Finite Group Databasebeta

← #33096487

Subgroups — #33096487

Order 18688.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988648C211yesmaximal, characteristic
2C2×#17988614C211yesmaximal, characteristic
3#22610655C211yesmaximal, characteristic, complemented
4#22610655C211yesmaximal, characteristic, complemented
5#22610650C211yesmaximal, characteristic, complemented
6#22610650C211yesmaximal, characteristic, complemented
7#22610116C211yesmaximal, characteristic
8#22610116C211yesmaximal, characteristic
9#22610111C211yesmaximal, characteristic
10#22610111C211yesmaximal, characteristic
11#22610085C211yesmaximal, characteristic, complemented
12#22610083C211yesmaximal, characteristic, complemented
13#22610051C211yesmaximal, characteristic, complemented
14#22610048C211yesmaximal, characteristic, complemented
15C73×#2298C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18#17988648—24no—
19#17988614—24no—
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×C4⋊#10596831C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×C4⋊#10596831C2211yescharacteristic
27C2×C4⋊#10596831C2211yescharacteristic
28C2×C4⋊#10596831C2211yescharacteristic
29C2×C4⋊#10596831C2211yescharacteristic
30C2×C4⋊#10596831C2211yescharacteristic
31C2×C4⋊#10596831C2211yescharacteristic
32C2×C4⋊#10596831C2211yescharacteristic
33C2×C4⋊#10596831C2211yescharacteristic
34C2×C22⋊#10596831C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×#14556502C2211yescharacteristic
37C2×C4×#10596831C2211yescharacteristic
38#17988342C2211yescharacteristic
39#17988342C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46C2×#117×C73C2211yescharacteristic
47#388×C73C411yescharacteristic
48#388×C73C411yescharacteristic
49#388×C73C411yescharacteristic
50#388×C73C411yescharacteristic
51#387×C73C411yescharacteristic
52#387×C73C411yescharacteristic
53#387×C73C411yescharacteristic
54#387×C73C411yescharacteristic
55C4×C4⋊C4×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57C4×C22⋊C4×C73C2211yescharacteristic
58C4×C22⋊C4×C73C2211yescharacteristic
59#376×C73C2211yescharacteristic
60C43×C73C2211yescharacteristic
61C2×#11924012—22no—
62C2×#11924012—41no—
63C2×#11924012—41no—
64C22×#10596831—22no—
65C22×#10596831—41no—
66C22×#10596831—41no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C4⋊#10596831—22no—
76C4⋊#10596831—22no—
77C4⋊#10596831—22no—
78C4⋊#10596831—22no—
79C4⋊#10596831—22no—
80C4⋊#10596831—22no—
81C4⋊#10596831—41no—
82C4⋊#10596831—41no—
83C4⋊#10596831—41no—
84C4⋊#10596831—41no—
85C4⋊#10596831—41no—
86C4⋊#10596831—41no—
87C4⋊#10596831—41no—
88C4⋊#10596831—41no—
89C22⋊#10596831—22no—
90C22⋊#10596831—22no—
91#14556502—22no—
92C4×#10596831—22no—
93C23×C4×C73C2311yescharacteristic
94#117×C73D414yes—
95#117×C73Q814yes—
96C2×C4⋊C4×C73C2×C411yescharacteristic
97C2×C4⋊C4×C73C2×C411yescharacteristic
98C2×C4⋊C4×C73C2×C411yescharacteristic
99C2×C4⋊C4×C73C2×C411yescharacteristic
100C2×C4⋊C4×C73C2×C411yescharacteristic
101C2×C4⋊C4×C73C2×C411yescharacteristic
102C2×C22⋊C4×C73C2×C411yescharacteristic
103C2×C22⋊C4×C73C2×C411yescharacteristic
104C2×C22⋊C4×C73C2×C411yescharacteristic
105C2×C22⋊C4×C73C2×C411yescharacteristic
106C2×C22⋊C4×C73C2×C411yescharacteristic
107C2×C22⋊C4×C73C2×C411yescharacteristic
108C2×C42×C73C2×C411yescharacteristic
109C2×C42×C73C2×C411yescharacteristic
110C2×C42×C73C2×C411yescharacteristic
