Finite Group Databasebeta

← #34027600

Subgroups — #34027600

Order 18688.

876 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626054C212yesmaximal
2#22626007C212yesmaximal, complemented
3#22626004C212yesmaximal, complemented
4#22625847C211yesmaximal, characteristic, complemented
5#22625823C211yesmaximal, characteristic, complemented
6#22625822C211yesmaximal, characteristic, complemented
7#22625726C212yesmaximal, complemented
8C4×#14556658C211yesmaximal, characteristic, complemented
9#22625658C211yesmaximal, characteristic, complemented
10#22625657C211yesmaximal, characteristic, complemented
11C4×#14556551C211yesmaximal, characteristic
12C2×#14556658C2212yes—
13C2×#14556658C2212yes—
14C2×#14556648C2212yes—
15C2×#14556648C2212yes—
16C2×C22⋊#10596833C2212yes—
17C2×C22⋊#10596833C2212yes—
18C2×#14556646C2212yes—
19C2×#14556646C2212yes—
20C2×C4×#10596833C2212yes—
21#17989453C2211yescharacteristic
22#17989453C2211yescharacteristic
23#17989453C2212yes—
24#17989453C2211yescharacteristic
25#17989453C2212yes—
26#17989453C2212yes—
27#17989453C2211yescharacteristic
28C2×C4×C22⋊D73C411yescharacteristic
29C2×#14556551C411yescharacteristic
30C2×#14556551C2211yescharacteristic
31C22×C4×Dic73C2211yescharacteristic
32C2×C42×D73C2211yescharacteristic
33C4×#11924007C411yescharacteristic
34#17988438C411yescharacteristic
35#17988438C2211yescharacteristic
36C22⋊C4×Dic73C411yescharacteristic
37C22⋊C4×Dic73C2211yescharacteristic
38C4×#11924005C411yescharacteristic
39#17988434C411yescharacteristic
40#17988434C2211yescharacteristic
41C42×Dic73C2211yescharacteristic
42C4×C22⋊C4×C73C411yescharacteristic
43C22×#10596833C2312yes—
44C22×#10596833C2312yes—
45C22×#10596833C2312yes—
46C22×#10596833C2312yes—
47#14556658—24no—
48#14556658—24no—
49#14556648—24no—
50#14556648—42no—
51C22⋊#10596833—24no—
52C22⋊#10596833—42no—
53#14556646—42no—
54#14556646—42no—
55C4×#10596833—24no—
56C22×C22⋊D73C2×C411yescharacteristic
57C23×Dic73C2×C411yescharacteristic
58C23×Dic73C2311yescharacteristic
59C22×C4×D73C2×C411yescharacteristic
60C22×C4×D73C2×C411yescharacteristic
61C22×C4×D73C2311yescharacteristic
62C4×C22⋊D73—24no—
63#14556551—24no—
64#14556551—22no—
65#14556551—22no—
66C2×#11924007C2×C411yescharacteristic
67C2×#11924007C2×C411yescharacteristic
68C2×#11924007C2×C411yescharacteristic
69C2×C22⋊Dic73C2×C411yescharacteristic
70C2×#11924005C2×C411yescharacteristic
71C2×#11924005C2×C411yescharacteristic
72C2×#11924005C2×C411yescharacteristic
73C2×C4×Dic73—42no—
74C2×C4×Dic73C2×C411yescharacteristic
75C2×C4×Dic73C2×C411yescharacteristic
76C2×C4×Dic73C2×C411yescharacteristic
77C2×C4×Dic73C2×C411yescharacteristic
78C2×C4×Dic73C2×C411yescharacteristic
79C2×C4×Dic73C2×C411yescharacteristic
80C2×C4×Dic73C2311yescharacteristic
81C2×C4×Dic73C2311yescharacteristic
82C2×C4×Dic73C2311yescharacteristic
83C2×C4×Dic73C2311yescharacteristic
84C2×C4×Dic73C2311yescharacteristic
85C42×D73—42no—
86#14556498C2×C411yescharacteristic
87#14556498C2×C411yescharacteristic
88#14556498C2×C411yescharacteristic
89#14556498C2×C411yescharacteristic
90C23×C4×C73C2×C411yescharacteristic
91C2×C22⋊C4×C73C2×C411yescharacteristic
92C2×C22⋊C4×C73C2×C411yescharacteristic
93C2×C42×C73C2×C411yescharacteristic
94C2×C42×C73C2×C411yescharacteristic
