Finite Group Databasebeta

← #33055319

Subgroups — #33055319

Order 18688.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619056C211yesmaximal, characteristic
2#22618898C211yesmaximal, characteristic
3#22608717C211yesmaximal, characteristic, complemented
4#22608714C211yesmaximal, characteristic, complemented
5#22608712C211yesmaximal, characteristic, complemented
6#22608709C211yesmaximal, characteristic, complemented
7#22608707C211yesmaximal, characteristic, complemented
8#22608705C211yesmaximal, characteristic, complemented
9#22608699C211yesmaximal, characteristic, complemented
10#22608696C211yesmaximal, characteristic, complemented
11#22608692C211yesmaximal, characteristic, complemented
12#22608684C211yesmaximal, characteristic, complemented
13#22608681C211yesmaximal, characteristic, complemented
14C2×#17988339C211yesmaximal, characteristic, complemented
15C73×#2990C211yesmaximal, characteristic
16#17988718—21no—
17#17988718C411yescharacteristic
18#17988718C411yescharacteristic
19#17988665C411yescharacteristic
20#17988665C411yescharacteristic
21#17988659—21no—
22#17988659—21no—
23#17988659C411yescharacteristic
24#17988659C411yescharacteristic
25#17988659C411yescharacteristic
26#17988659C411yescharacteristic
27D4×#10596831—21no—
28#17988644C2211yescharacteristic
29#17988644C2211yescharacteristic
30#17988640C2211yescharacteristic
31#17988640C2211yescharacteristic
32#17988640C2211yescharacteristic
33#17988640C2211yescharacteristic
34#17988611C2211yescharacteristic
35C2×C4⋊#10596831C2211yescharacteristic
36C2×C4⋊#10596831C2211yescharacteristic
37C4×#11924012C2211yescharacteristic
38C4×#11924012C2211yescharacteristic
39C2×C4×#10596831C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988339C2211yescharacteristic
43#17988339C2211yescharacteristic
44#17988339C2211yescharacteristic
45#17988339C2211yescharacteristic
46#17988339C2211yescharacteristic
47#17988339C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988337C2211yescharacteristic
53#17988337C2211yescharacteristic
54#17988337C2211yescharacteristic
55#17988337C2211yescharacteristic
56C4×#41×C73C2211yescharacteristic
57#446×C73—21no—
58#435×C73—21no—
59#435×C73—21no—
60C8×D4×C73—21no—
61#432×C73C2211yescharacteristic
62#432×C73C2211yescharacteristic
63#431×C73C2211yescharacteristic
64#423×C73C2211yescharacteristic
65C2×C4⋊C8×C73C2211yescharacteristic
66C2×C4⋊C8×C73C2211yescharacteristic
67C2×#11924012—21no—
68C2×#11924012C2×C411yescharacteristic
69C2×#11924012C2×C411yescharacteristic
70C2×#11924012C2×C411yescharacteristic
71C2×#11924012C2×C411yescharacteristic
72C22×#10596831—21no—
73C22×#10596831—21no—
74C22×#10596831C2×C411yescharacteristic
75C22×#10596831C2×C411yescharacteristic
76C4⋊#10596831—21no—
77C4⋊#10596831—21no—
78C4⋊#10596831—21no—
79C4⋊#10596831C2×C411yescharacteristic
80C4⋊#10596831C2×C411yescharacteristic
81C4⋊#10596831C2×C411yescharacteristic
82C4⋊#10596831C2×C411yescharacteristic
83C4⋊#10596831C2×C411yescharacteristic
84C4⋊#10596831C2×C411yescharacteristic
85C4⋊#10596831C2311yescharacteristic
86C4⋊#10596831C2311yescharacteristic
87C4⋊#10596831C2311yescharacteristic
88C4⋊#10596831C2311yescharacteristic
89C22⋊#10596831—21no—
90C22⋊#10596831—21no—
91C22⋊#10596831—21no—
92C22⋊#10596831C2×C411yescharacteristic
93C22⋊#10596831C2×C411yescharacteristic
94C22⋊#10596831C2×C411yescharacteristic
95C22⋊#10596831C2×C411yescharacteristic
96C22⋊#10596831C2×C411yescharacteristic
97C22⋊#10596831C2×C411yescharacteristic
98#14556502—21no—
99#14556502—21no—
100#14556502C2×C411yescharacteristic
