Finite Group Databasebeta

← #33057129

Subgroups — #33057129

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620003C211yesmaximal, characteristic
2#22618949C211yesmaximal, characteristic
3#22618878C211yesmaximal, characteristic, complemented
4#22608835C211yesmaximal, characteristic, complemented
5#22608823C211yesmaximal, characteristic, complemented
6#22608811C211yesmaximal, characteristic, complemented
7#22608804C211yesmaximal, characteristic, complemented
8#22608783C211yesmaximal, characteristic, complemented
9#22608776C211yesmaximal, characteristic, complemented
10#22608751C211yesmaximal, characteristic, complemented
11C8×Dic292C211yesmaximal, characteristic, complemented
12#22608716C211yesmaximal, characteristic, complemented
13#22608405C211yesmaximal, characteristic, complemented
14#22608319C211yesmaximal, characteristic
15C73×#1453C211yesmaximal, characteristic, complemented
16#17989144C2211yescharacteristic
17C4×#11924028C2211yescharacteristic
18#17988929C411yescharacteristic
19#17988929C411yescharacteristic
20#17988873C411yescharacteristic
21#17988868C411yescharacteristic
22#17988798C411yescharacteristic
23#17988793C411yescharacteristic
24#17988751C411yescharacteristic
25#17988751C411yescharacteristic
26#17988717C2211yescharacteristic
27#17988717C2211yescharacteristic
28#17988715—21no—
29#17988715—21no—
30C8×Dic146C2211yescharacteristic
31C8×Dic146C2211yescharacteristic
32C8×Dic146C2211yescharacteristic
33C8×Dic146C2211yescharacteristic
34C4×Dic292C2211yescharacteristic
35C4×Dic292C2211yescharacteristic
36C4×#11924017C2211yescharacteristic
37C4×#11924017C2211yescharacteristic
38#17988666C2211yescharacteristic
39#17988666C2211yescharacteristic
40#17988663—21no—
41#17988663—21no—
42#17988644C2211yescharacteristic
43#17988642—21no—
44#17988615—21no—
45C2×C4⋊#10596831C2211yescharacteristic
46#17988545—21no—
47#17988539—21no—
48#17988340C2211yescharacteristic
49#17988340C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988338C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988319C2211yescharacteristic
55#17988319C2211yescharacteristic
56#17988319C2211yescharacteristic
57#17988319C2211yescharacteristic
58#17988316C2211yescharacteristic
59#17988316C2211yescharacteristic
60#431×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62C4×M16×C73C2211yescharacteristic
63#322×C73C2211yescharacteristic
64#322×C73C2211yescharacteristic
65#322×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×Dic292C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×#11924017C2×C411yescharacteristic
72C2×#11924011—21no—
73C2×#11924011—21no—
74C22×#10596831—21no—
75#14556591C2×C411yescharacteristic
76#14556591C2×C411yescharacteristic
77#14556583—21no—
78#14556570—21no—
79#14556570C2×C411yescharacteristic
80#14556570C2×C411yescharacteristic
81C4×Dic146—21no—
82C4×Dic146C2×C411yescharacteristic
83C4×Dic146C2311yescharacteristic
84C4×Dic146C2311yescharacteristic
85C4×Dic146C2311yescharacteristic
86C4×D292C2×C411yescharacteristic
87C4×D292C2311yescharacteristic
88C4×C22⋊D73—21no—
89C4×C22⋊D73—21no—
90#14556550—21no—
91#14556550C2×C411yescharacteristic
92#14556548—21no—
93C42×D73—21no—
94#14556525C2×C411yescharacteristic
95#14556525C2×C411yescharacteristic
96#14556523C2×C411yescharacteristic
97#14556523C2×C411yescharacteristic
98C4⋊#10596831—21no—
99C4⋊#10596831C2311yescharacteristic
100C4⋊#10596831C2311yescharacteristic
101C4⋊#10596831C2311yescharacteristic
102C4⋊#10596831C2311yescharacteristic
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556520—21no—
108#14556520—21no—
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556516C2×C411yescharacteristic
112#14556516C2×C411yescharacteristic
113#14556516C2×C411yescharacteristic
114#14556516C2×C411yescharacteristic
115#14556513C2×C411yescharacteristic
116#14556513C2×C411yescharacteristic
117C22⋊#10596831—21no—
118#14556503—21no—
119#14556503—21no—
120#14556502—21no—
121#14556501—21no—
122#14556501—21no—
123C8×Dic73—21no—
124C8×Dic73—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C2×M16×C73D411yescharacteristic
128C2×M16×C73D411yescharacteristic
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73—21no—
131C4⋊C8×C73C2×C411yescharacteristic
132C4⋊C8×C73C2×C411yescharacteristic
133C22⋊C8×C73—21no—
134C22⋊C8×C73C2×C411yescharacteristic
135C22⋊C8×C73C2×C411yescharacteristic
