Finite Group Databasebeta

← C4×#17988968 #33094424

Subgroups — C4×#17988968 #33094424

Order 18688.

1150 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988968C211yesmaximal, characteristic
2C2×C4×#11924018C211yesmaximal, characteristic, complemented
3C2×C4×#11924017C211yesmaximal, characteristic, complemented
4C2×C4×#11924013C211yesmaximal, characteristic
5C4×#14556580C211yesmaximal, characteristic, complemented
6C4×#14556578C211yesmaximal, characteristic, complemented
7#22610794C211yesmaximal, characteristic
8#22610789C211yesmaximal, characteristic, complemented
9#22610787C211yesmaximal, characteristic, complemented
10#22610783C211yesmaximal, characteristic, complemented
11#22610741C211yesmaximal, characteristic, complemented
12#22610739C211yesmaximal, characteristic, complemented
13#22610092C211yesmaximal, characteristic, complemented
14C4×C8×Dic73C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
16C22×#11924018C2211yescharacteristic
17C22×#11924017C2211yescharacteristic
18C22×#11924013C2211yescharacteristic
19C2×#14556580C2211yescharacteristic
20C2×#14556578C2211yescharacteristic
21C2×C4×Dic146C2211yescharacteristic
22C2×C4×D292C2211yescharacteristic
23#17988968C418yesdirect product factor
24C4×#11924018—24no—
25C4×#11924017—24no—
26C4×#11924013—24no—
27C2×#14556524C2211yescharacteristic
28C2×#14556524C2211yescharacteristic
29C2×#14556523C2211yescharacteristic
30C2×#14556516C2211yescharacteristic
31C2×#14556515C2211yescharacteristic
32C2×#14556514C2211yescharacteristic
33C2×#14556513C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×#14556511C2211yescharacteristic
36C2×C4×#10596831C2211yescharacteristic
37C2×C8×Dic73C2211yescharacteristic
38C2×C8×Dic73C2211yescharacteristic
39C2×C8×Dic73C2211yescharacteristic
40C2×C8×Dic73C2211yescharacteristic
41#17988494C2211yescharacteristic
42#17988492C2211yescharacteristic
43#17988490C2211yescharacteristic
44#17988488C2211yescharacteristic
45#17988481—22no—
46#17988477—22no—
47#17988452C2211yescharacteristic
48#17988452C2211yescharacteristic
49C4×#11924005—22no—
50C4×C22⋊Dic73—22no—
51C42×Dic73C2211yescharacteristic
52C22×SD16×C73C2211yescharacteristic
53C2×C4×Q8×C73C2211yescharacteristic
54C2×C4×D4×C73C2211yescharacteristic
55C4×SD16×C73—24no—
56C2×#106×C73C2211yescharacteristic
57C2×#103×C73C2211yescharacteristic
58C2×#102×C73C2211yescharacteristic
59C2×C4×C8×C73C2211yescharacteristic
60C22×Dic146C2311yescharacteristic
61C22×D292C2311yescharacteristic
62C22×C4×D73—21no—
63C2×#11924018—22no—
64C2×#11924018—22no—
65C2×#11924018C2×C414yescomplemented
66C2×#11924017—22no—
67C2×#11924017—22no—
68C2×#11924017C2×C414yescomplemented
69C2×#11924013—22no—
70C2×#11924013—22no—
71C2×#11924013C2×C414yes—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74#14556580—22no—
75#14556580C2×C414yescomplemented
76#14556578—22no—
77#14556578C2×C414yescomplemented
78C4×Dic146—22no—
79C4×Dic146—22no—
80C4×D292—22no—
81C4×D292—22no—
