Finite Group Databasebeta

← #33055199

Subgroups — #33055199

Order 18688.

572 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619048C211yesmaximal, characteristic
2#22618575C211yesmaximal, characteristic
3#22608722C211yesmaximal, characteristic, complemented
4#22608719C211yesmaximal, characteristic, complemented
5#22608717C211yesmaximal, characteristic, complemented
6#22608714C211yesmaximal, characteristic, complemented
7#22608712C211yesmaximal, characteristic, complemented
8#22608709C211yesmaximal, characteristic, complemented
9#22608707C211yesmaximal, characteristic, complemented
10#22608705C211yesmaximal, characteristic, complemented
11#22608699C211yesmaximal, characteristic, complemented
12#22608696C211yesmaximal, characteristic, complemented
13#22608692C211yesmaximal, characteristic, complemented
14#22608689C211yesmaximal, characteristic, complemented
15C73×#2989C211yesmaximal, characteristic
16#17988718—21no—
17#17988665—21no—
18#17988659—21no—
19#17988659—21no—
20#17988648C412yes—
21#17988648C412yes—
22#17988644C2211yescharacteristic
23#17988644C2211yescharacteristic
24#17988640C2211yescharacteristic
25#17988640C2211yescharacteristic
26#17988640C2211yescharacteristic
27#17988640C2211yescharacteristic
28#17988640C2211yescharacteristic
29#17988614C412yes—
30#17988611C2211yescharacteristic
31#17988611C2211yescharacteristic
32C2×C4⋊#10596831C2211yescharacteristic
33#17988554C412yes—
34C4×#11924012C2211yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36#17988339C2211yescharacteristic
37#17988339C2211yescharacteristic
38#17988339C2211yescharacteristic
39#17988339C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988339C2211yescharacteristic
43#17988339C2211yescharacteristic
44#17988339C2211yescharacteristic
45#17988339C2211yescharacteristic
46#17988337C2211yescharacteristic
47#17988337C2211yescharacteristic
48#17988337C2211yescharacteristic
49#17988337C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52C4×#41×C73C2211yescharacteristic
53#446×C73—21no—
54#436×C73—21no—
55#435×C73—21no—
56#435×C73—21no—
57#432×C73C2211yescharacteristic
58#432×C73C2211yescharacteristic
59#431×C73C2211yescharacteristic
60#423×C73C2211yescharacteristic
61#423×C73C2211yescharacteristic
62C2×C4⋊C8×C73C2211yescharacteristic
63C2×#11924012—21no—
64C2×#11924012—21no—
65C2×#11924012C2×C412yes—
66C22×#10596831—21no—
67C22×#10596831C2×C412yes—
68C4⋊#10596831—21no—
69C4⋊#10596831—21no—
70C4⋊#10596831—21no—
71C4⋊#10596831C2×C412yes—
72C4⋊#10596831C2×C412yes—
73C4⋊#10596831C2×C412yes—
74C4⋊#10596831C2×C412yes—
75C4⋊#10596831C2311yescharacteristic
76C4⋊#10596831C2311yescharacteristic
77C4⋊#10596831C2311yescharacteristic
78C4⋊#10596831C2311yescharacteristic
79C22⋊#10596831—21no—
80C22⋊#10596831—21no—
81C22⋊#10596831—21no—
82C22⋊#10596831C2×C412yes—
83C22⋊#10596831C2×C412yes—
84C22⋊#10596831C2×C412yes—
85C22⋊#10596831C2×C412yes—
86#14556502—21no—
87#14556502—21no—
88#14556502C2×C412yes—
89C4×#10596831—21no—
90C4×#10596831C2×C412yes—
91C4×#10596831C2311yescharacteristic
92C4×#10596831C2311yescharacteristic
93C4×#10596831C2311yescharacteristic
94C4×#10596831C2311yescharacteristic
95C2×#41×C73C2×C411yescharacteristic
96C2×M16×C73—21no—
97C2×M16×C73—21no—
98C22×C8×C73—21no—
99C4×Q8×C73D411yescharacteristic
100C4×Q8×C73Q811yescharacteristic
101C4×D4×C73D411yescharacteristic
102C4×D4×C73D411yescharacteristic
