Finite Group Databasebeta

← #33022675

Subgroups — #33022675

Order 18688.

1250 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988529C212yesmaximal
2C2×#17988486C211yesmaximal, characteristic
3C2×#17988483C211yesmaximal, characteristic
4#22608192C212yesmaximal
5#22608189C212yesmaximal
6#22608187C212yesmaximal
7#22608161C211yesmaximal, characteristic
8#22608160C211yesmaximal, characteristic
9#22608160C211yesmaximal, characteristic
10C4×#14556498C211yesmaximal, characteristic
11C73×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2212yes—
14C22×C4⋊Dic73C2211yescharacteristic
15C22×#11924007C2212yes—
16C22×C4×Dic73C2211yescharacteristic
17C22×C4×Dic73C2211yescharacteristic
18#17988529—28no—
19#17988486—24no—
20#17988483—24no—
21C2×#14556498C2211yescharacteristic
22C2×#14556498C2211yescharacteristic
23C2×#14556498C2211yescharacteristic
24C2×#14556498C2212yes—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34C22×C4⋊C4×C73C2211yescharacteristic
35C22×C42×C73C2211yescharacteristic
36C2×#95×C73C2212yes—
37C2×#95×C73C2212yes—
38C23×Dic73C2312yes—
39C23×Dic73C2311yescharacteristic
40C23×Dic73C2311yescharacteristic
41C23×Dic73C2312yes—
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2311yescharacteristic
44C2×C4⋊Dic73—24no—
45C2×C4⋊Dic73—24no—
46C2×C4⋊Dic73—22no—
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—22no—
51C2×C4⋊Dic73—42no—
52C2×C4⋊Dic73D414yes—
53C2×#11924007—24no—
54C2×#11924007—24no—
55C2×#11924007—42no—
56C2×C4×Dic73—22no—
57C2×C4×Dic73—22no—
58C2×C4×Dic73—22no—
59C2×C4×Dic73—22no—
60C2×C4×Dic73—22no—
61C2×C4×Dic73—22no—
62#14556498—24no—
63#14556498—24no—
64#14556498—24no—
65#14556498—24no—
66#14556498—22no—
67#14556498—22no—
68#14556498—24no—
69#14556498—24no—
70#14556498—24no—
71#14556498—22no—
72#14556498—24no—
73#14556498D414yes—
74C23×C4×C73C2312yes—
75C23×C4×C73C2311yescharacteristic
76C23×C4×C73C2312yes—
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C2×C4⋊C4×C73—22no—
80C2×C4⋊C4×C73—22no—
81C2×C4⋊C4×C73—22no—
82C2×C4⋊C4×C73—22no—
83C2×C4⋊C4×C73—22no—
84C2×C4⋊C4×C73Q814yes—
85C2×C42×C73—22no—
86C2×C42×C73—22no—
87C2×C42×C73—22no—
88#95×C73—24no—
89#95×C73—42no—
90C22×Dic73—21no—
91C22×Dic73—21no—
92C22×Dic73—22no—
93C22×Dic73—21no—
94C22×Dic73—21no—
95C22×Dic73—21no—
96C22×Dic73—21no—
97C22×Dic73—21no—
98C22×Dic73—21no—
99C22×Dic73—22no—
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—21no—
111C22×Dic73—22no—
112C22×Dic73—21no—
113C22×Dic73—21no—
114C22×Dic73—21no—
115C22×Dic73—21no—
116C22×Dic73—21no—
117C22×Dic73—21no—
118C22×Dic73—22no—
119C22×Dic73—21no—
120C22×Dic73—22no—
121C22×Dic73—22no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—22no—
126C22×Dic73—22no—
127C22×Dic73C2×D412yes—
128C22×Dic73C2×D412yes—
129C22×Dic73C2×D414yes—
130C22×Dic73#4112yes—
131C22×Dic73#4112yes—
132C4⋊Dic73—28no—
133C4⋊Dic73—48no—
134C4⋊Dic73—44no—
135#11924007—48no—
136C4×Dic73—44no—
137C4×Dic73—44no—
138C24×C73C2411yescharacteristic
139C22×C4×C73—22no—
140C22×C4×C73—22no—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—22no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—22no—
151C22×C4×C73—21no—
152C22×C4×C73—22no—
153C22×C4×C73—21no—
154C22×C4×C73—22no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—22no—
158C22×C4×C73—22no—
159C22×C4×C73—22no—
160C22×C4×C73—22no—
161C22×C4×C73—22no—
162C22×C4×C73—22no—
163C22×C4×C73—22no—
164C22×C4×C73C2×D412yes—
165C22×C4×C73C2×D412yes—
166C22×C4×C73C2×Q814yes—
167C22×C4×C73C2×Q812yes—
168C22×C4×C73#4112yes—
