Finite Group Databasebeta

← #33093083

Subgroups — #33093083

Order 18688.

872 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988662C211yesmaximal, characteristic
2C2×#17988544C211yesmaximal, characteristic, complemented
3#22613192C211yesmaximal, characteristic
4#22610534C211yesmaximal, characteristic, complemented
5#22610495C211yesmaximal, characteristic, complemented
6#22610489C211yesmaximal, characteristic, complemented
7#22610220C211yesmaximal, characteristic
8#22610107C211yesmaximal, characteristic, complemented
9#22610001C211yesmaximal, characteristic, complemented
10#22609808C211yesmaximal, characteristic, complemented
11#22609792C211yesmaximal, characteristic, complemented
12#22609717C211yesmaximal, characteristic, complemented
13#22609715C211yesmaximal, characteristic, complemented
14#22609713C211yesmaximal, characteristic, complemented
15C73×#1924C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×#14556548C2211yescharacteristic
21#17988662—24no—
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27#17988544—24no—
28C2×#14556502C2211yescharacteristic
29C2×#14556501C2211yescharacteristic
30C2×C4×#10596831C2211yescharacteristic
31C2×C8×Dic73C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34#17988528C411yescharacteristic
35#17988523C411yescharacteristic
36#17988521C411yescharacteristic
37#17988516C411yescharacteristic
38#17988515C411yescharacteristic
39#17988514C411yescharacteristic
40#17988503C411yescharacteristic
41#17988502C411yescharacteristic
42C4×#11924007C2211yescharacteristic
43C4×C4⋊Dic73C2211yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×#97×C73C2211yescharacteristic
58C4×C22⋊C4×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C4×D73C2311yescharacteristic
63C2×#11924012—22no—
64C2×#11924012—22no—
65C2×#11924012—22no—
66C2×#11924011—22no—
67C2×#11924011—22no—
68C2×#11924011D414yes—
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C2×C8×D73—22no—
74C2×C8×D73—22no—
75C2×C8×D73—22no—
76C4×C22⋊D73—22no—
77C4×C22⋊D73—22no—
78#14556548—22no—
79#14556548—22no—
80C2×C4⋊Dic73C2×C411yescharacteristic
81C2×C4⋊Dic73C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×#11924007C2×C411yescharacteristic
85C2×#11924007C2×C411yescharacteristic
86C2×#11924007C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×C22⋊Dic73C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×#11924005C2×C411yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98#14556520—22no—
99#14556520—22no—
100C22⋊#10596831—22no—
101#14556503—22no—
102#14556503—22no—
103#14556502—22no—
104#14556501—22no—
105C4×#10596831—22no—
106C8×Dic73—22no—
107C8×Dic73—22no—
108C8×Dic73—22no—
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117C23×C4×C73C2311yescharacteristic
118C22×C8×C73C2311yescharacteristic
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C2×C22⋊C4×C73C2×C411yescharacteristic
123C2×C22⋊C4×C73C2×C411yescharacteristic
124C2×C42×C73C2311yescharacteristic
125C2×C42×C73C2311yescharacteristic
126C4⋊C8×C73—22no—
127C22⋊C8×C73—22no—
128C22⋊C8×C73—22no—
129#97×C73—22no—
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132C23×D73C22×C411yescharacteristic
133C2×C22⋊D73—22no—
134C2×C22⋊D73—22no—
135C2×C22⋊D73—41no—
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C22×C411yescharacteristic
140C22×Dic73C22×C411yescharacteristic
