Finite Group Databasebeta

← C2×#22619854 #33953762

Subgroups — C2×#22619854 #33953762

Order 18688.

2650 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989098C211yesmaximal, characteristic
2#22619854C2116yesmaximal, direct product factor
3C2×#17988922C212yesmaximal, complemented
4C2×#17988905C212yesmaximal, complemented
5C2×#17988917C212yesmaximal, complemented
6C2×#17988900C212yesmaximal, complemented
7C2×#17988627C212yesmaximal, complemented
8C2×#17988586C212yesmaximal, complemented
9C2×#17988551C211yesmaximal, characteristic, complemented
10C23×C4⋊C4×C73C211yesmaximal, characteristic, complemented
11C22×#11924028C2211yescharacteristic
12C22×#11924012C2212yes—
13#17989098—24no—
14#17989098C2218yes—
15C2×#14556574—21no—
16C2×#14556570C2211yescharacteristic
17C2×#14556570C2211yescharacteristic
18C2×#14556565C2211yescharacteristic
19C2×#14556565C2211yescharacteristic
20C2×#14556560—21no—
21C2×C4×C22⋊D73—21no—
22C2×C4×C22⋊D73—21no—
23C2×#14556550C2211yescharacteristic
24#17988922C22116yescomplemented
25#17988917C22116yescomplemented
26#17988905C22116yescomplemented
27#17988900C22116yescomplemented
28#17988627C22116yescomplemented
29C2×#14556524C2214yescomplemented
30C2×#14556522C2214yescomplemented
31#17988586C22116yescomplemented
32C2×#14556514C2214yescomplemented
33C2×#14556511C2214yescomplemented
34#17988551C2218yescomplemented
35C2×C22⋊#10596831C2212yes—
36C2×C22⋊#10596831C2212yes—
37C24×C4×C73—21no—
38C24×C4×C73C2211yescharacteristic
39C22×C4⋊C4×C73—24no—
40C22×C4⋊C4×C73—21no—
41C22×C4⋊C4×C73—21no—
42C22×C4⋊C4×C73—21no—
43C22×C4⋊C4×C73C2212yes—
44C22×C4⋊C4×C73C2212yes—
45C22×C4⋊C4×C73C2212yes—
46C22×C4⋊C4×C73C2218yescomplemented
47C2×#11924028—22no—
48C2×#11924028—28no—
49C2×#11924028C2314yes—
50C22×Dic146C2311yescharacteristic
51C22×D292C2311yescharacteristic
52C22×C22⋊D73—21no—
53C22×C22⋊D73—21no—
54C22×C22⋊D73—21no—
55C22×C4×D73—21no—
56C2×#11924012—28no—
57C2×#11924012C2318yes—
58C22×#10596831C2314yes—
59#14556574—28no—
60#14556570—22no—
61#14556570—22no—
62#14556570C2314yes—
63#14556570C2314yes—
64#14556565—22no—
65#14556565—22no—
66#14556565C2314yes—
67#14556565C2314yes—
68#14556560—28no—
69C4×C22⋊D73—28no—
70C4×C22⋊D73—28no—
71#14556550—22no—
72#14556550C2314yes—
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×#11924007—21no—
76C2×#11924007—21no—
77C2×C22⋊Dic73—21no—
78C2×C22⋊Dic73—21no—
79C2×C22⋊Dic73—21no—
80C2×#11924005—21no—
81C2×#11924005—21no—
82C2×C4×Dic73—21no—
83#14556524C23116yescomplemented
84#14556522C23116yescomplemented
85#14556514C23116yescomplemented
86#14556511C23116yescomplemented
87C22⋊#10596831C2318yes—
88C22⋊#10596831C2318yes—
89C25×C73D411yescharacteristic
90C23×C4×C73—28no—
91C23×C4×C73—22no—
92C23×C4×C73—22no—
93C23×C4×C73—22no—
