Finite Group Databasebeta

← #33017071

Subgroups — #33017071

Order 18688.

1342 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988459C211yesmaximal, characteristic
2#22608197C212yesmaximal, complemented
3#22608191C212yesmaximal, complemented
4#22608190C212yesmaximal, complemented
5#22608185C212yesmaximal, complemented
6#22608178C212yesmaximal
7#22608176C211yesmaximal, characteristic
8#22608153C212yesmaximal
9C73×#1439C211yesmaximal, characteristic
10C24×Dic73C2211yescharacteristic
11C22×C4⋊Dic73C2211yescharacteristic
12C22×#11924007C2212yes—
13C22×C22⋊Dic73C2211yescharacteristic
14C22×C22⋊Dic73C2212yes—
15#17988459C418yescomplemented
16C2×#14556498C2212yes—
17C2×#14556498C2212yes—
18C2×#14556498C2212yes—
19C2×#14556498C2212yes—
20C2×#14556498C2212yes—
21C2×#14556498C2211yescharacteristic
22C2×#14556498C2212yes—
23C2×#14556498C2212yes—
24C2×#14556498C2212yes—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C22×C4⋊C4×C73C2211yescharacteristic
28C22×C22⋊C4×C73C2212yes—
29C22×C22⋊C4×C73C2211yescharacteristic
30C2×#95×C73C2212yes—
31C2×#95×C73C2211yescharacteristic
32C23×Dic73—41no—
33C23×Dic73—41no—
34C23×Dic73—42no—
35C23×Dic73—42no—
36C23×Dic73C2×C414yes—
37C23×Dic73C2312yes—
38C23×Dic73C2312yes—
39C23×Dic73C2312yes—
40C23×Dic73C2312yes—
41C2×C4⋊Dic73—41no—
42C2×C4⋊Dic73—42no—
43C2×#11924007—42no—
44C2×#11924007—42no—
45C2×#11924007C2×C418yes—
46C2×C22⋊Dic73—22no—
47C2×C22⋊Dic73—22no—
48C2×C22⋊Dic73—24no—
49C2×C22⋊Dic73—42no—
50C2×C22⋊Dic73—42no—
51C2×C22⋊Dic73C2×C414yes—
52#14556498—41no—
53#14556498—42no—
54#14556498—42no—
55#14556498—42no—
56#14556498—42no—
57#14556498—42no—
58#14556498—42no—
59#14556498—42no—
60#14556498—42no—
61#14556498—42no—
62#14556498C2×C418yes—
63C25×C73C2311yescharacteristic
64C23×C4×C73C2312yes—
65C23×C4×C73C2312yes—
66C23×C4×C73C2311yescharacteristic
67C23×C4×C73C2311yescharacteristic
68C2×C4⋊C4×C73—41no—
69C2×C4⋊C4×C73—42no—
70C2×C22⋊C4×C73—24no—
71C2×C22⋊C4×C73—41no—
72C2×C22⋊C4×C73—41no—
73C2×C22⋊C4×C73—42no—
74C2×C22⋊C4×C73—42no—
75C2×C22⋊C4×C73C2×C414yes—
76#95×C73—41no—
77#95×C73—42no—
78C22×Dic73—22no—
79C22×Dic73—22no—
80C22×Dic73—22no—
81C22×Dic73—22no—
82C22×Dic73—22no—
83C22×Dic73—22no—
84C22×Dic73—22no—
85C22×Dic73—22no—
86C22×Dic73—22no—
87C22×Dic73—22no—
88C22×Dic73—22no—
89C22×Dic73—22no—
90C22×Dic73—22no—
91C22×Dic73—22no—
92C22×Dic73—22no—
93C22×Dic73—22no—
94C22×Dic73—22no—
95C22×Dic73—22no—
96C22×Dic73—22no—
97C22×Dic73—22no—
98C22×Dic73—22no—
99C22×Dic73—22no—
100C22×Dic73—22no—
101C22×Dic73—22no—
102C22×Dic73—22no—
103C22×Dic73—22no—
104C22×Dic73—48no—
105C22×Dic73—44no—
106C22×Dic73—44no—
107C22×Dic73—48no—
108C22×Dic73—44no—
109C22×Dic73C22×C414yes—
110C22×Dic73C22×C414yes—
111C4⋊Dic73—44no—
112#11924007—48no—
113C22⋊Dic73—28no—
114C22⋊Dic73—48no—
115C24×C73—22no—
116C24×C73—21no—
117C24×C73—21no—
118C24×C73—22no—
119C24×C73—22no—
120C24×C73—21no—
121C24×C73—21no—
122C24×C73—22no—
123C24×C73C22×C412yes—
