Finite Group Databasebeta

← #33022781

Subgroups — #33022781

Order 18688.

1106 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C73⋊#401C212yesmaximal
2#22608193C212yesmaximal
3#22608192C212yesmaximal
4#22608191C212yesmaximal
5#22608161C211yesmaximal, characteristic
6#22608160C211yesmaximal, characteristic
7#22608160C211yesmaximal, characteristic
8#22608160C211yesmaximal, characteristic
9#22608160C211yesmaximal, characteristic
10C4×#14556498C211yesmaximal, characteristic
11C73×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×C4×Dic73C2211yescharacteristic
15C22×C4×Dic73C2211yescharacteristic
16C73⋊#401—28no—
17C2×#14556498C2211yescharacteristic
18C2×#14556498C2211yescharacteristic
19C2×#14556498C2211yescharacteristic
20C2×#14556498C2212yes—
21C2×#14556498C2212yes—
22C2×#14556498C2212yes—
23C2×#14556498C2212yes—
24C2×#14556498C2212yes—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2211yescharacteristic
31C22×C4⋊C4×C73C2211yescharacteristic
32C22×C4⋊C4×C73C2211yescharacteristic
33C22×C42×C73C2211yescharacteristic
34C2×#95×C73C2212yes—
35C2×#95×C73C2212yes—
36C23×Dic73C2312yes—
37C23×Dic73C2312yes—
38C23×Dic73C2311yescharacteristic
39C23×Dic73C2311yescharacteristic
40C23×Dic73C2311yescharacteristic
41C23×Dic73C2311yescharacteristic
42C2×C4⋊Dic73—22no—
43C2×C4⋊Dic73—22no—
44C2×C4⋊Dic73—22no—
45C2×C4⋊Dic73—22no—
46C2×C4⋊Dic73—22no—
47C2×C4⋊Dic73—22no—
48C2×C4×Dic73—22no—
49C2×C4×Dic73—22no—
50C2×C4×Dic73—22no—
51C2×C4×Dic73—22no—
52C2×C4×Dic73—22no—
53C2×C4×Dic73—22no—
54#14556498—24no—
55#14556498—24no—
56#14556498—24no—
57#14556498—24no—
58#14556498—22no—
59#14556498—22no—
60#14556498—24no—
61#14556498—24no—
62#14556498—24no—
63#14556498—22no—
64#14556498—42no—
65#14556498—42no—
66#14556498—42no—
67#14556498D414yes—
68C23×C4×C73C2312yes—
69C23×C4×C73C2312yes—
70C23×C4×C73C2311yescharacteristic
71C23×C4×C73C2311yescharacteristic
72C23×C4×C73C2311yescharacteristic
73C2×C4⋊C4×C73—22no—
74C2×C4⋊C4×C73—22no—
75C2×C4⋊C4×C73—22no—
76C2×C4⋊C4×C73—22no—
77C2×C4⋊C4×C73—22no—
78C2×C4⋊C4×C73—22no—
79C2×C42×C73—22no—
80C2×C42×C73—22no—
81C2×C42×C73—22no—
82#95×C73—24no—
83#95×C73—24no—
84C22×Dic73—21no—
85C22×Dic73—21no—
86C22×Dic73—21no—
87C22×Dic73—21no—
88C22×Dic73—21no—
89C22×Dic73—21no—
90C22×Dic73—21no—
91C22×Dic73—21no—
92C22×Dic73—21no—
93C22×Dic73—21no—
94C22×Dic73—21no—
95C22×Dic73—21no—
96C22×Dic73—21no—
97C22×Dic73—21no—
98C22×Dic73—21no—
99C22×Dic73—21no—
100C22×Dic73—21no—
101C22×Dic73—21no—
102C22×Dic73—21no—
103C22×Dic73—21no—
104C22×Dic73—21no—
105C22×Dic73—21no—
106C22×Dic73—21no—
107C22×Dic73—21no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—22no—
120C22×Dic73—22no—
121C22×Dic73—22no—
122C22×Dic73C2×D412yes—
123C22×Dic73C2×D412yes—
124C22×Dic73#4112yes—
125C22×Dic73#4112yes—
126C4⋊Dic73—44no—
127C4⋊Dic73—44no—
128C4×Dic73—44no—
129C4×Dic73—44no—
130C24×C73C2411yescharacteristic
131C22×C4×C73—21no—
132C22×C4×C73—21no—
133C22×C4×C73—21no—
134C22×C4×C73—21no—
135C22×C4×C73—21no—
136C22×C4×C73—21no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—21no—
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—22no—
144C22×C4×C73—22no—
145C22×C4×C73—22no—
146C22×C4×C73—22no—
147C22×C4×C73—22no—
148C22×C4×C73—22no—
149C22×C4×C73—22no—
150C22×C4×C73—22no—
151C22×C4×C73—22no—
152C22×C4×C73—22no—
153C22×C4×C73—22no—
154C22×C4×C73—22no—
155C22×C4×C73—22no—
