Finite Group Databasebeta

← #33022765

Subgroups — #33022765

Order 18688.

1310 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×#17988528C212yesmaximal
2C2×#17988456C211yesmaximal, characteristic
3C2×C4×#11924007C211yesmaximal, characteristic
4#22608197C212yesmaximal
5#22608186C212yesmaximal
6#22608182C212yesmaximal
7#22608161C211yesmaximal, characteristic
8#22608160C211yesmaximal, characteristic
9#22608160C211yesmaximal, characteristic
10#22608160C211yesmaximal, characteristic
11C73×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×#11924007C2212yes—
15C22×#11924007C2211yescharacteristic
16C22×#11924007C2211yescharacteristic
17C22×#11924007C2212yes—
18C22×C4×Dic73C2211yescharacteristic
19C22×C4×Dic73C2211yescharacteristic
20#17988528—28no—
21#17988456—24no—
22C4×#11924007—24no—
23C2×#14556498C2212yes—
24C2×#14556498C2212yes—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2211yescharacteristic
29C2×#14556498C2211yescharacteristic
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
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—22no—
45C2×C4⋊Dic73—22no—
46C2×C4⋊Dic73—22no—
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73—22no—
50C2×#11924007—22no—
51C2×#11924007—22no—
52C2×#11924007—22no—
53C2×#11924007—22no—
54C2×#11924007—24no—
55C2×#11924007—24no—
56C2×#11924007—24no—
57C2×#11924007—24no—
58C2×#11924007—42no—
59C2×#11924007—42no—
60C2×#11924007D414yes—
61C2×#11924007Q814yes—
62C2×C4×Dic73—22no—
63C2×C4×Dic73—22no—
64C2×C4×Dic73—22no—
65C2×C4×Dic73—22no—
66C2×C4×Dic73D414yes—
67C2×C4×Dic73Q814yes—
68#14556498—22no—
69#14556498—22no—
70#14556498—24no—
71#14556498—24no—
72#14556498—24no—
73#14556498—24no—
74#14556498—24no—
75#14556498—42no—
76#14556498—42no—
77#14556498—42no—
78C23×C4×C73C2312yes—
79C23×C4×C73C2312yes—
80C23×C4×C73C2311yescharacteristic
81C23×C4×C73C2311yescharacteristic
82C23×C4×C73C2311yescharacteristic
83C2×C4⋊C4×C73—22no—
84C2×C4⋊C4×C73—22no—
85C2×C4⋊C4×C73—22no—
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—22no—
89C2×C42×C73—22no—
90C2×C42×C73—22no—
91C2×C42×C73—22no—
92#95×C73—24no—
93#95×C73—42no—
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×D412yes—
129C22×Dic73C2×D412yes—
130C22×Dic73C2×Q812yes—
131C22×Dic73C2×Q812yes—
132C22×Dic73C2×Q812yes—
133C22×Dic73C2×Q812yes—
134C22×Dic73#4112yes—
135C22×Dic73#4112yes—
136C4⋊Dic73—44no—
137C4⋊Dic73—44no—
138#11924007—28no—
139#11924007—28no—
140#11924007—48no—
141#11924007—48no—
142C4×Dic73—28no—
143C4×Dic73—28no—
144C24×C73C2411yescharacteristic
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
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×C73—22no—
165C22×C4×C73—22no—
166C22×C4×C73—22no—
167C22×C4×C73—22no—
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73C2×D412yes—
172C22×C4×C73C2×D412yes—
173C22×C4×C73C2×Q812yes—
174C22×C4×C73C2×Q812yes—
175C22×C4×C73#4112yes—
176C22×C4×C73#4112yes—
177C22×C4×C73#4112yes—
178C22×C4×C73#4112yes—
179C22×C4×C73#4112yes—
180C4⋊C4×C73—44no—
181C4⋊C4×C73—44no—
182C42×C73—44no—
183C23×C73C22×D411yescharacteristic
184C23×C73C22×D411yescharacteristic
185C23×C73C22×Q811yescharacteristic
186C23×C73C22×Q811yescharacteristic
