Finite Group Databasebeta

← C4×#17989191 #33245091

Subgroups — C4×#17989191 #33245091

Order 18688.

2518 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989191C211yesmaximal, characteristic
2#22612718C214yesmaximal, complemented
3#22612690C214yesmaximal, complemented
4#22612670C211yesmaximal, characteristic, complemented
5#22612657C211yesmaximal, characteristic, complemented
6#22612627C212yesmaximal, complemented
7#22612568C212yesmaximal, complemented
8#22612539C211yesmaximal, characteristic, complemented
9C4×#14556583C211yesmaximal, characteristic, complemented
10C4×#14556572C214yesmaximal, complemented
11C4×#14556563C214yesmaximal, complemented
12C4×#14556562C212yesmaximal, complemented
13C4×D4×Dic73C212yesmaximal, complemented
14C4×#14556548C211yesmaximal, characteristic, complemented
15C4×#127×C73C211yesmaximal, characteristic, complemented
16#17989191C4116yesdirect product factor
17C2×#14556583C2211yescharacteristic
18C2×#14556572C2214yes—
19C2×#14556563C2214yes—
20C2×#14556562C2212yes—
21C2×D4×Dic73C2212yes—
22C2×D4×Dic73C2212yes—
23C2×C4×C22⋊D73C2214yes—
24C2×#14556548C2211yescharacteristic
25C2×#14556548C2211yescharacteristic
26C22×C4×Dic73C2214yes—
27C2×C42×D73C2211yescharacteristic
28#17988490C2212yes—
29#17988487C2214yes—
30#17988485C2212yes—
31#17988483C2212yes—
32#17988482C2214yes—
33#17988481C2214yes—
34#17988477C2214yes—
35#17988475C2214yes—
36#17988475C2214yes—
37#17988475C2214yes—
38#17988471C2214yes—
39#17988468C2214yes—
40#17988468C2214yes—
41#17988467C2214yes—
42#17988467C2214yes—
43#17988464C2214yes—
44#17988463C2214yes—
45#17988459C2214yes—
46#17988453C2211yescharacteristic
47#17988448C2214yes—
48#17988445C2214yes—
49#17988444C2212yes—
50C4⋊C4×Dic73C2212yes—
51C4⋊C4×Dic73C2212yes—
52C4×#11924007C2214yes—
53C4×#11924007C2212yes—
54C4×#11924007C2212yes—
55C4×C4⋊Dic73C2212yes—
56C22⋊C4×Dic73C2214yes—
57C22⋊C4×Dic73C2214yes—
58C4×#11924005C2212yes—
59C4×#11924005C2212yes—
60C4×C22⋊Dic73C2214yes—
61C4×C22⋊Dic73C2214yes—
62#17988433C2211yescharacteristic
63#17988433C2211yescharacteristic
64C42×Dic73C2211yescharacteristic
65C2×#127×C73C2211yescharacteristic
66C2×C4×D4×C73C2212yes—
67C2×C4×D4×C73C2214yes—
68#390×C73C2212yes—
69#390×C73C2214yes—
70#384×C73C2211yescharacteristic
71C43×C73C2211yescharacteristic
72C22×C22⋊D73C2314yes—
73C23×Dic73C2314yes—
74C23×Dic73C2314yes—
75C22×C4×D73C2311yescharacteristic
76C22×C4×D73C2311yescharacteristic
77C22×C4×D73C2311yescharacteristic
78#14556583C2×C418yescomplemented
79#14556572C2×C4132yescomplemented
80#14556563C2×C4132yescomplemented
81#14556562C2×C4116yescomplemented
82D4×Dic73—28no—
83D4×Dic73C2×C4116yescomplemented
84C4×C22⋊D73—48no—
85#14556548—24no—
86#14556548C2×C418yescomplemented
87C2×C4⋊Dic73C2312yes—
88C2×C4⋊Dic73C2312yes—
89C2×#11924007C2312yes—
90C2×#11924007C2314yes—
91C2×#11924007C2314yes—
92C2×#11924007C2312yes—
93C2×#11924007C2314yes—