156C22×C4×C73—22no—
157C22×C4×C73C2×D412yes—
158C22×C4×C73#4112yes—
159C22×C4×C73#4112yes—
160C22×C4×C73#4112yes—
161C22×C4×C73#4112yes—
162C22×C4×C73#4112yes—
163C22×C4×C73#4112yes—
164C22×C4×C73#4112yes—
165C22×C4×C73#4112yes—
166C4⋊C4×C73—44no—
167C4⋊C4×C73—44no—
168C42×C73—44no—
169C23×C73C22×D411yescharacteristic
170C23×C73C2×#4111yescharacteristic
171C23×C73C2×#4111yescharacteristic
172C23×C73C2×#4111yescharacteristic
173C23×C73C2×#4111yescharacteristic
174C23×C73C2×#4111yescharacteristic
175C23×C73C2×#4111yescharacteristic
176C23×C73C2×#4111yescharacteristic
177C23×C73C2×#4111yescharacteristic
178C23×C73C2×#4111yescharacteristic
179C23×C73C2×#4111yescharacteristic
180C23×C73H(5,𝔽2)11yescharacteristic
181C23×C732−1+411yescharacteristic
182C23×C732−1+411yescharacteristic
183C23×C732−1+411yescharacteristic
184C2×C4×C73—22no—
185C2×C4×C73—22no—
186C2×C4×C73—22no—
187C2×C4×C73—22no—
188C2×C4×C73—22no—
189C2×C4×C73—22no—
190C2×C4×C73—41no—
191C2×C4×C73—41no—
192C2×C4×C73—41no—
193C2×C4×C73—41no—
194C2×C4×C73—41no—
195C2×C4×C73—41no—
196C2×C4×C73—41no—
197C2×C4×C73—41no—
198C2×C4×C73—42no—
199C2×C4×C73—42no—
200C2×C4×C73—42no—
201C2×C4×C73—42no—
202C2×C4×C73—42no—
203C2×C4×C73—42no—
204C2×C4×C73—42no—
205C2×C4×C73—42no—
206C2×C4×C73—42no—
207C2×C4×C73—42no—
208C2×C4×C73—42no—
209C2×C4×C73—42no—
210C2×C4×C73—42no—
211C2×C4×C73—42no—
212C2×C4×C73#12614yes—
213C2×C4×C73#12614yes—
214C2×C4×C73#12614yes—
215C2×C4×C73#12614yes—
216C2×C4×C73#12614yes—
217C2×C4×C73#12614yes—
218C2×C4×C73#12614yes—
219C2×Dic73—22no—
220C2×Dic73—22no—
221C2×Dic73—22no—
222C2×Dic73—22no—
223C2×Dic73—22no—
224C2×Dic73—22no—
225C2×Dic73—22no—
226C2×Dic73—22no—
227C2×Dic73—22no—
228C2×Dic73—22no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—41no—
232C2×Dic73—41no—
233C2×Dic73—41no—
234C2×Dic73—41no—
235C2×Dic73—41no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—42no—
248C2×Dic73—42no—
249C2×Dic73—42no—
250C2×Dic73—42no—
251C2×Dic73—42no—
252C2×Dic73—42no—
253C2×Dic73—42no—
254C2×Dic73—42no—
255C2×Dic73—42no—
256C2×Dic73—42no—
257C2×Dic73—42no—
258C2×Dic73—42no—
259C2×Dic73—42no—
260C2×Dic73—42no—
261C22×C73C2×#12611yescharacteristic
262C22×C73C2×#12611yescharacteristic
263C22×C73C2×#12611yescharacteristic
264C22×C73C2×#12611yescharacteristic
265C22×C73C2×#12611yescharacteristic
266C22×C73C2×#12611yescharacteristic
267C22×C73C2×#12611yescharacteristic
268C22×C73#52911yescharacteristic
269C22×C73#52911yescharacteristic
270C22×C73#52911yescharacteristic
271C22×C73#53211yescharacteristic
272C22×C73#53211yescharacteristic
273C22×C73#53211yescharacteristic
274C22×C73#54111yescharacteristic
275C22×C73#54111yescharacteristic
276C22×C73#54111yescharacteristic
277C22×C73#54211yescharacteristic
278C22×C73#54211yescharacteristic
279C22×C73#54211yescharacteristic
280C22×C73#54711yescharacteristic
281C22×C73#54711yescharacteristic
282C22×C73#54711yescharacteristic
283C22×C73#55011yescharacteristic
284C22×C73#55211yescharacteristic
285C22×C73#55211yescharacteristic
286C22×C73#55211yescharacteristic
287C22×C73#55311yescharacteristic
288C22×C73#55311yescharacteristic
289C22×C73#55311yescharacteristic
290C22×C73#55611yescharacteristic
291C22×C73#55611yescharacteristic
292C22×C73#55611yescharacteristic
293C22×C73#55611yescharacteristic
294C22×C73#55611yescharacteristic
295C22×C73#55611yescharacteristic
296C4×C73—42no—
