Finite Group Databasebeta

← #33093534

Subgroups — #33093534

Order 18688.

834 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988718C211yesmaximal, characteristic, complemented
2C2×#17988541C211yesmaximal, characteristic
3#22613201C211yesmaximal, characteristic
4#22610649C211yesmaximal, characteristic, complemented
5#22610498C211yesmaximal, characteristic, complemented
6#22610498C211yesmaximal, characteristic, complemented
7#22610110C211yesmaximal, characteristic
8#22610110C211yesmaximal, characteristic
9#22609912C211yesmaximal, characteristic
10#22609808C211yesmaximal, characteristic, complemented
11#22609804C211yesmaximal, characteristic, complemented
12#22609792C211yesmaximal, characteristic, complemented
13#22609713C211yesmaximal, characteristic
14#22609711C211yesmaximal, characteristic
15C73×#1984C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556548C2211yescharacteristic
19#17988718—24no—
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27#17988541—24no—
28C2×#14556502C2211yescharacteristic
29C2×#14556502C2211yescharacteristic
30C2×#14556501C2211yescharacteristic
31C2×#14556501C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34C2×C8×Dic73C2211yescharacteristic
35#17988525C411yescharacteristic
36#17988522C411yescharacteristic
37#17988520C411yescharacteristic
38#17988520C411yescharacteristic
39#17988509C411yescharacteristic
40#17988509C411yescharacteristic
41#17988506C411yescharacteristic
42#17988498C411yescharacteristic
43C4×#11924007C2211yescharacteristic
44C4×#11924007C2211yescharacteristic
45C4×C4⋊Dic73C2211yescharacteristic
46C4×#11924005C2211yescharacteristic
47C4×#11924005C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C2×C4×Q8×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic
56C2×C4×C8×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×C4×D73C2311yescharacteristic
62C2×#11924011—22no—
63C2×#11924011—22no—
64C2×#11924011Q814yescomplemented
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C2×C8×D73—22no—
70C2×C8×D73—22no—
71C2×C8×D73—22no—
72#14556548—22no—
73#14556548—22no—
74C2×C4⋊Dic73C2×C411yescharacteristic
75C2×C4⋊Dic73C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2×C411yescharacteristic
84C2×#11924005C2×C411yescharacteristic
85C2×#11924005C2×C411yescharacteristic
86C2×#11924005C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89C2×C4×Dic73C2311yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91C4⋊#10596831—22no—
92C4⋊#10596831—22no—
93C4⋊#10596831—22no—
94#14556520—22no—
95#14556520—22no—
96#14556503—22no—
97#14556503—22no—
98#14556502—22no—
99#14556502D414yes—
100#14556501—22no—
101#14556501—22no—
102C4×#10596831—22no—
103C8×Dic73—22no—
104C8×Dic73—22no—
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115C22×Q8×C73C2×C411yescharacteristic
116C22×C8×C73C2311yescharacteristic
117C22×C8×C73C2311yescharacteristic
118C22×C8×C73C2311yescharacteristic
119C22×C8×C73C2311yescharacteristic
120C4×Q8×C73—22no—
121C4×Q8×C73—22no—
122C2×C4⋊C4×C73C2×C411yescharacteristic
123C2×C4⋊C4×C73C2×C411yescharacteristic
124C2×C4⋊C4×C73C2×C411yescharacteristic
125C2×C42×C73C2311yescharacteristic
126C2×C42×C73C2311yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C4⋊C8×C73—22no—
129C4×C8×C73—22no—
130C23×D73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C2×C4×D73—21no—
139C2×C4×D73—21no—
140C2×C4×D73—21no—
141C2×C4×D73—21no—
142C2×C4×D73C2×Q812yes—
143C2×C4×D73#4112yes—
144#11924011—28no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831C2×D412yes—
154C2×#10596831C2×D412yes—
155C2×#10596831C2×Q812yes—
156C2×#10596831#4112yes—
157C8×D73—28no—
158C4⋊Dic73—22no—
159C4⋊Dic73—41no—
160#11924007—22no—
161#11924007—22no—
162#11924007—22no—
163#11924007—22no—
164#11924007—41no—
165#11924007—41no—
166#11924005—22no—
167#11924005—22no—
168#11924005—22no—
169#11924005—22no—
170#11924005—41no—
171#11924005—41no—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73—21no—
175C4×Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C2×Q8×C73—22no—
179C2×Q8×C73—22no—
180C2×Q8×C73—41no—
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C2411yescharacteristic
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73C2×Q812yes—
