Finite Group Databasebeta

← #33013168

Subgroups — #33013168

Order 18688.

1926 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556548C211yesmaximal, characteristic
2C2×#17988456C211yesmaximal, characteristic, complemented
3C2×#17988452C211yesmaximal, characteristic, complemented
4C2×#17988444C211yesmaximal, characteristic
5C2×#17988444C211yesmaximal, characteristic
6#22608182C214yesmaximal, complemented
7#22608175C214yesmaximal
8#22608161C211yesmaximal, characteristic, complemented
9C73×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×C4×D73C2211yescharacteristic
11C2×#14556548—24no—
12C2×#14556548—24no—
13C2×#14556548C418yescomplemented
14C22×C4⋊Dic73C2211yescharacteristic
15C22×C4⋊Dic73C2211yescharacteristic
16C22×#11924007C2212yes—
17C22×#11924007C2214yes—
18C22×#11924005C2212yes—
19C22×#11924005C2212yes—
20C22×#11924005C2212yes—
21C22×C4×Dic73C2211yescharacteristic
22#17988456—24no—
23#17988452—24no—
24#17988444—24no—
25#17988444—24no—
26C2×#14556498C2214yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2214yes—
30C22×C4⋊C4×C73C2211yescharacteristic
31C22×C4⋊C4×C73C2211yescharacteristic
32C22×C42×C73C2211yescharacteristic
33C2×#95×C73C2214yes—
34C24×D73C2311yescharacteristic
35C23×Dic73C2312yes—
36C23×Dic73C2312yes—
37C23×Dic73C2312yes—
38C23×Dic73C2311yescharacteristic
39C22×C4×D73—22no—
40C22×C4×D73—22no—
41C22×C4×D73—22no—
42C22×C4×D73—22no—
43C22×C4×D73C2×C414yes—
44C22×C4×D73D414yes—
45C22×C4×D73Q814yes—
46#14556548—232no—
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—22no—
51C2×C4⋊Dic73—22no—
52C2×C4⋊Dic73—22no—
53C2×#11924007—24no—
54C2×#11924007—24no—
55C2×#11924007—28no—
56C2×#11924007—44no—
57C2×#11924007—44no—
58C2×#11924007C2×C418yes—
59C2×#11924005—24no—
60C2×#11924005—24no—
61C2×#11924005—24no—
62C2×#11924005—24no—
63C2×#11924005—44no—
64C2×#11924005—44no—
65C2×#11924005C2×C418yes—
66C2×C4×Dic73C2×C414yes—
67C2×C4×Dic73D414yes—
68C2×C4×Dic73D414yes—
69#14556498—24no—
70#14556498—24no—
71#14556498—28no—
72#14556498—44no—
73C23×C4×C73C2312yes—
74C23×C4×C73C2312yes—
75C23×C4×C73C2312yes—
76C23×C4×C73C2311yescharacteristic
77C2×C4⋊C4×C73—22no—
78C2×C4⋊C4×C73—22no—
79C2×C4⋊C4×C73—22no—
80C2×C4⋊C4×C73—22no—
81C2×C4⋊C4×C73—22no—
82C2×C4⋊C4×C73—22no—
83C2×C42×C73—22no—
84C2×C42×C73—22no—
85C2×C42×C73C2×C414yes—
86#95×C73—44no—
87C23×D73—21no—
88C23×D73—21no—
89C23×D73—21no—
90C23×D73—21no—
91C23×D73—22no—
92C23×D73—22no—
93C23×D73—22no—
94C23×D73—22no—
95C23×D73C22×C412yes—
96C23×D73C2×D412yes—
97C23×D73C2×Q812yes—
98C22×Dic73—21no—
99C22×Dic73—21no—
100C22×Dic73—21no—
101C22×Dic73—21no—
102C22×Dic73—22no—
103C22×Dic73—22no—
