Finite Group Databasebeta

← #1528×D73 #33053888

Subgroups — #1528×D73 #33053888

Order 18688.

1050 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D73C211yesmaximal, characteristic
2#432×D73C211yesmaximal, characteristic
3C4×M16×D73C211yesmaximal, characteristic
4#22608534C211yesmaximal, characteristic, complemented
5#22608533C211yesmaximal, characteristic, complemented
6#22608532C211yesmaximal, characteristic, complemented
7#22608531C214yesmaximal, complemented
8#330×D73C214yesmaximal, complemented
9C73×#1528C211yesmaximal, characteristic, complemented
10C2×M16×D73—21no—
11C2×#14556583C2211yescharacteristic
12C2×#14556582C411yescharacteristic
13C2×#14556582C411yescharacteristic
14C2×#14556581—21no—
15C2×#14556581—21no—
16#125×D73—21no—
17#125×D73—21no—
18#125×D73—21no—
19#125×D73—21no—
20#125×D73C412yes—
21#125×D73C412yes—
22#125×D73C2212yes—
23#125×D73C2212yes—
24C2×C4⋊C4×D73—21no—
25C2×C4⋊C4×D73—21no—
26C2×C4⋊C4×D73C411yescharacteristic
27C2×C4⋊C4×D73C411yescharacteristic
28C2×C42×D73C2211yescharacteristic
29#17988644C2211yescharacteristic
30#17988643—21no—
31#17988642C2212yes—
32#17988641—21no—
33C4⋊C8×D73—21no—
34C22⋊C8×D73—21no—
35C4×#11924012C2211yescharacteristic
36#17988539C2212yes—
37M16×Dic73—21no—
38C4×#11924011—21no—
39#97×D73C2212yes—
40#97×D73C2212yes—
41C4×C8×D73—21no—
42#17988329C2214yescomplemented
43#17988328C2214yescomplemented
44#17988328C2214yescomplemented
45C2×#125×C73C2211yescharacteristic
46#432×C73C2211yescharacteristic
47C4×M16×C73C2211yescharacteristic
48#330×C73C2214yescomplemented
49C22×C4×D73—21no—
50C22×C4×D73—21no—
51C22×C4×D73C2×C411yescharacteristic
52C22×C4×D73D411yescharacteristic
53C22×C4×D73D411yescharacteristic
54C2×#11924012—21no—
55C2×#11924011—22no—
56M16×D73—28no—
57C2×C8×D73—22no—
58C2×C8×D73—22no—
59#14556583—21no—
60#14556583—21no—
61#14556583C2×C412yes—
62#14556583C2312yes—
63#14556582—21no—
64#14556582—21no—
65#14556582—21no—
66#14556582—21no—
67#14556582C2×C412yes—
68#14556582C2×C412yes—
69#14556582C2×C412yes—
70#14556582C2×C412yes—
71#14556581—22no—
72#14556581—22no—
73#14556581—22no—
74#14556581—22no—
75#14556581—22no—
76#14556581—22no—
77#14556581—22no—
78#14556581—22no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73—21no—
81C2×C4⋊Dic73C2×C411yescharacteristic
82C2×C4⋊Dic73C2×C411yescharacteristic
83C2×#11924007—21no—
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×#11924007—21no—
89C4⋊C4×D73—22no—
90C4⋊C4×D73—22no—
91C4⋊C4×D73—22no—
92C4⋊C4×D73—22no—
93C4⋊C4×D73—21no—
94C4⋊C4×D73—21no—
95C4⋊C4×D73—21no—
96C4⋊C4×D73—21no—
97C4⋊C4×D73—22no—
98C4⋊C4×D73—22no—
99C4⋊C4×D73—22no—
100C4⋊C4×D73—22no—
101C4⋊C4×D73C2×C412yes—
102C4⋊C4×D73C2×C412yes—
103C4⋊C4×D73C2×C412yes—
104C4⋊C4×D73C2×C412yes—
105C2×C4×Dic73C2×C411yescharacteristic
106C2×C4×Dic73D411yescharacteristic
107C2×C4×Dic73D411yescharacteristic