124C24×C73#4112yes—
125C24×C73#4112yes—
126C24×C73C2411yescharacteristic
127C22×C4×C73—21no—
128C22×C4×C73—22no—
129C22×C4×C73—21no—
130C22×C4×C73—21no—
131C22×C4×C73—21no—
132C22×C4×C73—22no—
133C22×C4×C73—22no—
134C22×C4×C73—22no—
135C22×C4×C73—22no—
136C22×C4×C73—22no—
137C22×C4×C73—22no—
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×C73C22×C412yes—
150C22×C4×C73C22×C412yes—
151C4⋊C4×C73—44no—
152C22⋊C4×C73—44no—
153C22⋊C4×C73—48no—
154C23×C73—22no—
155C23×C73—24no—
156C23×C73—22no—
157C23×C73—24no—
158C23×C73—24no—
159C23×C73—24no—
160C23×C73—24no—
161C23×C73—22no—
162C23×C73—22no—
163C23×C73—22no—
164C23×C73—22no—
165C23×C73—24no—
166C23×C73—41no—
167C23×C73—41no—
168C23×C73—42no—
169C23×C73—41no—
170C23×C73—42no—
171C23×C73—42no—
172C23×C73—42no—
173C23×C73—42no—
174C23×C73—42no—
175C23×C73—41no—
176C23×C73#11714yes—
177C23×C73C23×C411yescharacteristic
178C23×C73C2×#4111yescharacteristic
179C23×C73C2×#4111yescharacteristic
180C23×C73H(5,𝔽2)12yes—
181C23×C73H(5,𝔽2)11yescharacteristic
182C23×C73H(5,𝔽2)11yescharacteristic
183C23×C73H(5,𝔽2)12yes—
184C23×C73H(5,𝔽2)12yes—
185C23×C732−1+411yescharacteristic
186C23×C732−1+411yescharacteristic
187C23×C732−1+412yes—
188C2×C4×C73—22no—
189C2×C4×C73—22no—
190C2×C4×C73—24no—
191C2×C4×C73—24no—
192C2×C4×C73—41no—
193C2×C4×C73—41no—
194C2×C4×C73—42no—
195C2×C4×C73—41no—
196C2×C4×C73—42no—
197C2×C4×C73—41no—
198C2×C4×C73—42no—
199C2×C4×C73—42no—
200C2×C4×C73—42no—
201C2×C4×C73—42no—
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—42no—
212C2×Dic73—24no—
213C2×Dic73—24no—
214C2×Dic73—24no—
215C2×Dic73—24no—
216C2×Dic73—24no—
217C2×Dic73—24no—
218C2×Dic73—416no—
219C2×Dic73—42no—
220C2×Dic73—42no—
221C2×Dic73—42no—
222C2×Dic73—42no—
223C2×Dic73—42no—
224C2×Dic73—42no—
225C2×Dic73—42no—
226C2×Dic73—42no—
227C2×Dic73—42no—
228C2×Dic73—42no—
229C2×Dic73—42no—
230C2×Dic73—42no—
231C2×Dic73—42no—
232C2×Dic73—42no—
233C2×Dic73—42no—
234C2×Dic73—42no—
235C2×Dic73—42no—
236C2×Dic73—42no—
237C2×Dic73—42no—
238C2×Dic73—42no—
239C2×Dic73—42no—
240C2×Dic73—42no—
241C22×C73—24no—
242C22×C73—28no—
243C22×C73—42no—
244C22×C73—42no—
245C22×C73—44no—
246C22×C73—44no—
247C22×C73—42no—
248C22×C73—42no—
249C22×C73—42no—
250C22×C73—42no—
251C22×C73—44no—
252C22×C73C2×#11711yescharacteristic
253C22×C73#51812yes—
254C22×C73#51811yescharacteristic
255C22×C73#51911yescharacteristic
256C22×C73#52012yes—
257C22×C73#53812yes—
258C22×C73#53812yes—
259C22×C73#53912yes—
260C22×C73#53911yescharacteristic
261C22×C73#53911yescharacteristic
262C22×C73#53911yescharacteristic
263C22×C73#53911yescharacteristic
264C22×C73#53912yes—
265C22×C73#56011yescharacteristic
266C22×C73#56012yes—
267C22×C73#56011yescharacteristic
268C22×C73H(3,𝔽4)11yescharacteristic
269C22×C73#56212yes—
270C22×C73#56212yes—
271C22×C73#56212yes—
272C22×C73#56312yes—
273C22×C73#56312yes—
274C22×C73#56311yescharacteristic
275C4×C73—42no—
276C4×C73—42no—
277C4×C73—82no—
278C4×C73—82no—