141C22×Dic73C22×C411yescharacteristic
142C22×Dic73C22×C411yescharacteristic
143C2×C4×D73—21no—
144C2×C4×D73—21no—
145C2×C4×D73—21no—
146C2×C4×D73—21no—
147C2×C4×D73C2×D412yes—
148C2×C4×D73#4112yes—
149#11924012—44no—
150#11924011—28no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831C2×D412yes—
160C2×#10596831#4112yes—
161C2×#10596831#4112yes—
162C2×#10596831#4112yes—
163C8×D73—28no—
164C4⋊Dic73—22no—
165C4⋊Dic73—41no—
166#11924007—22no—
167#11924007—22no—
168#11924007—22no—
169#11924007—22no—
170#11924007—22no—
171C22⋊Dic73—22no—
172C22⋊Dic73—22no—
173C22⋊Dic73—41no—
174#11924005—22no—
175#11924005—22no—
176#11924005—22no—
177#11924005—22no—
178#11924005—41no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C24×C73C22×C411yescharacteristic
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C22×C411yescharacteristic
197C22×C4×C73C2411yescharacteristic
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73C2×D412yes—
209C2×C8×C73#4112yes—
210C22⋊C4×C73—41no—
211C22⋊C4×C73—41no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—21no—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73C23×C411yescharacteristic
224C22×D73—21no—
225C22×D73—21no—
226C22×D73—21no—
227C22×D73—21no—
228C22×D73—21no—
229C22×D73—21no—
230C22×D73C4×D412yes—
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—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73C22×D411yescharacteristic
251C2×C4×C73C2×#4111yescharacteristic
252C2×C4×C73C2×#4111yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×C4×C73C2×#4111yescharacteristic
256C22⋊D73—44no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73—21no—
269C2×Dic73—21no—
270C2×Dic73—21no—
271C2×Dic73—21no—
272C2×Dic73—21no—
273C2×Dic73—21no—
274C2×Dic73—21no—
275C2×Dic73C4×D412yes—
276C2×Dic73#13112yes—
277C2×Dic73#13112yes—
278C4×D73—22no—
279C4×D73—22no—
280C4×D73—22no—
281C4×D73—22no—
282C8×C73—22no—
283C8×C73—22no—
284C8×C73—41no—
285C8×C73—41no—
286#10596831—22no—
287#10596831—41no—
288#10596831—41no—
289#10596831#12314yes—
290C22×C73—41no—
291C22×C73—41no—
292C22×C73—41no—
293C22×C73—41no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73—41no—
297C22×C73C2×C4×D411yescharacteristic
298C22×C73C4×#4111yescharacteristic
299C22×C73C4×#4111yescharacteristic
300C22×C73C2×#13111yescharacteristic
301C22×C73C2×#13111yescharacteristic
302C22×C73#56811yescharacteristic
303C22×C73#56811yescharacteristic
304C2×D73—22no—
305C2×D73—22no—
306C2×D73—22no—
307C2×D73—41no—
308C2×D73—41no—
309C2×D73—41no—
310C2×D73—41no—
311C4×C73—41no—
312C4×C73—41no—
313C4×C73—41no—
314C4×C73—41no—
315C4×C73—41no—
316C4×C73C2×#12311yescharacteristic
317C4×C73#52511yescharacteristic
318C4×C73#52911yescharacteristic
319C4×C73#52911yescharacteristic
320Dic73—22no—
321Dic73—22no—
322Dic73—22no—
323Dic73—41no—
324Dic73—41no—
325Dic73—41no—
326Dic73—41no—
327#21571—731nomaximal, Sylow
328C2×C73—81no—
329C2×C73C4×#12311yescharacteristic
330C2×C73#293311yescharacteristic
331C2×C73#293511yescharacteristic
332C2×C73#296611yescharacteristic
333C2×C73#296711yescharacteristic
334C2×C73#296911yescharacteristic
335C2×C73#296911yescharacteristic
336D73—42no—
337C2×#436—731no—
338C2×#405—731no—
339#2395—731no—
340#1924D7311yescharacteristic, complemented
341#1923—731no—
342#1917—731no—
343#1916—731no—
344#1869—731no—
