Finite Group Databasebeta

← #33103687

Subgroups — #33103687

Order 18688.

810 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×#107×D73C211yesmaximal, characteristic
2#22612807C211yesmaximal, characteristic
3#22612804C211yesmaximal, characteristic
4#22610668C211yesmaximal, characteristic, complemented
5#22610666C211yesmaximal, characteristic, complemented
6#22610504C211yesmaximal, characteristic, complemented
7#22610503C211yesmaximal, characteristic, complemented
8#22610501C211yesmaximal, characteristic, complemented
9#22610020C211yesmaximal, characteristic
10#22610020C211yesmaximal, characteristic
11#22609955C211yesmaximal, characteristic
12#22609829C211yesmaximal, characteristic, complemented
13#22609827C211yesmaximal, characteristic, complemented
14#22609706C211yesmaximal, characteristic
15C73×#1918C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic
17C2×C4⋊C4×D73C2211yescharacteristic
18C2×C4⋊C4×D73C2211yescharacteristic
19C2×#14556525C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22#107×D73C418yescomplemented
23C2×#14556522C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556502C2211yescharacteristic
27C2×#14556501C2211yescharacteristic
28#17988486C2211yescharacteristic
29#17988485C2211yescharacteristic
30#17988483C2211yescharacteristic
31#17988474—21no—
32#17988471—21no—
33#17988469—21no—
34#17988468—21no—
35#17988446—21no—
36#17988444—21no—
37#17988444C2211yescharacteristic
38#17988444C2211yescharacteristic
39C4⋊C4×Dic73C2211yescharacteristic
40C4⋊C4×Dic73C2211yescharacteristic
41C4×C4⋊Dic73C2211yescharacteristic
42C4×#11924005—21no—
43C4×#11924005C2211yescharacteristic
44#17988434—21no—
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988341C2211yescharacteristic
53C2×#107×C73C2211yescharacteristic
54#389×C73C2211yescharacteristic
55C4×C4⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×C4×D73—21no—
61C22×C4×D73—21no—
62C22×C4×D73C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C2×C8×D73—22no—
66C2×C8×D73—22no—
67C2×C8×D73C2×C414yes—
68C2×C4⋊Dic73—21no—
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×#11924007—21no—
77C4⋊C4×D73—22no—
78C4⋊C4×D73—22no—
79C4⋊C4×D73C2×C414yes—
80C4⋊C4×D73C2×C414yes—
81C2×#11924005—21no—
82C2×#11924005—21no—
83C2×#11924005D411yescharacteristic
84C2×#11924005D411yescharacteristic
85C2×C4×Dic73—21no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73—21no—
88C2×C4×Dic73C2311yescharacteristic
89#14556525C2×C414yes—
90#14556524C2×C414yes—
91#14556524C2×C414yes—
92#14556522—22no—
93#14556522—22no—
94#14556503—22no—
95#14556502—22no—
96#14556501—22no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498D411yescharacteristic
106#14556498D411yescharacteristic
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C42×C73—21no—
115C2×C42×C73C2311yescharacteristic
116#107×C73C2×C414yes—
117#95×C73—21no—
118#95×C73—21no—
119C23×D73C2×D411yescharacteristic
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—21no—
124C22×Dic73C2×D411yescharacteristic
125C22×Dic73C2×D411yescharacteristic
126C22×Dic73C2×D411yescharacteristic
127C2×C4×D73—21no—
128C2×C4×D73—21no—
129C2×C4×D73—21no—
130C2×C4×D73—21no—
131C2×C4×D73—24no—
132C2×C4×D73—24no—
133C2×C4×D73—81no—
134C2×C4×D73—81no—
135C2×C4×D73—81no—
136C2×C4×D73—81no—
137C2×C4×D73C22×C412yes—
138C2×C4×D73#4112yes—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831C22×C412yes—
143C2×#10596831#4112yes—
144C2×#10596831#4112yes—
145C8×D73—28no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—81no—
153C4⋊Dic73C22×C412yes—
154C4⋊Dic73C22×C412yes—
155#11924007—24no—
156#11924007—24no—
157#11924007—81no—
158#11924007—81no—
159#11924005—22no—
160#11924005—22no—
161#11924005—42no—
162#11924005—42no—
163C4×Dic73—21no—
164C4×Dic73—21no—
165C4×Dic73—81no—
166C4×Dic73—81no—
167C4×Dic73—81no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2411yescharacteristic
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73C22×C412yes—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—81no—