95#95×C73C2×C411yescharacteristic
96#95×C73C2×C411yescharacteristic
97C2×#10596833—22no—
98C2×#10596833—22no—
99C2×#10596833—22no—
100C2×#10596833—22no—
101C2×#10596833—22no—
102C2×#10596833—22no—
103C2×#10596833—22no—
104C2×#10596833—22no—
105C2×#10596833—22no—
106C2×#10596833—22no—
107C2×#10596833—22no—
108C2×#10596833#4114yes—
109C23×D73C22×C411yescharacteristic
110C2×C22⋊D73—22no—
111C2×C22⋊D73—22no—
112C2×C22⋊D73M1614yes—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—21no—
116C22×Dic73—21no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—41no—
120C22×Dic73C22×C411yescharacteristic
121C22×Dic73C22×C411yescharacteristic
122C22×Dic73C22×C411yescharacteristic
123C22×Dic73C22×C411yescharacteristic
124C22×Dic73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C2411yescharacteristic
127C2×C4×D73—22no—
128C2×C4×D73—22no—
129C2×C4×D73—22no—
130C2×C4×D73—21no—
131C2×C4×D73—21no—
132C2×C4×D73—22no—
133C2×C4×D73—22no—
134C2×C4×D73—41no—
135C2×C4×D73—41no—
136C2×C4×D73—41no—
137#11924007—22no—
138#11924007—22no—
139#11924007—22no—
140C22⋊Dic73—22no—
141#11924005—22no—
142#11924005—22no—
143#11924005—22no—
144C4×Dic73—22no—
145C4×Dic73—22no—
146C4×Dic73—22no—
147C4×Dic73—22no—
148C4×Dic73—22no—
149C4×Dic73—22no—
150C4×Dic73—41no—
151C4×Dic73—41no—
152C4×Dic73—41no—
153C4×Dic73M1614yes—
154C4×Dic73#4112yes—
155C4×Dic73#4112yes—
156C24×C73C22×C411yescharacteristic
157C22×C4×C73—22no—
158C22×C4×C73—41no—
159C22×C4×C73—41no—
160C22×C4×C73C22×C411yescharacteristic
161C22×C4×C73C22×C411yescharacteristic
162C22×C4×C73C22×C411yescharacteristic
163C22×C4×C73C22×C411yescharacteristic
164C22×C4×C73C22×C411yescharacteristic
165C22×C4×C73C22×C411yescharacteristic
166C22⋊C4×C73—22no—
167C22⋊C4×C73—22no—
168C42×C73—41no—
169C42×C73—41no—
170C23×C73—21no—
171C23×C73—21no—
172C23×C73—21no—
173C23×C73—21no—
174C23×C73—21no—
175C23×C73—21no—
176C23×C73C2×M1612yes—
177C23×C73C23×C411yescharacteristic
178C22×D73—21no—
179C22×D73—21no—
180C22×D73—21no—
181C22×D73—21no—
182C22×D73—21no—
183C22×D73—21no—
184C22×D73C2×M1612yes—
185C2×C4×C73—21no—
186C2×C4×C73—21no—
187C2×C4×C73—21no—
188C2×C4×C73—21no—
189C2×C4×C73—21no—
190C2×C4×C73—21no—
191C2×C4×C73—21no—
192C2×C4×C73—21no—
193C2×C4×C73—21no—
194C2×C4×C73—21no—
195C2×C4×C73—21no—
196C2×C4×C73—21no—
197C2×C4×C73—21no—
198C2×C4×C73—21no—
199C2×C4×C73—21no—
200C2×C4×C73—21no—
201C2×C4×C73—44no—
202C2×C4×C73#11712yes—
203C2×C4×C73C2×M1612yes—
204C22⋊D73—28no—
205C2×Dic73—21no—
206C2×Dic73—21no—
207C2×Dic73—21no—
208C2×Dic73—21no—
209C2×Dic73—21no—
210C2×Dic73—21no—
211C2×Dic73—21no—
212C2×Dic73—21no—
213C2×Dic73—21no—
214C2×Dic73—21no—
215C2×Dic73—21no—
216C2×Dic73—21no—
217C2×Dic73—21no—
218C2×Dic73—44no—
219C2×Dic73—42no—
220C2×Dic73—42no—
221C2×Dic73#11712yes—
222C2×Dic73C2×M1612yes—
223C2×Dic73C2×M1612yes—
224C2×Dic73C2×M1612yes—
225C2×Dic73#13112yes—
226C2×Dic73C2×#4111yescharacteristic
227C2×Dic73C2×#4112yes—
228C2×Dic73C2×#4111yescharacteristic
229C2×Dic73H(5,𝔽2)12yes—
230C4×D73—44no—
231C4×D73—44no—
232C4×D73—42no—
233C4×D73—42no—
234#10596833—24no—
235#10596833—42no—
236#10596833—42no—
237#10596833—42no—
238C22×C73—22no—
239C22×C73—22no—
240C22×C73—22no—
241C22×C73—41no—
242C22×C73—41no—
243C22×C73—41no—
244C22×C73—41no—
245C22×C73C2×#11711yescharacteristic