101#14556502C2×C411yescharacteristic
102#14556502C2×C411yescharacteristic
103#14556502C2×C411yescharacteristic
104C4×#10596831—21no—
105C4×#10596831C2×C411yescharacteristic
106C4×#10596831C2×C411yescharacteristic
107C4×#10596831C2311yescharacteristic
108C4×#10596831C2311yescharacteristic
109C4×#10596831C2311yescharacteristic
110C4×#10596831C2311yescharacteristic
111C2×#41×C73Q811yescharacteristic
112C2×M16×C73—21no—
113C22×C8×C73—21no—
114C22×C8×C73—21no—
115C4×Q8×C73C2×C411yescharacteristic
116C4×Q8×C73D411yescharacteristic
117C4×D4×C73C2×C411yescharacteristic
118C4×D4×C73C2×C411yescharacteristic
119C4×D4×C73C2×C411yescharacteristic
120C4×D4×C73D411yescharacteristic
121C4×D4×C73D411yescharacteristic
122C4×D4×C73D411yescharacteristic
123#117×C73Q811yescharacteristic
124#117×C73Q811yescharacteristic
125#117×C73Q811yescharacteristic
126C2×C42×C73C2311yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73—21no—
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139#97×C73—21no—
140#97×C73—21no—
141C4×C8×C73—21no—
142#11924012—22no—
143#11924012—22no—
144#11924012—41no—
145#11924012—41no—
146#11924012—81no—
147C2×#10596831—22no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—41no—
153C2×#10596831—81no—
154C2×#10596831—81no—
155C2×#10596831C22×C411yescharacteristic
156C2×#10596831C22×C411yescharacteristic
157C2×#10596831C22×C411yescharacteristic
158C2×#10596831C22×C411yescharacteristic
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163#41×C73—42no—
164C2×Q8×C73C4⋊C411yescharacteristic
165C2×D4×C73C4⋊C411yescharacteristic
166C2×D4×C73C4⋊C411yescharacteristic
167C2×D4×C73C4⋊C411yescharacteristic
168C22×C4×C73C22×C411yescharacteristic
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×Q811yescharacteristic
175C22×C4×C73C2×Q811yescharacteristic
176C22×C4×C73C2×Q811yescharacteristic
177M16×C73—81no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—81no—
183C2×C8×C73—81no—
184C4⋊C4×C73C4⋊C411yescharacteristic
185C4⋊C4×C73C4⋊C411yescharacteristic
186C4⋊C4×C73C4⋊C411yescharacteristic
187C4⋊C4×C73C4⋊C411yescharacteristic
188C4⋊C4×C73C4⋊C411yescharacteristic
189C4⋊C4×C73C4⋊C411yescharacteristic
190C22⋊C4×C73C4⋊C411yescharacteristic
191C22⋊C4×C73C4⋊C411yescharacteristic
192C22⋊C4×C73C4⋊C411yescharacteristic
193C22⋊C4×C73C4⋊C411yescharacteristic
194C22⋊C4×C73C4⋊C411yescharacteristic
195C22⋊C4×C73C4⋊C411yescharacteristic
196C42×C73C22×C411yescharacteristic
197C42×C73C22×C411yescharacteristic
198C42×C73C22×C411yescharacteristic
199C42×C73C2×D411yescharacteristic
200C42×C73C2×D411yescharacteristic
201C42×C73C2×D411yescharacteristic
202C42×C73C2×Q811yescharacteristic
203C42×C73C2×Q811yescharacteristic
204C42×C73C2×Q811yescharacteristic
205C42×C73C2411yescharacteristic
206C23×C73C2×C4⋊C411yescharacteristic
207C23×C73C2×C4⋊C411yescharacteristic
208C23×C73C2×C4⋊C411yescharacteristic
209Q8×C73—41no—
210D4×C73—22no—
211D4×C73—22no—
212D4×C73—41no—
213C2×C4×C73—22no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73C2×C4⋊C411yescharacteristic
229C2×C4×C73C2×C4⋊C411yescharacteristic
230C2×C4×C73C2×C4⋊C411yescharacteristic
231C2×C4×C73C2×C4⋊C411yescharacteristic
232C2×C4×C73C2×C4⋊C411yescharacteristic
233C2×C4×C73C2×C4⋊C411yescharacteristic
234C2×C4×C73C2×C4⋊C411yescharacteristic
235C2×C4×C73C2×C4⋊C411yescharacteristic
236C2×C4×C73C2×C4⋊C411yescharacteristic
237C2×C4×C73C23×C411yescharacteristic
238C2×C4×C73C22×D411yescharacteristic
239C2×C4×C73C22×Q811yescharacteristic
240C8×C73—41no—
241C8×C73—41no—
242C8×C73—41no—
243C8×C73—41no—
244#10596831—21no—