188C4⋊C4×C73C22×C412yes—
189C4⋊C4×C73C22×C412yes—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73—81no—
193C23×C73C22×D411yescharacteristic
194C22×D73—21no—
195C22×D73—21no—
196C22×D73—21no—
197C22×D73—21no—
198C22×D73C4×D412yes—
199C22×D73#13712yes—
200C22×D73#13712yes—
201C2×C4×C73—22no—
202C2×C4×C73—22no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73C23×C411yescharacteristic
220C2×C4×C73C2×#4111yescharacteristic
221C2×C4×C73C2×#4111yescharacteristic
222C2×C4×C73C2×#4111yescharacteristic
223C2×C4×C732−1+411yescharacteristic
224C2×C4×C732−1+411yescharacteristic
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—22no—
228C2×Dic73—22no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—41no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73C4×D412yes—
246C4×D73—22no—
247C4×D73—22no—
248C4×D73—22no—
249C4×D73—22no—
250C4×D73—84no—
251C4×D73—84no—
252C8×C73—22no—
253C8×C73—41no—
254#10596831—41no—
255#10596831#11714yes—
256C22×C73C2×C4×D411yescharacteristic
257C22×C73#54711yescharacteristic
258C22×C73#54711yescharacteristic
259C22×C73C2×#13711yescharacteristic
260C22×C73C2×#13711yescharacteristic
261C22×C73#57611yescharacteristic
262C22×C73#57611yescharacteristic
263C2×D73—22no—
264C2×D73—22no—
265C2×D73—22no—
266C2×D73—22no—
267C2×D73—22no—
268C2×D73—22no—
269C2×D73#44114yes—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73—42no—
273C4×C73—42no—
274C4×C73—81no—
275C4×C73—81no—
276C4×C73C2×#11711yescharacteristic
277C4×C73#51911yescharacteristic
278C4×C73#55211yescharacteristic
279C4×C73#55211yescharacteristic
280Dic73—22no—
281Dic73—41no—
282Dic73—41no—
283Dic73—42no—
284Dic73—42no—
285Dic73—81no—
286Dic73—81no—
287#22618—731nomaximal, Sylow
288C2×C73#234411yescharacteristic
289C2×C73C2×#44111yescharacteristic
290C2×C73#294811yescharacteristic
291C2×C73#334611yescharacteristic
292C2×C73#334611yescharacteristic
293C2×C73#334611yescharacteristic
294C2×C73#334611yescharacteristic
295D73—24no—
296C22×#107—731no—
297#2345—731no—
298#2345—731no—
299#1943—731no—
300#1943—731no—
301#1918—731no—
302#1918—731no—
303#1918—731no—
304#1918D7311yescharacteristic, complemented
305#1824—731no—
306#1824—731no—
307#1807—731no—
308#1776—731no—
309#1776—731no—
310#1752—731no—
311C73#2261811yescharacteristic, complemented, Sylow
312C23×C8—731no—
313C22×C4⋊C4—731no—
314C22×C4⋊C4—731no—
315C2×#107—731no—
316C2×#107—731no—
317C2×#107—731no—
318C2×#107—738no—
319C2×#107C2×D7311yescharacteristic
320C2×#106—731no—
321C2×#106—731no—
322C2×C22⋊C8—731no—
323C2×#97—731no—
324C2×#97—731no—
325#389—731no—
326#389—731no—
327#389—731no—
328#389C2×D7311yescharacteristic
329#387—1461no—
330#387—1461no—
331#387—1461no—
332#387—1461no—
333#380—731no—
334#380—731no—
335#380—1461no—
336#380—1461no—
337C4×C4⋊C4—731no—
338C4×C4⋊C4—731no—
339C4×C4⋊C4—731no—
340C4×C4⋊C4C2×D7311yescharacteristic
341C4×C22⋊C4—731no—
342C4×C22⋊C4—1461no—
343C4×C22⋊C4—1461no—
344#340—731no—
345#340—731no—
346#340—731no—
347#340—731no—
348#340—731no—
349#340—731no—
350#340—731no—
351#340C2×D7311yescharacteristic
352#340C2×D7311yescharacteristic
353#340C2×D7311yescharacteristic
354#336—731no—
355#336C2×D7311yescharacteristic
356C23×C4—731no—
357C23×C4—1461no—
358C23×C4—1461no—
359C22×C8—731no—
360C22×C8—734no—
361C22×C8—731no—
362C22×C8—1462no—
363C22×C8—1462no—
364C22×C8C22×D7311yescharacteristic
365C22×C8C22×D7311yescharacteristic
366C2×C4⋊C4—21no—
367C2×C4⋊C4—731no—
368C2×C4⋊C4—731no—
369C2×C4⋊C4—734no—
370C2×C4⋊C4—734no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—1462no—
374C2×C4⋊C4—1462no—
375C2×C4⋊C4—1461no—
376C2×C4⋊C4—1461no—
377C2×C4⋊C4—1461no—
378C2×C4⋊C4—1461no—
379C2×C4⋊C4—1461no—
380C2×C4⋊C4C22×D7311yescharacteristic
381C2×C4⋊C4C22×D7311yescharacteristic
382C2×C4⋊C4C22×D7311yescharacteristic
383C2×C4⋊C4C22×D7311yescharacteristic
384C2×C22⋊C4—731no—
385C2×C22⋊C4—731no—
386C2×C22⋊C4—1461no—
387C2×C22⋊C4—1461no—