345#1850—731no—
346#1818—731no—
347#1771—731no—
348C8×C4⋊C4—731no—
349#1753—731no—
350#1753—731no—
351#1753—731no—
352C73#2157111yescharacteristic, complemented, Sylow
353C22×M16—731no—
354C22×M16—731no—
355C23×C8—731no—
356C2×C4×D4—731no—
357C2×#117—731no—
358#436—1464no—
359C2×C4⋊C8—731no—
360C2×C4⋊C8—731no—
361C2×C4⋊C8C2×D7311yescharacteristic
362C2×C22⋊C8—731no—
363C2×C22⋊C8—731no—
364C2×C22⋊C8—731no—
365C2×C22⋊C8C2×D7311yescharacteristic
366C2×C22⋊C8C2×D7311yescharacteristic
367#405—1464no—
368C2×#97—731no—
369C2×#97—731no—
370C2×#97C2×D7311yescharacteristic
371C2×C4×C8—731no—
372C2×C4×C8—731no—
373C2×C4×C8—731no—
374C2×C4×C8—731no—
375#400—731no—
376#399—731no—
377#398—731no—
378#397—731no—
379#397—731no—
380#397—731no—
381#394—731no—
382#394—731no—
383C4×C4⋊C4—731no—
384C4×C4⋊C4—731no—
385C4×C22⋊C4—731no—
386C4×C22⋊C4—731no—
387C4×C22⋊C4C2×D7311yescharacteristic
388#336—731no—
389#336—731no—
390#336—731no—
391#336—731no—
392#336—731no—
393#336—731no—
394#336—731no—
395#336—731no—
396#336C2×D7311yescharacteristic
397#336C2×D7311yescharacteristic
398C22×D4—731no—
399C23×C4—731no—
400C23×C4C22×D7311yescharacteristic
401C2×M16—734no—
402C2×M16—1462no—
403C2×M16—1462no—
404C2×M16—1462no—
405C2×M16—1462no—
406C2×M16—1462no—
407C22×C8—731no—
408C22×C8—731no—
409C22×C8—731no—
410C22×C8—731no—
411C22×C8—1462no—
412C22×C8—1462no—
413C22×C8—1462no—
414C22×C8C22×D7311yescharacteristic
415C22×C8C22×D7311yescharacteristic
416C22×C8C22×D7311yescharacteristic
417C22×C8C22×D7311yescharacteristic
418C4×D4—1462no—
419C4×D4—1462no—
420#117—1462no—
421#117—1462no—
422C2×C4⋊C4—731no—
423C2×C4⋊C4—731no—
424C2×C4⋊C4—731no—
425C2×C4⋊C4—731no—
426C2×C4⋊C4—731no—
427C2×C4⋊C4—731no—
428C2×C4⋊C4—731no—
429C2×C22⋊C4—731no—
430C2×C22⋊C4—731no—
431C2×C22⋊C4—731no—
432C2×C22⋊C4—731no—
433C2×C22⋊C4—731no—
434C2×C22⋊C4—731no—
435C2×C22⋊C4—731no—
436C2×C22⋊C4—731no—
437C2×C22⋊C4C4×D7311yescharacteristic
438C2×C22⋊C4C4×D7311yescharacteristic
439C2×C42—731no—
440C2×C42—731no—
441C2×C42—731no—
442C2×C42C22×D7311yescharacteristic
443C2×C42C22×D7311yescharacteristic
444C4⋊C8—22no—
445C4⋊C8—1462no—
446C4⋊C8—1462no—
447C22⋊C8—22no—
448C22⋊C8—22no—
449C22⋊C8—1462no—
450C22⋊C8—1462no—
451C22⋊C8—1462no—
452#97—22no—
453#97—1462no—
454#97—1462no—
455C4×C8—1462no—
456C4×C8—1462no—
457C4×C8—1462no—
458C4×C8—1462no—
459#95—731no—
460#95—731no—
461#95—731no—
462#95—731no—
463#95—731no—
464#95—731no—
465#95—731no—
466#95—731no—
467#95C4×D7311yescharacteristic
468#95C4×D7311yescharacteristic
469C24—731no—
470C24C2×C4×D7311yescharacteristic
471C2×D4—2921no—
472C2×D4—1462no—
473C2×D4—1462no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—731no—
481C22×C4—731no—
482C22×C4—731no—
483C22×C4—732no—
484C22×C4—732no—
485C22×C4—731no—
486C22×C4—731no—
487C22×C4—731no—
488C22×C4—731no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4C2×C4×D7311yescharacteristic
494C22×C4C2×C4×D7311yescharacteristic
495C22×C4C2×C4×D7311yescharacteristic
496C22×C4C2×C4×D7311yescharacteristic
497C22×C4C2×C4×D7311yescharacteristic
498C22×C4C23×D7311yescharacteristic
499M16—2924no—
500M16—1468no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—732no—
512C2×C8—732no—
513C2×C8—732no—
514C2×C8—732no—
515C2×C8—1468no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8—1461no—
520C2×C8—1461no—