246C22×C73C4×#4111yescharacteristic
247C22×C73#51811yescharacteristic
248C22×C73C22×M1611yescharacteristic
249C22×C73C22×M1611yescharacteristic
250C22×C73C2×#13111yescharacteristic
251C22×C73#56811yescharacteristic
252C2×D73—22no—
253C2×D73—22no—
254C2×D73—22no—
255C2×D73—41no—
256C2×D73—41no—
257C2×D73—41no—
258C2×D73—41no—
259C4×C73—22no—
260C4×C73—22no—
261C4×C73—41no—
262C4×C73—41no—
263C4×C73—41no—
264C4×C73—41no—
265Dic73—22no—
266Dic73—22no—
267Dic73—41no—
268Dic73—41no—
269Dic73—41no—
270Dic73#43214yes—
271Dic73#55312yes—
272Dic73#55912yes—
273#22839—731nomaximal, Sylow
274C2×C73—42no—
275C2×C73#235711yescharacteristic
276C2×C73C2×#43211yescharacteristic
277C2×C73#292511yescharacteristic
278C2×C73#296511yescharacteristic
279C2×C73#297011yescharacteristic
280C2×C73#297411yescharacteristic
281C2×C73#297511yescharacteristic
282D73—42no—
283C42×D4—731no—
284#1954—732no—
285#1924—732no—
286#1924—732no—
287#1831—731no—
288#1817—731no—
289#1817—731no—
290#1770—732no—
291C4×C4⋊C8—731no—
292#1749—731no—
293#1749—731no—
294C73#2283911yescharacteristic, complemented, Sylow
295C2×C4×D4—731no—
296C2×C4×D4—731no—
297C2×C4×D4—731no—
298C22×C42—731no—
299C22×C42—731no—
300C2×C4⋊C8—732no—
301C2×C4⋊C8—732no—
302C2×C22⋊C8—732no—
303C2×C22⋊C8—732no—
304C2×C22⋊C8—732no—
305C2×C22⋊C8—732no—
306C2×#97—732no—
307C2×#97—732no—
308C2×C4×C8—732no—
309C4×C4⋊C4—731no—
310C4×C4⋊C4—731no—
311C4×C4⋊C4—731no—
312C4×C22⋊C4—731no—
313C4×C22⋊C4—731no—
314C4×C22⋊C4—731no—
315C4×C22⋊C4—731no—
316C4×C22⋊C4—731no—
317C4×C22⋊C4#6440811yescharacteristic
318C43—731no—
319#336—731no—
320#336—731no—
321#336—731no—
322#336—732no—
323#336—732no—
324#336—732no—
325#336—731no—
326C22×D4—731no—
327C23×C4—731no—
328C23×C4—731no—
329C23×C4—731no—
330C23×C4—731no—
331C23×C4—731no—
332C23×C4C2×#6440811yescharacteristic
333C22×C8—732no—
334C22×C8—732no—
335C22×C8—732no—
336C22×C8—732no—
337C4×D4—1462no—
338C4×D4—1462no—
339C4×D4—1464no—
340C4×D4—1464no—
341C2×C4⋊C4—731no—
342C2×C4⋊C4—731no—
343C2×C4⋊C4—731no—
344C2×C22⋊C4—731no—
345C2×C22⋊C4—731no—
346C2×C22⋊C4—731no—
347C2×C22⋊C4—731no—
348C2×C22⋊C4C2×#6440811yescharacteristic
349C2×C22⋊C4C2×#6440811yescharacteristic
350C2×C42—2922no—
351C2×C42—2922no—
352C2×C42—731no—
353C2×C42—731no—
354C2×C42—731no—
355C2×C42—731no—
356C2×C42—731no—
357C2×C42—731no—
358C2×C42—731no—
359C2×C42—731no—
360C2×C42—731no—
361C2×C42—731no—
362C2×C42—731no—
363C2×C42C2×#6440811yescharacteristic
364C2×C42C2×#6440811yescharacteristic
365C4⋊C8—1464no—
366C4⋊C8—1464no—
367C22⋊C8—2922no—
368C22⋊C8—2922no—
369C22⋊C8—1464no—
370C22⋊C8—1464no—
371#97—2922no—
372#97—2922no—
373C4×C8—1464no—
374#95—731no—
375#95—731no—
376#95—731no—
377#95—731no—
378#95C2×#6440811yescharacteristic
379#95C2×#6440811yescharacteristic
380C24—731no—
381C24C22×#6440811yescharacteristic
382C2×D4—734no—
383C2×D4—1462no—
384C2×D4—1462no—
385C22×C4—22no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—2921no—
389C22×C4—2921no—
390C22×C4—2921no—
391C22×C4—2921no—
392C22×C4—731no—
393C22×C4—731no—
394C22×C4—731no—
395C22×C4—731no—
396C22×C4—731no—
397C22×C4—731no—
398C22×C4—731no—
399C22×C4—1462no—
400C22×C4—1462no—
401C22×C4—1461no—
402C22×C4—1461no—
403C22×C4—1462no—
404C22×C4—1462no—
405C22×C4—1462no—
406C22×C4—1462no—