108C42×D73C2×C411yescharacteristic
109C42×D73C2×C411yescharacteristic
110C42×D73D411yescharacteristic
111C42×D73D411yescharacteristic
112C42×D73D411yescharacteristic
113C42×D73D411yescharacteristic
114C42×D73C2311yescharacteristic
115C42×D73C2311yescharacteristic
116C4⋊#10596831—21no—
117#14556520—22no—
118C22⋊#10596831—21no—
119#14556503—22no—
120#14556502C2312yes—
121#14556502C2312yes—
122#14556501—22no—
123#14556501—22no—
124C4×#10596831—21no—
125C8×Dic73—22no—
126C2×M16×C73—21no—
127#125×C73—21no—
128#125×C73—21no—
129#125×C73C2×C412yes—
130#125×C73C2312yes—
131C2×C4⋊C4×C73—21no—
132C2×C4⋊C4×C73—21no—
133C2×C4⋊C4×C73C2×C411yescharacteristic
134C2×C4⋊C4×C73C2×C411yescharacteristic
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138#97×C73C2312yes—
139#97×C73C2312yes—
140C4×C8×C73—21no—
141C23×D73C22⋊C411yescharacteristic
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73C22⋊C411yescharacteristic
145C22×Dic73C22⋊C411yescharacteristic
146C22×Dic73C22⋊C411yescharacteristic
147C2×C4×D73—24no—
148C2×C4×D73—24no—
149C2×C4×D73—22no—
150C2×C4×D73—22no—
151C2×C4×D73—22no—
152C2×C4×D73—22no—
153C2×C4×D73—42no—
154C2×C4×D73—44no—
155C2×C4×D73—44no—
156C2×C4×D73C22⋊C411yescharacteristic
157C2×C4×D73C22⋊C411yescharacteristic
158C2×C4×D73C22⋊C411yescharacteristic
159C2×C4×D73C22⋊C411yescharacteristic
160C2×C4×D73C22⋊C411yescharacteristic
161C2×C4×D73C22⋊C411yescharacteristic
162C2×C4×D73C22×C411yescharacteristic
163C2×C4×D73C22×C411yescharacteristic
164C2×C4×D73C2×D411yescharacteristic
165C2×C4×D73C2×D411yescharacteristic
166C2×C4×D73C2×D411yescharacteristic
167C2×C4×D73C2×D411yescharacteristic
168#11924012—24no—
169#11924011—28no—
170C2×#10596831—22no—
171C2×#10596831—22no—
172C8×D73—28no—
173C8×D73—44no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—22no—
177C4⋊Dic73—22no—
178C4⋊Dic73—22no—
179C4⋊Dic73—22no—
180C4⋊Dic73C22×C412yes—
181C4⋊Dic73C22×C412yes—
182#11924007—22no—
183#11924007—22no—
184#11924007—22no—
185#11924007—22no—
186#11924007—22no—
187#11924007—22no—
188#11924007—22no—
189#11924007—22no—
190#11924007—22no—
191#11924007—22no—
192#11924007—22no—
193#11924007—22no—
194C4×Dic73C22⋊C411yescharacteristic
195C4×Dic73C22⋊C411yescharacteristic
196C4×Dic73C22⋊C411yescharacteristic
197C4×Dic73C22⋊C411yescharacteristic
198C4×Dic73C22⋊C411yescharacteristic
199C4×Dic73C22⋊C411yescharacteristic
200C4×Dic73C22×C411yescharacteristic
201C4×Dic73C22×C411yescharacteristic
202C4×Dic73C2×D411yescharacteristic
203C4×Dic73C2×D411yescharacteristic
204C4×Dic73C2×D411yescharacteristic
205C4×Dic73C2×D411yescharacteristic
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73C22×C411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×D411yescharacteristic
211M16×C73—24no—
212C2×C8×C73—22no—
213C2×C8×C73—22no—
214C4⋊C4×C73—22no—