94C23×C4×C73—28no—
95C23×C4×C73—48no—
96C23×C4×C73D411yescharacteristic
97C23×C4×C73D411yescharacteristic
98C23×C4×C73D411yescharacteristic
99C23×C4×C73D414yes—
100C23×C4×C73C2311yescharacteristic
101C23×C4×C73C2311yescharacteristic
102C23×C4×C73C2314yes—
103C23×C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73—22no—
105C2×C4⋊C4×C73—22no—
106C2×C4⋊C4×C73—24no—
107C2×C4⋊C4×C73—24no—
108C2×C4⋊C4×C73—22no—
109C2×C4⋊C4×C73—24no—
110C2×C4⋊C4×C73—28no—
111C2×C4⋊C4×C73—28no—
112C2×C4⋊C4×C73—28no—
113C2×C4⋊C4×C73C2314yes—
114C2×C4⋊C4×C73C2318yes—
115C2×C4⋊C4×C73C2318yes—
116C2×C4⋊C4×C73C2318yes—
117C23×D73—21no—
118#11924028—216no—
119#11924028—48no—
120C2×Dic146—24no—
121C2×Dic146—21no—
122C2×Dic146C2412yes—
123C2×D292—24no—
124C2×D292—21no—
125C2×D292C2412yes—
126C2×C22⋊D73—24no—
127C2×C22⋊D73—24no—
128C2×C22⋊D73—24no—
129C2×C22⋊D73—44no—
130C2×C22⋊D73—44no—
131C2×C22⋊D73—44no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C2×C4×D73—24no—
136C2×C4×D73—44no—
137#11924012—216no—
138C2×#10596831—28no—
139C2×#10596831C2418yes—
140C4⋊Dic73—21no—
141C4⋊Dic73—21no—
142C4⋊Dic73C2412yes—
143C4⋊Dic73C2412yes—
144#11924007—24no—
145#11924007—24no—
146C22⋊Dic73—24no—
147C22⋊Dic73—24no—
148C22⋊Dic73—24no—
149#11924005—24no—
150#11924005—24no—
151C4×Dic73—24no—
152C24×C73—24no—
153C24×C73—24no—
154C24×C73—24no—
155C24×C73C2×D414yes—
156C24×C73C2×D411yescharacteristic
157C24×C73C2×D411yescharacteristic
158C24×C73C2×D411yescharacteristic
159C22×C4×C73—24no—
160C22×C4×C73—24no—
161C22×C4×C73—24no—
162C22×C4×C73—216no—
163C22×C4×C73—24no—
164C22×C4×C73—24no—
165C22×C4×C73—216no—
166C22×C4×C73—28no—
167C22×C4×C73—28no—
168C22×C4×C73—28no—
169C22×C4×C73—24no—
170C22×C4×C73—48no—
171C22×C4×C73—48no—
172C22×C4×C73—432no—
173C22×C4×C73—48no—
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D414yes—
177C22×C4×C73C2×D414yes—
178C22×C4×C73C2×D412yes—
179C22×C4×C73C2×D412yes—
180C22×C4×C73C2×D414yes—
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D412yes—
183C22×C4×C73#4118yes—
184C22×C4×C73C2412yes—
185C22×C4×C73C2412yes—
186C22×C4×C73C2411yescharacteristic
187C22×C4×C73C2412yes—
188C4⋊C4×C73—28no—
189C4⋊C4×C73—28no—
190C4⋊C4×C73—28no—
191C4⋊C4×C73—24no—
192C4⋊C4×C73C2418yes—
193C23×C73—232no—
194C23×C73—28no—
195C23×C73—22no—
196C23×C73—22no—
197C23×C73—28no—
198C23×C73—22no—
199C23×C73—22no—
200C23×C73—28no—
201C23×C73—22no—
202C23×C73—22no—
203C23×C73#12314yes—
204C23×C73AGL(1,ℤ/8)14yes—
205C23×C73#13714yes—
206C23×C73C22×D412yes—
207C23×C73C22×D412yes—
208C23×C73C22×D412yes—
209C23×C73C22×D411yescharacteristic
210C22×D73—22no—
211C22×D73—42no—
212C22×D73—42no—
213C22×D73—42no—
214C2×C4×C73—28no—
215C2×C4×C73—22no—
216C2×C4×C73—22no—
217C2×C4×C73—24no—
218C2×C4×C73—24no—
219C2×C4×C73—28no—