104C22×Dic73—22no—
105C22×Dic73—22no—
106C22×Dic73—22no—
107C22×Dic73—22no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—24no—
113C22×Dic73—24no—
114C22×Dic73—24no—
115C22×Dic73—24no—
116C22×Dic73C22×C414yes—
117C22×Dic73C22×C412yes—
118C22×Dic73C2×D414yes—
119C22×Dic73C2×D414yes—
120C22×Dic73C2×D412yes—
121C22×Dic73C2×Q812yes—
122C2×C4×D73—28no—
123C2×C4×D73—28no—
124C2×C4×D73—28no—
125C2×C4×D73—28no—
126C2×C4×D73—28no—
127C2×C4×D73—28no—
128C2×C4×D73C4⋊C4116yescomplemented
129C4⋊Dic73—44no—
130C4⋊Dic73—44no—
131#11924007—216no—
132#11924007—416no—
133#11924005—216no—
134#11924005—48no—
135#11924005—48no—
136C4×Dic73C22⋊C4116yescomplemented
137C24×C73C2411yescharacteristic
138C22×C4×C73—22no—
139C22×C4×C73—22no—
140C22×C4×C73—22no—
141C22×C4×C73—22no—
142C22×C4×C73—22no—
143C22×C4×C73—22no—
144C22×C4×C73—22no—
145C22×C4×C73—22no—
146C22×C4×C73—22no—
147C22×C4×C73—22no—
148C22×C4×C73—22no—
149C22×C4×C73—22no—
150C22×C4×C73—24no—
151C22×C4×C73—24no—
152C22×C4×C73—24no—
153C22×C4×C73—24no—
154C22×C4×C73C22×C414yes—
155C22×C4×C73C22×C412yes—
156C22×C4×C73C2×D412yes—
157C22×C4×C73C2×D412yes—
158C22×C4×C73C2×D412yes—
159C22×C4×C73C2×Q812yes—
160C22×C4×C73#4112yes—
161C22×C4×C73#4112yes—
162C4⋊C4×C73—44no—
163C4⋊C4×C73—44no—
164C42×C73—28no—
165C23×C73C23×C411yescharacteristic
166C23×C73C22×D411yescharacteristic
167C23×C73C22×D411yescharacteristic
168C23×C73C22×D411yescharacteristic
169C23×C73C22×Q811yescharacteristic
170C23×C73C2×#4111yescharacteristic
171C23×C73C2×#4111yescharacteristic
172C23×C73H(5,𝔽2)12yes—
173C23×C73H(5,𝔽2)12yes—
174C23×C732−1+412yes—
175C23×C732−1+412yes—
176C22×D73—22no—
177C22×D73—22no—
178C22×D73—24no—
179C22×D73—24no—
180C22×D73—22no—
181C22×D73—22no—
182C22×D73—22no—
183C22×D73—22no—
184C22×D73—22no—
185C22×D73—22no—
186C22×D73—22no—
187C22×D73—22no—
188C22×D73—24no—
189C22×D73—24no—
190C22×D73—42no—
191C22×D73—42no—
192C22×D73—42no—
193C22×D73—42no—
194C22×D73—42no—
195C22×D73—42no—
196C22×D73—42no—
197C22×D73—42no—
198C22×D73C2×C4⋊C414yes—
199C2×C4×C73—24no—
200C2×C4×C73—24no—
201C2×C4×C73—24no—
202C2×C4×C73—42no—
203C2×C4×C73—42no—
204C2×C4×C73—42no—
205C2×C4×C73—42no—
206C2×C4×C73—42no—
207C2×C4×C73—42no—
208C2×C4×C73—42no—
209C2×C4×C73—42no—
210C2×C4×C73—42no—
211C2×C4×C73—44no—
212C2×C4×C73—42no—
213C2×C4×C73—44no—
214C2×C4×C73—44no—
215C2×C4×C73—44no—
216C2×C4×C73C2×C22⋊C414yes—
217C2×C4×C73C2×C4⋊C414yes—
218C2×C4×C73#11714yes—
219C2×C4×C73#12114yes—
220C2×C4×C73#12114yes—
221C2×C4×C73C22⋊Q814yes—
222C2×C4×C73C22⋊Q814yes—
223C2×Dic73—22no—
224C2×Dic73—22no—
225C2×Dic73—24no—
226C2×Dic73—24no—
227C2×Dic73—22no—