187C23×C73C2×#4111yescharacteristic
188C23×C73C2×#4111yescharacteristic
189C23×C73C2×#4111yescharacteristic
190C23×C73C2×#4111yescharacteristic
191C23×C73C2×#4111yescharacteristic
192C23×C73C2×#4111yescharacteristic
193C23×C73C2×#4111yescharacteristic
194C23×C73H(5,𝔽2)11yescharacteristic
195C23×C73H(5,𝔽2)11yescharacteristic
196C23×C732−1+411yescharacteristic
197C23×C732−1+411yescharacteristic
198C2×C4×C73—22no—
199C2×C4×C73—22no—
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—41no—
207C2×C4×C73—41no—
208C2×C4×C73—41no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—41no—
212C2×C4×C73—42no—
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×C73—42no—
221C2×C4×C73—42no—
222C2×C4×C73—42no—
223C2×C4×C73—42no—
224C2×C4×C73—42no—
225C2×C4×C73—42no—
226C2×C4×C73C22⋊Q814yes—
227C2×C4×C73#12314yes—
228C2×C4×C73#12414yes—
229C2×C4×C73#12514yes—
230C2×C4×C73#12514yes—
231C2×C4×C73#12614yes—
232C2×C4×C73#12614yes—
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—22no—
249C2×Dic73—22no—
250C2×Dic73—22no—
251C2×Dic73—22no—
252C2×Dic73—22no—
253C2×Dic73—22no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
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—42no—
271C2×Dic73—42no—
272C2×Dic73#12114yes—
273C2×Dic73C22⋊Q814yes—
274C2×Dic73C4⋊Q814yes—
275C22×C73C2×#12111yescharacteristic
276C22×C73C2×C22⋊Q811yescharacteristic
277C22×C73C2×C22⋊Q811yescharacteristic
278C22×C73C2×#12311yescharacteristic
279C22×C73C2×#12411yescharacteristic
280C22×C73C2×#12511yescharacteristic
281C22×C73C2×#12511yescharacteristic
282C22×C73C2×#12611yescharacteristic
283C22×C73C2×#12611yescharacteristic
284C22×C73C2×C4⋊Q811yescharacteristic
285C22×C73#53211yescharacteristic
286C22×C73#53311yescharacteristic
287C22×C73#53311yescharacteristic
288C22×C73#53511yescharacteristic
289C22×C73#53611yescharacteristic
290C22×C73#54211yescharacteristic
291C22×C73#54211yescharacteristic
292C22×C73#54411yescharacteristic
293C22×C73#54411yescharacteristic
294C22×C73#54711yescharacteristic
295C22×C73#54711yescharacteristic
296C22×C73#55011yescharacteristic
297C22×C73#55011yescharacteristic
298C22×C73#55211yescharacteristic
299C22×C73#55211yescharacteristic
300C22×C73#55311yescharacteristic
301C22×C73#55311yescharacteristic
302C22×C73#55411yescharacteristic
303C22×C73#55411yescharacteristic
304C22×C73#55611yescharacteristic
305C22×C73#55611yescharacteristic
306C22×C73#55711yescharacteristic
307C22×C73#55711yescharacteristic
308C22×C73#55911yescharacteristic
309C22×C73#55911yescharacteristic
310C4×C73—42no—
311C4×C73—42no—
312C4×C73—82no—
313C4×C73—82no—
314C4×C73#40018yescomplemented
315Dic73—24no—
316Dic73—24no—
317Dic73—24no—
318Dic73—42no—
319Dic73—82no—
320Dic73—82no—
321#15152—731nomaximal, Sylow
322C2×C73C2×#40011yescharacteristic
323C2×C73#248611yescharacteristic
324C2×C73#248711yescharacteristic
325C2×C73#251111yescharacteristic
326C2×C73#251111yescharacteristic
327C2×C73#251211yescharacteristic
328C2×C73#251211yescharacteristic
329C2×C73#254811yescharacteristic
330C2×C73#255211yescharacteristic
331C2×C73#255211yescharacteristic
332C2×C73#256811yescharacteristic
333C2×C73#257011yescharacteristic
334C2×C73#257011yescharacteristic