521C2×C8—1461no—
522C2×C8—1461no—
523C2×C8—1461no—
524C2×C8D4×D7312yes—
525C2×C8#1192402712yes—
526C4⋊C4—2921no—
527C4⋊C4—1462no—
528C4⋊C4—1462no—
529C4⋊C4—1462no—
530C4⋊C4—1462no—
531C4⋊C4—1462no—
532C4⋊C4—1462no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—2921no—
536C22⋊C4—2921no—
537C22⋊C4—1462no—
538C22⋊C4—1462no—
539C22⋊C4—1462no—
540C22⋊C4—1462no—
541C22⋊C4—1462no—
542C22⋊C4—1462no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—1461no—
548C42—1461no—
549C42—1461no—
550C42—1461no—
551C42—1461no—
552C42—1461no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—732no—
561C23—1461no—
562C23—1461no—
563C23—1461no—
564C23—1461no—
565C23—1461no—
566C23—1461no—
567C23C22×C4×D7311yescharacteristic
568D4—2924no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—732no—
589C2×C4—732no—
590C2×C4—732no—
591C2×C4—1461no—
592C2×C4—1461no—
593C2×C4—1461no—
594C2×C4—1461no—
595C2×C4—1461no—
596C2×C4—1461no—
597C2×C4—1461no—
598C2×C4—1461no—
599C2×C4—1461no—
600C2×C4—1461no—
601C2×C4—1461no—
602C2×C4—1461no—
603C2×C4—1461no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4—1461no—
607C2×C4—1461no—
608C2×C4—1461no—
609C2×C4—1462no—
610C2×C4—1462no—
611C2×C4—1462no—
612C2×C4—1462no—
613C2×C4C2×D4×D7311yescharacteristic
614C2×C4#41×D7311yescharacteristic
615C2×C4#41×D7311yescharacteristic
616C2×C4#41×D7311yescharacteristic
617C2×C4#41×D7311yescharacteristic
618C2×C4C2×#1192402711yescharacteristic
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—2921no—
624C8—2921no—
625C8—734no—
626C8—1462no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—2921no—
635C22—2921no—
636C22—2921no—
637C22—2921no—
638C22—1462no—
639C22—1462no—
640C22—1462no—
641C22C4×D4×D7311yescharacteristic
642C22C4×#1192402711yescharacteristic
643C22#1798905511yescharacteristic
644C22#131×D7311yescharacteristic
645C22#131×D7311yescharacteristic
646C22#1798935311yescharacteristic
647C22#1798935311yescharacteristic
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—2921no—
654C4—2921no—
655C4—2921no—
656C4—2921no—
657C4—1462no—
658C4—1462no—
659C4—1462no—
660C4#123×D7311yescharacteristic
661C4#1798909711yescharacteristic
662C4#1798911611yescharacteristic
663C4#1798912011yescharacteristic
664C2—81no—
665C2—2922no—
666C2#2261245811yescharacteristic
667C2#2261866011yescharacteristic
668C2#2261867211yescharacteristic
669C2#2261890411yescharacteristic
670C2#2261891111yescharacteristic
671C2#2261892811yescharacteristic
672C2#2261892811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1924C2
prime radicalC22×C22⋊D73C2×C4
cosocleC22×C4×C73C24
hypercenter#1924D73
hypocenterC73#21571
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
2. C2×#17988544C2semidirect
4. #22610534C2semidirect
5. #22610495C2semidirect
6. #22610489C2semidirect
8. #22610107C2semidirect
9. #22610001C2semidirect
10. #22609808C2semidirect
11. #22609792C2semidirect
12. #22609717C2semidirect
13. #22609715C2semidirect
14. #22609713C2semidirect
15. C73×#1924C2semidirect
340. #1924D73semidirect
352. C73#21571semidirect

Maximal subgroups

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

subgroupindex
C2×#179886622
C2×#179885442
#226131922
#226105342
#226104952
#226104892
#226102202
#226101072
#226100012
#226098082
#226097922
#226097172
#226097152
#226097132
C73×#19242
#2157173