Finite Group Databasebeta

← #33022718

Subgroups — #33022718

Order 18688.

1294 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988527C212yesmaximal
2C2×#17988486C211yesmaximal, characteristic
3C2×#17988456C211yesmaximal, characteristic
4#22608186C212yesmaximal
5#22608186C212yesmaximal
6#22608185C212yesmaximal
7#22608161C211yesmaximal, characteristic
8#22608160C211yesmaximal, characteristic
9#22608160C211yesmaximal, characteristic
10C4×#14556498C211yesmaximal, characteristic
11C73×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×C4⋊Dic73C2212yes—
15C22×#11924007C2212yes—
16C22×#11924007C2212yes—
17C22×C4×Dic73C2211yescharacteristic
18C22×C4×Dic73C2211yescharacteristic
19#17988527—28no—
20#17988486—24no—
21#17988456—24no—
22C2×#14556498C2211yescharacteristic
23C2×#14556498C2211yescharacteristic
24C2×#14556498C2212yes—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34C22×C4⋊C4×C73C2211yescharacteristic
35C22×C42×C73C2211yescharacteristic
36C2×#95×C73C2212yes—
37C2×#95×C73C2212yes—
38C23×Dic73C2312yes—
39C23×Dic73C2312yes—
40C23×Dic73C2311yescharacteristic
41C23×Dic73C2311yescharacteristic
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2311yescharacteristic
44C2×C4⋊Dic73—24no—
45C2×C4⋊Dic73—22no—
46C2×C4⋊Dic73—24no—
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—22no—
51C2×C4⋊Dic73—22no—
52C2×C4⋊Dic73—42no—
53C2×#11924007—24no—
54C2×#11924007—24no—
55C2×#11924007—24no—
56C2×#11924007—24no—
57C2×#11924007—42no—
58C2×#11924007—42no—
59C2×C4×Dic73—22no—
60C2×C4×Dic73—22no—
61C2×C4×Dic73—22no—
62C2×C4×Dic73—22no—
63C2×C4×Dic73—22no—
64C2×C4×Dic73Q814yes—
65#14556498—24no—
66#14556498—24no—
67#14556498—22no—
68#14556498—22no—
69#14556498—24no—
70#14556498—24no—
71#14556498—24no—
72#14556498—42no—
73#14556498—42no—
74#14556498D414yes—
75#14556498Q814yes—
76C23×C4×C73C2312yes—
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2312yes—
79C23×C4×C73C2311yescharacteristic
80C23×C4×C73C2311yescharacteristic
81C2×C4⋊C4×C73—22no—
82C2×C4⋊C4×C73—22no—
83C2×C4⋊C4×C73—22no—
84C2×C4⋊C4×C73—22no—
85C2×C4⋊C4×C73—22no—
86C2×C4⋊C4×C73D414yes—
87C2×C42×C73—22no—
88C2×C42×C73—22no—
89C2×C42×C73—22no—
90#95×C73—24no—
91#95×C73—42no—
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—21no—
109C22×Dic73—21no—
110C22×Dic73—21no—
111C22×Dic73—21no—
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×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—22no—
126C22×Dic73C2×D412yes—
127C22×Dic73C2×D412yes—
128C22×Dic73C2×Q812yes—
129C22×Dic73C2×Q812yes—
130C22×Dic73C2×Q812yes—
131C22×Dic73C2×Q812yes—
132C22×Dic73#4112yes—
133C22×Dic73#4112yes—
134C4⋊Dic73—48no—
135C4⋊Dic73—44no—
136C4⋊Dic73—44no—
137#11924007—48no—
138#11924007—48no—
139C4×Dic73—28no—
140C4×Dic73—44no—
141C24×C73C2411yescharacteristic
142C22×C4×C73—22no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—22no—
150C22×C4×C73—22no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—22no—
154C22×C4×C73—21no—
155C22×C4×C73—22no—
156C22×C4×C73—21no—
157C22×C4×C73—22no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—22no—
161C22×C4×C73—22no—
162C22×C4×C73—22no—
163C22×C4×C73—22no—
164C22×C4×C73—22no—
165C22×C4×C73—22no—
166C22×C4×C73—22no—
167C22×C4×C73C2×D412yes—
168C22×C4×C73C2×D414yes—
169C22×C4×C73C2×D412yes—
170C22×C4×C73C2×Q812yes—
171C22×C4×C73C2×Q812yes—
172C22×C4×C73#4112yes—
173C22×C4×C73#4112yes—
174C22×C4×C73#4112yes—
175C22×C4×C73#4112yes—
176C22×C4×C73#4112yes—
177C4⋊C4×C73—28no—
