D7911yescharacteristic, complemented
369C2×C4×SD16—791no—
370C79C2×#336911yescharacteristic, complemented, Sylow
371C22×Q16—791no—
372C22×Q16C2×D7911yescharacteristic
373C22×SD16—791no—
374Q82—798no—
375Q82—1584no—
376#556—798no—
377#556—1584no—
378C2×C4⋊Q8—791no—
379C2×C4⋊Q8—791no—
380C2×C4⋊Q8—791no—
381C2×C4⋊Q8—791no—
382C2×C4⋊Q8—1581no—
383C2×C4⋊Q8—1581no—
384C2×C4⋊Q8—1581no—
385C2×#126—1581no—
386C2×#126—1581no—
387C2×#124—791no—
388C2×#124—791no—
389C2×C22⋊Q8—1581no—
390C2×C4×Q8—791no—
391C2×C4×Q8—791no—
392C2×C4×Q8—791no—
393C2×C4×Q8—791no—
394C2×C4×Q8—1581no—
395C2×C4×Q8C2×D7911yescharacteristic
396C2×C4×Q8C2×D7911yescharacteristic
397C2×C4×D4—791no—
398C2×#117—1581no—
399#489—798no—
400#489—798no—
401#487—798no—
402#476—798no—
403#475—798no—
404#475—798no—
405#464—798no—
406#464—798no—
407#462—798no—
408#446—798no—
409#441—798no—
410#441C2×D7918yescomplemented
411C4×SD16—798no—
412C2×#106—791no—
413C2×#106—791no—
414C2×#106C2×D7911yescharacteristic
415C2×C4⋊C8—791no—
416C2×C4⋊C8—791no—
417C2×C4⋊C8—791no—
418C2×#103—791no—
419C2×#103—791no—
420C2×#103—791no—
421C2×#103—791no—
422C2×#103—791no—
423C2×#103C2×D7911yescharacteristic
424C2×#103C2×D7911yescharacteristic
425C2×#102—791no—
426C2×#102—791no—
427C2×#102—791no—
428C2×#97—791no—
429C2×#97C2×D7911yescharacteristic
430C2×C4×C8—791no—
431C22×Q8—791no—
432C22×Q8—791no—
433C22×Q8—1581no—
434C22×Q8—1581no—
435C22×Q8—1581no—
436C22×Q8C22×D7911yescharacteristic
437C22×Q8C22×D7911yescharacteristic
438C22×D4—791no—
439C23×C4—1581no—
440C2×Q16—24no—
441C2×Q16—794no—
442C2×Q16—1584no—
443C2×Q16C22×D7914yes—
444C2×SD16—794no—
445C2×SD16—1584no—
446C22×C8—791no—
447C22×C8—791no—
448C22×C8C22×D7911yescharacteristic
449C22×C8C22×D7911yescharacteristic
450C4⋊Q8—794no—
451C4⋊Q8—794no—
452C4⋊Q8—794no—
453C4⋊Q8—794no—
454C4⋊Q8—1588no—
455C4⋊Q8—1582no—
456C4⋊Q8—1582no—
457C4⋊Q8—1582no—
458C4⋊Q8—1588no—
459C4⋊Q8—1588no—
460C4⋊Q8—1582no—
461#126—1588no—
462#126—1588no—
463#124—794no—
464#124—794no—
465#124—1582no—
466#124—1582no—
467C22⋊Q8—1588no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8—794no—
471C4×Q8—794no—
472C4×Q8—794no—
473C4×Q8—794no—
474C4×Q8—794no—
475C4×Q8—1588no—
476C4×Q8—1582no—
477C4×Q8—1582no—
478C4×Q8—1582no—
479C4×Q8C22×D7914yes—
480C4×Q8C22×D7914yes—
481C4×D4—794no—
482C4×D4—1582no—
483#117—1588no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—791no—
487C2×C4⋊C4—791no—
488C2×C4⋊C4—791no—
489C2×C4⋊C4—791no—
490C2×C4⋊C4—791no—
491C2×C4⋊C4—1581no—
492C2×C4⋊C4—1581no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4—1581no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C22⋊C4—1581no—
502C2×C22⋊C4—1581no—
503C2×C22⋊C4—1581no—
504C2×C22⋊C4—1581no—
505C2×C22⋊C4—1581no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—791no—
509C2×C42—791no—
510C2×C42—1581no—
511C2×C42—1581no—
512C2×C42—1581no—
513C2×C42C22×D7911yescharacteristic
514#106—794no—
515#106—794no—
516#106C22×D7914yes—
517C4⋊C8—794no—
518C4⋊C8—794no—
519C4⋊C8—794no—
520#103—794no—
521#103—794no—
522#103—794no—
523#103—794no—
524#103—794no—
525#103C22×D7914yes—
526#103C22×D7914yes—
527#102—794no—
528#102—794no—
529#102—794no—
530#97—794no—
531#97C22×D7914yes—
532C4×C8—794no—
533C24—1581no—
534C2×Q8—22no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—794no—
540C2×Q8—792no—
541C2×Q8—6322no—
542C2×Q8—6322no—
543C2×Q8—6322no—
544C2×Q8—1584no—
545C2×Q8—1584no—
546C2×Q8—1584no—
547C2×Q8—1582no—
548C2×Q8—1582no—
549C2×Q8—1581no—
550C2×Q8—1584no—
551C2×Q8#1192962414yes—
552C2×Q8C23×D7912yes—
553C2×Q8C23×D7912yes—
554C2×D4—792no—
555C2×D4—1582no—
556C2×D4—1582no—