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×#11924007—21no—
85C2×C22⋊Dic73—22no—
86C2×C22⋊Dic73—22no—
87C2×#11924005—22no—
88C2×#11924005—22no—
89C2×#11924005—21no—
90C2×C4×Dic73—21no—
91C2×C4×Dic73D412yes—
92C2×C4×Dic73D412yes—
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95#14556524—22no—
96#14556524—22no—
97#14556523—22no—
98#14556516—22no—
99#14556515—22no—
100#14556514—22no—
101#14556513—22no—
102#14556512—22no—
103#14556511—22no—
104C4×#10596831D414yes—
105C8×Dic73—22no—
106C8×Dic73—22no—
107C8×Dic73—22no—
108C8×Dic73C2×C414yescomplemented
109#14556498—22no—
110#14556498—22no—
111#14556498—22no—
112#14556498—22no—
113C22×Q8×C73C2311yescharacteristic
114C22×D4×C73C2311yescharacteristic
115C23×C4×C73—21no—
116C2×SD16×C73—22no—
117C2×SD16×C73—22no—
118C2×SD16×C73C2×C414yescomplemented
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C4×Q8×C73—22no—
122C4×Q8×C73—22no—
123C4×D4×C73—22no—
124C4×D4×C73—22no—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C22⋊C4×C73—21no—
129C2×C42×C73—21no—
130C2×C42×C73C2311yescharacteristic
131#106×C73—22no—
132#103×C73—22no—
133#102×C73—22no—
134C4×C8×C73D414yes—
135C23×D73—21no—
136C2×Dic146—21no—
137C2×Dic146—21no—
138C2×Dic146—21no—
139C2×Dic146—21no—
140C2×Dic146—21no—
141C2×Dic146C22×C412yes—
142C2×D292—21no—
143C2×D292—21no—
144C2×D292—21no—
145C2×D292—21no—
146C2×D292—21no—
147C2×D292C22×C412yes—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73C2×D412yes—
152C22×Dic73C2×D412yes—
153C2×C4×D73—42no—
154C2×C4×D73—44no—
155#11924018—28no—
156#11924017—28no—
157#11924013—28no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831C22×C412yes—
161C2×#10596831C2×D412yes—
162C2×#10596831C2×D412yes—
163C2×#10596831#4112yes—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168#11924007—42no—
169C22⋊Dic73—28no—
170C22⋊Dic73—44no—
171#11924005—28no—
172#11924005—42no—
173#11924005—44no—
174C4×Dic73—24no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—24no—
178C4×Dic73—42no—
179C4×Dic73C22×C412yes—
180C4×Dic73#4112yes—
181C24×C73—21no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—21no—
186C2×Q8×C73—21no—
187C2×Q8×C73C22×C412yes—
188C2×D4×C73—21no—
189C2×D4×C73—21no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73C22×C412yes—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—42no—
198C22×C4×C73—44no—
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2411yescharacteristic
202SD16×C73—28no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73C22×C412yes—
206C2×C8×C73C2×D412yes—
207C2×C8×C73C2×D412yes—
208C2×C8×C73#4112yes—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—42no—
214C22⋊C4×C73—42no—
215C42×C73—42no—
216C42×C73C2×D412yes—
217C42×C73C2×D412yes—
218C23×C73—22no—
219C23×C73—41no—
220C23×C73—41no—
221C23×C73—42no—
222C23×C73—42no—
223C23×C73C22×D411yescharacteristic
224C22×D73—22no—
225C22×D73—41no—
226C22×D73—41no—
227C22×D73—42no—
228C22×D73—42no—
229Q8×C73—22no—
230Q8×C73—22no—
231Q8×C73—41no—
232Q8×C73—41no—