178C4⋊C4×C73—44no—
179C42×C73—44no—
180C23×C73C22×D411yescharacteristic
181C23×C73C22×D411yescharacteristic
182C23×C73C22×Q811yescharacteristic
183C23×C73C22×Q811yescharacteristic
184C23×C73C2×#4111yescharacteristic
185C23×C73C2×#4111yescharacteristic
186C23×C73C2×#4111yescharacteristic
187C23×C73C2×#4111yescharacteristic
188C23×C73C2×#4111yescharacteristic
189C23×C73C2×#4111yescharacteristic
190C23×C73C2×#4111yescharacteristic
191C23×C73H(5,𝔽2)11yescharacteristic
192C23×C73H(5,𝔽2)11yescharacteristic
193C23×C732−1+411yescharacteristic
194C23×C732−1+411yescharacteristic
195C2×C4×C73—24no—
196C2×C4×C73—22no—
197C2×C4×C73—22no—
198C2×C4×C73—24no—
199C2×C4×C73—24no—
200C2×C4×C73—22no—
201C2×C4×C73—22no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—41no—
205C2×C4×C73—41no—
206C2×C4×C73—42no—
207C2×C4×C73—42no—
208C2×C4×C73—41no—
209C2×C4×C73—41no—
210C2×C4×C73—42no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—42no—
216C2×C4×C73—42no—
217C2×C4×C73—42no—
218C2×C4×C73—42no—
219C2×C4×C73—42no—
220C2×C4×C73—42no—
221C2×C4×C73—42no—
222C2×C4×C73—42no—
223C2×C4×C73C22⋊Q814yes—
224C2×C4×C73#12314yes—
225C2×C4×C73#12414yes—
226C2×C4×C73#12514yes—
227C2×C4×C73#12514yes—
228C2×C4×C73#12614yes—
229C2×C4×C73#12614yes—
230C2×Dic73—22no—
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—22no—
234C2×Dic73—22no—
235C2×Dic73—22no—
236C2×Dic73—22no—
237C2×Dic73—22no—
238C2×Dic73—22no—
239C2×Dic73—22no—
240C2×Dic73—22no—
241C2×Dic73—22no—
242C2×Dic73—22no—
243C2×Dic73—22no—
244C2×Dic73—22no—
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—22no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—42no—
257C2×Dic73—42no—
258C2×Dic73—42no—
259C2×Dic73—42no—
260C2×Dic73—42no—
261C2×Dic73—42no—
262C2×Dic73—42no—
263C2×Dic73—42no—
264C2×Dic73—42no—
265C2×Dic73—42no—
266C2×Dic73—42no—
267C2×Dic73—42no—
268C2×Dic73—42no—
269C2×Dic73—42no—
270C2×Dic73#12514yes—
271C2×Dic73C4⋊Q814yes—
272C22×C73C2×C22⋊Q811yescharacteristic
273C22×C73C2×#12311yescharacteristic
274C22×C73C2×#12411yescharacteristic
275C22×C73C2×#12511yescharacteristic
276C22×C73C2×#12511yescharacteristic
277C22×C73C2×#12511yescharacteristic
278C22×C73C2×#12611yescharacteristic
279C22×C73C2×#12611yescharacteristic
280C22×C73C2×C4⋊Q811yescharacteristic
281C22×C73#53211yescharacteristic
282C22×C73#53211yescharacteristic
283C22×C73#53311yescharacteristic
284C22×C73#53311yescharacteristic
285C22×C73#54011yescharacteristic
286C22×C73#54111yescharacteristic
287C22×C73#54211yescharacteristic
288C22×C73#54211yescharacteristic
289C22×C73#54411yescharacteristic
290C22×C73#54411yescharacteristic
291C22×C73D4211yescharacteristic
292C22×C73#54611yescharacteristic
293C22×C73#54711yescharacteristic
294C22×C73#54711yescharacteristic
295C22×C73#54811yescharacteristic
296C22×C73D4×Q811yescharacteristic
297C22×C73#55011yescharacteristic
298C22×C73#55211yescharacteristic
299C22×C73#55311yescharacteristic
300C22×C73#55411yescharacteristic
301C22×C73#55411yescharacteristic
302C22×C73#55511yescharacteristic
303C22×C73#55611yescharacteristic
304C22×C73#55611yescharacteristic
305C22×C73#55711yescharacteristic
306C22×C73#55911yescharacteristic
307C4×C73—44no—
308C4×C73—42no—
309C4×C73—42no—
310C4×C73—82no—
311C4×C73#40018yescomplemented
312Dic73—24no—
313Dic73—24no—
314Dic73—42no—
315Dic73—42no—
316Dic73—82no—
317Dic73—82no—
318#15146—731nomaximal, Sylow
319C2×C73C2×#40011yescharacteristic
320C2×C73#244011yescharacteristic