245#10596831—21no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255#10596831#13112yes—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—21no—
264C22×C73#43012yes—
265C22×C73C22×C4⋊C411yescharacteristic
266C4×C73—21no—
267C4×C73—21no—
268C4×C73—21no—
269C4×C73—21no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—21no—
275C4×C73—21no—
276C4×C73C2×#13111yescharacteristic
277C4×C73#56811yescharacteristic
278C4×C73#57611yescharacteristic
279C4×C73#57811yescharacteristic
280#17840—731nomaximal, Sylow
281C2×C73—22no—
282C2×C73—41no—
283C2×C73—41no—
284C2×C73#290611yescharacteristic
285C2×C73#291311yescharacteristic
286C2×C73C2×#43011yescharacteristic
287#2990—731no—
288#2990D7311yescharacteristic
289#2965—731no—
290#1573—731no—
291#1573—731no—
292#1572—731no—
293#1572—731no—
294#1571—731no—
295#1571—731no—
296#1569—731no—
297#1569—731no—
298#1568—731no—
299#1565—731no—
300#1565—731no—
301C2×#335—731no—
302C73#1784011yescharacteristic, complemented, Sylow
303C4×#41C2×D7311yescharacteristic
304#446—21no—
305#446—731no—
306#446—731no—
307#446—1461no—
308#436—731no—
309#436—731no—
310#435—21no—
311#435—21no—
312#435—731no—
313#435—731no—
314#435—731no—
315#435—731no—
316#435—1461no—
317#435—1461no—
318C8×D4—21no—
319C8×D4—1461no—
320#432—731no—
321#432—731no—
322#432C2×D7311yescharacteristic
323#432C2×D7311yescharacteristic
324#431—731no—
325#431—731no—
326#431—731no—
327#431—731no—
328#431C2×D7311yescharacteristic
329#423—731no—
330#423C2×D7311yescharacteristic
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8C2×D7311yescharacteristic
334C2×C4⋊C8C2×D7311yescharacteristic
335C4×M16—731no—
336C4×M16—731no—
337C2×C4×C8—731no—
338#335—731no—
339#335—731no—
340#335—731no—
341#335—731no—
342#335—731no—
343#335—731no—
344#335—731no—
345#335—731no—
346#335—731no—
347#335—731no—
348#334—731no—
349#334—731no—
350#334—731no—
351#334—731no—
352#334—731no—
353#334—731no—
354C2×#41Dic14611yescharacteristic
355C2×M16—21no—
356C2×M16—731no—
357C2×M16—731no—
358C2×M16—731no—
359C2×M16—731no—
360C2×M16—1461no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—1461no—
366C22×C8—1461no—
367C4×Q8C4×D7311yescharacteristic
368C4×Q8C22⋊D7311yescharacteristic
369C4×D4C4×D7311yescharacteristic
370C4×D4C4×D7311yescharacteristic
371C4×D4C4×D7311yescharacteristic
372C4×D4C22⋊D7311yescharacteristic
373C4×D4C22⋊D7311yescharacteristic
374C4×D4C22⋊D7311yescharacteristic
375#117Dic14611yescharacteristic
376#117Dic14611yescharacteristic
377#117Dic14611yescharacteristic
378C2×C42C22×D7311yescharacteristic
379C2×C42C22×D7311yescharacteristic
380C2×C42C22×D7311yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—731no—
391C4⋊C8—731no—
392C4⋊C8—731no—
393C4⋊C8—731no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8C22×D7311yescharacteristic
398C4⋊C8C22×D7311yescharacteristic
399C4⋊C8C22×D7311yescharacteristic
400C4⋊C8C22×D7311yescharacteristic
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—731no—
405C22⋊C8—731no—
406C22⋊C8—731no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—731no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—21no—
414#97—21no—
415#97—731no—
416#97—731no—
417#97—731no—
418#97—731no—
419#97—1461no—
420#97—1461no—
421C4×C8—21no—
422C4×C8—731no—
423C4×C8—731no—
424C4×C8—731no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—1461no—
429#41—42no—
430C2×Q8#1192400711yescharacteristic
431C2×D4#1192400711yescharacteristic
432C2×D4#1192400711yescharacteristic
433C2×D4#1192400711yescharacteristic
434C22×C4C2×C4×D7311yescharacteristic
435C22×C4C2×C4×D7311yescharacteristic