111C2×C42×C73C2×C411yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120#95×C73C2×C411yescharacteristic
121#95×C73C2×C411yescharacteristic
122#95×C73C2×C411yescharacteristic
123#95×C73C2×C411yescharacteristic
124#95×C73C2×C411yescharacteristic
125#95×C73C2×C411yescharacteristic
126#95×C73C2×C411yescharacteristic
127#95×C73C2×C411yescharacteristic
128#95×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130#11924012—44no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
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×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—44no—
156C24×C73C22×C411yescharacteristic
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73C22×C411yescharacteristic
162C22×C4×C73C22×C411yescharacteristic
163C22×C4×C73C22×C411yescharacteristic
164C22×C4×C73C22×C411yescharacteristic
165C22×C4×C73C22×C411yescharacteristic
166C22×C4×C73C22×C411yescharacteristic
167C22×C4×C73C22×C411yescharacteristic
168C22×C4×C73C22×C411yescharacteristic
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C22×C411yescharacteristic
172C22×C4×C73C22×C411yescharacteristic
173C22×C4×C73C22×C411yescharacteristic
174C22×C4×C73C2×D412yes—
175C22×C4×C73C2×Q812yes—
176C22×C4×C73C2411yescharacteristic
177C4⋊C4×C73—22no—
178C4⋊C4×C73—22no—
179C4⋊C4×C73—41no—
180C4⋊C4×C73—41no—
181C4⋊C4×C73C4⋊C414yes—
182C4⋊C4×C73C4⋊C414yes—
183C22⋊C4×C73—22no—
184C22⋊C4×C73—22no—
185C22⋊C4×C73—41no—
186C22⋊C4×C73—41no—
187C22⋊C4×C73C4⋊C414yes—
188C22⋊C4×C73C4⋊C414yes—
189C42×C73—22no—
190C42×C73—22no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—21no—
195C42×C73—21no—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—21no—
199C42×C73—41no—
200C42×C73—41no—
201C42×C73C2×D412yes—
202C42×C73C2×D412yes—
203C42×C73C2×Q812yes—
204C42×C73C2×Q812yes—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73—21no—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73—21no—
211C23×C73C2×C4⋊C412yes—
212C23×C73C23×C411yescharacteristic
213C2×C4×C73—21no—
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—21no—
227C2×C4×C73—22no—
228C2×C4×C73—22no—
229C2×C4×C73—22no—
230C2×C4×C73—22no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73C2×C4⋊C412yes—
250C2×C4×C73C2×C4⋊C412yes—
251C2×C4×C73C2×C4⋊C412yes—
252C2×C4×C73C2×C4⋊C412yes—
253C2×C4×C73C2×C4⋊C412yes—
254C2×C4×C73#13112yes—
255C2×C4×C73#13112yes—
256C2×C4×C73C22×D411yescharacteristic
257C2×C4×C73C22×Q811yescharacteristic
258C2×C4×C73H(5,𝔽2)11yescharacteristic
259C2×C4×C73H(5,𝔽2)11yescharacteristic
260C2×C4×C732−1+411yescharacteristic
261C2×C4×C732−1+411yescharacteristic
262#10596831—41no—
263#10596831—41no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267#10596831—41no—
268#10596831—41no—
269#10596831—41no—
270C22×C73—22no—
271C22×C73—22no—
272C22×C73—22no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73C22×C4⋊C411yescharacteristic
278C22×C73#52011yescharacteristic
279C22×C73#52011yescharacteristic
280C22×C73C2×#13111yescharacteristic
281C22×C73C2×#13111yescharacteristic
282C22×C73#56811yescharacteristic
283C22×C73#56811yescharacteristic
284C4×C73—22no—
285C4×C73—22no—
286C4×C73—22no—
287C4×C73—22no—
288C4×C73—22no—
289C4×C73—22no—
290C4×C73—22no—
291C4×C73—41no—
292C4×C73—41no—
293C4×C73—41no—
294C4×C73—41no—
295C4×C73—41no—
296C4×C73—41no—
297C4×C73#53511yescharacteristic
298C4×C73#53611yescharacteristic
299C4×C73#54411yescharacteristic