388C2×C42—21no—
389C2×C42—731no—
390C2×C42—1461no—
391C2×C42—1461no—
392C2×C42—1461no—
393C2×C42C22×D7311yescharacteristic
394#107—734no—
395#107—734no—
396#107—734no—
397#107C4×D7314yes—
398#106—1462no—
399#106—1462no—
400C22⋊C8—1462no—
401#97—1462no—
402#97—1462no—
403#95—21no—
404#95—21no—
405#95—731no—
406#95—731no—
407#95—1461no—
408#95—1461no—
409#95—1461no—
410#95—1461no—
411#95—1461no—
412#95—1461no—
413#95—1461no—
414#95—1461no—
415C24—731no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—5841no—
421C22×C4—5841no—
422C22×C4—5841no—
423C22×C4—5841no—
424C22×C4—731no—
425C22×C4—732no—
426C22×C4—732no—
427C22×C4—731no—
428C22×C4—731no—
429C22×C4—1464no—
430C22×C4—1464no—
431C22×C4—1461no—
432C22×C4—1461no—
433C22×C4—1461no—
434C22×C4—1461no—
435C22×C4—1461no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4D4×D7311yescharacteristic
440C22×C4D4×D7311yescharacteristic
441C22×C4C23×D7311yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—732no—
448C2×C8—732no—
449C2×C8—732no—
450C2×C8—1468no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8C2×C4×D7312yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—5841no—
463C4⋊C4—5841no—
464C4⋊C4—5841no—
465C4⋊C4—732no—
466C4⋊C4—732no—
467C4⋊C4—1464no—
468C4⋊C4—1464no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4C2×C4×D7312yes—
476C4⋊C4C2×C4×D7312yes—
477C22⋊C4—2922no—
478C22⋊C4—2922no—
479C22⋊C4—1462no—
480C22⋊C4—1462no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—5841no—
485C42—5841no—
486C42—5841no—
487C42—1461no—
488C42—1461no—
489C23—732no—
490C23—732no—
491C23—732no—
492C23—1461no—
493C23—1461no—
494C23—1461no—
495C23—1461no—
496C23C2×D4×D7311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—2921no—
516C2×C4—2921no—
517C2×C4—2921no—
518C2×C4—2921no—
519C2×C4—2921no—
520C2×C4—2921no—
521C2×C4—2921no—
522C2×C4—2921no—
523C2×C4—2921no—
524C2×C4—2921no—
525C2×C4—5844no—
526C2×C4—5844no—
527C2×C4—732no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1462no—
535C2×C4—1462no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1462no—
539C2×C4—1462no—
540C2×C4—1462no—
541C2×C4—1462no—
542C2×C4C22×C4×D7311yescharacteristic
543C2×C4#41×D7311yescharacteristic
544C2×C4#41×D7311yescharacteristic
545C2×C4#41×D7311yescharacteristic
546C2×C4#1455663811yescharacteristic
547C2×C4#1455663911yescharacteristic
548C8—22no—
549C8—41no—
550C8—2921no—
551C8—734no—
552C22—734no—
553C22—1462no—
554C22—1462no—
555C22—1462no—
556C22—1462no—
557C22—1462no—
558C22—1462no—
559C22C4×D4×D7311yescharacteristic
560C22#1798923511yescharacteristic
561C22#1798923911yescharacteristic
562C22#137×D7311yescharacteristic
563C22#137×D7311yescharacteristic
564C22#1798938811yescharacteristic
565C22#1798938911yescharacteristic
566C4—42no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—2922no—
573C4—2922no—
574C4—2921no—
575C4—2921no—
576C4—5841no—
577C4—5841no—
578C4—1462no—
579C4#117×D7311yescharacteristic
580C4#1798906311yescharacteristic
581C4#1798926911yescharacteristic
582C4#1798927311yescharacteristic
583C2—1464no—
584C2#2261279711yescharacteristic
585C2#441×D7311yescharacteristic
586C2#2261877811yescharacteristic
587C2#2262240911yescharacteristic
588C2#2262241311yescharacteristic
589C2#2262241911yescharacteristic
590C2#2262242311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1918C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1918D73
hypocenterC73#22618
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #22610668C2semidirect
5. #22610666C2semidirect
6. #22610504C2semidirect
7. #22610503C2semidirect
8. #22610501C2semidirect
12. #22609829C2semidirect
13. #22609827C2semidirect
15. C73×#1918C2semidirect
22. #107×D73C4semidirect
304. #1918D73semidirect
311. C73#22618semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D732
#226128072
#226128042
#226106682
#226106662
#226105042
#226105032
#226105012
#226100202
#226099552
#226098292
#226098272
#226097062
C73×#19182
#2261873