228C2×Dic73—22no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—24no—
232C2×Dic73—24no—
233C2×Dic73—24no—
234C2×Dic73—24no—
235C2×Dic73—42no—
236C2×Dic73—42no—
237C2×Dic73—42no—
238C2×Dic73—42no—
239C2×Dic73—44no—
240C2×Dic73—42no—
241C2×Dic73—42no—
242C2×Dic73—44no—
243C2×Dic73—44no—
244C2×Dic73—44no—
245C2×Dic73C2×C22⋊C418yes—
246C2×Dic73C2×C4⋊C414yes—
247C4×D73—232no—
248C22×C73C22×C22⋊C411yescharacteristic
249C22×C73C22×C4⋊C411yescharacteristic
250C22×C73C2×#11711yescharacteristic
251C22×C73#52012yes—
252C22×C73#52012yes—
253C22×C73C2×#12111yescharacteristic
254C22×C73C2×#12111yescharacteristic
255C22×C73C2×C22⋊Q811yescharacteristic
256C22×C73C2×C22⋊Q811yescharacteristic
257C22×C73#53511yescharacteristic
258C22×C73#53512yes—
259C22×C73#53511yescharacteristic
260C22×C73#53611yescharacteristic
261C22×C73#53612yes—
262C22×C73#53611yescharacteristic
263C22×C73#53712yes—
264C22×C73#53712yes—
265C22×C73#54012yes—
266C22×C73#54112yes—
267C22×C73#54212yes—
268C22×C73#54212yes—
269C22×C73#54412yes—
270C22×C73#54412yes—
271C2×D73—24no—
272C2×D73—24no—
273C2×D73—24no—
274C2×D73—44no—
275C2×D73—44no—
276C2×D73—42no—
277C2×D73—42no—
278C2×D73—42no—
279C2×D73—42no—
280C2×D73—44no—
281C2×D73—44no—
282C4×C73—44no—
283C4×C73—82no—
284C4×C73—82no—
285C4×C73#38018yes—
286Dic73—28no—
287Dic73—24no—
288Dic73—82no—
289Dic73—82no—
290#14340—731nomaximal, Sylow
291C2×C73C2×#38011yescharacteristic
292C2×C73#231112yes—
293C2×C73#231412yes—
294C2×C73#231711yescharacteristic
295C2×C73#231711yescharacteristic
296C2×C73#261911yescharacteristic
297C2×C73#262011yescharacteristic
298C2×C73#262011yescharacteristic
299C2×C73#262111yescharacteristic
300C2×C73#262812yes—
301C2×C73#262912yes—
302D73—44no—
303C22×#117—731no—
304C2×#384—731no—
305C2×#382—731no—
306C2×#380—731no—
307C2×#380—731no—
308#1441—734no—
309#1439—734no—
310C4⋊#95—731no—
311C4⋊#95D7311yescharacteristic, complemented
312C73#1434011yescharacteristic, complemented, Sylow
313C24×C4—731no—
314C2×#117—738no—
315C2×#117—1464no—
316C2×#117—1464no—
317C22×C4⋊C4—734no—
318C22×C4⋊C4—732no—
319C22×C4⋊C4—731no—
320C22×C4⋊C4—731no—
321C22×C4⋊C4C2×D7311yescharacteristic
322C22×C4⋊C4C2×D7311yescharacteristic
323C22×C22⋊C4—732no—
324C22×C22⋊C4—732no—
325C22×C22⋊C4—732no—
326C22×C42—731no—
327C22×C42C2×D7311yescharacteristic
328#384—1464no—
329#382—1464no—
330#380—1464no—
331#380—1464no—
332C2×#95—734no—
333C2×#95—734no—
334C2×#95—732no—
335C2×#95—732no—
336C2×#95C2×D7314yes—
337C25—731no—
338C23×C4—732no—
339C23×C4—731no—
340C23×C4—734no—
341C23×C4—734no—
342C23×C4—734no—
343C23×C4—732no—
344C23×C4—732no—
345C23×C4—1462no—