407C22×C4—1461no—
408C22×C4—1461no—
409C22×C4—1462no—
410C22×C4—1462no—
411C22×C4—1462no—
412C22×C4C22×#6440811yescharacteristic
413C22×C4C22×#6440811yescharacteristic
414C22×C4C22×#6440811yescharacteristic
415C22×C4C22×#6440811yescharacteristic
416C22×C4C22×#6440811yescharacteristic
417C22×C4C22×#6440811yescharacteristic
418C2×C8—734no—
419C2×C8—1462no—
420C2×C8—1462no—
421C2×C8—1462no—
422C2×C8—1462no—
423C2×C8—1462no—
424C2×C8—1462no—
425C2×C8—1462no—
426C2×C8—1462no—
427C2×C8—1462no—
428C2×C8—1462no—
429C2×C8—1462no—
430C4⋊C4—1462no—
431C4⋊C4—1462no—
432C4⋊C4—1462no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—1462no—
436C22⋊C4—1462no—
437C22⋊C4—1462no—
438C22⋊C4—1462no—
439C42—41no—
440C42—41no—
441C42—2921no—
442C42—2921no—
443C42—2921no—
444C42—734no—
445C42—732no—
446C42—732no—
447C42—1462no—
448C42—1462no—
449C42—1462no—
450C42—1462no—
451C42—1462no—
452C42—1462no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—732no—
460C23—1461no—
461C23—1461no—
462C23—1461no—
463C23—1461no—
464C23—1461no—
465C23—1461no—
466C23D73⋊M1612yes—
467C23C23×#6440811yescharacteristic
468D4—1468no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—44no—
486C2×C4—2924no—
487C2×C4—2922no—
488C2×C4—2922no—
489C2×C4—2924no—
490C2×C4—2922no—
491C2×C4—2922no—
492C2×C4—2924no—
493C2×C4—732no—
494C2×C4—731no—
495C2×C4—731no—
496C2×C4—732no—
497C2×C4—732no—
498C2×C4—732no—
499C2×C4—732no—
500C2×C4—732no—
501C2×C4—732no—
502C2×C4—1461no—
503C2×C4—1461no—
504C2×C4—1461no—
505C2×C4—1461no—
506C2×C4—1461no—
507C2×C4—1461no—
508C2×C4—1461no—
509C2×C4—1461no—
510C2×C4—1461no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4#1455667012yes—
516C2×C4D73⋊M1612yes—
517C8—2922no—
518C8—2922no—
519C8—2922no—
520C8—1464no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—2921no—
529C22—2921no—
530C22—2921no—
531C22—2921no—
532C22—1462no—
533C22—1462no—
534C22—1462no—
535C22C2×#1455667011yescharacteristic
536C22#41×#6440811yescharacteristic
537C22#1798965411yescharacteristic
538C22C2×D73⋊M1611yescharacteristic
539C22C2×D73⋊M1611yescharacteristic
540C22D73⋊#13111yescharacteristic
541C22#1798966511yescharacteristic
542C4—22no—
543C4—22no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—2921no—
549C4—2921no—
550C4—2921no—
551C4—734no—
552C4—732no—
553C4—732no—
554C4—1462no—
555C4—1462no—
556C2—42no—
557C2—2922no—
558C2#2262645211yescharacteristic
559C2D73⋊#43211yescharacteristic
560C2#2262662911yescharacteristic
561C2#2262674211yescharacteristic
562C2#2262677111yescharacteristic
563C2#2262678811yescharacteristic
564C2#2262679511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
FittingC4×C22⋊C4×C73C4
prime radicalC22×C22⋊D73C2×C4
cosocleC22×Dic73C24
hypercenterC4×C22⋊C4#64408
hypocenterC73#22839
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #22626007C2semidirect
3. #22626004C2semidirect
4. #22625847C2semidirect
5. #22625823C2semidirect
6. #22625822C2semidirect
7. #22625726C2semidirect
8. C4×#14556658C2semidirect
9. #22625658C2semidirect
10. #22625657C2semidirect
294. C73#22839semidirect

Maximal subgroups

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

subgroupindex
#226260542
#226260072
#226260042
#226258472
#226258232
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