103C4×D4×C73D411yescharacteristic
104C4×D4×C73Q811yescharacteristic
105C4×D4×C73Q811yescharacteristic
106C4×D4×C73Q811yescharacteristic
107#117×C73C2×C411yescharacteristic
108#117×C73C2×C411yescharacteristic
109#117×C73C2×C411yescharacteristic
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C4⋊C8×C73—21no—
114C4⋊C8×C73—21no—
115C4⋊C8×C73—21no—
116C4⋊C8×C73C2311yescharacteristic
117C4⋊C8×C73C2311yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2311yescharacteristic
120C22⋊C8×C73—21no—
121C22⋊C8×C73—21no—
122C22⋊C8×C73—21no—
123#97×C73—21no—
124#97×C73—21no—
125C4×C8×C73—21no—
126#11924012—42no—
127#11924012—81no—
128#11924012—81no—
129C2×#10596831—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—42no—
134C2×#10596831—81no—
135C2×#10596831C22×C412yes—
136C2×#10596831C22×C412yes—
137C2×#10596831C22×C412yes—
138C2×#10596831C22×C412yes—
139#41×C73—42no—
140C2×Q8×C73C4⋊C411yescharacteristic
141C2×D4×C73C4⋊C411yescharacteristic
142C2×D4×C73C4⋊C411yescharacteristic
143C2×D4×C73C4⋊C411yescharacteristic
144C22×C4×C73C22×C411yescharacteristic
145C22×C4×C73C22×C411yescharacteristic
146C22×C4×C73C22×C411yescharacteristic
147C22×C4×C73C2×D411yescharacteristic
148C22×C4×C73C2×D411yescharacteristic
149C22×C4×C73C2×D411yescharacteristic
150C22×C4×C73C2×Q811yescharacteristic
151C22×C4×C73C2×Q811yescharacteristic
152C22×C4×C73C2×Q811yescharacteristic
153M16×C73—81no—
154M16×C73—81no—
155C2×C8×C73—21no—
156C2×C8×C73—21no—
157C2×C8×C73—21no—
158C2×C8×C73—21no—
159C2×C8×C73—81no—
160C4⋊C4×C73C4⋊C411yescharacteristic
161C4⋊C4×C73C4⋊C411yescharacteristic
162C4⋊C4×C73C4⋊C411yescharacteristic
163C4⋊C4×C73C4⋊C411yescharacteristic
164C4⋊C4×C73C4⋊C411yescharacteristic
165C4⋊C4×C73C4⋊C411yescharacteristic
166C22⋊C4×C73C4⋊C411yescharacteristic
167C22⋊C4×C73C4⋊C411yescharacteristic
168C22⋊C4×C73C4⋊C411yescharacteristic
169C22⋊C4×C73C4⋊C411yescharacteristic
170C22⋊C4×C73C4⋊C411yescharacteristic
171C22⋊C4×C73C4⋊C411yescharacteristic
172C42×C73C22×C411yescharacteristic
173C42×C73C22×C411yescharacteristic
174C42×C73C22×C411yescharacteristic
175C42×C73C2×D411yescharacteristic
176C42×C73C2×D411yescharacteristic
177C42×C73C2×D411yescharacteristic
178C42×C73C2×Q811yescharacteristic
179C42×C73C2×Q811yescharacteristic
180C42×C73C2×Q811yescharacteristic
181C42×C73C2411yescharacteristic
182C23×C73C2×C4⋊C411yescharacteristic
183C23×C73C2×C4⋊C411yescharacteristic
184C23×C73C2×C4⋊C411yescharacteristic
185Q8×C73—41no—
186D4×C73—41no—
187D4×C73—41no—
188D4×C73—41no—
189C2×C4×C73—22no—
190C2×C4×C73—22no—
191C2×C4×C73—22no—
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—41no—
199C2×C4×C73—41no—
200C2×C4×C73—41no—
201C2×C4×C73C2×C4⋊C411yescharacteristic
202C2×C4×C73C2×C4⋊C411yescharacteristic
203C2×C4×C73C2×C4⋊C411yescharacteristic
204C2×C4×C73C2×C4⋊C411yescharacteristic
205C2×C4×C73C2×C4⋊C411yescharacteristic
206C2×C4×C73C2×C4⋊C411yescharacteristic
207C2×C4×C73C2×C4⋊C411yescharacteristic
208C2×C4×C73C2×C4⋊C411yescharacteristic
209C2×C4×C73C2×C4⋊C411yescharacteristic
210C2×C4×C73C23×C411yescharacteristic
211C2×C4×C73C22×D411yescharacteristic
212C2×C4×C73C22×Q811yescharacteristic
213C8×C73—41no—
214C8×C73—41no—
215C8×C73—41no—
216C8×C73—41no—
217#10596831—22no—
218#10596831—22no—
219#10596831—22no—
220#10596831—22no—
221#10596831—41no—
222#10596831—41no—
223#10596831—41no—
224#10596831—41no—