94C2×C22⋊Dic73C2314yes—
95C2×C22⋊Dic73C2314yes—
96C2×C22⋊Dic73C2314yes—
97C2×C22⋊Dic73C2314yes—
98C2×C22⋊Dic73C2314yes—
99C2×#11924005C2312yes—
100C2×#11924005C2314yes—
101C2×#11924005C2312yes—
102C2×C4×Dic73—48no—
103C2×C4×Dic73C2312yes—
104C2×C4×Dic73C2311yescharacteristic
105C2×C4×Dic73C2311yescharacteristic
106C2×C4×Dic73C2314yes—
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2312yes—
109C2×C4×Dic73C2314yes—
110C2×C4×Dic73C2314yes—
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C42×D73—24no—
114#14556498C2312yes—
115#14556498C2312yes—
116#14556498C2312yes—
117#14556498C2312yes—
118#14556498C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125C22×D4×C73C2312yes—
126C22×D4×C73C2314yes—
127C23×C4×C73C2314yes—
128#127×C73C2×C418yescomplemented
129C4×D4×C73—28no—
130C4×D4×C73—48no—
131C2×C4⋊C4×C73C2312yes—
132C2×C4⋊C4×C73C2314yes—
133C2×C22⋊C4×C73C2314yes—
134C2×C22⋊C4×C73C2314yes—
135C2×C22⋊C4×C73C2314yes—
136C2×C42×C73C2311yescharacteristic
137C2×C42×C73C2312yes—
138C2×C42×C73C2312yes—
139C2×C42×C73C2311yescharacteristic
140C2×C42×C73C2311yescharacteristic
141C23×D73C2411yescharacteristic
142C2×C22⋊D73—44no—
143C2×C22⋊D73—44no—
144C2×C22⋊D73C22×C4116yes—
145C22×Dic73—28no—
146C22×Dic73—44no—
147C22×Dic73—44no—
148C22×Dic73—44no—
149C22×Dic73—44no—
150C22×Dic73C22×C4116yes—
151C22×Dic73C2411yescharacteristic
152C22×Dic73C2414yes—
153C22×Dic73C2411yescharacteristic
154C22×Dic73C2412yes—
155C22×Dic73C2411yescharacteristic
156C22×Dic73C2414yes—
157C22×Dic73C2412yes—
158C2×C4×D73—22no—
159C2×C4×D73—22no—
160C2×C4×D73—22no—
161C2×C4×D73—22no—
162C2×C4×D73—24no—
163C2×C4×D73—42no—
164C2×C4×D73C22×C414yes—
165C4⋊Dic73—24no—
166C4⋊Dic73C22×C418yes—
167#11924007—24no—
168#11924007—44no—
169#11924007—44no—
170#11924007C22×C418yes—
171#11924007C22×C4116yes—
172C22⋊Dic73—28no—
173C22⋊Dic73—44no—
174C22⋊Dic73—44no—
175C22⋊Dic73C22×C4116yes—
176C22⋊Dic73C22×C4116yes—
177#11924005—24no—
178#11924005—44no—
179#11924005C22×C418yes—
180C4×Dic73—22no—
181C4×Dic73—22no—
182C4×Dic73—22no—
183C4×Dic73—24no—
184C4×Dic73—28no—
185C4×Dic73—44no—
186C4×Dic73—44no—
187C4×Dic73—42no—
188C4×Dic73C22×C414yes—
189C4×Dic73#4114yes—
190C24×C73C2414yes—
191C2×D4×C73—24no—
192C2×D4×C73—24no—
193C2×D4×C73—44no—
194C2×D4×C73—44no—
195C2×D4×C73C22×C418yes—
196C2×D4×C73C22×C4116yes—
197C22×C4×C73—28no—
198C22×C4×C73—28no—
199C22×C4×C73—28no—
200C22×C4×C73C2412yes—
201C22×C4×C73C2414yes—
202C22×C4×C73C2412yes—
203C22×C4×C73C2411yescharacteristic
204C22×C4×C73C2411yescharacteristic
205C22×C4×C73C2411yescharacteristic
206C4⋊C4×C73—24no—
207C4⋊C4×C73—44no—
208C22⋊C4×C73—28no—
209C22⋊C4×C73—44no—
210C22⋊C4×C73—44no—
211C42×C73—22no—
212C42×C73—24no—
213C42×C73—42no—
214C42×C73C22×C414yes—
215C42×C73#4114yes—
216C23×C73—24no—
217C23×C73—24no—
218C23×C73—24no—
219C23×C73—24no—
220C23×C73—24no—
221C23×C73—24no—
222C23×C73C23×C418yes—
