Finite Group Databasebeta

← #33090971

Subgroups — #33090971

Order 18688.

1186 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989117C211yesmaximal, characteristic
2C2×#17988637C211yesmaximal, characteristic, complemented
3C2×M16×Dic73C211yesmaximal, characteristic, complemented
4#22610865C212yesmaximal, complemented
5#22610723C212yesmaximal, complemented
6#22610229C211yesmaximal, characteristic, complemented
7#22610228C211yesmaximal, characteristic, complemented
8#22610226C211yesmaximal, characteristic, complemented
9#22609699C212yesmaximal, complemented
10#22609696C212yesmaximal, complemented
11C73×#1870C211yesmaximal, characteristic, complemented
12C22×#11924012C2211yescharacteristic
13#17989117—24no—
14#17989117—24no—
15C2×#14556586C411yescharacteristic
16C2×#14556584C411yescharacteristic
17C2×#14556581C411yescharacteristic
18C2×#14556577C411yescharacteristic
19C2×#14556575C411yescharacteristic
20C2×#14556572C411yescharacteristic
21C2×#14556568C411yescharacteristic
22C2×#14556563C411yescharacteristic
23C2×C4×Dic146C2211yescharacteristic
24C2×C4×C22⋊D73C2211yescharacteristic
25C2×C4×C22⋊D73C2211yescharacteristic
26C2×#14556550C2211yescharacteristic
27C2×#14556548C2211yescharacteristic
28C22×C4×Dic73C2211yescharacteristic
29#17988637—24no—
30C2×#14556520C2212yes—
31C2×C22⋊#10596831C2212yes—
32C2×C22⋊#10596831C2211yescharacteristic
33C2×#14556503C2212yes—
34C2×#14556503C2212yes—
35M16×Dic73—24no—
36C2×#14556501C2212yes—
37C2×C8×Dic73C2212yes—
38C2×C8×Dic73C2212yes—
39#17988342C2212yes—
40#17988341C2212yes—
41#17988341C2212yes—
42C22×M16×C73C2211yescharacteristic
43C2×C4×D4×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2212yes—
45C2×C22⋊C8×C73C2211yescharacteristic
46#336×C73C2212yes—
47C22×Dic146C2×C411yescharacteristic
48C22×C22⋊D73C2×C411yescharacteristic
49C22×C22⋊D73C2×C411yescharacteristic
50C23×Dic73C2×C411yescharacteristic
51C23×Dic73C2×C411yescharacteristic
52C22×C4×D73C2311yescharacteristic
53C2×#11924012—24no—
54C2×#11924012—22no—
55C22×#10596831C2312yes—
56C22×#10596831C2312yes—
57#14556586—24no—
58#14556584—24no—
59#14556581—24no—
60#14556577—24no—
61#14556575—24no—
62#14556572—24no—
63#14556568—24no—
64#14556563—24no—
65C4×Dic146—22no—
66C4×Dic146—22no—
67C4×C22⋊D73—22no—
68C4×C22⋊D73—22no—
69C4×C22⋊D73—22no—
70C4×C22⋊D73—22no—
71#14556550—22no—
72#14556550—22no—
73#14556548—22no—
74#14556548—22no—
75C2×C4⋊Dic73C2×C411yescharacteristic
76C2×C4⋊Dic73C2×C411yescharacteristic
77C2×C4⋊Dic73C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×C4×Dic73C2×C411yescharacteristic
93C2×C4×Dic73C2×C411yescharacteristic
94C2×C4×Dic73D414yes—
95C2×C4×Dic73D414yes—
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99#14556520—24no—
100C22⋊#10596831—24no—
101C22⋊#10596831—22no—
102#14556503—24no—
103#14556503—24no—
104#14556501—24no—
105C8×Dic73—24no—
106C8×Dic73—24no—
107C22×D4×C73C2×C411yescharacteristic
108C23×C4×C73C2311yescharacteristic
109C23×C4×C73C2311yescharacteristic
110C2×M16×C73—22no—
111C2×M16×C73—24no—
112C22×C8×C73C2312yes—
113C22×C8×C73C2312yes—
114C4×D4×C73—22no—
115C4×D4×C73—22no—
116C2×C4⋊C4×C73C2×C411yescharacteristic
117C2×C22⋊C4×C73C2×C411yescharacteristic
118C2×C22⋊C4×C73C2×C411yescharacteristic
119C2×C42×C73C2311yescharacteristic
120C22⋊C8×C73—22no—
121C22⋊C8×C73—24no—
122C23×D73C22×C411yescharacteristic
123C2×Dic146—22no—
124C2×Dic146—24no—
125C2×C22⋊D73—22no—