225C22×C73—21no—
226C22×C73—21no—
227C22×C73—21no—
228C22×C73—21no—
229C22×C73—21no—
230C22×C73—21no—
231C22×C73—21no—
232C22×C73—21no—
233C22×C73—21no—
234C22×C73C22×C4⋊C411yescharacteristic
235C4×C73—21no—
236C4×C73—21no—
237C4×C73—21no—
238C4×C73—21no—
239C4×C73—21no—
240C4×C73—21no—
241C4×C73—21no—
242C4×C73—21no—
243C4×C73—21no—
244C4×C73—21no—
245C4×C73#56812yes—
246C4×C73#57611yescharacteristic
247C4×C73#57811yescharacteristic
248#17825—731nomaximal, Sylow
249C2×C73—41no—
250C2×C73—41no—
251C2×C73—41no—
252C2×C73#290511yescharacteristic
253C2×C73#291311yescharacteristic
254C2×C73#291611yescharacteristic
255#2989—731no—
256#2989D7311yescharacteristic
257#2922—731no—
258#1574—731no—
259#1574—731no—
260#1573—731no—
261#1573—731no—
262#1572—731no—
263#1572—731no—
264#1571—731no—
265#1571—731no—
266#1569—731no—
267#1569—731no—
268#1568—731no—
269#1567—731no—
270C73#1782511yescharacteristic, complemented, Sylow
271C4×#41C2×D7311yescharacteristic
272#446—21no—
273#446—1461no—
274#436—21no—
275#436—1461no—
276#435—21no—
277#435—21no—
278#435—1461no—
279#435—1461no—
280#433—732no—
281#433—732no—
282#432—731no—
283#432—731no—
284#432C2×D7311yescharacteristic
285#432C2×D7311yescharacteristic
286#431—731no—
287#431—731no—
288#431—731no—
289#431—731no—
290#431—731no—
291#431C2×D7311yescharacteristic
292#424—732no—
293#423—731no—
294#423—731no—
295#423C2×D7311yescharacteristic
296#423C2×D7311yescharacteristic
297C2×C4⋊C8—731no—
298C2×C4⋊C8C2×D7311yescharacteristic
299#408—732no—
300C4×M16—731no—
301C2×C4×C8—731no—
302#335—731no—
303#335—731no—
304#335—731no—
305#335—731no—
306#335—731no—
307#335—731no—
308#335—731no—
309#335—731no—
310#335—731no—
311#335—731no—
312#334—731no—
313#334—731no—
314#334—731no—
315#334—731no—
316#334—731no—
317#334—731no—
318C2×#41C4×D7311yescharacteristic
319C2×M16—21no—
320C2×M16—21no—
321C2×M16—732no—
322C2×M16—1461no—
323C2×M16—1461no—
324C22×C8—21no—
325C22×C8—732no—
326C22×C8—1461no—
327C4×Q8Dic14611yescharacteristic
328C4×Q8C22⋊D7311yescharacteristic
329C4×D4Dic14611yescharacteristic
330C4×D4Dic14611yescharacteristic
331C4×D4Dic14611yescharacteristic
332C4×D4C22⋊D7311yescharacteristic
333C4×D4C22⋊D7311yescharacteristic
334C4×D4C22⋊D7311yescharacteristic
335#117C4×D7311yescharacteristic
336#117C4×D7311yescharacteristic
337#117C4×D7311yescharacteristic
338C2×C42C22×D7311yescharacteristic
339C2×C42C22×D7311yescharacteristic
340C2×C42C22×D7311yescharacteristic
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8—732no—
345C4⋊C8—732no—
346C4⋊C8—732no—
347C4⋊C8—732no—
348C4⋊C8—731no—
349C4⋊C8—731no—
350C4⋊C8—731no—
351C4⋊C8—731no—
352C4⋊C8—1461no—
353C4⋊C8—1461no—
354C4⋊C8—1461no—
355C4⋊C8C22×D7311yescharacteristic
356C4⋊C8C22×D7311yescharacteristic
357C4⋊C8C22×D7311yescharacteristic
358C4⋊C8C22×D7311yescharacteristic
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—732no—
363C22⋊C8—732no—
364C22⋊C8—732no—
365C22⋊C8—732no—
366C22⋊C8—1461no—
367C22⋊C8—1461no—
368C22⋊C8—1461no—
369#97—21no—
370#97—21no—
371#97—732no—
372#97—1461no—
373#97—1461no—
374C4×C8—21no—
375C4×C8—732no—
376C4×C8—731no—
377C4×C8—731no—
378C4×C8—731no—
379C4×C8—731no—
380C4×C8—1461no—
381#41—42no—
382C2×Q8#1192400711yescharacteristic
383C2×D4#1192400711yescharacteristic
384C2×D4#1192400711yescharacteristic
385C2×D4#1192400711yescharacteristic
386C22×C4C2×C4×D7311yescharacteristic