169C22×C4×C73#4112yes—
170C22×C4×C73#4112yes—
171C22×C4×C73#4112yes—
172C22×C4×C73#4112yes—
173C22×C4×C73#4112yes—
174C4⋊C4×C73—28no—
175C4⋊C4×C73—44no—
176C42×C73—44no—
177C23×C73C22×D411yescharacteristic
178C23×C73C22×D411yescharacteristic
179C23×C73C22×Q811yescharacteristic
180C23×C73C2×#4111yescharacteristic
181C23×C73C2×#4111yescharacteristic
182C23×C73C2×#4111yescharacteristic
183C23×C73C2×#4111yescharacteristic
184C23×C73C2×#4111yescharacteristic
185C23×C73C2×#4111yescharacteristic
186C23×C73C2×#4111yescharacteristic
187C23×C73C2×#4111yescharacteristic
188C23×C73H(5,𝔽2)11yescharacteristic
189C23×C732−1+411yescharacteristic
190C23×C732−1+411yescharacteristic
191C23×C732−1+411yescharacteristic
192C2×C4×C73—24no—
193C2×C4×C73—22no—
194C2×C4×C73—22no—
195C2×C4×C73—22no—
196C2×C4×C73—22no—
197C2×C4×C73—24no—
198C2×C4×C73—22no—
199C2×C4×C73—22no—
200C2×C4×C73—24no—
201C2×C4×C73—41no—
202C2×C4×C73—41no—
203C2×C4×C73—42no—
204C2×C4×C73—41no—
205C2×C4×C73—42no—
206C2×C4×C73—41no—
207C2×C4×C73—42no—
208C2×C4×C73—42no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—42no—
214C2×C4×C73—42no—
215C2×C4×C73—42no—
216C2×C4×C73—42no—
217C2×C4×C73—42no—
218C2×C4×C73—42no—
219C2×C4×C73—42no—
220C2×C4×C73C22⋊Q814yes—
221C2×C4×C73#12314yes—
222C2×C4×C73#12414yes—
223C2×C4×C73#12514yes—
224C2×C4×C73#12514yes—
225C2×C4×C73#12614yes—
226C2×C4×C73#12614yes—
227C2×Dic73—24no—
228C2×Dic73—22no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—24no—
234C2×Dic73—22no—
235C2×Dic73—22no—
236C2×Dic73—22no—
237C2×Dic73—24no—
238C2×Dic73—22no—
239C2×Dic73—22no—
240C2×Dic73—22no—
241C2×Dic73—22no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—42no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—42no—
252C2×Dic73—42no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73—41no—
259C2×Dic73—42no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—42no—
263C2×Dic73—42no—
264C2×Dic73—42no—
265C2×Dic73—42no—
266C2×Dic73—42no—
267C2×Dic73—42no—
268C2×Dic73—42no—
269C22×C73C2×C22⋊Q811yescharacteristic
270C22×C73C2×#12311yescharacteristic
271C22×C73C2×#12411yescharacteristic
272C22×C73C2×#12511yescharacteristic
273C22×C73C2×#12511yescharacteristic
274C22×C73C2×#12611yescharacteristic
275C22×C73C2×#12611yescharacteristic
276C22×C73#52911yescharacteristic
277C22×C73#52911yescharacteristic
278C22×C73#52911yescharacteristic
279C22×C73#53211yescharacteristic
280C22×C73#53211yescharacteristic
281C22×C73#53211yescharacteristic
282C22×C73#54111yescharacteristic
283C22×C73#54111yescharacteristic
284C22×C73#54111yescharacteristic
285C22×C73#54211yescharacteristic
286C22×C73#54211yescharacteristic
287C22×C73#54211yescharacteristic
288C22×C73D4211yescharacteristic
289C22×C73#54711yescharacteristic
290C22×C73#54711yescharacteristic
291C22×C73#54711yescharacteristic
292C22×C73#54811yescharacteristic
293C22×C73#54811yescharacteristic
294C22×C73D4×Q811yescharacteristic
295C22×C73#55211yescharacteristic
296C22×C73#55211yescharacteristic
297C22×C73#55211yescharacteristic
298C22×C73#55311yescharacteristic
299C22×C73#55411yescharacteristic
300C22×C73#55511yescharacteristic
301C22×C73#55611yescharacteristic
302C22×C73#55711yescharacteristic
303C22×C73#55711yescharacteristic
304C4×C73—44no—
305C4×C73—42no—
306C4×C73—42no—
307C4×C73—82no—
308C4×C73#40018yescomplemented
309Dic73—42no—
310Dic73—44no—
311Dic73—42no—
312Dic73—42no—
313Dic73—42no—
314Dic73—82no—
315#15139—731nomaximal, Sylow
316C2×C73C2×#40011yescharacteristic
317C2×C73#242111yescharacteristic