126C2×C22⋊D73—22no—
127C2×C22⋊D73—24no—
128C2×C22⋊D73—41no—
129C2×C22⋊D73—41no—
130C22×Dic73—24no—
131C22×Dic73—41no—
132C22×Dic73—41no—
133C22×Dic73C22⋊C414yes—
134C22×Dic73C22⋊C414yes—
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C22×Dic73C22×C411yescharacteristic
139C22×Dic73C22×C411yescharacteristic
140C22×Dic73C22×C411yescharacteristic
141C22×Dic73C22×C411yescharacteristic
142C2×C4×D73—21no—
143C2×C4×D73—21no—
144C2×C4×D73—22no—
145C2×C4×D73—22no—
146#11924012—28no—
147C2×#10596831—22no—
148C2×#10596831—22no—
149C2×#10596831—22no—
150C2×#10596831—22no—
151C2×#10596831—22no—
152C2×#10596831#4114yes—
153C4⋊Dic73—22no—
154C4⋊Dic73—22no—
155C4⋊Dic73—22no—
156#11924007—22no—
157#11924007—22no—
158#11924007—22no—
159#11924007—22no—
160#11924007—22no—
161#11924007—22no—
162C22⋊Dic73—22no—
163C22⋊Dic73—22no—
164C22⋊Dic73—22no—
165C22⋊Dic73—22no—
166#11924005—22no—
167#11924005—22no—
168#11924005—22no—
169#11924005—22no—
170C4×Dic73—21no—
171C4×Dic73—21no—
172C4×Dic73C22⋊C414yes—
173C4×Dic73C22⋊C414yes—
174C4×Dic73C2×D412yes—
175C4×Dic73C2×D412yes—
176C4×Dic73C2×D412yes—
177C4×Dic73C2×D412yes—
178C24×C73C22×C411yescharacteristic
179C24×C73C22×C411yescharacteristic
180C2×D4×C73—22no—
181C2×D4×C73—41no—
182C2×D4×C73—41no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—22no—
188C22×C4×C73—22no—
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C2×D412yes—
194C22×C4×C73C2×D412yes—
195C22×C4×C73C2411yescharacteristic
196M16×C73—28no—
197C2×C8×C73—22no—
198C2×C8×C73—22no—
199C2×C8×C73—22no—
200C2×C8×C73—22no—
201C2×C8×C73—22no—
202C2×C8×C73#4114yes—
203C4⋊C4×C73—22no—
204C22⋊C4×C73—22no—
205C22⋊C4×C73—22no—
206C42×C73—21no—
207C42×C73—21no—
208C23×C73—22no—
209C23×C73—22no—
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—22no—
214C23×C73—22no—
215C23×C73—21no—
216C23×C73—21no—
217C23×C73C2×C22⋊C412yes—
218C23×C73C23×C411yescharacteristic
219C22×D73—21no—
220C22×D73—22no—
221C22×D73—22no—
222C22×D73—21no—
223C22×D73—21no—
224D4×C73—44no—
225C2×C4×C73—22no—
226C2×C4×C73—22no—
227C2×C4×C73—22no—
228C2×C4×C73—24no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—22no—
233C2×C4×C73—22no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—42no—
239C2×C4×C73C2×C22⋊C412yes—
240C2×C4×C73C22×D411yescharacteristic
241C2×C4×C73C22×D411yescharacteristic
242C2×C4×C73C2×#4112yes—
243C2×C4×C73C2×#4112yes—
244C22⋊D73—44no—
245C22⋊D73—44no—
246C2×Dic73—22no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—28no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—22no—
256C2×Dic73—22no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—44no—
260C2×Dic73C2×C22⋊C412yes—
261C2×Dic73C2×C22⋊C412yes—
262C2×Dic73C2×C22⋊C412yes—
263C2×Dic73C2×C22⋊C412yes—
264C2×Dic73#13114yes—
265C4×D73—41no—
266C4×D73—41no—
267C4×D73—42no—
268Dic146—44no—
269C8×C73—24no—
270C8×C73—42no—
271#10596831—24no—
272#10596831—42no—
273C22×C73—22no—
274C22×C73—22no—
275C22×C73—22no—
276C22×C73—42no—
277C22×C73—42no—
278C22×C73—41no—
279C22×C73—41no—
280C22×C73—42no—
281C22×C73—42no—
282C22×C73—41no—
283C22×C73C22×C22⋊C411yescharacteristic
284C22×C73C4×#4112yes—
285C22×C73C2×#13112yes—
286C22×C73#56811yescharacteristic
287C22×C73#56811yescharacteristic
288C2×D73—41no—
289C2×D73—41no—
290C2×D73—42no—
291C2×D73—42no—
292C2×D73—41no—
293C4×C73—22no—
294C4×C73—41no—
295C4×C73—41no—
296C4×C73—41no—
297C4×C73#52511yescharacteristic