215C4⋊C4×C73—22no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—22no—
219C4⋊C4×C73—22no—
220C4⋊C4×C73C22×C412yes—
221C4⋊C4×C73C22×C412yes—
222C42×C73C22×C411yescharacteristic
223C42×C73C2×D411yescharacteristic
224C42×C73C2×D411yescharacteristic
225C42×C73C2411yescharacteristic
226C23×C73C2×C22⋊C411yescharacteristic
227C22×D73—22no—
228C22×D73—22no—
229C22×D73#10414yes—
230C22×D73C2×C22⋊C411yescharacteristic
231C22×D73C2×C22⋊C411yescharacteristic
232C2×C4×C73—22no—
233C2×C4×C73—22no—
234C2×C4×C73—22no—
235C2×C4×C73—22no—
236C2×C4×C73—41no—
237C2×C4×C73—42no—
238C2×C4×C73—42no—
239C2×C4×C73C2×C22⋊C411yescharacteristic
240C2×C4×C73C2×C22⋊C411yescharacteristic
241C2×C4×C73C2×C22⋊C411yescharacteristic
242C2×C4×C73C23×C411yescharacteristic
243C2×C4×C73C22×D411yescharacteristic
244C2×C4×C73C22×D411yescharacteristic
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—22no—
248C2×Dic73—22no—
249C2×Dic73—41no—
250C2×Dic73—42no—
251C2×Dic73—42no—
252C2×Dic73C2×C22⋊C411yescharacteristic
253C2×Dic73C2×C22⋊C411yescharacteristic
254C2×Dic73C2×C22⋊C411yescharacteristic
255C2×Dic73C2×C22⋊C411yescharacteristic
256C2×Dic73C2×C22⋊C411yescharacteristic
257C2×Dic73C2×C22⋊C411yescharacteristic
258C4×D73—22no—
259C4×D73—22no—
260C4×D73—22no—
261C4×D73—22no—
262C4×D73—22no—
263C4×D73—22no—
264C4×D73—22no—
265C4×D73—22no—
266C4×D73—22no—
267C4×D73—41no—
268C4×D73—41no—
269C4×D73—44no—
270C4×D73—44no—
271C4×D73—44no—
272C4×D73—44no—
273C4×D73#10114yes—
274C8×C73—24no—
275C8×C73—42no—
276#10596831—24no—
277#10596831—42no—
278C22×C73—21no—
279C22×C73—21no—
280C22×C73C2×#10412yes—
281C22×C73C22×C22⋊C411yescharacteristic
282C2×D73—21no—
283C2×D73—21no—
284C2×D73—28no—
285C2×D73C2×#10112yes—
286C2×D73C2×#10412yes—
287C2×D73C2×#10412yes—
288C2×D73#42112yes—
289C4×C73—21no—
290C4×C73—21no—
291C4×C73—21no—
292C4×C73—21no—
293C4×C73—21no—
294C4×C73—42no—
295C4×C73—42no—
296C4×C73C2×#10112yes—
297Dic73—21no—
298Dic73—21no—
299Dic73—21no—
300Dic73—21no—
301Dic73—21no—
302Dic73—42no—
303Dic73—42no—
304Dic73C2×#10112yes—
305C2×#1528—731nomaximal, Sylow
306C2×C73—22no—
307C2×C73C22×#10111yescharacteristic
308C2×C73C22×#10411yescharacteristic
309C2×C73C2×#42111yescharacteristic
310D73—22no—
311D73#152814yesdirect product factor
312C22×#125—731no—
313C2×#432—731no—
314C2×C4×M16—731no—
315#1528—731no—
316#1528—731no—
317#1528—734no—
318#1528—731no—
319#1528D7311yescharacteristic, direct product factor
320C2×#330—734no—
321C73C2×#152811yescharacteristic, complemented, Sylow
322C22×M16—1461no—
323C2×#125—732no—
324C2×#125—732no—
325C2×#125—732no—
326C2×#125—732no—
327C2×#125—731no—
328C2×#125—731no—
329C2×#125—731no—
330C2×#125—1461no—
331C2×#125—1461no—
332C2×#125—1461no—
333C2×#125—1461no—
334C2×#125—1461no—
335C2×#125—1461no—
336C2×#125C2×D7311yescharacteristic
337C22×C4⋊C4—731no—
338C22×C4⋊C4—731no—
339C22×C4⋊C4—1461no—
340C22×C4⋊C4—1461no—