279Dic73—44no—
280Dic73—44no—
281Dic73—82no—
282Dic73—82no—
283#14669—731nomaximal, Sylow
284C2×C73—44no—
285C2×C73#231311yescharacteristic
286C2×C73#231812yes—
287C2×C73#237511yescharacteristic
288C2×C73#237611yescharacteristic
289C2×C73#237812yes—
290C2×C73#282411yescharacteristic
291C2×C73#282611yescharacteristic
292C2×C73#282712yes—
293C2×C73#282712yes—
294C2×C73#283411yescharacteristic
295C2×C73#283511yescharacteristic
296C2×#385—731no—
297#1445—732no—
298#1443—732no—
299#1442—732no—
300#1441—732no—
301#1440—732no—
302#1439—731no—
303#1439D7311yescharacteristic
304C22⋊#95—732no—
305C73#1466911yescharacteristic, complemented, Sylow
306C24×C4—731no—
307C22×C4⋊C4—731no—
308C22×C4⋊C4—732no—
309C22×C4⋊C4C2×D7311yescharacteristic
310C22×C22⋊C4—732no—
311C22×C22⋊C4—731no—
312C22×C22⋊C4C2×D7312yes—
313C22×C22⋊C4C2×D7311yescharacteristic
314#385—738no—
315C2×#95—732no—
316C2×#95—732no—
317C2×#95—732no—
318C2×#95—732no—
319C2×#95—732no—
320C2×#95—731no—
321C2×#95—732no—
322C2×#95—732no—
323C2×#95—732no—
324C2×#95—732no—
325C2×#95—732no—
326C2×#95C2×D7312yes—
327C2×#95C2×D7311yescharacteristic
328C25C22×D7311yescharacteristic
329C23×C4—2921no—
330C23×C4—2921no—
331C23×C4—2922no—
332C23×C4—2922no—
333C23×C4—734no—
334C23×C4—732no—
335C23×C4—732no—
336C23×C4—732no—
337C23×C4—732no—
338C23×C4C22×D7312yes—
339C23×C4C22×D7312yes—
340C23×C4C22×D7311yescharacteristic
341C23×C4C22×D7311yescharacteristic
342C2×C4⋊C4—42no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—2922no—
345C2×C4⋊C4—2922no—
346C2×C4⋊C4—2921no—
347C2×C4⋊C4—2922no—
348C2×C4⋊C4—738no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—2922no—
355C2×C22⋊C4—2922no—
356C2×C22⋊C4—734no—
357C2×C22⋊C4—1464no—
358C2×C22⋊C4—1462no—
359C2×C22⋊C4—1462no—
360C2×C22⋊C4C4×D7314yes—
361#95—41no—
362#95—42no—
363#95—2921no—
364#95—2922no—
365#95—2922no—
366#95—2922no—
367#95—2922no—
368#95—2922no—
369#95—2922no—
370#95—2922no—
371#95—2922no—
372#95—2922no—
373#95—738no—
374C24—22no—
375C24—22no—
376C24—21no—
377C24—21no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—21no—
382C24C2×C4×D7312yes—
383C24#1192402712yes—
384C24#1192402912yes—
385C24C23×D7311yescharacteristic
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—2924no—
409C22×C4—2928no—
410C22×C4—2924no—
411C22×C4—2928no—
412C22×C4—2924no—
413C22×C4—734no—
414C22×C4—734no—
415C22×C4—1462no—
416C22×C4—1462no—
417C22×C4—1462no—
418C22×C4—1462no—
419C22×C4—1462no—
420C22×C4—1462no—
421C22×C4—1462no—
422C22×C4—1462no—
423C22×C4—1462no—
424C22×C4—1462no—
425C22×C4—1462no—
426C22×C4—1462no—
427C22×C4—1462no—
428C22×C4—1462no—
429C22×C4—1462no—
430C22×C4—1462no—
431C22×C4—1462no—
432C22×C4—1462no—
433C22×C4—1462no—
434C22×C4—1462no—
435C22×C4—1462no—
436C22×C4—1462no—
437C22×C4—1462no—
438C22×C4—1462no—
439C22×C4—1462no—
440C22×C4—1462no—
441C22×C4C2×C4×D7312yes—
442C22×C4C2×C4×D7312yes—
443C4⋊C4—44no—
444C4⋊C4—2928no—
445C4⋊C4—2924no—
446C22⋊C4—44no—