298C4×C73#52511yescharacteristic
299C4×C73#53212yes—
300Dic73—22no—
301Dic73—22no—
302Dic73—22no—
303Dic73—41no—
304Dic73—41no—
305Dic73—41no—
306Dic73#40814yes—
307#21378—731nomaximal, Sylow
308C2×C73—42no—
309C2×C73—81no—
310C2×C73#229711yescharacteristic
311C2×C73C2×#40811yescharacteristic
312C2×C73#287911yescharacteristic
313C2×C73#296912yes—
314C2×C73#296912yes—
315D73—81no—
316C2×#529—731no—
317C2×#431—731no—
318C2×C4×M16—731no—
319#1984—732no—
320#1954—732no—
321#1870—731no—
322#1870—731no—
323#1870—731no—
324#1870D7311yescharacteristic, complemented
325#1750—732no—
326#1750—732no—
327C73#2137811yescharacteristic, complemented, Sylow
328C22×M16—731no—
329C22×M16C2×D7311yescharacteristic
330#529—1464no—
331#529—1464no—
332C2×#126—731no—
333C2×#126—731no—
334C2×#125—731no—
335C2×#124—731no—
336C2×#123—731no—
337C2×#123—731no—
338C2×C22⋊Q8—731no—
339C2×#121—731no—
340C2×C4×Q8—731no—
341C2×C4×D4—731no—
342C2×C4×D4—731no—
343C2×C4×D4C2×D7311yescharacteristic
344C2×#117—731no—
345C2×#117—731no—
346C22×C42—731no—
347#431—1464no—
348C2×C4⋊C8—732no—
349C2×C22⋊C8—731no—
350C2×C22⋊C8—732no—
351C2×C22⋊C8—732no—
352C2×C22⋊C8—732no—
353C2×C22⋊C8C2×D7311yescharacteristic
354C2×C22⋊C8C2×D7312yes—
355C4×M16—1464no—
356C2×#97—732no—
357C2×C4×C8—732no—
358C2×C4×C8—732no—
359#336—732no—
360#336—732no—
361#336—732no—
362#336C2×D7312yes—
363C22×Q8—731no—
364C22×D4—731no—
365C22×D4—731no—
366C22×D4C4×D7311yescharacteristic
367C23×C4—731no—
368C23×C4—731no—
369C23×C4—731no—
370C23×C4C22×D7311yescharacteristic
371C23×C4C22×D7311yescharacteristic
372C2×M16—22no—
373C2×M16—24no—
374C2×M16—1464no—
375C2×M16—1462no—
376C22×C8—732no—
377C22×C8—732no—
378C22×C8C22×D7312yes—
379C22×C8C22×D7312yes—
380#126—1464no—
381#126—1464no—
382#125—1464no—
383#124—1464no—
384#123—1464no—
385#123—1464no—
386C22⋊Q8—1464no—
387#121—1464no—
388C4×Q8—1462no—
389C4×Q8—1462no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—1462no—
393C4×D4—1462no—
394C4×D4—1462no—
395C4×D4—1462no—
396#117—1462no—
397#117—1462no—
398#117—1462no—
399#117—1462no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4—731no—
405C2×C4⋊C4—731no—
406C2×C4⋊C4—731no—
407C2×C4⋊C4—731no—
408C2×C4⋊C4—731no—
409C2×C4⋊C4C4×D7311yescharacteristic
410C2×C22⋊C4—731no—
411C2×C22⋊C4—731no—
412C2×C22⋊C4—731no—
413C2×C22⋊C4—731no—
414C2×C22⋊C4—731no—
415C2×C22⋊C4—731no—
416C2×C22⋊C4—731no—
417C2×C22⋊C4—731no—
418C2×C22⋊C4C4×D7311yescharacteristic
419C2×C22⋊C4C4×D7311yescharacteristic
420C2×C42—731no—
421C2×C42—731no—
422C2×C42—734no—
423C2×C42—734no—
424C2×C42—731no—
425C2×C42—731no—
426C2×C42—731no—
427C2×C42C22×D7311yescharacteristic
428C4⋊C8—1464no—
429C22⋊C8—22no—
430C22⋊C8—24no—
431C22⋊C8—1464no—
432C22⋊C8—1464no—
433C22⋊C8—1462no—
434C22⋊C8—1464no—
435#97—1464no—
436C4×C8—1464no—
437C4×C8—1464no—
438C24—731no—
439C24C2×C4×D7311yescharacteristic
440C24C2×C4×D7311yescharacteristic
441C2×Q8—1462no—
442C2×Q8—1464no—
443C2×D4—22no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—2921no—
447C2×D4—2921no—
448C2×D4—1462no—
449C2×D4—1464no—
450C2×D4—1462no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—2921no—
458C22×C4—2921no—
459C22×C4—734no—
460C22×C4—731no—
461C22×C4—734no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—731no—
466C22×C4—731no—
467C22×C4—731no—
468C22×C4—1461no—
469C22×C4—1461no—
470C22×C4—1462no—
471C22×C4—1462no—
472C22×C4—1464no—