233D4×C73—22no—
234D4×C73—22no—
235D4×C73—41no—
236D4×C73—41no—
237C2×C4×C73—22no—
238C2×C4×C73—22no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—42no—
244C2×C4×C73—42no—
245C2×C4×C73—84no—
246C2×C4×C73#12712yes—
247C2×C4×C73#12712yes—
248C2×C4×C73#13514yes—
249C2×C4×C73C23×C411yescharacteristic
250C2×C4×C73C22×D411yescharacteristic
251C2×C4×C73C22×D411yescharacteristic
252C2×C4×C73C2×#4111yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×Dic73—22no—
256C2×Dic73—22no—
257C2×Dic73—22no—
258C2×Dic73—22no—
259C2×Dic73—22no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—42no—
265C2×Dic73—42no—
266C2×Dic73C4×D414yes—
267C2×Dic73#13514yes—
268D292—22no—
269D292—22no—
270D292—41no—
271D292—41no—
272C4×D73—84no—
273Dic146—22no—
274Dic146—22no—
275Dic146—41no—
276Dic146—41no—
277C8×C73—22no—
278C8×C73C4×D414yes—
279#10596831—22no—
280#10596831C4×D414yes—
281C22×C73—42no—
282C22×C73—44no—
283C22×C73—81no—
284C22×C73—81no—
285C22×C73—82no—
286C22×C73C2×C4×D411yescharacteristic
287C22×C73C2×#12711yescharacteristic
288C22×C73#53211yescharacteristic
289C22×C73C2×#13512yes—
290C22×C73C2×#13512yes—
291C2×D73—42no—
292C2×D73—44no—
293C2×D73—81no—
294C2×D73—81no—
295C2×D73—82no—
296C4×C73—22no—
297C4×C73—42no—
298C4×C73—81no—
299C4×C73—81no—
300C4×C73#49514yescomplemented
301C4×C73C2×C4×D411yescharacteristic
302C4×C73C2×C4×D411yescharacteristic
303C4×C73#53211yescharacteristic
304C4×C73#53211yescharacteristic
305Dic73—24no—
306Dic73—24no—
307Dic73—42no—
308Dic73—81no—
309Dic73—81no—
310C4×#495—731nomaximal, Sylow
311C2×C73—82no—
312C2×C73C4×#12711yescharacteristic
313C2×C73C4×#13512yes—
314C2×C73C2×#49511yescharacteristic
315C2×C73#314711yescharacteristic
316C2×C73#316812yes—
317D73—82no—
318C2×#495—731no—
319C2×C4×Q16—731no—
320C2×C4×SD16—731no—
321C2×C4×SD16D7311yescharacteristic, complemented
322C2×C4×D8—731no—
323C4×#124—731no—
324C4×#124—731no—
325#1970—731no—
326#1969—731no—
327#1968—731no—
328#1968—731no—
329#1958—731no—
330#1958—731no—
331#1846—731no—
332C42×C8—731no—
333C73C4×#49511yescharacteristic, complemented, Sylow
334C22×Q16—731no—
335C22×SD16—731no—
336C22×SD16C2×D7311yescharacteristic
337C22×D8—731no—
338C2×#124—731no—
339C2×#124—731no—
340C2×C4×Q8—731no—
341C2×C4×Q8C2×D7311yescharacteristic
342C2×C4×D4—731no—
343C2×C4×D4C2×D7311yescharacteristic
344#495—738no—
345C4×Q16—1464no—
346C4×SD16—24no—
347C4×SD16—1464no—
348C4×D8—1464no—
349C2×#107—731no—
350C2×#107—731no—
351C2×#106—731no—
352C2×#106C2×D7311yescharacteristic
353C2×#103—731no—
354C2×#103—731no—
355C2×#103—731no—
356C2×#103C2×D7311yescharacteristic
357C2×#102—731no—
358C2×#102—731no—
359C2×#102—731no—
360C2×#102C2×D7311yescharacteristic
361C2×C4×C8—731no—
362C2×C4×C8—731no—
363C2×C4×C8—731no—
364C2×C4×C8—731no—
365C2×C4×C8—731no—
366C2×C4×C8C2×D7311yescharacteristic
367#391—731no—
368#391—731no—
369#390—731no—
370#390—731no—
371#388—1462no—
372#388—1462no—
373#382—731no—
374#382—731no—
375C4×C22⋊C4—1462no—