220C2×C4×C73—28no—
221C2×C4×C73—24no—
222C2×C4×C73—24no—
223C2×C4×C73—28no—
224C2×C4×C73—416no—
225C2×C4×C73—416no—
226C2×C4×C73—416no—
227C2×C4×C73—48no—
228C2×C4×C73#12314yes—
229C2×C4×C73#12318yes—
230C2×C4×C73C22×D412yes—
231C2×C4×C73C22×D412yes—
232C2×C4×C73C22×D412yes—
233C2×C4×C73C22×D411yescharacteristic
234C2×C4×C73C2×#4114yes—
235C2×C4×C73C2×#4118yes—
236C2×C4×C73C2511yescharacteristic
237C22⋊D73—48no—
238C22⋊D73—48no—
239C22⋊D73—48no—
240C2×Dic73—22no—
241C2×Dic73—22no—
242C2×Dic73—22no—
243C2×Dic73—42no—
244C2×Dic73—42no—
245C2×Dic73—42no—
246D292—24no—
247D292—42no—
248C4×D73—48no—
249Dic146—24no—
250Dic146—42no—
251#10596831—28no—
252C22×C73—232no—
253C22×C73—28no—
254C22×C73—28no—
255C22×C73—28no—
256C22×C73—22no—
257C22×C73—22no—
258C22×C73—22no—
259C22×C73—22no—
260C22×C73—22no—
261C22×C73—22no—
262C22×C73C2×#12314yes—
263C22×C73C2×#12312yes—
264C22×C73C2×AGL(1,ℤ/8)14yes—
265C22×C73C2×AGL(1,ℤ/8)12yes—
266C22×C73C2×#13714yes—
267C22×C73C2×#13712yes—
268C22×C73C23×D411yescharacteristic
269C2×D73—42no—
270C2×D73—42no—
271C2×D73—42no—
272C2×D73—84no—
273C4×C73—22no—
274C4×C73—22no—
275C4×C73—48no—
276C4×C73C2×#12312yes—
277C4×C73C2×#12314yes—
278C4×C73C22×#4112yes—
279Dic73—42no—
280Dic73—42no—
281Dic73—42no—
282C2×#3092—731nomaximal, Sylow
283C2×C73—24no—
284C2×C73—24no—
285C2×C73—24no—
286C2×C73#309214yescomplemented
287C2×C73C22×#12311yescharacteristic
288C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
289C2×C73C22×#13711yescharacteristic
290D73—82no—
291C2×#525—731no—
292C23×C4⋊C4D7311yescharacteristic, complemented
293#3092—7316no—
294C2×#484—732no—
295C2×#481—732no—
296C2×#483—732no—
297C2×#480—732no—
298C2×#428—732no—
299C2×#417—732no—
300C2×#407—731no—
301C73C2×#309211yescharacteristic, complemented, Sylow
302C22×#41—731no—
303C24×C4—21no—
304C24×C4C2×D7311yescharacteristic
305C22×M16—732no—
306#525—738no—
307#525—1464no—
308C2×#123—1461no—
309C2×C22⋊Q8—731no—
310C2×C22⋊Q8—731no—
311C2×#121—731no—
312C2×#121—731no—
313C2×#120—1461no—
314C2×C4×D4—1461no—
315C2×C4×D4—1461no—
316C2×#117—731no—
317C22×C4⋊C4—24no—
318C22×C4⋊C4—21no—
319C22×C4⋊C4—21no—
320C22×C4⋊C4—21no—
321C22×C4⋊C4C2×D7312yes—
322C22×C4⋊C4C2×D7312yes—
323C22×C4⋊C4C2×D7312yes—
324C22×C4⋊C4C2×D7318yescomplemented
325#484—7316no—
326#483—7316no—
327#481—7316no—
328#480—7316no—
329#428—7316no—
330C2×#107—734no—
331C2×#106—734no—
332#417—7316no—
333C2×#103—734no—
334C2×#102—734no—
335#407—738no—
336C2×C22⋊C8—732no—
337C2×C22⋊C8—732no—
338C25C22⋊D7311yescharacteristic
339C2×#41—734no—
340C2×#41—1468no—
341C2×#41—1462no—
342C22×Q8—731no—
343C22×D4—731no—
344C22×D4—1461no—
345C22×D4—1461no—
346C22×D4—1461no—
347C23×C4—28no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—28no—
352C23×C4—48no—