346C23×C4—1462no—
347C23×C4—1462no—
348C23×C4—1462no—
349C23×C4C22×D7312yes—
350C23×C4C22×D7312yes—
351C23×C4C22×D7312yes—
352C23×C4C22×D7311yescharacteristic
353#117—14632no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—2924no—
361C2×C4⋊C4—2924no—
362C2×C4⋊C4—738no—
363C2×C4⋊C4—1468no—
364C2×C4⋊C4—1462no—
365C2×C4⋊C4—1462no—
366C2×C4⋊C4—1462no—
367C2×C4⋊C4—1462no—
368C2×C4⋊C4—1462no—
369C2×C4⋊C4—1462no—
370C2×C4⋊C4—1464no—
371C2×C4⋊C4—1464no—
372C2×C22⋊C4—2924no—
373C2×C22⋊C4—2924no—
374C2×C22⋊C4—738no—
375C2×C22⋊C4—1464no—
376C2×C22⋊C4—1464no—
377C2×C22⋊C4—1464no—
378C2×C22⋊C4—1464no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—734no—
382C2×C42—734no—
383C2×C42—734no—
384C2×C42C4×D7314yes—
385#95—44no—
386#95—2924no—
387#95—1464no—
388#95—1464no—
389#95—1468no—
390C24—732no—
391C24—732no—
392C24—732no—
393C24—1461no—
394C24—1461no—
395C24—1461no—
396C24—1461no—
397C24—1462no—
398C24—1462no—
399C24—1462no—
400C24—1462no—
401C24C23×D7311yescharacteristic
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—734no—
419C22×C4—732no—
420C22×C4—732no—
421C22×C4—734no—
422C22×C4—734no—
423C22×C4—732no—
424C22×C4—7316no—
425C22×C4—1462no—
426C22×C4—1462no—
427C22×C4—1462no—
428C22×C4—1462no—
429C22×C4—1462no—
430C22×C4—1462no—
431C22×C4—1464no—
432C22×C4—1464no—
433C22×C4—1464no—
434C22×C4—1464no—
435C22×C4—1461no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4—1462no—
440C22×C4—1462no—
441C22×C4—1462no—
442C22×C4—1462no—
443C22×C4—1468no—
444C22×C4—1468no—
445C22×C4—1468no—
446C22×C4—1468no—
447C22×C4—1468no—
448C22×C4—1468no—
449C22×C4C2×C4×D7314yes—
450C22×C4C2×C4×D7312yes—
451C22×C4D4×D7312yes—
452C22×C4D4×D7312yes—
453C22×C4D4×D7312yes—
454C22×C4Q8×D7312yes—
455C22×C4#1192402812yes—
456C22×C4#1192402812yes—
457C4⋊C4—44no—
458C4⋊C4—44no—
459C4⋊C4—29216no—
460C4⋊C4—2924no—
461C4⋊C4—2924no—
462C4⋊C4—14616no—
463C22⋊C4—2928no—
464C22⋊C4—2928no—
465C22⋊C4—14616no—
466C42—28no—
467C42—7316no—
468C23—2922no—
469C23—2922no—
470C23—2922no—
471C23—2922no—
472C23—2922no—
473C23—2922no—
474C23—2922no—
475C23—2922no—
476C23—734no—
477C23—1462no—
478C23—1462no—
479C23—1462no—
480C23—1462no—
481C23—1464no—
482C23—1464no—
483C23—1462no—
484C23—1462no—
485C23—1464no—
486C23—1464no—
487C23—1462no—
488C23—1462no—
489C23—1462no—
490C23—1462no—
491C23C22×C4×D7311yescharacteristic
492C23C2×D4×D7311yescharacteristic
493C23C2×D4×D7311yescharacteristic
494C23C2×D4×D7311yescharacteristic
495C23C2×Q8×D7311yescharacteristic
496C23C2×#1192402811yescharacteristic
497C23C2×#1192402811yescharacteristic
498C23#1455663612yes—
499C23#1455663712yes—
500C23#1455663812yes—