318C2×C73#242211yescharacteristic
319C2×C73#245211yescharacteristic
320C2×C73#245311yescharacteristic
321C2×C73#248911yescharacteristic
322C2×C73#249111yescharacteristic
323C2×C73#249511yescharacteristic
324C2×C73#249611yescharacteristic
325C2×C73#250611yescharacteristic
326C2×C73#250611yescharacteristic
327C2×C73#250811yescharacteristic
328C2×C73#250911yescharacteristic
329C2×C73#264511yescharacteristic
330C2×C73#286011yescharacteristic
331C2×#400—732no—
332C2×#389—731no—
333C2×#389—731no—
334#1443—732no—
335#1442—732no—
336#1442—732no—
337C4⋊#95—731no—
338C4⋊#95—731no—
339C4⋊#95—731no—
340C4⋊#95D7311yescharacteristic
341C4×#95—731no—
342C73#1513911yescharacteristic, complemented, Sylow
343C22×C4⋊C4—732no—
344C22×C4⋊C4—732no—
345C22×C4⋊C4—731no—
346C22×C4⋊C4—731no—
347C22×C4⋊C4C2×D7311yescharacteristic
348C22×C4⋊C4C2×D7311yescharacteristic
349C22×C42—731no—
350C22×C42—731no—
351C22×C42C2×D7311yescharacteristic
352#400—1468no—
353#389—1464no—
354#389—1464no—
355C2×#95—731no—
356C2×#95—732no—
357C2×#95—732no—
358C2×#95—732no—
359C2×#95—731no—
360C2×#95—731no—
361C2×#95—731no—
362C2×#95—732no—
363C2×#95—732no—
364C2×#95—732no—
365C2×#95—732no—
366C2×#95—732no—
367C2×#95C2×D7312yes—
368C2×#95C2×D7312yes—
369C23×C4—732no—
370C23×C4—731no—
371C23×C4—731no—
372C23×C4—731no—
373C23×C4—731no—
374C23×C4—732no—
375C23×C4C22×D7312yes—
376C23×C4C22×D7311yescharacteristic
377C23×C4C22×D7312yes—
378C23×C4C22×D7311yescharacteristic
379C23×C4C22×D7311yescharacteristic
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—2922no—
386C2×C4⋊C4—2922no—
387C2×C4⋊C4—734no—
388C2×C4⋊C4—1464no—
389C2×C4⋊C4—1464no—
390C2×C4⋊C4—1464no—
391C2×C4⋊C4—1464no—
392C2×C4⋊C4—1462no—
393C2×C4⋊C4—1462no—
394C2×C4⋊C4—1462no—
395C2×C4⋊C4—1462no—
396C2×C4⋊C4—1462no—
397C2×C4⋊C4Dic14614yes—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—1462no—
402C2×C42—1462no—
403C2×C42—1462no—
404C2×C42—1462no—
405C2×C42—1462no—
406C2×C42—1462no—
407#95—24no—
408#95—42no—
409#95—734no—
410#95—1464no—
411#95—1462no—
412#95—1462no—
413#95—1464no—
414#95—1464no—
415#95—1464no—
416#95—1464no—
417#95—1464no—
418#95—1464no—
419#95—1464no—
420#95—1462no—
421C24C23×D7311yescharacteristic
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—732no—
448C22×C4—732no—
449C22×C4—734no—
450C22×C4—732no—
451C22×C4—732no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4—1462no—
455C22×C4—1462no—
456C22×C4—1462no—
457C22×C4—1462no—
458C22×C4—1462no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1462no—
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—1462no—
473C22×C4—1462no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4—1462no—
479C22×C4—1461no—
480C22×C4—1462no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4—1462no—
488C22×C4—1461no—
489C22×C4D4×D7312yes—
490C22×C4D4×D7312yes—
491C22×C4C2×Dic14614yes—
492C22×C4C2×Dic14612yes—
493C22×C4#1192402712yes—
494C22×C4#1192402712yes—
495C22×C4#1192402812yes—
496C22×C4#1192402812yes—
497C22×C4#1192402912yes—
498C22×C4#1192402912yes—
499C4⋊C4—28no—
500C4⋊C4—44no—
501C4⋊C4—2928no—
502C4⋊C4—2928no—
503C4⋊C4—2924no—
504C4⋊C4—1468no—
505C42—44no—
506C42—2924no—
507C42—2924no—
508C23C2×D4×D7311yescharacteristic
509C23C2×D4×D7311yescharacteristic
510C23C22×Dic14611yescharacteristic
511C23#41×D7311yescharacteristic
512C23#41×D7311yescharacteristic
513C23C2×#1192402711yescharacteristic
514C23C2×#1192402711yescharacteristic
515C23C2×#1192402811yescharacteristic
516C23C2×#1192402811yescharacteristic