447C22⋊C4—48no—
448C22⋊C4—2928no—
449C22⋊C4—1468no—
450C23—24no—
451C23—24no—
452C23—24no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—24no—
458C23—24no—
459C23—22no—
460C23—22no—
461C23—24no—
462C23—41no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—41no—
471C23—42no—
472C23#1455654914yes—
473C23C22×C4×D7311yescharacteristic
474C23C2×#1192402711yescharacteristic
475C23C2×#1192402911yescharacteristic
476C23#1455663612yes—
477C23#1455663612yes—
478C23#1455663611yescharacteristic
479C23#1455663611yescharacteristic
480C23#1455663712yes—
481C23#1455663812yes—
482C23#1455663811yescharacteristic
483C23#1455663811yescharacteristic
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—29216no—
509C2×C4—2922no—
510C2×C4—2922no—
511C2×C4—2922no—
512C2×C4—2922no—
513C2×C4—2922no—
514C2×C4—2922no—
515C2×C4—2922no—
516C2×C4—2922no—
517C2×C4—2922no—
518C2×C4—2922no—
519C2×C4—2922no—
520C2×C4—2922no—
521C2×C4—2922no—
522C2×C4—2922no—
523C2×C4—2922no—
524C2×C4—2922no—
525C2×C4—2922no—
526C2×C4—2922no—
527C2×C4—2922no—
528C2×C4—2922no—
529C2×C4—2922no—
530C2×C4—2922no—
531C2×C4—1464no—
532C2×C4—1464no—
533C2×C4—1464no—
534C2×C4—1464no—
535C2×C4—1464no—
536C2×C4—1464no—
537C22—24no—
538C22—28no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—42no—
545C22—42no—
546C22—44no—
547C22—44no—
548C22C2×#1455654911yescharacteristic
549C22#1798905912yes—
550C22#1798906011yescharacteristic
551C22#1798906411yescharacteristic
552C22#1798906612yes—
553C22#1798917212yes—
554C22#1798917712yes—
555C22#1798918112yes—
556C22#1798918211yescharacteristic
557C22#1798918211yescharacteristic
558C22#1798918611yescharacteristic
559C22#1798918612yes—
560C22#1798918611yescharacteristic
561C22#1798932411yescharacteristic
562C22#1798932512yes—
563C22#1798932611yescharacteristic
564C22#1798932911yescharacteristic
565C22#1798933112yes—
566C22#1798933212yes—
567C22#1798933212yes—
568C22#1798933912yes—
569C22#1798934011yescharacteristic
570C22#1798934012yes—
571C4—42no—
572C4—42no—
573C4—82no—
574C4—82no—
575C4—2924no—
576C4—2924no—
577C4—5842no—
578C4—5842no—
579C2—44no—
580C2#2261253311yescharacteristic
581C2#2261255912yes—
582C2#2261306811yescharacteristic
583C2#2261307411yescharacteristic
584C2#2261309812yes—
585C2#2261801511yescharacteristic
586C2#2261803011yescharacteristic
587C2#2261803912yes—
588C2#2261804512yes—
589C2#2261811711yescharacteristic
590C2#2261812111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1439C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenter#1439D73
hypocenterC73#14669
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #22608197C2semidirect
3. #22608191C2semidirect
4. #22608190C2semidirect
5. #22608185C2semidirect
15. #17988459C4semidirect
305. C73#14669semidirect

Maximal subgroups

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

subgroupindex
C2×#179884592
#226081972
#226081912
#226081902
#226081852
#226081782
#226081762
#226081532
C73×#14392
#1466973