Finite Group Databasebeta

← C4×#17988913 #33093141

Subgroups — C4×#17988913 #33093141

Order 18688.

972 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988913C211yesmaximal, characteristic
2C4×#14556566C211yesmaximal, characteristic
3C4×#14556549C211yesmaximal, characteristic, complemented
4#22610557C211yesmaximal, characteristic, complemented
5#22610549C211yesmaximal, characteristic, complemented
6#22610526C211yesmaximal, characteristic, complemented
7#22610518C211yesmaximal, characteristic, complemented
8#22610252C211yesmaximal, characteristic
9#22610129C211yesmaximal, characteristic, complemented
10#22610024C211yesmaximal, characteristic, complemented
11C4×#14556524C211yesmaximal, characteristic, complemented
12C4×#14556511C211yesmaximal, characteristic, complemented
13C4×#14556513C211yesmaximal, characteristic, complemented
14C4×#14556503C211yesmaximal, characteristic, complemented
15C4×#106×C73C211yesmaximal, characteristic, complemented
16C2×#14556566C2211yescharacteristic
17C2×C4×D292—21no—
18C2×C4×D292C2211yescharacteristic
19C2×#14556549C2211yescharacteristic
20C2×#14556549C2211yescharacteristic
21C2×C42×D73C2211yescharacteristic
22#17988913C418yesdirect product factor
23C2×#14556524C2211yescharacteristic
24C2×#14556524C2211yescharacteristic
25C2×#14556513C2211yescharacteristic
26C2×#14556513C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556511C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×C4×#10596831C2211yescharacteristic
32#17988488C2211yescharacteristic
33#17988486C2211yescharacteristic
34#17988479—21no—
35#17988465—21no—
36#17988444C2211yescharacteristic
37C4⋊C4×Dic73C2211yescharacteristic
38C4⋊C4×Dic73C2211yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40C4×#11924005—21no—
41C4×#11924005—21no—
42#17988434—21no—
43#17988432—21no—
44C42×Dic73—21no—
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53C2×#106×C73C2211yescharacteristic
54C2×#106×C73C2211yescharacteristic
55C2×C4×C8×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60C22×D292—21no—
61C22×D292C2311yescharacteristic
62C22×C4×D73—21no—
63C22×C4×D73D411yescharacteristic
64C22×C4×D73D411yescharacteristic
65C22×C4×D73C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68#14556566—22no—
69#14556566C2×C414yes—
70C4×D292—22no—
71C4×D292—22no—
72C4×D292—44no—
73#14556549—22no—
74#14556549—22no—
75#14556549—22no—
76#14556549C2×C414yescomplemented
77C2×C4⋊Dic73—21no—
78C2×C4⋊Dic73C2311yescharacteristic
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×#11924005—21no—
82C2×#11924005—21no—
83C2×#11924005—21no—
84C2×#11924005—21no—
85C2×#11924005—21no—
86C2×#11924005—21no—
87C2×#11924005—21no—
88C2×C4×Dic73—21no—
89C2×C4×Dic73—21no—
90C2×C4×Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73D411yescharacteristic
94C2×C4×Dic73D411yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C42×D73—22no—
97C42×D73—22no—
98#14556524—22no—
99#14556524C2×C414yescomplemented
100#14556513—22no—
101#14556513C2×C414yescomplemented
102#14556511—22no—
103#14556511C2×C414yescomplemented
104#14556503—22no—
105#14556503C2×C414yescomplemented
106C4×#10596831—22no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112C22×C8×C73C2311yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C42×C73—21no—
119C2×C42×C73—21no—
120C2×C42×C73C2311yescharacteristic
121#106×C73—22no—
122#106×C73C2×C414yescomplemented
123C4×C8×C73—22no—
124#95×C73—21no—
125#95×C73—21no—
126C23×D73—21no—
127C23×D73C2×D411yescharacteristic
128C2×D292—21no—
129C2×D292—21no—
130C2×D292—21no—
131C2×D292—21no—
132C2×D292—24no—
133C2×D292—21no—
134C2×D292—42no—
135C2×D292—42no—