199C2×C8×C73#4112yes—
200C4⋊C4×C73—22no—
201C4⋊C4×C73—22no—
202C4⋊C4×C73—22no—
203C42×C73—21no—
204C42×C73—21no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73C2×D412yes—
208C42×C73#4112yes—
209C23×C73C23×C411yescharacteristic
210C22×D73—21no—
211C22×D73—21no—
212C22×D73—21no—
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73C4×Q812yes—
217Q8×C73—44no—
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—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73C4×D412yes—
234C2×C4×C73C4×D412yes—
235C2×C4×C73#13112yes—
236C2×C4×C73C22×D411yescharacteristic
237C2×C4×C73C22×Q811yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
239C2×C4×C73C2×#4111yescharacteristic
240C2×C4×C73C2×#4111yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73C4×Q812yes—
262C2×Dic73#13112yes—
263C4×D73—22no—
264C4×D73—22no—
265C4×D73—22no—
266C4×D73—22no—
267C8×C73—22no—
268C8×C73—22no—
269C8×C73—41no—
270C8×C73—41no—
271#10596831—22no—
272#10596831—41no—
273#10596831—41no—
274#10596831C22⋊Q814yes—
275C22×C73C2×C4×D411yescharacteristic
276C22×C73C2×C4×Q811yescharacteristic
277C22×C73C4×#4111yescharacteristic
278C22×C73C2×#13111yescharacteristic
279C22×C73C2×#13111yescharacteristic
280C22×C73#56811yescharacteristic
281C22×C73#56811yescharacteristic
282C2×D73—22no—
283C2×D73—22no—
284C2×D73—22no—
285C2×D73—41no—
286C2×D73—41no—
287C2×D73—41no—
288C2×D73—41no—
289C4×C73—22no—
290C4×C73—22no—
291C4×C73—22no—
292C4×C73—41no—
293C4×C73—41no—
294C4×C73—41no—
295C4×C73C2×C22⋊Q811yescharacteristic
296C4×C73#52511yescharacteristic
297C4×C73#52911yescharacteristic
298C4×C73#53311yescharacteristic
299Dic73—22no—
300Dic73—22no—
301Dic73—41no—
302Dic73—41no—
303Dic73—41no—
304Dic73—41no—
305Dic73—41no—
306#21606—731nomaximal, Sylow
307C2×C73C4×C22⋊Q811yescharacteristic
308C2×C73#293311yescharacteristic
309C2×C73#293511yescharacteristic
310C2×C73#296211yescharacteristic
311C2×C73#296211yescharacteristic
312C2×C73#296611yescharacteristic
313C2×C73#296711yescharacteristic
314D73—42no—
315C2×#446—731no—
316C2×#405—731no—
317#2396—731no—
318#1984D7311yescharacteristic, complemented
319#1939—731no—
320#1917—731no—
321#1917—731no—
322#1850—731no—
323#1850—731no—
324#1798—731no—
325#1771—731no—
326#1771—731no—
327C8×C4⋊C4—731no—
328#1753—731no—
329#1753—731no—
330C73#2160611yescharacteristic, complemented, Sylow
331C22×M16—731no—
332C23×C8—731no—
333C2×C4×Q8C2×D7311yescharacteristic
334C2×#117—731no—
335#446—1464no—
336C2×C4⋊C8—731no—
337C2×C4⋊C8—731no—
338C2×C4⋊C8—731no—
339C2×C4⋊C8—731no—
340C2×C4⋊C8—731no—
341C2×C4⋊C8C2×D7311yescharacteristic
342C2×C22⋊C8—731no—
343C2×C22⋊C8—731no—
344#405—1464no—
345C2×#97—731no—
346C2×#97—731no—
347C2×#97—731no—
348C2×#97—731no—
349C2×C4×C8—731no—
350C2×C4×C8—731no—
351C2×C4×C8—731no—
352C2×C4×C8C2×D7311yescharacteristic
353#400—731no—
354#399—731no—
355#398—731no—
356#398—731no—
357#396—731no—
358#396—731no—
359#395—731no—
360#393—731no—
361C4×C4⋊C4—731no—
362C4×C4⋊C4—731no—
363C4×C4⋊C4—731no—
364C4×C22⋊C4—731no—
365C4×C22⋊C4—731no—
366#336—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370#336—731no—
371#336—731no—
372#336C2×D7311yescharacteristic
373#336C2×D7311yescharacteristic
374#336C2×D7311yescharacteristic
375#336C2×D7311yescharacteristic
376C22×Q8C4×D7311yescharacteristic
377C23×C4—731no—
378C2×M16—734no—
379C2×M16—1462no—
380C2×M16—1462no—
381C22×C8—731no—
382C22×C8—731no—
383C22×C8—731no—
384C22×C8—731no—
385C22×C8—1462no—
386C22×C8—1462no—
387C22×C8—1462no—
388C22×C8C22×D7311yescharacteristic
389C22×C8C22×D7311yescharacteristic
390C22×C8C22×D7311yescharacteristic
391C22×C8C22×D7311yescharacteristic
392C4×Q8—22no—
393C4×Q8—22no—
394#117—1462no—
395#117—1462no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—731no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4C4×D7311yescharacteristic
405C2×C4⋊C4C4×D7311yescharacteristic
406C2×C4⋊C4C4×D7311yescharacteristic
407C2×C22⋊C4—731no—
408C2×C22⋊C4—731no—
409C2×C22⋊C4—731no—
410C2×C22⋊C4—731no—
411C2×C22⋊C4—731no—
412C2×C22⋊C4—731no—
413C2×C42—731no—
414C2×C42—731no—
415C2×C42—731no—
416C2×C42C22×D7311yescharacteristic
417C2×C42C22×D7311yescharacteristic
418C2×C42C22×D7311yescharacteristic
419C4⋊C8—22no—