517C23C2×#1192402911yescharacteristic
518C23C2×#1192402911yescharacteristic
519C23#1455663611yescharacteristic
520C23#1455663811yescharacteristic
521C23#1455663811yescharacteristic
522C23#1455663911yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—2922no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—2921no—
555C2×C4—2921no—
556C2×C4—2922no—
557C2×C4—2922no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2922no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—2921no—
568C2×C4—2921no—
569C2×C4—2921no—
570C2×C4—2921no—
571C2×C4—2922no—
572C2×C4—2922no—
573C2×C4—2922no—
574C2×C4—2922no—
575C2×C4—2922no—
576C2×C4—2922no—
577C2×C4—2922no—
578C2×C4—1462no—
579C2×C4—1462no—
580C2×C4—1462no—
581C2×C4—1462no—
582C2×C4—1462no—
583C2×C4—1464no—
584C2×C4—1462no—
585C2×C4—1462no—
586C2×C4—1462no—
587C2×C4—1464no—
588C2×C4—1462no—
589C2×C4—1462no—
590C2×C4—1462no—
591C2×C4—1462no—
592C2×C4—1464no—
593C2×C4#1455656814yes—
594C2×C4#1455657614yes—
595C2×C4#1455657714yes—
596C2×C4#1455658214yes—
597C2×C4#1455658314yes—
598C2×C4#1455658414yes—
599C2×C4#1455658614yes—
600C22C2×#1455656811yescharacteristic
601C22C2×#1455657611yescharacteristic
602C22C2×#1455657711yescharacteristic
603C22C2×#1455658211yescharacteristic
604C22C2×#1455658311yescharacteristic
605C22C2×#1455658411yescharacteristic
606C22C2×#1455658611yescharacteristic
607C22#1798912211yescharacteristic
608C22#1798912311yescharacteristic
609C22#1798912411yescharacteristic
610C22#1798913211yescharacteristic
611C22#1798913411yescharacteristic
612C22#1798913811yescharacteristic
613C22#1798919511yescharacteristic
614C22#1798919711yescharacteristic
615C22#1798920011yescharacteristic
616C22#1798920211yescharacteristic
617C22#1798920411yescharacteristic
618C22#1798921111yescharacteristic
619C22#1798922211yescharacteristic
620C22#1798923711yescharacteristic
621C22#1798923811yescharacteristic
622C22#1798924011yescharacteristic
623C22#1798924511yescharacteristic
624C22#1798924511yescharacteristic
625C22D4×Dic14611yescharacteristic
626C22#1798927111yescharacteristic
627C22#1798927611yescharacteristic
628C22#1798927911yescharacteristic
629C22#1798928511yescharacteristic
630C22#1798929611yescharacteristic
631C22#1798930111yescharacteristic
632C22#1798930511yescharacteristic
633C22#1798931311yescharacteristic
634C22#1798931611yescharacteristic
635C4—44no—
636C4—42no—
637C4—42no—
638C4—82no—
639C4—2922no—
640C4—2922no—
641C4—2922no—
642C4—2924no—
643C4—2922no—
644C4—5842no—
645C4#1798852918yescomplemented
646C2C2×#1798852911yescharacteristic
647C2#2261343711yescharacteristic
648C2#2261344811yescharacteristic
649C2#2261378411yescharacteristic
650C2#2261379511yescharacteristic
651C2#2261427311yescharacteristic
652C2#2261429511yescharacteristic
653C2#2261433811yescharacteristic
654C2#2261434911yescharacteristic
655C2#2261444111yescharacteristic
656C2#2261444911yescharacteristic
657C2#2261447111yescharacteristic
658C2#2261447411yescharacteristic
659C2#2261589911yescharacteristic
660C2#2261829911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, prime radical, cosocleC24×C73C24
FittingC73×C4⋊#95C2
hypercenterC4⋊#95D73
hypocenterC73#15139
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
308. C4×C73#400semidirect
342. C73#15139semidirect
645. C4#17988529semidirect

Maximal subgroups

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

subgroupindex
C2×#179885292
C2×#179884862
C2×#179884832
#226081922
#226081892
#226081872
#226081612
#226081602
C4×#145564982
C73×C4⋊#952
#1513973