436C22×C4C2×C4×D7311yescharacteristic
437C22×C4C2×C22⋊D7311yescharacteristic
438C22×C4C2×C22⋊D7311yescharacteristic
439C22×C4C2×C22⋊D7311yescharacteristic
440C22×C4C2×Dic14611yescharacteristic
441C22×C4C2×Dic14611yescharacteristic
442C22×C4C2×Dic14611yescharacteristic
443M16—81no—
444M16—2921no—
445M16—2921no—
446M16—5841no—
447M16—1462no—
448M16—1462no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8—81no—
455C2×C8—2921no—
456C2×C8—5841no—
457C2×C8—5841no—
458C2×C8—731no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—731no—
462C2×C8—731no—
463C2×C8—731no—
464C2×C8—731no—
465C2×C8—731no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1462no—
471C4⋊C4#1192400711yescharacteristic
472C4⋊C4#1192400711yescharacteristic
473C4⋊C4#1192400711yescharacteristic
474C4⋊C4#1192400711yescharacteristic
475C4⋊C4#1192400711yescharacteristic
476C4⋊C4#1192400711yescharacteristic
477C22⋊C4#1192400711yescharacteristic
478C22⋊C4#1192400711yescharacteristic
479C22⋊C4#1192400711yescharacteristic
480C22⋊C4#1192400711yescharacteristic
481C22⋊C4#1192400711yescharacteristic
482C22⋊C4#1192400711yescharacteristic
483C42C2×C4×D7311yescharacteristic
484C42C2×C4×D7311yescharacteristic
485C42C2×C4×D7311yescharacteristic
486C42C2×C22⋊D7311yescharacteristic
487C42C2×C22⋊D7311yescharacteristic
488C42C2×C22⋊D7311yescharacteristic
489C42C2×Dic14611yescharacteristic
490C42C2×Dic14611yescharacteristic
491C42C2×Dic14611yescharacteristic
492C42C23×D7311yescharacteristic
493C23C2×#1192400711yescharacteristic
494C23C2×#1192400711yescharacteristic
495C23C2×#1192400711yescharacteristic
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4C2×#1192400711yescharacteristic
516C2×C4C2×#1192400711yescharacteristic
517C2×C4C2×#1192400711yescharacteristic
518C2×C4C2×#1192400711yescharacteristic
519C2×C4C2×#1192400711yescharacteristic
520C2×C4C2×#1192400711yescharacteristic
521C2×C4C2×#1192400711yescharacteristic
522C2×C4C2×#1192400711yescharacteristic
523C2×C4C2×#1192400711yescharacteristic
524C2×C4C22×C4×D7311yescharacteristic
525C2×C4C22×C22⋊D7311yescharacteristic
526C2×C4C22×Dic14611yescharacteristic
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—2921no—
532C8—2921no—
533C8—2921no—
534C8—2921no—
535C8—732no—
536C8—1461no—
537C8—1461no—
538C8—1461no—
539C8—1461no—
540C8—1461no—
541C8—1461no—
542C8—1461no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22#1798863512yes—
552C22C22×#1192400711yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4#131×D7311yescharacteristic
564C4#1798935211yescharacteristic
565C4#1798939011yescharacteristic
566C4#1798940211yescharacteristic
567C2—22no—
568C2—41no—
569C2—41no—
570C2#2261849711yescharacteristic
571C2#2261852911yescharacteristic
572C2C2×#1798863511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2990C2
socleC22×C73C22×C4⋊C4
prime radicalC2×#41×C73Q8
cosocleC42×C73C24
hypercenter#2990D73
hypocenterC73#17840
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
3. #22608717C2semidirect
4. #22608714C2semidirect
5. #22608712C2semidirect
6. #22608709C2semidirect
7. #22608707C2semidirect
8. #22608705C2semidirect
9. #22608699C2semidirect
10. #22608696C2semidirect
11. #22608692C2semidirect
12. #22608684C2semidirect
13. #22608681C2semidirect
14. C2×#17988339C2semidirect
302. C73#17840semidirect

Maximal subgroups

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

subgroupindex
#226190562
#226188982
#226087172
#226087142
#226087122
#226087092
#226087072
#226087052
#226086992
#226086962
#226086922
#226086842
#226086812
C2×#179883392
C73×#29902
#1784073