420C4⋊C8—1462no—
421C4⋊C8—1462no—
422C4⋊C8—1462no—
423C4⋊C8—1462no—
424C4⋊C8—1462no—
425C22⋊C8—1462no—
426C22⋊C8—1462no—
427#97—734no—
428#97—1462no—
429#97—1462no—
430#97—1462no—
431C4×C8—22no—
432C4×C8—1462no—
433C4×C8—1462no—
434C4×C8—1462no—
435#95—731no—
436#95—731no—
437#95—731no—
438#95—731no—
439#95—731no—
440#95—731no—
441#95—731no—
442#95—731no—
443#95—731no—
444#95—731no—
445C24—731no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—41no—
449C22×C4—731no—
450C22×C4—731no—
451C22×C4—732no—
452C22×C4—732no—
453C22×C4—731no—
454C22×C4—731no—
455C22×C4—731no—
456C22×C4—731no—
457C22×C4—731no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4C2×C4×D7311yescharacteristic
463C22×C4C2×C4×D7311yescharacteristic
464C22×C4C2×C4×D7311yescharacteristic
465C22×C4C2×C4×D7311yescharacteristic
466C22×C4C2×C4×D7311yescharacteristic
467C22×C4C2×C4×D7311yescharacteristic
468C22×C4C23×D7311yescharacteristic
469M16—1468no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—732no—
481C2×C8—732no—
482C2×C8—732no—
483C2×C8—732no—
484C2×C8—1468no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8Q8×D7312yes—
494C2×C8#1192402912yes—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—2921no—
499C4⋊C4—2921no—
500C4⋊C4—2921no—
501C4⋊C4—1462no—
502C4⋊C4—1462no—
503C4⋊C4—1462no—
504C4⋊C4—1462no—
505C4⋊C4—1462no—
506C22⋊C4—2921no—
507C22⋊C4—2921no—
508C22⋊C4—1462no—
509C22⋊C4—1462no—
510C22⋊C4—1462no—
511C22⋊C4—1462no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—1461no—
517C42—1461no—
518C42—1461no—
519C42—1461no—
520C42—1461no—
521C42—1461no—
522C42D4×D7312yes—
523C42#1192402712yes—
524C23—732no—
525C23—1461no—
526C23—1461no—
527C23—1461no—
528C23—1461no—
529C23—1461no—
530C23—1461no—
531C23C22×C4×D7311yescharacteristic
532Q8—44no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—732no—
549C2×C4—732no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4—1461no—
557C2×C4—1461no—
558C2×C4—1461no—
559C2×C4—1461no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1462no—
570C2×C4—1462no—
571C2×C4—1462no—
572C2×C4—1462no—
573C2×C4#1455655112yes—
574C2×C4#1455655112yes—
575C2×C4#1455659712yes—
576C2×C4C2×D4×D7311yescharacteristic
577C2×C4C2×Q8×D7311yescharacteristic
578C2×C4#41×D7311yescharacteristic
579C2×C4#41×D7311yescharacteristic
580C2×C4C2×#1192402711yescharacteristic
581C2×C4C2×#1192402911yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C8—2921no—
587C8—2921no—
588C8—734no—
589C8—1462no—
590C22—2921no—
591C22—2921no—
592C22—2921no—
593C22—2921no—
594C22—1462no—
595C22—1462no—
596C22—1462no—
597C22C2×#1455655111yescharacteristic
598C22C4×Q8×D7311yescharacteristic
599C22C4×#1192402911yescharacteristic
600C22#131×D7311yescharacteristic
601C22C2×#1455659711yescharacteristic
602C22#1798935211yescharacteristic
603C22#1798935311yescharacteristic
604C4—22no—
605C4—22no—
606C4—22no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—2921no—
611C4—2921no—
612C4—2921no—
613C4—2921no—
614C4—2921no—
615C4—1462no—
616C4—1462no—
617C4C22⋊Q8×D7311yescharacteristic
618C4#1798910011yescharacteristic
619C4#1798911611yescharacteristic
620C4#1798914211yescharacteristic
621C2—2922no—
622C2#2261246911yescharacteristic
623C2#2261865211yescharacteristic
624C2#2261867111yescharacteristic
625C2#2261887311yescharacteristic
626C2#2261887611yescharacteristic
627C2#2261890811yescharacteristic
628C2#2261891511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1984C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1984D73
hypocenterC73#21606
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1984

Complements

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

NH ≅ G/Ntype
1. C2×#17988718C2semidirect
4. #22610649C2semidirect
5. #22610498C2semidirect
6. #22610498C2semidirect
10. #22609808C2semidirect
11. #22609804C2semidirect
12. #22609792C2semidirect
15. C73×#1984C2semidirect
64. C2×#11924011Q8semidirect
318. #1984D73semidirect
330. C73#21606semidirect

Maximal subgroups

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

subgroupindex
C2×#179887182
C2×#179885412
#226132012
#226106492
#226104982
#226101102
#226099122
#226098082
#226098042
#226097922
#226097132
#226097112
C73×#19842
#2160673