136#97×C73D411yescharacteristic
137#97×C73D411yescharacteristic
138C4×C8×C73C2311yescharacteristic
139C4×C8×C73C2311yescharacteristic
140C4×C8×C73C2311yescharacteristic
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—41no—
146C2×Dic146—21no—
147C2×Dic146C22×C411yescharacteristic
148C2×Dic146C22×C411yescharacteristic
149C2×Dic146C22×C411yescharacteristic
150C2×D292C22×C411yescharacteristic
151C2×C22⋊D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155Dic292—22no—
156Dic292—22no—
157#11924017—41no—
158#11924017—41no—
159#11924011—42no—
160#11924011—42no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—42no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73C22×C411yescharacteristic
170C4⋊Dic73C22×C411yescharacteristic
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173#11924007—21no—
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179C22⋊Dic73—21no—
180C22⋊Dic73—21no—
181C22⋊Dic73—21no—
182#11924005—21no—
183#11924005—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73#4111yescharacteristic
192M16×C73—22no—
193M16×C73—41no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73C22×C411yescharacteristic
197C2×C8×C73C22×C411yescharacteristic
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C2×C8×C73C2×D411yescharacteristic
204C42×C73C22×C411yescharacteristic
205C42×C73C2×D411yescharacteristic
206C42×C73#4111yescharacteristic
207C42×C73C2411yescharacteristic
208C23×C73C4×D411yescharacteristic
209C22×D73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—41no—
215C2×C4×C73C4×D411yescharacteristic
216C2×C4×C73C4×D411yescharacteristic
217C2×C4×C73C4×D411yescharacteristic
218C2×C4×C73C23×C411yescharacteristic
219C2×C4×C73C22×D411yescharacteristic
220C2×C4×C73C2×#4111yescharacteristic
221C22⋊D73—42no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229D292—21no—
230D292—21no—
231C4×D73—42no—
232C4×D73—41no—
233C4×D73—41no—
234C4×D73—81no—
235Dic146—21no—
236Dic146—21no—
237Dic146—21no—
238Dic146—21no—
239Dic146—21no—
240Dic146—81no—
241Dic146#13112yes—
242C8×C73—21no—
243C8×C73—21no—
244C8×C73—21no—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73#13712yes—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255#10596831—41no—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73C2×C4×D411yescharacteristic
260C2×D73—41no—
261C2×D73—41no—
262C2×D73—41no—
263C4×C73—21no—
264C4×C73—21no—
265C4×C73—21no—
266C4×C73—21no—
267C4×C73C2×#13111yescharacteristic
268C4×C73#56811yescharacteristic
269C4×C73C2×#13711yescharacteristic
270C4×C73#57511yescharacteristic
271Dic73—22no—
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276Dic73—41no—
277Dic73—41no—
278#18013—731nomaximal, Sylow
279C2×C73—41no—
280C2×C73#293311yescharacteristic
281C2×C73C4×#13711yescharacteristic
282C2×C73#295711yescharacteristic
283D73—81no—
284#3107—731no—
285#2971—731no—
286#2962—731no—
287#1592—731no—
288#1590—731no—
289#1588—731no—
290#1587—731no—
291#1584—731no—
292#1583—731no—
293#1579—731no—
294C8×Q16—731no—
295#1573—731no—
296#1497—731no—
297#1477—731no—
298#1453D7311yescharacteristic, complemented
299C73#1801311yescharacteristic, complemented, Sylow
300#533—731no—
301C4×#41—731no—
302#485—731no—
303#485—731no—
304#475—731no—
305#474—731no—
306#462—731no—
307#461—731no—
308#452—731no—
309#452—731no—
310#446—731no—
311#446—731no—
312#446—1461no—
313#446—1461no—
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—731no—
317C8×Q8—731no—
318C4×Q16—731no—
319C4×Q16—731no—
320C4×SD16—731no—
321C4×SD16—731no—
322#436—731no—
323#436—731no—
324#436—1461no—
325#436—1461no—
326#432—731no—
327#432—1461no—
328#431C2×D7311yescharacteristic
329#431C2×D7311yescharacteristic
330#424—1461no—
331C2×C4⋊C8—731no—
332#405—1461no—
333C4×M16—1461no—
334C4×M16C2×D7311yescharacteristic
335#335—731no—
336#335—731no—
337#334—731no—
338#334—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343Q8⋊C8—731no—
344Q8⋊C8—731no—
345D4⋊C8—731no—
346D4⋊C8—731no—
347#322C2×D7311yescharacteristic
348#322C2×D7311yescharacteristic
349#322C2×D7311yescharacteristic
350C82C2×D7311yescharacteristic
351C2×#41—731no—
352C2×Q16—731no—
353C2×Q16—731no—
354C2×SD16—731no—
355C2×SD16—731no—
356C2×M16—1461no—
357C2×M16—1461no—
358C2×M16D29211yescharacteristic
359C2×M16D29211yescharacteristic
360C22×C8—1461no—
361C4⋊Q8—731no—
362C4⋊Q8—731no—