136C2×D292C22×C412yes—
137C22×Dic73—21no—
138C22×Dic73—21no—
139C22×Dic73—21no—
140C22×Dic73C2×D411yescharacteristic
141C22×Dic73C2×D411yescharacteristic
142C22×Dic73C2×D411yescharacteristic
143C2×C4×D73—21no—
144C2×C4×D73—21no—
145C2×C4×D73—21no—
146C2×C4×D73—21no—
147C2×C4×D73—22no—
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—22no—
151C2×C4×D73—22no—
152C2×C4×D73—41no—
153C2×C4×D73—42no—
154C2×C4×D73—42no—
155C2×C4×D73—42no—
156C2×C4×D73C22×C412yes—
157C2×C4×D73#4112yes—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831C22×C412yes—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—42no—
169C4⋊Dic73C22×C412yes—
170C4⋊Dic73#4112yes—
171#11924005—24no—
172#11924005—24no—
173#11924005—24no—
174#11924005—42no—
175#11924005—42no—
176#11924005—42no—
177#11924005—42no—
178C4×Dic73—24no—
179C4×Dic73—22no—
180C4×Dic73—22no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—24no—
184C4×Dic73—42no—
185C4×Dic73—42no—
186C4×Dic73—42no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2411yescharacteristic
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73C22×C412yes—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73C22×C412yes—
206C4⋊C4×C73C22×C412yes—
207C4⋊C4×C73#4112yes—
208C42×C73—42no—
209C42×C73—42no—
210C42×C73#4112yes—
211C42×C73#4112yes—
212C23×C73C22×D411yescharacteristic
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—21no—
217C22×D73—21no—
218C22×D73—21no—
219C22×D73—22no—
220C22×D73—41no—
221C22×D73—41no—
222C22×D73—41no—
223C22×D73—41no—
224C22×D73—41no—
225C22×D73—41no—
226C22×D73C4×D412yes—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—22no—
230C2×C4×C73—22no—
231C2×C4×C73—22no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73#12312yes—
242C2×C4×C73#12312yes—
243C2×C4×C73#13512yes—
244C2×C4×C73AGL(1,ℤ/8)12yes—
245C2×C4×C73C23×C411yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73C2×#4111yescharacteristic
248C2×C4×C73C2×#4111yescharacteristic
249C2×C4×C73C2×#4111yescharacteristic
250C2×C4×C73C2×#4111yescharacteristic
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—22no—
256C2×Dic73—21no—
257C2×Dic73—22no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73C4×D412yes—
268C2×Dic73#13512yes—
269D292—22no—
270D292—22no—
271D292—48no—
272D292—41no—
273D292—41no—
274C4×D73—22no—
275C4×D73—22no—
276C4×D73—22no—
277C4×D73—22no—
278C4×D73—44no—
279C4×D73—44no—
280C4×D73—84no—
281C8×C73—22no—
282C8×C73—41no—
283#10596831—22no—
284#10596831—41no—
285C22×C73C2×C4×D411yescharacteristic
286C22×C73C2×#12311yescharacteristic
287C22×C73#52511yescharacteristic
288C22×C73C2×#13511yescharacteristic
289C22×C73C2×#13511yescharacteristic
290C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C73#57511yescharacteristic
292C2×D73—22no—
293C2×D73—22no—
294C2×D73—22no—
295C2×D73—41no—
296C2×D73—41no—
297C2×D73—41no—
298C2×D73—41no—
299C2×D73—42no—
300C2×D73—42no—
301C2×D73—42no—
302C2×D73—81no—
303C2×D73—81no—
304C2×D73—81no—
305C2×D73—81no—
306C4×C73—22no—
307C4×C73—42no—
308C4×C73—42no—
309C4×C73—42no—
310C4×C73—81no—
311C4×C73#48214yescomplemented
312C4×C73C4×#4111yescharacteristic
313C4×C73C4×#4111yescharacteristic
314C4×C73#52911yescharacteristic
315C4×C73#52911yescharacteristic
316Dic73—22no—
317Dic73—22no—
318Dic73—41no—
319Dic73—42no—
320Dic73—42no—
321Dic73—81no—
322C4×#482—731nomaximal, Sylow
323C2×C73C4×#12311yescharacteristic
324C2×C73C4×#13511yescharacteristic
325C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
326C2×C73C2×#48211yescharacteristic
327C2×C73#309111yescharacteristic
328C2×C73#310211yescharacteristic
329C2×C73#310611yescharacteristic
330D73—42no—