387C22×C4C2×C4×D7311yescharacteristic
388C22×C4C2×C4×D7311yescharacteristic
389C22×C4C2×C22⋊D7311yescharacteristic
390C22×C4C2×C22⋊D7311yescharacteristic
391C22×C4C2×C22⋊D7311yescharacteristic
392C22×C4C2×Dic14611yescharacteristic
393C22×C4C2×Dic14611yescharacteristic
394C22×C4C2×Dic14611yescharacteristic
395M16—81no—
396M16—81no—
397M16—2922no—
398M16—5841no—
399M16—5841no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—81no—
405C2×C8—2922no—
406C2×C8—5841no—
407C2×C8—732no—
408C2×C8—732no—
409C2×C8—732no—
410C2×C8—732no—
411C2×C8—1461no—
412C2×C8—1461no—
413C2×C8—1461no—
414C2×C8—1461no—
415C4⋊C4#1192400711yescharacteristic
416C4⋊C4#1192400711yescharacteristic
417C4⋊C4#1192400711yescharacteristic
418C4⋊C4#1192400711yescharacteristic
419C4⋊C4#1192400711yescharacteristic
420C4⋊C4#1192400711yescharacteristic
421C22⋊C4#1192400711yescharacteristic
422C22⋊C4#1192400711yescharacteristic
423C22⋊C4#1192400711yescharacteristic
424C22⋊C4#1192400711yescharacteristic
425C22⋊C4#1192400711yescharacteristic
426C22⋊C4#1192400711yescharacteristic
427C42C2×C4×D7311yescharacteristic
428C42C2×C4×D7311yescharacteristic
429C42C2×C4×D7311yescharacteristic
430C42C2×C22⋊D7311yescharacteristic
431C42C2×C22⋊D7311yescharacteristic
432C42C2×C22⋊D7311yescharacteristic
433C42C2×Dic14611yescharacteristic
434C42C2×Dic14611yescharacteristic
435C42C2×Dic14611yescharacteristic
436C42C23×D7311yescharacteristic
437C23C2×#1192400711yescharacteristic
438C23C2×#1192400711yescharacteristic
439C23C2×#1192400711yescharacteristic
440Q8—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4C2×#1192400711yescharacteristic
457C2×C4C2×#1192400711yescharacteristic
458C2×C4C2×#1192400711yescharacteristic
459C2×C4C2×#1192400711yescharacteristic
460C2×C4C2×#1192400711yescharacteristic
461C2×C4C2×#1192400711yescharacteristic
462C2×C4C2×#1192400711yescharacteristic
463C2×C4C2×#1192400711yescharacteristic
464C2×C4C2×#1192400711yescharacteristic
465C2×C4C22×C4×D7311yescharacteristic
466C2×C4C22×C22⋊D7311yescharacteristic
467C2×C4C22×Dic14611yescharacteristic
468C8—41no—
469C8—41no—
470C8—41no—
471C8—41no—
472C8—2921no—
473C8—2921no—
474C8—2921no—
475C8—2921no—
476C8—1462no—
477C8—1462no—
478C8—1462no—
479C8—1462no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22C22×#1192400711yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4#1798935312yes—
501C4#1798939011yescharacteristic
502C4#1798940211yescharacteristic
503C2—41no—
504C2—41no—
505C2—41no—
506C2#2261849411yescharacteristic
507C2#2261852911yescharacteristic
508C2#2261854011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2989C2
socleC22×C73C22×C4⋊C4
prime radicalC2×#41×C73C2×C4
cosocleC42×C73C24
hypercenter#2989D73
hypocenterC73#17825
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
3. #22608722C2semidirect
4. #22608719C2semidirect
5. #22608717C2semidirect
6. #22608714C2semidirect
7. #22608712C2semidirect
8. #22608709C2semidirect
9. #22608707C2semidirect
10. #22608705C2semidirect
11. #22608699C2semidirect
12. #22608696C2semidirect
13. #22608692C2semidirect
14. #22608689C2semidirect
270. C73#17825semidirect

Maximal subgroups

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

subgroupindex
#226190482
#226185752
#226087222
#226087192
#226087172
#226087142
#226087122
#226087092
#226087072
#226087052
#226086992
#226086962
#226086922
#226086892
C73×#29892
#1782573