321C2×C73#244211yescharacteristic
322C2×C73#244511yescharacteristic
323C2×C73#244611yescharacteristic
324C2×C73#249111yescharacteristic
325C2×C73#249211yescharacteristic
326C2×C73#249611yescharacteristic
327C2×C73#249711yescharacteristic
328C2×C73#251111yescharacteristic
329C2×C73#251211yescharacteristic
330C2×C73#255211yescharacteristic
331C2×C73#257111yescharacteristic
332C2×C73#264711yescharacteristic
333C2×C73#285911yescharacteristic
334C2×#400—732no—
335C2×#389—731no—
336C2×#384—731no—
337#1442—732no—
338#1442—732no—
339#1441—732no—
340C4⋊#95—731no—
341C4⋊#95—731no—
342C4⋊#95—731no—
343C4⋊#95D7311yescharacteristic
344C4×#95—731no—
345C73#1514611yescharacteristic, complemented, Sylow
346C22×C4⋊C4—732no—
347C22×C4⋊C4—732no—
348C22×C4⋊C4—732no—
349C22×C4⋊C4—731no—
350C22×C4⋊C4—731no—
351C22×C4⋊C4C2×D7311yescharacteristic
352C22×C4⋊C4C2×D7311yescharacteristic
353C22×C42—731no—
354C22×C42—731no—
355C22×C42C2×D7311yescharacteristic
356#400—1468no—
357#389—1464no—
358#384—1464no—
359C2×#95—732no—
360C2×#95—732no—
361C2×#95—731no—
362C2×#95—731no—
363C2×#95—732no—
364C2×#95—732no—
365C2×#95—732no—
366C2×#95—731no—
367C2×#95—731no—
368C2×#95—732no—
369C2×#95—732no—
370C2×#95C2×D7312yes—
371C2×#95C2×D7312yes—
372C23×C4—731no—
373C23×C4—731no—
374C23×C4—731no—
375C23×C4—731no—
376C23×C4—732no—
377C23×C4—732no—
378C23×C4C22×D7312yes—
379C23×C4C22×D7311yescharacteristic
380C23×C4C22×D7312yes—
381C23×C4C22×D7311yescharacteristic
382C23×C4C22×D7311yescharacteristic
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—2922no—
389C2×C4⋊C4—2922no—
390C2×C4⋊C4—2922no—
391C2×C4⋊C4—1464no—
392C2×C4⋊C4—1464no—
393C2×C4⋊C4—1464no—
394C2×C4⋊C4—1464no—
395C2×C4⋊C4—1464no—
396C2×C4⋊C4—1462no—
397C2×C4⋊C4—1464no—
398C2×C4⋊C4—1462no—
399C2×C4⋊C4—1462no—
400C2×C4⋊C4—1462no—
401C2×C4⋊C4—1462no—
402C2×C4⋊C4—1462no—
403C2×C4⋊C4D29214yes—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—734no—
408C2×C42—1462no—
409C2×C42—1462no—
410C2×C42—1462no—
411C2×C42—1462no—
412C2×C42—1462no—
413#95—24no—
414#95—42no—
415#95—2922no—
416#95—2922no—
417#95—734no—
418#95—734no—
419#95—1462no—
420#95—1462no—
421#95—1464no—
422#95—1464no—
423#95—1464no—
424#95—1464no—
425#95—1464no—
426C24C23×D7311yescharacteristic
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—732no—
453C22×C4—732no—
454C22×C4—732no—
455C22×C4—732no—
456C22×C4—732no—
457C22×C4—732no—
458C22×C4—732no—
459C22×C4—732no—
460C22×C4—1462no—
461C22×C4—1462no—
462C22×C4—1462no—
463C22×C4—1462no—
464C22×C4—1462no—
465C22×C4—1462no—
466C22×C4—1462no—
467C22×C4—1462no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4—1462no—
471C22×C4—1462no—
472C22×C4—1462no—
473C22×C4—1462no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4—1461no—
488C22×C4—1461no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4D4×D7312yes—
495C22×C4C2×D29214yes—
496C22×C4C2×D29212yes—
497C22×C4Q8×D7312yes—
498C22×C4Q8×D7312yes—
499C22×C4#1192402712yes—
500C22×C4#1192402712yes—
501C22×C4#1192402712yes—
502C22×C4#1192402812yes—
503C22×C4#1192402812yes—
504C4⋊C4—28no—
505C4⋊C4—44no—
506C4⋊C4—2928no—
507C4⋊C4—2928no—
508C4⋊C4—2928no—
509C4⋊C4—2924no—
510C4⋊C4—2924no—
511C42—44no—
512C42—2924no—
513C42—1468no—
514C23C2×D4×D7311yescharacteristic
515C23C22×D29211yescharacteristic
516C23C2×Q8×D7311yescharacteristic
517C23C2×Q8×D7311yescharacteristic
518C23#41×D7311yescharacteristic
519C23#41×D7311yescharacteristic
520C23C2×#1192402711yescharacteristic
521C23C2×#1192402711yescharacteristic