297C4×C73—42no—
298C4×C73—82no—
299C4×C73—82no—
300C4×C73#40118yescomplemented
301Dic73—42no—
302Dic73—42no—
303Dic73—42no—
304Dic73—42no—
305Dic73—82no—
306Dic73—82no—
307C4⋊#401—731nomaximal, Sylow
308C2×C73C2×#40111yescharacteristic
309C2×C73#249411yescharacteristic
310C2×C73#249411yescharacteristic
311C2×C73#249411yescharacteristic
312C2×C73#249611yescharacteristic
313C2×C73#249611yescharacteristic
314C2×C73#249611yescharacteristic
315C2×C73#251211yescharacteristic
316C2×C73#251211yescharacteristic
317C2×C73#251211yescharacteristic
318C2×C73#251411yescharacteristic
319C2×C73#251411yescharacteristic
320C2×C73#251411yescharacteristic
321C2×C73#264511yescharacteristic
322C2×C73#286011yescharacteristic
323C2×#401—732no—
324#1443—732no—
325#1443—732no—
326#1443—732no—
327C4⋊#95—731no—
328C4⋊#95—731no—
329C4⋊#95—731no—
330C4⋊#95—731no—
331C4⋊#95—731no—
332C4⋊#95D7311yescharacteristic
333C4×#95—731no—
334C73C4⋊#40111yescharacteristic, complemented, Sylow
335C22×C4⋊C4—731no—
336C22×C4⋊C4—731no—
337C22×C4⋊C4C2×D7311yescharacteristic
338C22×C4⋊C4C2×D7311yescharacteristic
339C22×C42—731no—
340C22×C42—731no—
341C22×C42C2×D7311yescharacteristic
342#401—1468no—
343C2×#95—732no—
344C2×#95—732no—
345C2×#95—732no—
346C2×#95—731no—
347C2×#95—732no—
348C2×#95—732no—
349C2×#95—732no—
350C2×#95—732no—
351C2×#95—732no—
352C2×#95—731no—
353C2×#95—731no—
354C2×#95—731no—
355C2×#95—732no—
356C2×#95—732no—
357C2×#95C2×D7312yes—
358C2×#95C2×D7312yes—
359C23×C4—731no—
360C23×C4—731no—
361C23×C4—731no—
362C23×C4—731no—
363C23×C4—732no—
364C23×C4—732no—
365C23×C4C22×D7312yes—
366C23×C4C22×D7312yes—
367C23×C4C22×D7311yescharacteristic
368C23×C4C22×D7311yescharacteristic
369C23×C4C22×D7311yescharacteristic
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—1462no—
377C2×C4⋊C4—1462no—
378C2×C4⋊C4—1462no—
379C2×C4⋊C4—1462no—
380C2×C4⋊C4—1462no—
381C2×C4⋊C4—1462no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—1462no—
386C2×C42—1462no—
387C2×C42—1462no—
388C2×C42—1462no—
389C2×C42—1462no—
390C2×C42—1462no—
391#95—24no—
392#95—24no—
393#95—2922no—
394#95—2922no—
395#95—2922no—
396#95—734no—
397#95—1462no—
398#95—1462no—
399#95—1464no—
400#95—1464no—
401#95—1464no—
402#95—1464no—
403#95—1464no—
404#95—1464no—
405#95—1464no—
406#95—1462no—
407C24C23×D7311yescharacteristic
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—732no—
435C22×C4—732no—
436C22×C4—732no—
437C22×C4—732no—
438C22×C4—1462no—
439C22×C4—1462no—
440C22×C4—1462no—
441C22×C4—1462no—
442C22×C4—1462no—
443C22×C4—1462no—
444C22×C4—1462no—
445C22×C4—1462no—
446C22×C4—1462no—
447C22×C4—1462no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4—1461no—
465C22×C4—1461no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1461no—
469C22×C4—1461no—
470C22×C4—1461no—
471C22×C4—1461no—
472C22×C4—1461no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4D4×D7312yes—
477C22×C4#1192402712yes—
478C22×C4#1192402712yes—
479C22×C4#1192402712yes—
480C22×C4#1192402712yes—
481C22×C4#1192402812yes—
482C22×C4#1192402812yes—
483C22×C4#1192402812yes—
484C22×C4#1192402912yes—
485C4⋊C4—44no—
486C4⋊C4—44no—
487C4⋊C4—2924no—
488C4⋊C4—2924no—
489C42—44no—
490C42—2924no—
491C42—2924no—
492C23C2×D4×D7311yescharacteristic
493C23#41×D7311yescharacteristic
494C23#41×D7311yescharacteristic
495C23C2×#1192402711yescharacteristic
496C23C2×#1192402711yescharacteristic