353C23×C4—1461no—
354C23×C4C22⋊D7311yescharacteristic
355C23×C4C22⋊D7311yescharacteristic
356C23×C4C22⋊D7311yescharacteristic
357C23×C4C22⋊D7314yes—
358C23×C4C22×D7311yescharacteristic
359C23×C4C22×D7311yescharacteristic
360C23×C4C22×D7314yes—
361C23×C4C22×D7311yescharacteristic
362C2×M16—738no—
363C2×M16—1468no—
364C22×C8—734no—
365#123—1468no—
366C22⋊Q8—734no—
367C22⋊Q8—734no—
368C22⋊Q8—1462no—
369C22⋊Q8—1462no—
370#121—734no—
371#121—734no—
372#121—1462no—
373#121—1462no—
374#120—1468no—
375C4×D4—1468no—
376C4×D4—1468no—
377#117—734no—
378#117—1462no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—731no—
390C2×C4⋊C4—1461no—
391C2×C4⋊C4—1461no—
392C2×C4⋊C4C22×D7314yes—
393C2×C4⋊C4C22×D7318yes—
394C2×C4⋊C4C22×D7318yes—
395C2×C4⋊C4C22×D7318yes—
396C2×C22⋊C4—1461no—
397C2×C22⋊C4—1461no—
398C2×C22⋊C4—1461no—
399C2×C22⋊C4—1461no—
400C2×C22⋊C4—1461no—
401C2×C42—1461no—
402#107—7316no—
403#106—7316no—
404#103—7316no—
405#102—7316no—
406C22⋊C8—738no—
407C22⋊C8—738no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—1461no—
412C24C2×C22⋊D7314yes—
413C24C2×C22⋊D7311yescharacteristic
414C24C2×C22⋊D7311yescharacteristic
415C24C2×C22⋊D7311yescharacteristic
416#41—2928no—
417#41—14616no—
418C2×Q8—732no—
419C2×Q8—1464no—
420C2×Q8—1461no—
421C2×D4—2924no—
422C2×D4—2924no—
423C2×D4—2924no—
424C2×D4—732no—
425C2×D4—1464no—
426C2×D4—1464no—
427C2×D4—1464no—
428C2×D4—1461no—
429C2×D4—1464no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—216no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—216no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—24no—
441C22×C4—48no—
442C22×C4—48no—
443C22×C4—432no—
444C22×C4—48no—
445C22×C4—2924no—
446C22×C4—1461no—
447C22×C4—1461no—
448C22×C4—1461no—
449C22×C4—1464no—
450C22×C4C2×C22⋊D7314yes—
451C22×C4C2×C22⋊D7314yes—
452C22×C4C2×C22⋊D7312yes—
453C22×C4C2×C22⋊D7312yes—
454C22×C4C2×C22⋊D7314yes—
455C22×C4C2×C22⋊D7311yescharacteristic
456C22×C4C2×C22⋊D7311yescharacteristic
457C22×C4C2×C22⋊D7312yes—
458C22×C4C2×C22⋊D7311yescharacteristic
459C22×C4#1192402818yes—
460C22×C4C23×D7312yes—
461C22×C4C23×D7312yes—
462C22×C4C23×D7312yes—
463C22×C4C23×D7311yescharacteristic
464M16—14616no—
465C2×C8—738no—
466C2×C8—1468no—
467C4⋊C4—28no—
468C4⋊C4—28no—
469C4⋊C4—28no—
470C4⋊C4—24no—
471C4⋊C4—732no—
472C4⋊C4—732no—
473C4⋊C4—1464no—
474C4⋊C4—1464no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4C23×D7318yes—
478C22⋊C4—1464no—
479C22⋊C4—1464no—
480C22⋊C4—1464no—
481C22⋊C4—1464no—
482C22⋊C4—1464no—
483C42—1464no—
484C23—232no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—28no—
489C23—22no—
490C23—22no—
491C23—28no—
492C23—22no—
493C23—22no—
494C23—2922no—
495C23—2922no—
496C23—2922no—
497C23—1462no—
498C23#1455657414yes—
499C23#1455661714yes—
500C23#1455662214yes—