341C22×C42—731no—
342#432—731no—
343#432—732no—
344#432—1461no—
345#432—1461no—
346#432C2×D7311yescharacteristic
347C2×C4⋊C8—1461no—
348C2×C22⋊C8—1461no—
349C4×M16—731no—
350C4×M16—732no—
351C4×M16—1461no—
352C4×M16—1461no—
353C4×M16C2×D7311yescharacteristic
354C2×#97—732no—
355C2×#97—732no—
356C2×C4×C8—1461no—
357#330—734no—
358#330—734no—
359#330—734no—
360#330C2×D7314yescomplemented
361C23×C4—731no—
362C23×C4—731no—
363C23×C4—731no—
364C23×C4—1461no—
365C23×C4—1461no—
366C2×M16—21no—
367C2×M16—1462no—
368C2×M16—1468no—
369C2×M16—1461no—
370C22×C8—1462no—
371C22×C8—1462no—
372#125—21no—
373#125—21no—
374#125—732no—
375#125—732no—
376#125—732no—
377#125—732no—
378#125—732no—
379#125—732no—
380#125—1462no—
381#125—1462no—
382#125—1462no—
383#125—1462no—
384#125—1462no—
385#125—1462no—
386#125—1462no—
387#125—1462no—
388#125—1461no—
389#125—1461no—
390#125—1461no—
391#125—1461no—
392#125—1461no—
393#125—1461no—
394#125C4×D7312yes—
395#125C22×D7312yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—732no—
401C2×C4⋊C4—732no—
402C2×C4⋊C4—732no—
403C2×C4⋊C4—732no—
404C2×C4⋊C4—1461no—
405C2×C4⋊C4—1461no—
406C2×C4⋊C4—1461no—
407C2×C4⋊C4—1461no—
408C2×C4⋊C4—1462no—
409C2×C4⋊C4—1462no—
410C2×C4⋊C4—1462no—
411C2×C4⋊C4—1462no—
412C2×C4⋊C4—1462no—
413C2×C4⋊C4—1462no—
414C2×C4⋊C4—1462no—
415C2×C4⋊C4—1462no—
416C2×C4⋊C4—1461no—
417C2×C4⋊C4—1461no—
418C2×C4⋊C4—1461no—
419C2×C4⋊C4—1461no—
420C2×C4⋊C4—1461no—
421C2×C4⋊C4—1461no—
422C2×C4⋊C4—1461no—
423C2×C4⋊C4—1461no—
424C2×C4⋊C4C4×D7311yescharacteristic
425C2×C4⋊C4C4×D7311yescharacteristic
426C2×C42—731no—
427C2×C42—731no—
428C2×C42—731no—
429C2×C42—731no—
430C2×C42—731no—
431C2×C42—731no—
432C2×C42—731no—
433C2×C42—731no—
434C2×C42—731no—
435C2×C42—731no—
436C2×C42—731no—
437C2×C42C22×D7311yescharacteristic
438C4⋊C8—21no—
439C4⋊C8—1462no—
440C4⋊C8—1461no—
441C22⋊C8—21no—
442C22⋊C8—1462no—
443C22⋊C8—1461no—
444#97—732no—
445#97—732no—
446#97—1462no—
447#97—1462no—
448#97C22×D7312yes—
449#97C22×D7312yes—
450C4×C8—21no—
451C4×C8—1462no—
452C4×C8—1461no—
453C24—731no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—2924no—
457C22×C4—2924no—
458C22×C4—2922no—
459C22×C4—731no—
460C22×C4—731no—
461C22×C4—731no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—731no—
466C22×C4—731no—
467C22×C4—731no—
468C22×C4—731no—
469C22×C4—731no—
470C22×C4—731no—
471C22×C4—731no—
472C22×C4—731no—
473C22×C4—731no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4—1462no—
477C22×C4—1462no—
478C22×C4—1464no—
479C22×C4—1464no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4C2×C4×D7311yescharacteristic
483C22×C4D4×D7311yescharacteristic
484C22×C4D4×D7311yescharacteristic
485M16—24no—
486M16—1468no—
487M16—1464no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—2924no—
491C2×C8—1468no—
492C2×C8—1462no—