501C23#1455663912yes—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—2922no—
520C2×C4—2924no—
521C2×C4—2922no—
522C2×C4—2922no—
523C2×C4—2922no—
524C2×C4—2924no—
525C2×C4—2924no—
526C2×C4—2924no—
527C2×C4—2922no—
528C2×C4—2922no—
529C2×C4—738no—
530C2×C4—734no—
531C2×C4—1464no—
532C2×C4—1464no—
533C2×C4—1464no—
534C2×C4—1464no—
535C2×C4—1462no—
536C2×C4—1462no—
537C2×C4—1464no—
538C2×C4—1464no—
539C2×C4—1462no—
540C2×C4—1462no—
541C2×C4—1462no—
542C2×C4—1462no—
543C2×C4—14632no—
544C2×C4C22⋊C4×D7314yes—
545C2×C4C4⋊C4×D7314yes—
546C2×C4#1455654814yes—
547C2×C4#1455656414yes—
548C2×C4#1455656414yes—
549C2×C4#1455656914yes—
550C2×C4#1455656914yes—
551C22—2924no—
552C22—2924no—
553C22—2922no—
554C22—2922no—
555C22—2922no—
556C22—2922no—
557C22—2924no—
558C22—2924no—
559C22—1464no—
560C22—1464no—
561C22—1464no—
562C22C2×C22⋊C4×D7311yescharacteristic
563C22C2×C4⋊C4×D7311yescharacteristic
564C22C2×#1455654811yescharacteristic
565C22#1798906712yes—
566C22#1798906812yes—
567C22C2×#1455656411yescharacteristic
568C22C2×#1455656411yescharacteristic
569C22C2×#1455656911yescharacteristic
570C22C2×#1455656911yescharacteristic
571C22#1798915011yescharacteristic
572C22#1798915312yes—
573C22#1798915511yescharacteristic
574C22#1798915711yescharacteristic
575C22#1798916012yes—
576C22#1798916211yescharacteristic
577C22#1798916612yes—
578C22#1798916712yes—
579C22#1798918812yes—
580C22#1798919512yes—
581C22#1798920212yes—
582C22#1798920912yes—
583C22#1798921412yes—
584C22#1798921712yes—
585C4—44no—
586C4—82no—
587C4—82no—
588C4—5842no—
589C4—5842no—
590C4—1468no—
591C4—1464no—
592C4#1798844618yes—
593C2—2924no—
594C2C2×#1798844611yescharacteristic
595C2#2261252012yes—
596C2#2261253612yes—
597C2#2261255211yescharacteristic
598C2#2261255611yescharacteristic
599C2#2261568611yescharacteristic
600C2#2261569411yescharacteristic
601C2#2261569511yescharacteristic
602C2#2261570211yescharacteristic
603C2#2261575812yes—
604C2#2261576612yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×C4⋊#95C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenterC4⋊#95D73
hypocenterC73#14340
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#17988456C2semidirect
3. C2×#17988452C2semidirect
6. #22608182C2semidirect
8. #22608161C2semidirect
9. C73×C4⋊#95C2semidirect
13. C2×#14556548C4semidirect
128. C2×C4×D73C4⋊C4semidirect
136. C4×Dic73C22⋊C4semidirect
311. C4⋊#95D73semidirect
312. C73#14340semidirect

Maximal subgroups

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

subgroupindex
C22×#145565482
C2×#179884562
C2×#179884522
C2×#179884442
#226081822
#226081752
#226081612
C73×C4⋊#952
#1434073