473C22×C4C2×C4×D7311yescharacteristic
474C22×C4C2×C4×D7311yescharacteristic
475C22×C4C2×C4×D7311yescharacteristic
476C22×C4C2×C4×D7311yescharacteristic
477C22×C4D4×D7312yes—
478C22×C4D4×D7312yes—
479C22×C4C23×D7311yescharacteristic
480M16—28no—
481M16—1468no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—734no—
488C2×C8—1462no—
489C2×C8—1462no—
490C2×C8—1462no—
491C2×C8—1462no—
492C2×C8—1462no—
493C2×C8#1192402714yes—
494C4⋊C4—22no—
495C4⋊C4—1462no—
496C4⋊C4—1462no—
497C4⋊C4—1462no—
498C4⋊C4—1462no—
499C4⋊C4—1462no—
500C4⋊C4—1462no—
501C4⋊C4—1462no—
502C4⋊C4—1462no—
503C4⋊C4—1462no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—1462no—
507C22⋊C4—1462no—
508C22⋊C4—1462no—
509C22⋊C4—1462no—
510C22⋊C4—1462no—
511C22⋊C4—1462no—
512C22⋊C4—1462no—
513C22⋊C4—1462no—
514C42—21no—
515C42—21no—
516C42—734no—
517C42—734no—
518C42—732no—
519C42—732no—
520C42—732no—
521C42—732no—
522C42—1461no—
523C42—1461no—
524C23—22no—
525C23—22no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—22no—
530C23—22no—
531C23—21no—
532C23—21no—
533C23—1461no—
534C23—1462no—
535C23—1462no—
536C23—1461no—
537C23—1461no—
538C23C22⋊C4×D7312yes—
539C23C22×C4×D7311yescharacteristic
540Q8—2924no—
541D4—44no—
542D4—2924no—
543D4—2924no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—2922no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2924no—
562C2×C4—732no—
563C2×C4—734no—
564C2×C4—732no—
565C2×C4—732no—
566C2×C4—732no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1462no—
571C2×C4—1462no—
572C2×C4—1461no—
573C2×C4—1461no—
574C2×C4—1468no—
575C2×C4—1462no—
576C2×C4—1461no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4C22⋊C4×D7312yes—
581C2×C4C2×D4×D7311yescharacteristic
582C2×C4C2×D4×D7311yescharacteristic
583C2×C4#41×D7312yes—
584C2×C4C2×#1192402712yes—
585C8—24no—
586C8—42no—
587C8—2922no—
588C8—1464no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—42no—
593C22—42no—
594C22—41no—
595C22—41no—
596C22—42no—
597C22—42no—
598C22—41no—
599C22—2921no—
600C22—2921no—
601C22—2922no—
602C22—2922no—
603C22—2921no—
604C22C2×C22⋊C4×D7311yescharacteristic
605C22C4×#1192402712yes—
606C22#131×D7312yes—
607C22#1798935311yescharacteristic
608C22#1798935311yescharacteristic
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—2921no—
614C4—2921no—
615C4—2921no—
616C4—734no—
617C4—1462no—
618C4—1462no—
619C4—1462no—
620C4#1798909311yescharacteristic
621C4#1798909511yescharacteristic
622C4#1798913212yes—
623C2—42no—
624C2—81no—
625C2—5841no—
626C2#2261241611yescharacteristic
627C2#408×D7311yescharacteristic
628C2#2261837411yescharacteristic
629C2#2261892812yes—
630C2#2261893012yes—
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1870C2
prime radicalC2×#14556563C4
cosocleC22×C4×C73C24
hypercenter#1870D73
hypocenterC73#21378
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#17988637C2semidirect
3. C2×M16×Dic73C2semidirect
4. #22610865C2semidirect
5. #22610723C2semidirect
6. #22610229C2semidirect
7. #22610228C2semidirect
8. #22610226C2semidirect
9. #22609699C2semidirect
10. #22609696C2semidirect
11. C73×#1870C2semidirect
324. #1870D73semidirect
327. C73#21378semidirect

Maximal subgroups

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

subgroupindex
C2×#179891172
C2×#179886372
C2×M16×Dic732
#226108652
#226107232
#226102292
#226102282
#226102262
#226096992
#226096962
C73×#18702
#2137873