493C2×C8—1462no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—732no—
501C4⋊C4—732no—
502C4⋊C4—1462no—
503C4⋊C4—1462no—
504C4⋊C4—1462no—
505C4⋊C4—1462no—
506C4⋊C4—1462no—
507C4⋊C4—1462no—
508C4⋊C4—1462no—
509C4⋊C4—1462no—
510C4⋊C4—1462no—
511C4⋊C4—1462no—
512C4⋊C4—1462no—
513C4⋊C4—1462no—
514C4⋊C4—1462no—
515C4⋊C4—1462no—
516C4⋊C4—1461no—
517C4⋊C4—1461no—
518C4⋊C4—1462no—
519C4⋊C4—1462no—
520C4⋊C4C2×C4×D7312yes—
521C4⋊C4C2×C4×D7312yes—
522C42—731no—
523C42—731no—
524C42—731no—
525C42—731no—
526C42—731no—
527C42—731no—
528C42—731no—
529C42—731no—
530C42—731no—
531C42—731no—
532C42—731no—
533C42—731no—
534C42C2×C4×D7311yescharacteristic
535C42D4×D7311yescharacteristic
536C42D4×D7311yescharacteristic
537C42C23×D7311yescharacteristic
538C23—731no—
539C23—731no—
540C23—734no—
541C23—1462no—
542C23—1462no—
543C23C22⋊C4×D7311yescharacteristic
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—2924no—
554C2×C4—2924no—
555C2×C4—2924no—
556C2×C4—2924no—
557C2×C4—2922no—
558C2×C4—2922no—
559C2×C4—2921no—
560C2×C4—731no—
561C2×C4—734no—
562C2×C4—731no—
563C2×C4—731no—
564C2×C4—731no—
565C2×C4—731no—
566C2×C4—731no—
567C2×C4—1462no—
568C2×C4—1462no—
569C2×C4—1462no—
570C2×C4—1462no—
571C2×C4—1462no—
572C2×C4—1462no—
573C2×C4—1462no—
574C2×C4—1462no—
575C2×C4—1462no—
576C2×C4—1462no—
577C2×C4—1462no—
578C2×C4—1462no—
579C2×C4—1462no—
580C2×C4C22⋊C4×D7311yescharacteristic
581C2×C4C22⋊C4×D7311yescharacteristic
582C2×C4C22⋊C4×D7311yescharacteristic
583C2×C4C22×C4×D7311yescharacteristic
584C2×C4C2×D4×D7311yescharacteristic
585C2×C4C2×D4×D7311yescharacteristic
586C8—24no—
587C8—42no—
588C8—2922no—
589C8—1464no—
590C22—21no—
591C22—21no—
592C22—732no—
593C22—732no—
594C22—732no—
595C22—732no—
596C22—1468no—
597C22—1461no—
598C22—1461no—
599C22#104×D7312yes—
600C22C2×C22⋊C4×D7311yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—2922no—
609C4—2922no—
610C4—732no—
611C4—1461no—
612C4—1461no—
613C4—1461no—
614C4—1461no—
615C4—1461no—
616C4#101×D7312yes—
617C2—22no—
618C2—734no—
619C2—1462no—
620C2C2×#101×D7311yescharacteristic
621C2C2×#104×D7311yescharacteristic
622C2#421×D7311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1528C2
socleC22×C73C22×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC42×C73C24
hypercenter#1528D73
hypocenterC73C2×#1528
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
4. #22608534C2semidirect
5. #22608533C2semidirect
6. #22608532C2semidirect
7. #22608531C2semidirect
8. #330×D73C2semidirect
9. C73×#1528C2semidirect
42. #17988329C22semidirect
43. #17988328C22semidirect
44. #17988328C22semidirect
48. #330×C73C22semidirect
311. D73#1528direct (N × H)
319. #1528D73direct (N × H)
321. C73C2×#1528semidirect
360. #330C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D732
#432×D732
C4×M16×D732
#226085342
#226085332
#226085322
#226085312
#330×D732
C73×#15282
C2×#152873