223C23×C73C2511yescharacteristic
224C22×D73—21no—
225C22×D73—21no—
226C22×D73—22no—
227C22×D73—22no—
228C22×D73C23×C412yes—
229D4×C73—216no—
230D4×C73—416no—
231C2×C4×C73—22no—
232C2×C4×C73—22no—
233C2×C4×C73—22no—
234C2×C4×C73—22no—
235C2×C4×C73—24no—
236C2×C4×C73—22no—
237C2×C4×C73—24no—
238C2×C4×C73—24no—
239C2×C4×C73—22no—
240C2×C4×C73—416no—
241C2×C4×C73C23×C414yes—
242C2×C4×C73C23×C412yes—
243C2×C4×C73C2×#4112yes—
244C2×C4×C73C2×#4112yes—
245C2×C4×C73C2×#4112yes—
246C2×C4×C73C2×#4112yes—
247C2×C4×C73H(5,𝔽2)14yes—
248C22⋊D73—416no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—22no—
252C2×Dic73—22no—
253C2×Dic73—24no—
254C2×Dic73—22no—
255C2×Dic73—22no—
256C2×Dic73—24no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—24no—
260C2×Dic73—24no—
261C2×Dic73—22no—
262C2×Dic73—22no—
263C2×Dic73—24no—
264C2×Dic73—416no—
265C2×Dic73—416no—
266C2×Dic73C23×C414yes—
267C2×Dic73C23×C412yes—
268C2×Dic73C23×C418yes—
269C2×Dic73C2×#4114yes—
270C4×D73—28no—
271C4×D73—44no—
272C4×D73—44no—
273C22×C73—28no—
274C22×C73—28no—
275C22×C73—28no—
276C22×C73—44no—
277C22×C73—44no—
278C22×C73—44no—
279C22×C73—44no—
280C22×C73C24×C411yescharacteristic
281C22×C73C22×#4111yescharacteristic
282C22×C73C22×#4111yescharacteristic
283C22×C73C2×H(5,𝔽2)12yes—
284C22×C73#58512yes—
285C2×D73—22no—
286C2×D73—24no—
287C2×D73—41no—
288C2×D73—41no—
289C2×D73—42no—
290C4×C73—24no—
291C4×C73—22no—
292C4×C73—44no—
293C4×C73—42no—
294C4×C73C4×#4114yes—
295C4×C73#54014yescomplemented
296Dic73—22no—
297Dic73—24no—
298Dic73—28no—
299Dic73—24no—
300Dic73—41no—
301Dic73—41no—
302Dic73—44no—
303C4×#540—731nomaximal, Sylow
304C2×C73—48no—
305C2×C73C2×C4×#4111yescharacteristic
306C2×C73C4×H(5,𝔽2)12yes—
307C2×C73C2×#54011yescharacteristic
308C2×C73#345511yescharacteristic
309C2×C73#346012yes—
310D73—42no—
311C2×#540—731no—
312#2335—734no—
313#2333—734no—
314#2330—731no—
315#2328—731no—
316#2324—732no—
317#2319—732no—
318#2314—731no—
319C4×#127D7311yescharacteristic, complemented
320C4×#125—731no—
321C4×#123—734no—
322C4×#121—732no—
323C4×#121—734no—
324C42×D4—732no—
325C4×#117—731no—
326C73C4×#54011yescharacteristic, complemented, Sylow
327#540—7316no—
328C2×#127C2×D7311yescharacteristic
329C2×#125—731no—
330C2×#123—734no—
331C2×#121—732no—
332C2×#121—734no—
333C2×C4×D4—734no—
334C2×C4×D4—732no—
335C2×C4×D4—732no—
336C2×C4×D4C2×D7312yes—
337C2×C4×D4C2×D7314yes—
338C2×#117—731no—
339C2×#117—731no—
340C22×C42—734no—
341C22×C42—731no—
342#390—732no—
343#390—734no—
344#390C2×D7312yes—
345#390C2×D7314yes—
346#389—732no—
347#389—734no—
348#389—732no—
349#388—734no—
350#388—734no—
351#388—734no—
352#388—734no—
353#388—734no—
354#387—734no—
355#387—734no—
356#387—734no—
357#386—734no—
358#386—734no—
359#386—734no—
360#386—734no—
361#385—734no—
362#384C2×D7311yescharacteristic
363#382—731no—
364#381—734no—
365#380—732no—
366#380—734no—
