Finite Group Databasebeta

← #33136158

Subgroups — #33136158

Order 18688.

850 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×#17988894C211yesmaximal, characteristic, complemented
2C2×D4×#10596831C211yesmaximal, characteristic
3#22615097C211yesmaximal, characteristic
4#22611367C211yesmaximal, characteristic, complemented
5#22611357C211yesmaximal, characteristic, complemented
6#22611131C211yesmaximal, characteristic, complemented
7#22611124C211yesmaximal, characteristic, complemented
8#22610895C211yesmaximal, characteristic, complemented
9#22610697C211yesmaximal, characteristic, complemented
10#22610355C211yesmaximal, characteristic, complemented
11#22610355C211yesmaximal, characteristic, complemented
12#22609958C211yesmaximal, characteristic, complemented
13#22609954C211yesmaximal, characteristic, complemented
14C4×#14556515C211yesmaximal, characteristic, complemented
15C73×#2536C211yesmaximal, characteristic
16C23×#10596831C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556583C2211yescharacteristic
19#17988894—24no—
20D4×#10596831—24no—
21C2×#14556524C2211yescharacteristic
22C2×#14556524C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556515C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33#17988525—21no—
34#17988501—21no—
35#17988481—21no—
36#17988481—21no—
37#17988447C2211yescharacteristic
38#17988447C2211yescharacteristic
39#17988447C2211yescharacteristic
40#17988447C2211yescharacteristic
41C4×C4⋊Dic73C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50C2×C22⋊Q8×C73C2211yescharacteristic
51C2×C22⋊Q8×C73C2211yescharacteristic
52C2×C4×Q8×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54#398×C73—21no—
55#394×C73—21no—
56#388×C73—21no—
57#388×C73—21no—
58#382×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60#380×C73C2211yescharacteristic
61C22×#10596831—22no—
62C22×#10596831—22no—
63C22×#10596831—22no—
64C22×#10596831—22no—
65C22×#10596831—41no—
66C22×#10596831—41no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556583—22no—
72#14556583—22no—
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C4⋊Dic73C2311yescharacteristic
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×C22⋊Dic73—21no—
80C2×C22⋊Dic73—21no—
81C2×C22⋊Dic73—21no—
82C2×C22⋊Dic73—21no—
83C2×C4×Dic73—21no—
84#14556524—22no—
85#14556524—41no—
86#14556522—22no—
87#14556522—41no—
88C4⋊#10596831D414yes—
89#14556515—22no—
90#14556515—22no—
91#14556515—22no—
92#14556515—22no—
93C22⋊#10596831—22no—
94C22⋊#10596831—22no—
95C4×#10596831—22no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101C22×Q8×C73C2311yescharacteristic
102C22×D4×C73D411yescharacteristic
103C23×C4×C73C2311yescharacteristic
104C23×C4×C73C2311yescharacteristic
105C22⋊Q8×C73—22no—
106C22⋊Q8×C73—22no—
107C22⋊Q8×C73—41no—
108C22⋊Q8×C73—41no—
109C4×Q8×C73—22no—
110C4×Q8×C73—22no—
111C4×D4×C73—22no—
112C4×D4×C73—22no—
113C2×C4⋊C4×C73—21no—
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73D411yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73D411yescharacteristic
125C2×C22⋊C4×C73D411yescharacteristic
126C2×C42×C73—21no—
127C2×C42×C73C2311yescharacteristic
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—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—44no—
146C2×#10596831—44no—
147C2×#10596831C2×D412yes—
148C2×#10596831C2×D412yes—
149C2×#10596831#4112yes—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158#11924007—42no—
159#11924007—42no—
160C22⋊Dic73—42no—
161C22⋊Dic73—42no—
162C22⋊Dic73—81no—
163C22⋊Dic73—81no—
164C4×Dic73—81no—
165C24×C73C2×D411yescharacteristic
166C24×C73C2×D411yescharacteristic
167C2×Q8×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73—21no—
172C2×Q8×C73#4112yes—
173C2×D4×C73—22no—
174C2×D4×C73—22no—
175C2×D4×C73—22no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2411yescharacteristic
197C4⋊C4×C73—22no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—42no—
205C4⋊C4×C73—42no—
206C4⋊C4×C73—42no—
207C22⋊C4×C73—22no—