376C4×C22⋊C4—1462no—
377C43—731no—
378C22×Q8—731no—
379C22×Q8C22×D7311yescharacteristic
380C22×D4—731no—
381C22×D4C22×D7311yescharacteristic
382C23×C4—21no—
383C23×C4—1461no—
384C2×Q16—734no—
385C2×Q16—1462no—
386C2×Q16—1462no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—734no—
390C2×SD16—1462no—
391C2×SD16—1462no—
392C2×SD16C4×D7314yescomplemented
393C2×D8—734no—
394C2×D8—1462no—
395C2×D8—1462no—
396C22×C8—731no—
397C22×C8—731no—
398C22×C8C22×D7311yescharacteristic
399C22×C8C22×D7311yescharacteristic
400#124—734no—
401#124—734no—
402#124—1462no—
403#124—1462no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—1462no—
407C4×Q8—1462no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—1462no—
411C4×D4—1462no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—731no—
414C2×C4⋊C4—731no—
415C2×C4⋊C4—1461no—
416C2×C4⋊C4C22×D7311yescharacteristic
417C2×C4⋊C4C22×D7311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—1462no—
420C2×C22⋊C4—1462no—
421C2×C22⋊C4—1461no—
422C2×C22⋊C4—1462no—
423C2×C22⋊C4—1462no—
424C2×C42—21no—
425C2×C42—731no—
426C2×C42—732no—
427C2×C42—732no—
428C2×C42—731no—
429C2×C42—1461no—
430C2×C42C22×D7311yescharacteristic
431#107—1462no—
432#107—1462no—
433#106—22no—
434#106—1462no—
435#103—22no—
436#103—1462no—
437#103—1462no—
438#103—1462no—
439#102—22no—
440#102—1462no—
441#102—1462no—
442#102—1462no—
443C4×C8—734no—
444C4×C8—734no—
445C4×C8—1462no—
446C4×C8—1462no—
447C4×C8—1462no—
448C4×C8C22⋊D7314yes—
449#95—1462no—
450#95—1462no—
451#95—1462no—
452#95—1462no—
453C24—21no—
454C24—1461no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—732no—
461C2×Q8—1461no—
462C2×Q8—1461no—
463C2×Q8—1461no—
464C2×Q8—1461no—
465C2×Q8—1461no—
466C2×Q8C2×C4×D7312yes—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—732no—
473C2×D4—1461no—
474C2×D4—1461no—
475C2×D4—1461no—
476C2×D4—1461no—
477C2×D4—1461no—
478C2×D4C2×C4×D7312yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—44no—
484C22×C4—2922no—
485C22×C4—2924no—
486C22×C4—732no—
487C22×C4—732no—
488C22×C4—1461no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4D4×D7311yescharacteristic
492C22×C4D4×D7311yescharacteristic
493C22×C4C23×D7311yescharacteristic
494Q16—1468no—
495SD16—28no—
496SD16—1468no—
497D8—1468no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—732no—
501C2×C8—732no—
502C2×C8—732no—
503C2×C8—732no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8C2×C4×D7312yes—
507C2×C8C2×C22⋊D7312yes—
508C2×C8C2×C22⋊D7312yes—
509C2×C8#1192402812yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—2922no—
516C4⋊C4—1461no—
517C4⋊C4—1461no—
518C4⋊C4—1461no—
519C4⋊C4—1461no—
520C22⋊C4—42no—
521C22⋊C4—2924no—
522C22⋊C4—2924no—
523C22⋊C4—2922no—
524C22⋊C4—1468no—
525C22⋊C4—1468no—
526C42—42no—
527C42—2922no—
528C42—732no—
529C42—732no—
530C42—1464no—
531C42—1464no—
532C42—1461no—
533C42—1461no—
534C42D4×D7312yes—
535C42C2×C22⋊D7312yes—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—42no—
540C23—42no—