335C2×C73#262811yescharacteristic
336C2×C73#285711yescharacteristic
337C2×#400—732no—
338C2×#384—731no—
339C2×C4×C4⋊C4—731no—
340#1445—732no—
341#1442—732no—
342#1441—732no—
343C4⋊#95—731no—
344C4⋊#95—731no—
345C4⋊#95—731no—
346C4⋊#95—731no—
347C4⋊#95D7311yescharacteristic
348C73#1515211yescharacteristic, complemented, Sylow
349C22×C4⋊C4—732no—
350C22×C4⋊C4—731no—
351C22×C4⋊C4—731no—
352C22×C4⋊C4—732no—
353C22×C4⋊C4—731no—
354C22×C4⋊C4—731no—
355C22×C4⋊C4C2×D7311yescharacteristic
356C22×C4⋊C4C2×D7311yescharacteristic
357C22×C42—731no—
358C22×C42—731no—
359C22×C42C2×D7311yescharacteristic
360#400—1468no—
361#384—1464no—
362C4×C4⋊C4—1464no—
363C2×#95—732no—
364C2×#95—732no—
365C2×#95—732no—
366C2×#95—732no—
367C2×#95—732no—
368C2×#95—732no—
369C2×#95—732no—
370C2×#95—732no—
371C2×#95—731no—
372C2×#95—731no—
373C2×#95C2×D7312yes—
374C2×#95C2×D7312yes—
375C23×C4—731no—
376C23×C4—731no—
377C23×C4—731no—
378C23×C4—731no—
379C23×C4—732no—
380C23×C4—732no—
381C23×C4C22×D7312yes—
382C23×C4C22×D7312yes—
383C23×C4C22×D7311yescharacteristic
384C23×C4C22×D7311yescharacteristic
385C23×C4C22×D7311yescharacteristic
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—2922no—
393C2×C4⋊C4—2922no—
394C2×C4⋊C4—734no—
395C2×C4⋊C4—734no—
396C2×C4⋊C4—1464no—
397C2×C4⋊C4—1464no—
398C2×C4⋊C4—1464no—
399C2×C4⋊C4—1464no—
400C2×C4⋊C4—1462no—
401C2×C4⋊C4—1462no—
402C2×C4⋊C4—1462no—
403C2×C4⋊C4—1462no—
404C2×C4⋊C4—1462no—
405C2×C4⋊C4—1462no—
406C2×C4⋊C4—1462no—
407C2×C4⋊C4—1462no—
408C2×C4⋊C4—1462no—
409C2×C4⋊C4—1462no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—734no—
414C2×C42—734no—
415C2×C42—1462no—
416C2×C42—1462no—
417C2×C42—1462no—
418C2×C42—1462no—
419#95—24no—
420#95—42no—
421#95—2922no—
422#95—2922no—
423#95—2922no—
424#95—1464no—
425#95—1462no—
426#95—1462no—
427#95—1464no—
428#95—1464no—
429#95—1464no—
430#95—1464no—
431C24C23×D7311yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—732no—
459C22×C4—732no—
460C22×C4—732no—
461C22×C4—732no—
462C22×C4—732no—
463C22×C4—732no—
464C22×C4—732no—
465C22×C4—732no—
466C22×C4—732no—
467C22×C4—732no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4—1462no—
471C22×C4—1462no—
472C22×C4—1462no—
473C22×C4—1462no—
474C22×C4—1462no—
475C22×C4—1462no—
476C22×C4—1462no—
477C22×C4—1462no—
478C22×C4—1462no—
479C22×C4—1462no—
480C22×C4—1462no—
481C22×C4—1462no—
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×C4—1461no—
495C22×C4—1461no—
496C22×C4—1461no—
497C22×C4—1461no—
498C22×C4—1461no—
499C22×C4—1461no—
500C22×C4D4×D7312yes—
501C22×C4D4×D7312yes—
502C22×C4Q8×D7312yes—
503C22×C4Q8×D7312yes—
504C22×C4#1192402712yes—
505C22×C4#1192402712yes—
506C22×C4#1192402812yes—
507C22×C4#1192402812yes—
508C22×C4#1192402812yes—
509C4⋊C4—44no—
510C4⋊C4—44no—
511C4⋊C4—2928no—
512C4⋊C4—2928no—
513C4⋊C4—2924no—
514C4⋊C4—2924no—
515C4⋊C4—1468no—
516C4⋊C4—1468no—
517C42—44no—
518C42—1468no—
519C42—1468no—
520C23C2×D4×D7311yescharacteristic
521C23C2×D4×D7311yescharacteristic
522C23C2×Q8×D7311yescharacteristic
523C23C2×Q8×D7311yescharacteristic
524C23#41×D7311yescharacteristic
525C23#41×D7311yescharacteristic
526C23C2×#1192402711yescharacteristic
527C23C2×#1192402711yescharacteristic