300C4×C73#54411yescharacteristic
301#21980—731nomaximal, Sylow
302C2×C73—42no—
303C2×C73#231711yescharacteristic
304C2×C73#290611yescharacteristic
305C2×C73#290611yescharacteristic
306C2×C73#299211yescharacteristic
307C2×C73#299311yescharacteristic
308C2×C73#299411yescharacteristic
309C2×C73#299511yescharacteristic
310C2×#433—731no—
311C2×#424—731no—
312#2298D7311yescharacteristic
313#1940—731no—
314#1940—731no—
315#1939—731no—
316#1939—731no—
317#1851—731no—
318#1851—731no—
319#1850—731no—
320#1850—731no—
321#1843—731no—
322#1842—731no—
323#1832—731no—
324#1831—731no—
325C73#2198011yescharacteristic, complemented, Sylow
326C22×M16—731no—
327C23×C8—731no—
328C2×#117C2×D7311yescharacteristic
329#433—1464no—
330#424—1464no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8—731no—
337C2×C4⋊C8—731no—
338C2×C4⋊C8—731no—
339C2×C4⋊C8—731no—
340C2×C4⋊C8—731no—
341C2×C4⋊C8—731no—
342C2×C4⋊C8—731no—
343C2×C4⋊C8—731no—
344C2×C4⋊C8—731no—
345C2×C22⋊C8—731no—
346C2×C22⋊C8—731no—
347C2×#97—731no—
348C2×C4×C8—731no—
349#388Dic7311yescharacteristic
350#388Dic7311yescharacteristic
351#388Dic7311yescharacteristic
352#388Dic7311yescharacteristic
353#387Dic7311yescharacteristic
354#387Dic7311yescharacteristic
355#387Dic7311yescharacteristic
356#387Dic7311yescharacteristic
357C4×C4⋊C4C2×D7311yescharacteristic
358C4×C4⋊C4C2×D7311yescharacteristic
359C4×C22⋊C4C2×D7311yescharacteristic
360C4×C22⋊C4C2×D7311yescharacteristic
361#376C2×D7311yescharacteristic
362C43C2×D7311yescharacteristic
363#336—731no—
364#336—731no—
365#336—731no—
366#336—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370#336—731no—
371C23×C4C22×D7311yescharacteristic
372C2×M16—2921no—
373C2×M16—2921no—
374C2×M16—1462no—
375C22×C8—2921no—
376C22×C8—2921no—
377C22×C8—731no—
378C22×C8—731no—
379C22×C8—731no—
380C22×C8—731no—
381C22×C8—731no—
382C22×C8—731no—
383C22×C8—731no—
384C22×C8—731no—
385C22×C8—1462no—
386#117Dic14614yes—
387#117D29214yes—
388C2×C4⋊C4C2×Dic7311yescharacteristic
389C2×C4⋊C4C2×Dic7311yescharacteristic
390C2×C4⋊C4C2×Dic7311yescharacteristic
391C2×C4⋊C4C2×Dic7311yescharacteristic
392C2×C4⋊C4C2×Dic7311yescharacteristic
393C2×C4⋊C4C2×Dic7311yescharacteristic
394C2×C22⋊C4C2×Dic7311yescharacteristic
395C2×C22⋊C4C2×Dic7311yescharacteristic
396C2×C22⋊C4C2×Dic7311yescharacteristic
397C2×C22⋊C4C2×Dic7311yescharacteristic
398C2×C22⋊C4C2×Dic7311yescharacteristic
399C2×C22⋊C4C2×Dic7311yescharacteristic
400C2×C42C2×Dic7311yescharacteristic
401C2×C42C2×Dic7311yescharacteristic
402C2×C42C2×Dic7311yescharacteristic
403C2×C42C2×Dic7311yescharacteristic
404C2×C42C22×D7311yescharacteristic
405C2×C42C22×D7311yescharacteristic
406C2×C42C22×D7311yescharacteristic
407C2×C42C22×D7311yescharacteristic
408C2×C42C22×D7311yescharacteristic
409C2×C42C22×D7311yescharacteristic
410C4⋊C8—2921no—
411C4⋊C8—2921no—
412C4⋊C8—2921no—
413C4⋊C8—2921no—
414C4⋊C8—2921no—
415C4⋊C8—2921no—
416C4⋊C8—2921no—
417C4⋊C8—2921no—
418C4⋊C8—1462no—
419C4⋊C8—1462no—
420C4⋊C8—1462no—
421C4⋊C8—1462no—
422C4⋊C8—1462no—
423C4⋊C8—1462no—
424C22⋊C8—1462no—
425C22⋊C8—1462no—
426#97—1462no—
427C4×C8—1462no—
428#95C2×Dic7311yescharacteristic
429#95C2×Dic7311yescharacteristic
430#95C2×Dic7311yescharacteristic
431#95C2×Dic7311yescharacteristic
432#95C2×Dic7311yescharacteristic
433#95C2×Dic7311yescharacteristic
434#95C2×Dic7311yescharacteristic
435#95C2×Dic7311yescharacteristic