208C22⋊C4×C73—22no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—42no—
213C42×C73—42no—
214C42×C73C2×D412yes—
215C42×C73#4112yes—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73#13512yes—
229C23×C73#13512yes—
230C23×C73C22×D411yescharacteristic
231Q8×C73—22no—
232Q8×C73—22no—
233Q8×C73—41no—
234Q8×C73—41no—
235D4×C73—28no—
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—22no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73#12112yes—
267C2×C4×C73#12112yes—
268C2×C4×C73C22×D411yescharacteristic
269C2×C4×C73C2×#4111yescharacteristic
270C2×C4×C73C2×#4111yescharacteristic
271C2×C4×C73C2×#4111yescharacteristic
272C2×C4×C73H(5,𝔽2)11yescharacteristic
273C2×C4×C732−1+411yescharacteristic
274C2×Dic73—41no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73—41no—
279C2×Dic73—41no—
280C2×Dic73—41no—
281C2×Dic73—41no—
282C2×Dic73—41no—
283C2×Dic73—41no—
284C2×Dic73—41no—
285C2×Dic73—41no—
286#10596831—22no—
287#10596831—22no—
288#10596831—22no—
289#10596831—41no—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—22no—
294C22×C73—22no—
295C22×C73—22no—
296C22×C73—41no—
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73C2×#12111yescharacteristic
305C22×C73#54611yescharacteristic
306C22×C73#54711yescharacteristic
307C22×C73C2×#13511yescharacteristic
308C22×C73C2×#13511yescharacteristic
309C22×C73#57711yescharacteristic
310C22×C73#57811yescharacteristic
311C4×C73—22no—
312C4×C73—22no—
313C4×C73—41no—
314C4×C73—41no—
315C4×C73—42no—
316C4×C73—81no—
317C4×C73—81no—
318C4×C73—81no—
319C4×C73#52911yescharacteristic
320C4×C73#54211yescharacteristic
321C4×C73#54611yescharacteristic
322C4×C73#54811yescharacteristic
323Dic73—81no—
324Dic73—81no—
325Dic73—81no—
326Dic73—81no—
327#25343—731nomaximal, Sylow
328C2×C73—42no—
329C2×C73—42no—
330C2×C73#242711yescharacteristic
331C2×C73#305011yescharacteristic
332C2×C73#306311yescharacteristic
333C2×C73#330011yescharacteristic
334C2×C73#330111yescharacteristic
335C2×C73#333611yescharacteristic
336C2×C73#333711yescharacteristic
337C2×#479—731no—
338C2×C8×D4—731no—
339#2562—731no—
340#2536D7311yescharacteristic
341#2077—731no—
342#2075—731no—
343#2036—731no—
344#2035—731no—
345#1991—731no—
346#1949—731no—
347#1892—731no—
348#1892—731no—
349#1808—731no—
350#1807—731no—
351C4×#103—731no—
352C73#2534311yescharacteristic, complemented, Sylow
353C23×C8—731no—
354C23×C8—731no—
355C2×#125—731no—
356C2×C22⋊Q8C2×D7311yescharacteristic
357C2×C22⋊Q8C2×D7311yescharacteristic
358C2×C4×Q8C2×D7311yescharacteristic
359C2×C4×D4C2×D7311yescharacteristic
360#479—1464no—
361C8×D4—1464no—
362C2×#107—731no—
363C2×#107—731no—
364C2×#106—731no—
365C2×#106—731no—
366C2×C4⋊C8—731no—
367C2×#103—731no—
368C2×#103—731no—
369C2×#103—731no—
370C2×#103—731no—
371C2×C22⋊C8—731no—
372C2×C22⋊C8—731no—
373C2×C4×C8—731no—
374#400—1461no—
375#398—21no—
376#394—21no—
377#394—1461no—
378#388—21no—
379#388—21no—
380#388—1461no—
381#388—1461no—
382#382C2×D7311yescharacteristic
383#380—731no—
384#380—731no—
385#380—731no—
386#380—731no—
387#380C2×D7311yescharacteristic
388#380C2×D7311yescharacteristic
389C4×C4⋊C4—731no—
390#340—731no—
391#340—731no—
392#340—731no—
393#340—731no—
394#340—731no—
395#340—731no—
396#340—731no—
397#340—731no—
398C22×Q8C22×D7311yescharacteristic
399C22×D4C22⋊D7311yescharacteristic
400C23×C4C22×D7311yescharacteristic
401C23×C4C22×D7311yescharacteristic
402C22×C8—2921no—
403C22×C8—2921no—
404C22×C8—731no—
405C22×C8—731no—
406C22×C8—731no—
407C22×C8—731no—
408C22×C8—1462no—
409C22×C8—1462no—
410C22×C8—1462no—
411C22×C8—1462no—
412#125—1462no—
413#125—1462no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—41no—
417C22⋊Q8—41no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×D4—22no—
421C4×D4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—731no—
426C2×C4⋊C4—731no—
427C2×C4⋊C4—731no—
428C2×C4⋊C4—731no—
429C2×C4⋊C4—1461no—
430C2×C4⋊C4—1461no—
431C2×C4⋊C4C22⋊D7311yescharacteristic
432C2×C4⋊C4C22×D7311yescharacteristic
433C2×C4⋊C4C22×D7311yescharacteristic