522C23C2×#1192402711yescharacteristic
523C23C2×#1192402811yescharacteristic
524C23C2×#1192402811yescharacteristic
525C23#1455663611yescharacteristic
526C23#1455663711yescharacteristic
527C23#1455663811yescharacteristic
528C23#1455663911yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2922no—
566C2×C4—2922no—
567C2×C4—2922no—
568C2×C4—2922no—
569C2×C4—2922no—
570C2×C4—2922no—
571C2×C4—2922no—
572C2×C4—2922no—
573C2×C4—2922no—
574C2×C4—2922no—
575C2×C4—2922no—
576C2×C4—2922no—
577C2×C4—2922no—
578C2×C4—2922no—
579C2×C4—734no—
580C2×C4—734no—
581C2×C4—1462no—
582C2×C4—1462no—
583C2×C4—1462no—
584C2×C4—1462no—
585C2×C4—1462no—
586C2×C4—1462no—
587C2×C4—1462no—
588C2×C4—1462no—
589C2×C4—1462no—
590C2×C4—1462no—
591C2×C4—1462no—
592C2×C4—1462no—
593C2×C4—1462no—
594C2×C4—1462no—
595C2×C4—1462no—
596C2×C4—1462no—
597C2×C4—1462no—
598C2×C4—1462no—
599C2×C4#1455657114yes—
600C2×C4#1455657514yes—
601C2×C4#1455657914yes—
602C2×C4#1455658114yes—
603C2×C4#1455658114yes—
604C2×C4#1455658414yes—
605C2×C4#1455658414yes—
606C22C2×#1455657111yescharacteristic
607C22C2×#1455657511yescharacteristic
608C22C2×#1455657911yescharacteristic
609C22#125×D7311yescharacteristic
610C22C2×#1455658111yescharacteristic
611C22C2×#1455658111yescharacteristic
612C22C2×#1455658411yescharacteristic
613C22C2×#1455658411yescharacteristic
614C22C4⋊Q8×D7311yescharacteristic
615C22#1798913211yescharacteristic
616C22#1798913411yescharacteristic
617C22#1798913911yescharacteristic
618C22#1798914111yescharacteristic
619C22#1798919011yescharacteristic
620C22#1798919711yescharacteristic
621C22#1798920211yescharacteristic
622C22#1798920911yescharacteristic
623C22#1798921411yescharacteristic
624C22#1798921711yescharacteristic
625C22D4×D29211yescharacteristic
626C22#1798923211yescharacteristic
627C22#1798923711yescharacteristic
628C22#1798923811yescharacteristic
629C22#1798924911yescharacteristic
630C22Q8×D29211yescharacteristic
631C22#1798925711yescharacteristic
632C22#1798927111yescharacteristic
633C22#1798928411yescharacteristic
634C22#1798929211yescharacteristic
635C22#1798929511yescharacteristic
636C22#1798930011yescharacteristic
637C22#1798930511yescharacteristic
638C22#1798930611yescharacteristic
639C22#1798931211yescharacteristic
640C22#1798931911yescharacteristic
641C4—42no—
642C4—42no—
643C4—44no—
644C4—82no—
645C4—2922no—
646C4—2922no—
647C4—5842no—
648C4—5842no—
649C4—1464no—
650C4—1464no—
651C4#1798852718yescomplemented
652C2C2×#1798852711yescharacteristic
653C2#2261363111yescharacteristic
654C2#2261365311yescharacteristic
655C2#2261369411yescharacteristic
656C2#2261370511yescharacteristic
657C2#2261428811yescharacteristic
658C2#2261429911yescharacteristic
659C2#2261434911yescharacteristic
660C2#2261436011yescharacteristic
661C2#2261450711yescharacteristic
662C2#2261451811yescharacteristic
663C2#2261496411yescharacteristic
664C2#2261517111yescharacteristic
665C2#2261590711yescharacteristic
666C2#2261829011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, prime radical, cosocleC24×C73C24
FittingC73×C4⋊#95C2
hypercenterC4⋊#95D73
hypocenterC73#15146
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
311. C4×C73#400semidirect
345. C73#15146semidirect
651. C4#17988527semidirect

Maximal subgroups

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

subgroupindex
C2×#179885272
C2×#179884862
C2×#179884562
#226081862
#226081852
#226081612
#226081602
C4×#145564982
C73×C4⋊#952
#1514673