528C23C2×#1192402811yescharacteristic
529C23C2×#1192402811yescharacteristic
530C23C2×#1192402811yescharacteristic
531C23#1455663611yescharacteristic
532C23#1455663711yescharacteristic
533C23#1455663811yescharacteristic
534C23#1455663911yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
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—2922no—
580C2×C4—2922no—
581C2×C4—734no—
582C2×C4—734no—
583C2×C4—734no—
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—1462no—
600C2×C4—1462no—
601C2×C4—1462no—
602C2×C4—1462no—
603C2×C4—1462no—
604C2×C4—1462no—
605C2×C4#1455656914yes—
606C2×C4#1455657314yes—
607C2×C4#1455657714yes—
608C2×C4#1455658114yes—
609C2×C4#1455658114yes—
610C2×C4#1455658414yes—
611C2×C4#1455658514yes—
612C22#121×D7311yescharacteristic
613C22C22⋊Q8×D7311yescharacteristic
614C22C2×#1455656911yescharacteristic
615C22C2×#1455657311yescharacteristic
616C22C2×#1455657711yescharacteristic
617C22C2×#1455658111yescharacteristic
618C22C2×#1455658111yescharacteristic
619C22C2×#1455658411yescharacteristic
620C22C2×#1455658511yescharacteristic
621C22C4⋊Q8×D7311yescharacteristic
622C22#1798913411yescharacteristic
623C22#1798914111yescharacteristic
624C22#1798914311yescharacteristic
625C22#1798915311yescharacteristic
626C22#1798916011yescharacteristic
627C22#1798920211yescharacteristic
628C22#1798920911yescharacteristic
629C22#1798921411yescharacteristic
630C22#1798921711yescharacteristic
631C22#1798923711yescharacteristic
632C22#1798923811yescharacteristic
633C22#1798925711yescharacteristic
634C22#1798925811yescharacteristic
635C22#1798927111yescharacteristic
636C22#1798927611yescharacteristic
637C22#1798928111yescharacteristic
638C22#1798928411yescharacteristic
639C22#1798929211yescharacteristic
640C22#1798929511yescharacteristic
641C22#1798930611yescharacteristic
642C22#1798930911yescharacteristic
643C22#1798931211yescharacteristic
644C22#1798931511yescharacteristic
645C22#1798931911yescharacteristic
646C22#1798932011yescharacteristic
647C4—42no—
648C4—42no—
649C4—82no—
650C4—82no—
651C4—2922no—
652C4—5842no—
653C4—5842no—
654C4—1464no—
655C4—1464no—
656C4—1464no—
657C4#1798852818yescomplemented
658C2C2×#1798852811yescharacteristic
659C2#2261423511yescharacteristic
660C2#2261424411yescharacteristic
661C2#2261450011yescharacteristic
662C2#2261450711yescharacteristic
663C2#2261451111yescharacteristic
664C2#2261451811yescharacteristic
665C2#2261493211yescharacteristic
666C2#2261496411yescharacteristic
667C2#2261496511yescharacteristic
668C2#2261514511yescharacteristic
669C2#2261516311yescharacteristic
670C2#2261516811yescharacteristic
671C2#2261575811yescharacteristic
672C2#2261828211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, prime radical, cosocleC24×C73C24
FittingC73×C4⋊#95C2
hypercenterC4⋊#95D73
hypocenterC73#15152
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
314. C4×C73#400semidirect
348. C73#15152semidirect
657. C4#17988528semidirect

Maximal subgroups

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

subgroupindex
C2×#179885282
C2×#179884562
C2×C4×#119240072
#226081972
#226081862
#226081822
#226081612
#226081602
C73×C4⋊#952
#1515273