436#95C2×Dic7311yescharacteristic
437#95C2×Dic7311yescharacteristic
438#95C2×Dic7311yescharacteristic
439#95C2×Dic7311yescharacteristic
440C24C22×Dic7311yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C22×Dic7311yescharacteristic
446C22×C4C22×Dic7311yescharacteristic
447C22×C4C22×Dic7311yescharacteristic
448C22×C4C22×Dic7311yescharacteristic
449C22×C4C22×Dic7311yescharacteristic
450C22×C4C22×Dic7311yescharacteristic
451C22×C4C22×Dic7311yescharacteristic
452C22×C4C22×Dic7311yescharacteristic
453C22×C4C22×Dic7311yescharacteristic
454C22×C4C22×Dic7311yescharacteristic
455C22×C4C22×Dic7311yescharacteristic
456C22×C4C22×Dic7311yescharacteristic
457C22×C4C22×Dic7311yescharacteristic
458C22×C4C2×D29212yes—
459C22×C4C2×Dic14612yes—
460C22×C4C23×D7311yescharacteristic
461M16—2924no—
462C2×C8—2924no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8—1461no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C4⋊Dic7314yes—
492C4⋊C4C4⋊Dic7314yes—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4C4⋊Dic7314yes—
498C22⋊C4C4⋊Dic7314yes—
499C42—22no—
500C42—22no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—41no—
510C42—41no—
511C42C2×D29212yes—
512C42C2×D29212yes—
513C42C2×Dic14612yes—
514C42C2×Dic14612yes—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23C2×C4⋊Dic7312yes—
522C23C23×Dic7311yescharacteristic
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4C2×C4⋊Dic7312yes—
560C2×C4C2×C4⋊Dic7312yes—
561C2×C4C2×C4⋊Dic7312yes—
562C2×C4C2×C4⋊Dic7312yes—
563C2×C4C2×C4⋊Dic7312yes—
564C2×C4#1455659812yes—
565C2×C4#1455659812yes—
566C2×C4C22×D29211yescharacteristic
567C2×C4C22×Dic14611yescharacteristic
568C2×C4#1455663711yescharacteristic
569C2×C4#1455663711yescharacteristic
570C2×C4#1455663811yescharacteristic
571C2×C4#1455663811yescharacteristic
572C8—2921no—
573C8—2921no—
574C8—2921no—
575C8—2921no—
576C8—2921no—
577C8—2921no—
578C8—2921no—
579C8—2921no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C22×C4⋊Dic7311yescharacteristic
588C22#1798907011yescharacteristic
589C22#1798907011yescharacteristic
590C22C2×#1455659811yescharacteristic
591C22C2×#1455659811yescharacteristic
592C22#1798935411yescharacteristic
593C22#1798935411yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—22no—
599C4—22no—
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4#1798915611yescharacteristic
608C4#1798916311yescharacteristic
609C4#1798921511yescharacteristic
610C4#1798921511yescharacteristic
611C2—42no—
612C2#2261255411yescharacteristic
613C2#2261849911yescharacteristic
614C2#2261849911yescharacteristic
615C2#2261907011yescharacteristic
616C2#2261908011yescharacteristic
617C2#2261909111yescharacteristic
618C2#2261910111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#2298C2
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenter#2298D73
hypocenterC73#21980
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
3. #22610655C2semidirect
4. #22610655C2semidirect
5. #22610650C2semidirect
6. #22610650C2semidirect
11. #22610085C2semidirect
12. #22610083C2semidirect
13. #22610051C2semidirect
14. #22610048C2semidirect
325. C73#21980semidirect

Maximal subgroups

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

subgroupindex
C2×#179886482
C2×#179886142
#226106552
#226106502
#226101162
#226101112
#226100852
#226100832
#226100512
#226100482
C73×#22982
#2198073