331D73—82no—
332C2×#482—731no—
333C4×#121—731no—
334C4×#117—731no—
335#1926—731no—
336#1925—731no—
337#1921—731no—
338#1920—731no—
339#1875—731no—
340#1854—731no—
341#1825—731no—
342C4×#107—731no—
343C4×#106D7311yescharacteristic, complemented
344C4×#102—731no—
345C4×#102—731no—
346C4×C22⋊C8—731no—
347C73C4×#48211yescharacteristic, complemented, Sylow
348C2×#121—731no—
349C2×C4×D4—731no—
350C2×C4×D4—1461no—
351C2×#117—731no—
352C2×#117—731no—
353C22×C42—731no—
354#482—738no—
355C2×#107—731no—
356C2×#107—731no—
357C2×#106C2×D7311yescharacteristic
358C2×#106C2×D7311yescharacteristic
359C2×#102—731no—
360C2×#102—731no—
361C2×#102—731no—
362C2×#102—731no—
363C2×C22⋊C8—731no—
364C2×C22⋊C8—731no—
365C2×C4×C8—731no—
366C2×C4×C8C2×D7311yescharacteristic
367#390—731no—
368#389—731no—
369#388—1461no—
370#386—1461no—
371#380—731no—
372C4×C4⋊C4—731no—
373C4×C4⋊C4—731no—
374C4×C4⋊C4—731no—
375C4×C4⋊C4C2×D7311yescharacteristic
376C4×C4⋊C4C2×D7311yescharacteristic
377C4×C22⋊C4—1461no—
378C4×C22⋊C4—1461no—
379C4×C22⋊C4—1461no—
380#376—1461no—
381C43—1461no—
382#340—731no—
383#340—731no—
384#340—731no—
385#340—731no—
386#340—731no—
387#340—731no—
388#340C2×D7311yescharacteristic
389#340C2×D7311yescharacteristic
390#336—731no—
391#336—731no—
392C22×D4—731no—
393C22×D4—1461no—
394C23×C4—731no—
395C23×C4—731no—
396C23×C4—731no—
397C23×C4—1461no—
398C22×C8—731no—
399C22×C8—731no—
400C22×C8C22×D7311yescharacteristic
401C22×C8C22×D7311yescharacteristic
402#121—734no—
403#121—1462no—
404C4×D4—2924no—
405C4×D4—1462no—
406C4×D4—1462no—
407#117—734no—
408#117—1462no—
409#117—1462no—
410#117—1462no—
411C2×C4⋊C4—731no—
412C2×C4⋊C4—731no—
413C2×C4⋊C4—731no—
414C2×C4⋊C4—1461no—
415C2×C4⋊C4C22×D7311yescharacteristic
416C2×C4⋊C4C22×D7311yescharacteristic
417C2×C4⋊C4C22×D7311yescharacteristic
418C2×C4⋊C4C22×D7311yescharacteristic
419C2×C22⋊C4—1461no—
420C2×C22⋊C4—1461no—
421C2×C22⋊C4—1461no—
422C2×C22⋊C4—1461no—
423C2×C22⋊C4—1461no—
424C2×C22⋊C4—1461no—
425C2×C22⋊C4—1461no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—731no—
429C2×C42—731no—
430C2×C42—731no—
431C2×C42—1461no—
432C2×C42—1461no—
433C2×C42—1461no—
434C2×C42—1461no—
435C2×C42—1461no—
436C2×C42—1462no—
437C2×C42—1462no—
438C2×C42C22×D7311yescharacteristic
439#107—734no—
440#107—1462no—
441#106—22no—
442#106C4×D7314yescomplemented
443#102—734no—
444#102—734no—
445#102—1462no—
446#102—1462no—
447C22⋊C8—734no—
448C22⋊C8—1462no—
449C4×C8—22no—
450C4×C8—1462no—
451#95—21no—
452#95—21no—
453#95—1461no—
454#95—1461no—
455#95—1461no—
456#95—1461no—
457#95—1461no—
458C24—731no—
459C24—1461no—
460C2×D4—2922no—
461C2×D4—2922no—
462C2×D4—732no—
463C2×D4—1464no—
464C2×D4—1461no—
465C2×D4—1461no—
466C2×D4—1461no—
467C2×D4—1461no—
468C2×D4—1461no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—2921no—
474C22×C4—2922no—
475C22×C4—2922no—
476C22×C4—2922no—
477C22×C4—731no—
478C22×C4—731no—
479C22×C4—732no—
480C22×C4—732no—
481C22×C4—731no—
482C22×C4—1462no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1462no—
487C22×C4—1462no—
488C22×C4—1462no—
489C22×C4—1462no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4D4×D7311yescharacteristic
495C22×C4D4×D7311yescharacteristic
496C22×C4C23×D7311yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—732no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8C2×C4×D7312yes—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—2922no—
515C4⋊C4—732no—
516C4⋊C4—732no—
517C4⋊C4—1461no—
518C4⋊C4—1461no—
519C4⋊C4—1461no—
520C4⋊C4—1461no—
521C4⋊C4C2×C4×D7312yes—
522C4⋊C4C2×C4×D7312yes—
523C4⋊C4#1192402812yes—
524C22⋊C4—2922no—
525C22⋊C4—2922no—