363#125—1461no—
364C22⋊Q8—731no—
365C22⋊Q8—731no—
366C22⋊Q8—1461no—
367C4×Q8—731no—
368C4×Q8—731no—
369C4×Q8—731no—
370C4×Q8—731no—
371C4×Q8—1461no—
372C4×D4—731no—
373C4×D4—731no—
374C4×D4—1461no—
375C4×D4—1461no—
376#117—731no—
377#117—1461no—
378#117—1461no—
379C2×C42—1461no—
380C2×C42C22×D7311yescharacteristic
381#107—731no—
382#107—731no—
383#106—731no—
384#106—731no—
385C4⋊C8—21no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8C4×D7311yescharacteristic
398C4⋊C8C4×D7311yescharacteristic
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#103—731no—
404#103—731no—
405#102—731no—
406#102—731no—
407C22⋊C8—21no—
408C22⋊C8—1461no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8C4×D7311yescharacteristic
412C22⋊C8C4×D7311yescharacteristic
413#97—1461no—
414#97—1461no—
415#97—1461no—
416#97D29211yescharacteristic
417#97D29211yescharacteristic
418C4×C8—1461no—
419C4×C8—1461no—
420C4×C8—1461no—
421C4×C8—1461no—
422C4×C8C22×D7311yescharacteristic
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C4×C8C22×D7311yescharacteristic
426C4×C8C22×D7311yescharacteristic
427C4×C8C22×D7311yescharacteristic
428#41—2921no—
429#41—1462no—
430C2×Q8—731no—
431C2×Q8—731no—
432C2×Q8—731no—
433C2×Q8—1461no—
434C2×D4—731no—
435C2×D4—1461no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4C2×C4×D7311yescharacteristic
440C22×C4C2×D29211yescharacteristic
441C22×C4#1192402811yescharacteristic
442Q16—1462no—
443Q16—1462no—
444SD16—2921no—
445SD16—2921no—
446M16—22no—
447M16—41no—
448M16—2922no—
449M16—2922no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—2922no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8C2×C4×D7311yescharacteristic
458C2×C8C2×C4×D7311yescharacteristic
459C2×C8C2×C4×D7311yescharacteristic
460C2×C8C2×C4×D7311yescharacteristic
461C2×C8C2×D29211yescharacteristic
462C2×C8C2×D29211yescharacteristic
463C2×C8C2×D29211yescharacteristic
464C2×C8C2×D29211yescharacteristic
465C4⋊C4—731no—
466C4⋊C4—731no—
467C4⋊C4—731no—
468C4⋊C4—731no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C22⋊C4—1461no—
482C22⋊C4—1461no—
483C42—1461no—
484C42—1461no—
485C42—1461no—
486C42—1461no—
487C42—1461no—
488C42C2×C4×D7311yescharacteristic
489C42C2×D29211yescharacteristic
490C42#1192402811yescharacteristic
491C42C23×D7311yescharacteristic
492C23—1461no—
493C23C4×D29211yescharacteristic
494Q8—5841no—
495Q8—732no—
496Q8—1461no—
497Q8—1461no—
498Q8—1461no—
499Q8—1461no—
500Q8—1461no—
501D4—2922no—
502D4—1461no—
503D4—1461no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—2922no—
510C2×C4—2921no—
511C2×C4—2921no—
512C2×C4—5841no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4C4×D29211yescharacteristic
521C2×C4C4×D29211yescharacteristic
522C2×C4C4×D29211yescharacteristic
523C2×C4C22×C4×D7311yescharacteristic
524C2×C4C22×D29211yescharacteristic
525C2×C4C2×#1192402811yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—2921no—
536C8—2921no—
537C8—2921no—
538C8—2921no—
539C8#1455662412yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—2921no—
544C22—2921no—
545C22—2921no—
546C22C2×C4×D29211yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—2921no—
552C4—2921no—
553C4—2921no—
554C4—2921no—
555C4—2921no—
556C4—2921no—
557C4—1462no—
558C4#131×D7311yescharacteristic
559C4#1798935211yescharacteristic
560C4C2×#1455662411yescharacteristic
561C4#1798938711yescharacteristic
562C2—41no—
563C2—5841no—
564C2#2261865911yescharacteristic
565C2C4×#1455662411yescharacteristic
566C2#2261884911yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1453C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C2×C4
cosocleC42×C73C24
hypercenter#1453D73
hypocenterC73#18013
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. #22618878C2semidirect
4. #22608835C2semidirect
5. #22608823C2semidirect
6. #22608811C2semidirect
7. #22608804C2semidirect
8. #22608783C2semidirect
9. #22608776C2semidirect
10. #22608751C2semidirect
11. C8×Dic292C2semidirect
12. #22608716C2semidirect
13. #22608405C2semidirect
15. C73×#1453C2semidirect
298. #1453D73semidirect
299. C73#18013semidirect

Maximal subgroups

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

subgroupindex
#226200032
#226189492
#226188782
#226088352
#226088232
#226088112
#226088042
#226087832
#226087762
#226087512
C8×Dic2922
#226087162
#226084052
#226083192
C73×#14532
#1801373