367C4×C4⋊C4—732no—
368C4×C4⋊C4—732no—
369C4×C4⋊C4—732no—
370C4×C4⋊C4—734no—
371C4×C4⋊C4—732no—
372C4×C4⋊C4—732no—
373C4×C22⋊C4—734no—
374C4×C22⋊C4—734no—
375C4×C22⋊C4—734no—
376C4×C22⋊C4—734no—
377C4×C22⋊C4—732no—
378C4×C22⋊C4—732no—
379#376—731no—
380#376—731no—
381C43—731no—
382C43C2×D7311yescharacteristic
383C22×D4—734no—
384C22×D4C22×D7312yes—
385C22×D4C22×D7314yes—
386C23×C4—734no—
387C23×C4—734no—
388C23×C4—731no—
389C23×C4—731no—
390C23×C4—731no—
391C23×C4C22×D7314yes—
392#127C4×D7318yescomplemented
393#125—738no—
394#123—7332no—
395#121—7316no—
396#121—7332no—
397C4×D4—28no—
398C4×D4—48no—
399C4×D4—2928no—
400C4×D4—7316no—
401C4×D4—1468no—
402#117—738no—
403#117—1464no—
404C2×C4⋊C4—734no—
405C2×C4⋊C4—734no—
406C2×C4⋊C4—732no—
407C2×C4⋊C4—732no—
408C2×C4⋊C4—734no—
409C2×C4⋊C4—732no—
410C2×C4⋊C4—732no—
411C2×C4⋊C4C22×D7312yes—
412C2×C4⋊C4C22×D7314yes—
413C2×C22⋊C4—734no—
414C2×C22⋊C4—734no—
415C2×C22⋊C4—734no—
416C2×C22⋊C4—734no—
417C2×C22⋊C4—734no—
418C2×C22⋊C4—732no—
419C2×C22⋊C4—734no—
420C2×C22⋊C4—732no—
421C2×C22⋊C4C22×D7314yes—
422C2×C22⋊C4C22×D7314yes—
423C2×C22⋊C4C22×D7314yes—
424C2×C42—2928no—
425C2×C42—732no—
426C2×C42—734no—
427C2×C42—734no—
428C2×C42—731no—
429C2×C42—731no—
430C2×C42—731no—
431C2×C42—731no—
432C2×C42—734no—
433C2×C42—732no—
434C2×C42—731no—
435C2×C42—1464no—
436C2×C42C22×D7311yescharacteristic
437C2×C42C22×D7312yes—
438C2×C42C22×D7312yes—
439C2×C42C22×D7311yescharacteristic
440C2×C42C22×D7311yescharacteristic
441#95—732no—
442#95—732no—
443#95—732no—
444#95—732no—
445#95—734no—
446#95—734no—
447#95—734no—
448#95—734no—
449#95—734no—
450#95—734no—
451#95—734no—
452C24—731no—
453C24C23×D7314yes—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—2924no—
459C2×D4—2924no—
460C2×D4—7316no—
461C2×D4C2×C4×D7318yes—
462C2×D4C2×C4×D73116yes—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—2922no—
467C22×C4—2924no—
468C22×C4—2924no—
469C22×C4—2924no—
470C22×C4—2924no—
471C22×C4—7316no—
472C22×C4—732no—
473C22×C4—732no—
474C22×C4—731no—
475C22×C4—734no—
476C22×C4—734no—
477C22×C4—731no—
478C22×C4—734no—
479C22×C4—731no—
480C22×C4—1468no—
481C22×C4—1462no—
482C22×C4—1462no—
483C22×C4—1464no—
484C22×C4—1462no—
485C22×C4—1462no—
486C22×C4C23×D7314yes—
487C22×C4C23×D7312yes—
488C22×C4C23×D7312yes—
489C22×C4C23×D7311yescharacteristic
490C22×C4C23×D7311yescharacteristic
491C22×C4C23×D7311yescharacteristic
492C4⋊C4—24no—
493C4⋊C4—44no—
494C4⋊C4—2924no—
495C4⋊C4—2924no—
496C4⋊C4—738no—
497C4⋊C4—7316no—
498C4⋊C4—738no—
499C4⋊C4—1464no—
500C4⋊C4—1464no—
501C22⋊C4—28no—
502C22⋊C4—44no—
503C22⋊C4—44no—
504C22⋊C4—2924no—
505C22⋊C4—2924no—
506C22⋊C4—2924no—
507C22⋊C4—7316no—
508C22⋊C4—7316no—
509C22⋊C4—738no—
510C22⋊C4—1464no—
511C22⋊C4—1468no—
512C42—22no—
513C42—24no—
514C42—42no—
515C42—2924no—
516C42—2924no—
517C42—2922no—
518C42—734no—
519C42—734no—
520C42—1462no—
521C42—1462no—
522C42—1462no—