526C22⋊C4—2922no—
527C22⋊C4—2922no—
528C22⋊C4—1464no—
529C22⋊C4—1464no—
530C22⋊C4—1464no—
531C42—42no—
532C42—42no—
533C42—2922no—
534C42—2922no—
535C42—2922no—
536C42—1464no—
537C42—1464no—
538C42—1462no—
539C42—1462no—
540C42—1461no—
541C42—1461no—
542C42#1192402812yes—
543C42#1192402912yes—
544C23—2921no—
545C23—2921no—
546C23—2921no—
547C23—2921no—
548C23—2921no—
549C23—2921no—
550C23—732no—
551C23—1462no—
552C23—1461no—
553C23—1461no—
554C23—1461no—
555C23—1461no—
556C23—1461no—
557C23—1461no—
558C23C2×D4×D7311yescharacteristic
559D4—2928no—
560D4—2921no—
561D4—2921no—
562D4—1462no—
563D4—1462no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—2924no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—2924no—
584C2×C4—2921no—
585C2×C4—2921no—
586C2×C4—2921no—
587C2×C4—5844no—
588C2×C4—732no—
589C2×C4—732no—
590C2×C4—1462no—
591C2×C4—1461no—
592C2×C4—1462no—
593C2×C4—1461no—
594C2×C4—1461no—
595C2×C4—1461no—
596C2×C4—1461no—
597C2×C4—1461no—
598C2×C4—1461no—
599C2×C4—1462no—
600C2×C4—1462no—
601C2×C4—1462no—
602C2×C4—1462no—
603C2×C4#1455657612yes—
604C2×C4#1455657612yes—
605C2×C4#1455661212yes—
606C2×C4#1455661812yes—
607C2×C4C22×C4×D7311yescharacteristic
608C2×C4#41×D7311yescharacteristic
609C2×C4#41×D7311yescharacteristic
610C2×C4C2×#1192402811yescharacteristic
611C2×C4C2×#1192402811yescharacteristic
612C2×C4C2×#1192402911yescharacteristic
613C8—22no—
614C8—41no—
615C8—2921no—
616C8—1462no—
617C22—2921no—
618C22—2921no—
619C22—2921no—
620C22—2921no—
621C22—2922no—
622C22—2922no—
623C22—2922no—
624C22—5841no—
625C22—5841no—
626C22—5841no—
627C22—5841no—
628C22—1462no—
629C22—1462no—
630C22—1462no—
631C22C4×D4×D7311yescharacteristic
632C22C2×#1455657611yescharacteristic
633C22#1798909611yescharacteristic
634C22#135×D7311yescharacteristic
635C22C2×#1455661211yescharacteristic
636C22C2×#1455661811yescharacteristic
637C22#1798938411yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—81no—
643C4—2922no—
644C4—2922no—
645C4—2921no—
646C4—5841no—
647C4—1462no—
648C4—1462no—
649C4#1798891314yesdirect product factor
650C4C4×#1192402811yescharacteristic
651C4C4×#1192402911yescharacteristic
652C4#1798911511yescharacteristic
653C4#1798912411yescharacteristic
654C2—2922no—
655C2—5842no—
656C2C4×#1455657611yescharacteristic
657C2C4×#1455661211yescharacteristic
658C2C4×#1455661811yescharacteristic
659C2C2×#1798891311yescharacteristic
660C2#2261984811yescharacteristic
661C2#2261995311yescharacteristic
662C2#2261998911yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC4×#106×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556566C22
cosocleC22×C4×C73C24
hypercenterC4×#106D73
hypocenterC73C4×#482
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
3. C4×#14556549C2semidirect
4. #22610557C2semidirect
5. #22610549C2semidirect
6. #22610526C2semidirect
7. #22610518C2semidirect
9. #22610129C2semidirect
10. #22610024C2semidirect
11. C4×#14556524C2semidirect
12. C4×#14556511C2semidirect
13. C4×#14556513C2semidirect
14. C4×#14556503C2semidirect
15. C4×#106×C73C2semidirect
22. #17988913C4direct (N × H)
76. #14556549C2×C4semidirect
99. #14556524C2×C4semidirect
101. #14556513C2×C4semidirect
103. #14556511C2×C4semidirect
105. #14556503C2×C4semidirect
122. #106×C73C2×C4semidirect
311. C4×C73#482semidirect
343. C4×#106D73semidirect
347. C73C4×#482semidirect
442. #106C4×D73semidirect
649. C4#17988913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889132
C4×#145565662
C4×#145565492
#226105572
#226105492
#226105262
#226105182
#226102522
#226101292
#226100242
C4×#145565242
C4×#145565112
C4×#145565132
C4×#145565032
C4×#106×C732
C4×#48273