541C23—2921no—
542C23—2921no—
543C23—2922no—
544C23—2922no—
545C23—1462no—
546C23C2×D4×D7311yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—41no—
550Q8—41no—
551Q8—2921no—
552Q8—2921no—
553Q8—1462no—
554Q8—1462no—
555D4—22no—
556D4—22no—
557D4—41no—
558D4—41no—
559D4—2921no—
560D4—2921no—
561D4—1462no—
562D4—1462no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—84no—
572C2×C4—2921no—
573C2×C4—2921no—
574C2×C4—2921no—
575C2×C4—2921no—
576C2×C4—2922no—
577C2×C4—2922no—
578C2×C4—5844no—
579C2×C4—734no—
580C2×C4—734no—
581C2×C4—1462no—
582C2×C4—1462no—
583C2×C4—1462no—
584C2×C4—1462no—
585C2×C4—1462no—
586C2×C4#1455658712yes—
587C2×C4#1455658712yes—
588C2×C4#1455661214yes—
589C2×C4C22×C4×D7311yescharacteristic
590C2×C4C2×D4×D7311yescharacteristic
591C2×C4C22×C22⋊D7311yescharacteristic
592C2×C4#41×D7311yescharacteristic
593C2×C4#41×D7311yescharacteristic
594C2×C4C2×#1192402811yescharacteristic
595C8—22no—
596C8—734no—
597C8—1462no—
598C8C4×C22⋊D7314yes—
599C22—42no—
600C22—44no—
601C22—82no—
602C22—81no—
603C22—81no—
604C22—2922no—
605C22—2924no—
606C22—5842no—
607C22—5841no—
608C22—5841no—
609C22C4×D4×D7311yescharacteristic
610C22C2×#1455658711yescharacteristic
611C22#1798913411yescharacteristic
612C22#135×D7312yes—
613C22C2×#1455661212yes—
614C4—22no—
615C4—42no—
616C4—81no—
617C4—81no—
618C4—2922no—
619C4—5841no—
620C4—5841no—
621C4—1464no—
622C4—1464no—
623C4#1798896814yesdirect product factor
624C4C4×D4×D7311yescharacteristic
625C4C2×C4×C22⋊D7311yescharacteristic
626C4#1798913311yescharacteristic
627C4#1798913411yescharacteristic
628C2—82no—
629C2—5842no—
630C2C4×#1455658711yescharacteristic
631C2C4×#1455661212yes—
632C2C2×#1798896811yescharacteristic
633C2#2262035511yescharacteristic
634C2#2262049712yes—
subgroupG/H
centerC22×C4D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×C4×SD16×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924013C22
cosocleC22×C4×C73C24
hypercenterC2×C4×SD16D73
hypocenterC73C4×#495
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11924018C2semidirect
3. C2×C4×#11924017C2semidirect
5. C4×#14556580C2semidirect
6. C4×#14556578C2semidirect
8. #22610789C2semidirect
9. #22610787C2semidirect
10. #22610783C2semidirect
11. #22610741C2semidirect
12. #22610739C2semidirect
13. #22610092C2semidirect
14. C4×C8×Dic73C2semidirect
15. C2×C4×SD16×C73C2semidirect
23. #17988968C4direct (N × H)
65. C2×#11924018C2×C4semidirect
68. C2×#11924017C2×C4semidirect
75. #14556580C2×C4semidirect
77. #14556578C2×C4semidirect
108. C8×Dic73C2×C4semidirect
118. C2×SD16×C73C2×C4semidirect
300. C4×C73#495semidirect
321. C2×C4×SD16D73semidirect
333. C73C4×#495semidirect
392. C2×SD16C4×D73semidirect
623. C4#17988968direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889682
C2×C4×#119240182
C2×C4×#119240172
C2×C4×#119240132
C4×#145565802
C4×#145565782
#226107942
#226107892
#226107872
#226107832
#226107412
#226107392
#226100922
C4×C8×Dic732
C2×C4×SD16×C732
C4×#49573