557C2×D4—1581no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—3164no—
563C22×C4—791no—
564C22×C4—791no—
565C22×C4—791no—
566C22×C4—791no—
567C22×C4—1584no—
568C22×C4—1581no—
569C22×C4—1581no—
570C22×C4—1581no—
571C22×C4D4×D7911yescharacteristic
572C22×C4D4×D7911yescharacteristic
573C22×C4C23×D7911yescharacteristic
574Q16—28no—
575Q16—1588no—
576SD16—1588no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—792no—
580C2×C8—792no—
581C2×C8—1582no—
582C2×C8—1582no—
583C2×C8C23×D7912yes—
584C2×C8C23×D7912yes—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—794no—
590C4⋊C4—794no—
591C4⋊C4—794no—
592C4⋊C4—792no—
593C4⋊C4—792no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1584no—
597C4⋊C4—1584no—
598C4⋊C4—1584no—
599C4⋊C4—1584no—
600C4⋊C4—1584no—
601C4⋊C4—1581no—
602C4⋊C4—1581no—
603C4⋊C4—1584no—
604C4⋊C4C23×D7912yes—
605C4⋊C4C23×D7912yes—
606C22⋊C4—1584no—
607C22⋊C4—1584no—
608C22⋊C4—1584no—
609C22⋊C4—1584no—
610C22⋊C4—1584no—
611C42—24no—
612C42—24no—
613C42—792no—
614C42—792no—
615C42—792no—
616C42—792no—
617C42—1584no—
618C42—1584no—
619C42—1584no—
620C42D4×D7912yes—
621C42C23×D7912yes—
622C23—3162no—
623C23—3162no—
624C23—3162no—
625C23—1582no—
626C23C2×D4×D7911yescharacteristic
627Q8—22no—
628Q8—24no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—3162no—
633Q8—6324no—
634Q8—6324no—
635Q8—6324no—
636Q8—1588no—
637Q8—1582no—
638Q8—1582no—
639Q8C2×#1192962414yes—
640D4—3162no—
641D4—1582no—
642D4—1582no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—3168no—
654C2×C4—3162no—
655C2×C4—3162no—
656C2×C4—3162no—
657C2×C4—794no—
658C2×C4—792no—
659C2×C4—792no—
660C2×C4—792no—
661C2×C4—792no—
662C2×C4—1582no—
663C2×C4—1582no—
664C2×C4—1582no—
665C2×C4—1582no—
666C2×C4—1582no—
667C2×C4—1582no—
668C2×C4C2×D4×D7912yes—
669C2×C4C2×D4×D7912yes—
670C2×C4C2×D4×D7911yescharacteristic
671C2×C4C2×#1192962412yes—
672C2×C4#1457920812yes—
673C2×C4C24×D7911yescharacteristic
674C8—22no—
675C8—22no—
676C8—1582no—
677C8—1582no—
678C22—3162no—
679C22—3162no—
680C22—3162no—
681C22—6324no—
682C22#1909922212yes—
683C22#137×D7912yes—
684C22#1909937212yes—
685C22C22×D4×D7911yescharacteristic
686C4—22no—
687C4—24no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—3162no—
693C4—3162no—
694C4—3162no—
695C4—794no—
696C4—1582no—
697C4—1582no—
698C4—1582no—
699C4#1909922212yes—
700C4C22×#1192962411yescharacteristic
701C4C2×#1457920811yescharacteristic
702C2—6322no—
703C2#2377614114yesdirect product factor
704C2C2×#1909922211yescharacteristic
705C2C2×#137×D7911yescharacteristic
706C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#441×C79C2
socleC23×C79C22×D4
prime radicalC22×D316C23
hypercenterC2×#441D79
hypocenterC79C2×#3369
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic158C2semidirect
3. #23776141C2direct (N × H)
6. C2×#19098912C2semidirect
7. C2×#19098848C2semidirect
8. C2×#19098847C2semidirect
12. C2×#19098771C2semidirect
13. C2×#19098691C2semidirect
14. C2×#19098667C2semidirect
16. C2×#441×C79C2semidirect
20. Q8×Dic158C22semidirect
44. #19098912C22semidirect
46. #19098848C22semidirect
47. #19098847C22semidirect
50. #19098771C22semidirect
51. #19098691C22semidirect
52. #19098667C22semidirect
72. #441×C79C22semidirect
349. C2×C79#3369semidirect
368. C2×#441D79semidirect
370. C79C2×#3369semidirect
410. #441C2×D79semidirect
703. C2#23776141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1582
C2×#190992852
#237761412
C2×#190989242
C2×#190989232
C2×#190989122
C2×#190988482
C2×#190988472
C2×#190988522
C2×#190987872
C2×#190987852
C2×#190987712
C2×#190986912
C2×#190986672
C2×#190986482
C2×#441×C792
C2×#336979