497C23C2×#1192402711yescharacteristic
498C23C2×#1192402711yescharacteristic
499C23C2×#1192402811yescharacteristic
500C23C2×#1192402811yescharacteristic
501C23C2×#1192402811yescharacteristic
502C23C2×#1192402911yescharacteristic
503C23#1455663711yescharacteristic
504C23#1455663811yescharacteristic
505C23#1455663911yescharacteristic
506C23#1455663911yescharacteristic
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—2921no—
536C2×C4—2921no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—2922no—
552C2×C4—2922no—
553C2×C4—2922no—
554C2×C4—2922no—
555C2×C4—2922no—
556C2×C4—2922no—
557C2×C4—2922no—
558C2×C4—2922no—
559C2×C4—2922no—
560C2×C4—2922no—
561C2×C4—2922no—
562C2×C4—2922no—
563C2×C4—2922no—
564C2×C4—2922no—
565C2×C4—1462no—
566C2×C4—1462no—
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#1455658414yes—
578C2×C4#1455658414yes—
579C2×C4#1455658414yes—
580C2×C4#1455658514yes—
581C2×C4#1455658614yes—
582C2×C4#1455658614yes—
583C2×C4#1455658614yes—
584C22C2×#1455658411yescharacteristic
585C22C2×#1455658411yescharacteristic
586C22C2×#1455658411yescharacteristic
587C22C2×#1455658511yescharacteristic
588C22C2×#1455658611yescharacteristic
589C22C2×#1455658611yescharacteristic
590C22C2×#1455658611yescharacteristic
591C22#1798911611yescharacteristic
592C22#1798911811yescharacteristic
593C22#1798911911yescharacteristic
594C22#1798913211yescharacteristic
595C22#1798913411yescharacteristic
596C22#1798913511yescharacteristic
597C22#1798919511yescharacteristic
598C22#1798919711yescharacteristic
599C22#1798919811yescharacteristic
600C22#1798920611yescharacteristic
601C22#1798920911yescharacteristic
602C22#1798921011yescharacteristic
603C22#1798923711yescharacteristic
604C22#1798923811yescharacteristic
605C22#1798924011yescharacteristic
606C22#1798925811yescharacteristic
607C22#1798927111yescharacteristic
608C22#1798927211yescharacteristic
609C22#1798927511yescharacteristic
610C22#1798928111yescharacteristic
611C22#1798928911yescharacteristic
612C22#1798929011yescharacteristic
613C22#1798930511yescharacteristic
614C22#1798930711yescharacteristic
615C22#1798930811yescharacteristic
616C22#1798930911yescharacteristic
617C22#1798930911yescharacteristic
618C22#1798931111yescharacteristic
619C4—42no—
620C4—42no—
621C4—82no—
622C4—82no—
623C4—2922no—
624C4—2922no—
625C4—2922no—
626C4—2922no—
627C4—5842no—
628C4—5842no—
629C4C73⋊#40118yescomplemented
630C2C2×C73⋊#40111yescharacteristic
631C2#2261432711yescharacteristic
632C2#2261433211yescharacteristic
633C2#2261433411yescharacteristic
634C2#2261434911yescharacteristic
635C2#2261435411yescharacteristic
636C2#2261435611yescharacteristic
637C2#2261451111yescharacteristic
638C2#2261451911yescharacteristic
639C2#2261452011yescharacteristic
640C2#2261453311yescharacteristic
641C2#2261454111yescharacteristic
642C2#2261454211yescharacteristic
643C2#2261589711yescharacteristic
644C2#2261829511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, prime radical, cosocleC24×C73C24
FittingC73×C4⋊#95C2
hypercenterC4⋊#95D73
hypocenterC73C4⋊#401
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
300. C4×C73#401semidirect
334. C73C4⋊#401semidirect
629. C4C73⋊#401semidirect

Maximal subgroups

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

subgroupindex
C2×C73⋊#4012
#226081932
#226081922
#226081912
#226081612
#226081602
C4×#145564982
C73×C4⋊#952
C4⋊#40173