434C2×C4⋊C4C22×D7311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—1461no—
440C2×C22⋊C4—1461no—
441C2×C22⋊C4—1461no—
442C2×C22⋊C4—1461no—
443C2×C22⋊C4C22⋊D7311yescharacteristic
444C2×C22⋊C4C22⋊D7311yescharacteristic
445C2×C42—21no—
446C2×C42—1461no—
447C2×C42C22×D7311yescharacteristic
448#107—2921no—
449#107—1462no—
450#106—2921no—
451#106—1462no—
452C4⋊C8—734no—
453#103—1462no—
454#103—1462no—
455#103—1462no—
456#103—1462no—
457C22⋊C8—1462no—
458C22⋊C8—1462no—
459C4×C8—1462no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—1461no—
465#95—1461no—
466#95—1461no—
467#95—1461no—
468#95—1461no—
469C24C2×C22⋊D7311yescharacteristic
470C24C2×C22⋊D7311yescharacteristic
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8#1192402712yes—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—1461no—
497C22×C4—1461no—
498C22×C4—1461no—
499C22×C4—1461no—
500C22×C4C2×C22⋊D7311yescharacteristic
501C22×C4C2×C22⋊D7311yescharacteristic
502C22×C4C2×C22⋊D7311yescharacteristic
503C22×C4C2×C22⋊D7311yescharacteristic
504C22×C4C23×D7311yescharacteristic
505C2×C8—2924no—
506C2×C8—2924no—
507C2×C8—732no—
508C2×C8—732no—
509C2×C8—732no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—2922no—
530C4⋊C4—2922no—
531C4⋊C4—1461no—
532C4⋊C4—1461no—
533C4⋊C4—1461no—
534C4⋊C4—1461no—
535C4⋊C4—1461no—
536C4⋊C4—1461no—
537C4⋊C4—1461no—
538C4⋊C4—1461no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—2922no—
546C22⋊C4—2922no—
547C22⋊C4—5841no—
548C22⋊C4—5841no—
549C42—42no—
550C42—5841no—
551C42D4×D7312yes—
552C42#1192402712yes—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#1455661112yes—
566C23#1455661112yes—
567C23C22×C22⋊D7311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—28no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
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—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—2921no—
604C2×C4—2921no—
605C2×C4—2921no—
606C2×C4—2921no—
607C2×C4—2921no—
608C2×C4—2921no—
609C2×C4—2921no—
610C2×C4—2921no—
611C2×C4—2921no—
612C2×C4—2921no—
613C2×C4—2921no—
614C2×C4—2921no—
615C2×C4#1455656312yes—
616C2×C4#1455656312yes—
617C2×C4C2×D4×D7311yescharacteristic
618C2×C4#41×D7311yescharacteristic
619C2×C4C2×#1192402711yescharacteristic
620C2×C4C2×#1192402711yescharacteristic
621C2×C4#1455663611yescharacteristic
622C2×C4#1455663811yescharacteristic
623C8—2921no—
624C8—1462no—
625C8—1462no—
626C8—1462no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×#1455656311yescharacteristic
642C22#1798923111yescharacteristic
643C22#1798923611yescharacteristic
644C22C2×#1455661111yescharacteristic
645C22C2×#1455661111yescharacteristic
646C22#1798939511yescharacteristic
647C22#1798940211yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—5841no—
657C4—5841no—
658C4—5841no—
659C4—5841no—
660C4#1798911811yescharacteristic
661C4#1798920411yescharacteristic
662C4#1798923411yescharacteristic
663C4#1798924311yescharacteristic
664C2—42no—
665C2—42no—
666C2#2261351011yescharacteristic
667C2#2261950911yescharacteristic
668C2#2261961811yescharacteristic
669C2#2262181811yescharacteristic
670C2#2262183311yescharacteristic
671C2#2262229311yescharacteristic
672C2#2262231011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2536C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
hypercenter#2536D73
hypocenterC73#25343
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. C2×#17988894C2semidirect
4. #22611367C2semidirect
5. #22611357C2semidirect
6. #22611131C2semidirect
7. #22611124C2semidirect
8. #22610895C2semidirect
9. #22610697C2semidirect
10. #22610355C2semidirect
11. #22610355C2semidirect
12. #22609958C2semidirect
13. #22609954C2semidirect
14. C4×#14556515C2semidirect
352. C73#25343semidirect

Maximal subgroups

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

subgroupindex
C2×#179888942
C2×D4×#105968312
#226150972
#226113672
#226113572
#226111312
#226111242
#226108952
#226106972
#226103552
#226099582
#226099542
C4×#145565152
C73×#25362
#2534373