501C23C22×C22⋊D7312yes—
502C23C22×C22⋊D7312yes—
503C23C22×C22⋊D7312yes—
504C23C22×C22⋊D7311yescharacteristic
505Q8—2922no—
506Q8—1464no—
507D4—2928no—
508D4—2928no—
509D4—2928no—
510D4—2922no—
511D4—1464no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—28no—
518C2×C4—28no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—28no—
522C2×C4—416no—
523C2×C4—416no—
524C2×C4—416no—
525C2×C4—48no—
526C2×C4—2922no—
527C2×C4—2922no—
528C2×C4—2922no—
529C2×C4—2928no—
530C2×C4—1462no—
531C2×C4—1462no—
532C2×C4—1462no—
533C2×C4#1455657414yes—
534C2×C4#1455657418yes—
535C2×C4C22×C22⋊D7312yes—
536C2×C4C22×C22⋊D7312yes—
537C2×C4C22×C22⋊D7312yes—
538C2×C4C22×C22⋊D7311yescharacteristic
539C2×C4C2×#1192402814yes—
540C2×C4C2×#1192402818yes—
541C2×C4C24×D7311yescharacteristic
542C8—1468no—
543C22—232no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—28no—
551C22—28no—
552C22—28no—
553C22—2922no—
554C22—2922no—
555C22—2922no—
556C22—5844no—
557C22C2×#1455657414yes—
558C22C2×#1455657412yes—
559C22C2×#1455661714yes—
560C22C2×#1455661712yes—
561C22C2×#1455662214yes—
562C22C2×#1455662212yes—
563C22C23×C22⋊D7311yescharacteristic
564C4—22no—
565C4—22no—
566C4—48no—
567C4—2922no—
568C4—2922no—
569C4—2922no—
570C4C2×#1455657414yes—
571C4C2×#1455657412yes—
572C4C22×#1192402812yes—
573C2—24no—
574C2—24no—
575C2—24no—
576C2—5842no—
577C2#2261985414yesdirect product factor
578C2C22×#1455657411yescharacteristic
579C2C22×#1455661711yescharacteristic
580C2C22×#1455662211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC23×C4⋊C4×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989098C2
hypercenterC23×C4⋊C4D73
hypocenterC73C2×#3092
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #22619854C2direct (N × H)
3. C2×#17988922C2semidirect
4. C2×#17988905C2semidirect
5. C2×#17988917C2semidirect
6. C2×#17988900C2semidirect
7. C2×#17988627C2semidirect
8. C2×#17988586C2semidirect
9. C2×#17988551C2semidirect
10. C23×C4⋊C4×C73C2semidirect
24. #17988922C22semidirect
25. #17988917C22semidirect
26. #17988905C22semidirect
27. #17988900C22semidirect
28. #17988627C22semidirect
29. C2×#14556524C22semidirect
30. C2×#14556522C22semidirect
31. #17988586C22semidirect
32. C2×#14556514C22semidirect
33. C2×#14556511C22semidirect
34. #17988551C22semidirect
46. C22×C4⋊C4×C73C22semidirect
83. #14556524C23semidirect
84. #14556522C23semidirect
85. #14556514C23semidirect
86. #14556511C23semidirect
286. C2×C73#3092semidirect
292. C23×C4⋊C4D73semidirect
301. C73C2×#3092semidirect
324. C22×C4⋊C4C2×D73semidirect
577. C2#22619854direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890982
#226198542
C2×#179889222
C2×#179889052
C2×#179889172
C2×#179889002
C2×#179886272
C2×#179885862
C2×#179885512
C23×C4⋊C4×C732
C2×#309273