523C42—1464no—
524C42—1468no—
525C42C2×C4×D7314yes—
526C42#1192402714yes—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—732no—
534C23—1461no—
535C23—1461no—
536C23—1462no—
537C23—1462no—
538C23C22×C4×D7318yes—
539C23C24×D7311yescharacteristic
540D4—216no—
541D4—416no—
542D4—29216no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—416no—
553C2×C4—2924no—
554C2×C4—29216no—
555C2×C4—2924no—
556C2×C4—29216no—
557C2×C4—734no—
558C2×C4—732no—
559C2×C4—738no—
560C2×C4—734no—
561C2×C4—1464no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1464no—
565C2×C4—1462no—
566C2×C4—1462no—
567C2×C4—1464no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1462no—
571C2×C4—1462no—
572C2×C4—1464no—
573C2×C4—1462no—
574C2×C4—1462no—
575C2×C4—1464no—
576C2×C4—1468no—
577C2×C4C22×C4×D7314yes—
578C2×C4C22×C4×D7312yes—
579C2×C4#41×D7312yes—
580C2×C4C2×#1192402712yes—
581C2×C4C2×#1192402712yes—
582C2×C4C2×#1192402712yes—
583C2×C4#1455663614yes—
584C22—28no—
585C22—28no—
586C22—28no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—2921no—
592C22—2921no—
593C22—2922no—
594C22—1462no—
595C22—1464no—
596C22C23×C4×D7311yescharacteristic
597C22C2×#41×D7311yescharacteristic
598C22C22×#1192402711yescharacteristic
599C22C2×#1455663612yes—
600C22#1798942312yes—
601C4—22no—
602C4—24no—
603C4—44no—
604C4—42no—
605C4—2921no—
606C4—2921no—
607C4—2924no—
608C4—1464no—
609C4—1462no—
610C4—1464no—
611C4—1468no—
612C4C4×#1192402714yes—
613C4#1798919114yesdirect product factor
614C2—48no—
615C2—2922no—
616C2C2×C4×#1192402711yescharacteristic
617C2C4×#1455663612yes—
618C2C2×#1798919111yescharacteristic
619C2#2262332011yescharacteristic
620C2#2262334512yes—
subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC4×#127×C73C2
socle, cosocleC23×C73C25
prime radicalC2×#17989191C2
hypercenterC4×#127D73
hypocenterC73C4×#540
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
2. #22612718C2semidirect
3. #22612690C2semidirect
4. #22612670C2semidirect
5. #22612657C2semidirect
6. #22612627C2semidirect
7. #22612568C2semidirect
8. #22612539C2semidirect
9. C4×#14556583C2semidirect
10. C4×#14556572C2semidirect
11. C4×#14556563C2semidirect
12. C4×#14556562C2semidirect
13. C4×D4×Dic73C2semidirect
14. C4×#14556548C2semidirect
15. C4×#127×C73C2semidirect
16. #17989191C4direct (N × H)
78. #14556583C2×C4semidirect
79. #14556572C2×C4semidirect
80. #14556563C2×C4semidirect
81. #14556562C2×C4semidirect
83. D4×Dic73C2×C4semidirect
86. #14556548C2×C4semidirect
128. #127×C73C2×C4semidirect
295. C4×C73#540semidirect
319. C4×#127D73semidirect
326. C73C4×#540semidirect
392. #127C4×D73semidirect
613. C4#17989191direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891912
#226127182
#226126902
#226126702
#226126572
#226126272
#226125682
#226125392
C4×#145565832
C4×#145565722
C4×#145565632
C4×#145565622
C4×D4×Dic732
C4×#145565482
C4×#127×C732
C4×#54073