Finite Group Databasebeta

← #33022740

Subgroups — #33022740

Order 18688.

1410 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988518C211yesmaximal, characteristic
2C2×#17988482C212yesmaximal
3C2×#17988482C211yesmaximal, characteristic
4C2×C4⋊C4×Dic73C211yesmaximal, characteristic
5#22608190C212yesmaximal
6#22608189C212yesmaximal
7#22608185C211yesmaximal, characteristic
8#22608184C211yesmaximal, characteristic
9#22608159C212yesmaximal
10#22608159C211yesmaximal, characteristic
11C2×#398×C73C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×#11924007C2211yescharacteristic
14C22×#11924007C2211yescharacteristic
15C22×#11924007C2212yes—
16C22×#11924007C2211yescharacteristic
17C22×#11924007C2212yes—
18C22×C4×Dic73C2212yes—
19C22×C4×Dic73C2211yescharacteristic
20#17988518—24no—
21#17988482—28no—
22#17988482—24no—
23C4⋊C4×Dic73—24no—
24C2×#14556498C2212yes—
25C2×#14556498C2211yescharacteristic
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2212yes—
34C22×C4⋊C4×C73C2211yescharacteristic
35C22×C4⋊C4×C73C2212yes—
36C22×C4⋊C4×C73C2211yescharacteristic
37#398×C73—24no—
38C2×#95×C73C2211yescharacteristic
39C2×#95×C73C2212yes—
40C23×Dic73C2311yescharacteristic
41C23×Dic73C2311yescharacteristic
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2312yes—
44C23×Dic73C2312yes—
45C23×Dic73C2311yescharacteristic
46C2×C4⋊Dic73—24no—
47C2×C4⋊Dic73—22no—
48C2×#11924007—22no—
49C2×#11924007—24no—
50C2×#11924007—22no—
51C2×#11924007—24no—
52C2×#11924007—24no—
53C2×#11924007—22no—
54C2×#11924007—24no—
55C2×#11924007—22no—
56C2×#11924007—24no—
57C2×#11924007—22no—
58C2×#11924007—22no—
59C2×#11924007—42no—
60C2×#11924007D414yes—
61C2×#11924007Q818yes—
62C2×C4×Dic73—24no—
63C2×C4×Dic73—24no—
64C2×C4×Dic73—24no—
65C2×C4×Dic73—24no—
66C2×C4×Dic73D414yes—
67#14556498—24no—
68#14556498—24no—
69#14556498—22no—
70#14556498—22no—
71#14556498—24no—
72#14556498—24no—
73#14556498—24no—
74#14556498—24no—
75#14556498—22no—
76#14556498—42no—
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C23×C4×C73C2312yes—
80C23×C4×C73C2312yes—
81C23×C4×C73C2311yescharacteristic
82C2×C4⋊C4×C73—22no—
83C2×C4⋊C4×C73—22no—
84C2×C4⋊C4×C73—24no—
85C2×C4⋊C4×C73—22no—
86C2×C4⋊C4×C73—24no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—42no—
90C2×C4⋊C4×C73D414yes—
91#95×C73—22no—
92#95×C73—24no—
93C22×Dic73—22no—
94C22×Dic73—22no—
95C22×Dic73—22no—
96C22×Dic73—21no—
97C22×Dic73—22no—
98C22×Dic73—21no—
99C22×Dic73—22no—
100C22×Dic73—22no—
101C22×Dic73—22no—
102C22×Dic73—21no—
103C22×Dic73—22no—
104C22×Dic73—21no—
105C22×Dic73—22no—
106C22×Dic73—21no—
107C22×Dic73—22no—
108C22×Dic73—21no—
109C22×Dic73—21no—
110C22×Dic73—21no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—21no—
116C22×Dic73—21no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—21no—
120C22×Dic73C2×D412yes—
121C22×Dic73C2×D412yes—
122C22×Dic73C2×D412yes—
123C22×Dic73C2×D412yes—
124C22×Dic73C2×Q814yes—
125C22×Dic73C2×Q814yes—
126C22×Dic73#4114yes—
127C22×Dic73#4112yes—
128C22×Dic73#4114yes—
129C4⋊Dic73—28no—
130#11924007—28no—
131#11924007—216no—
132#11924007—48no—
133#11924007—44no—
134#11924007—44no—
135C4×Dic73—28no—
136C4×Dic73—48no—
137C24×C73C2411yescharacteristic
138C22×C4×C73—22no—
139C22×C4×C73—22no—
140C22×C4×C73—22no—
141C22×C4×C73—21no—
142C22×C4×C73—22no—
143C22×C4×C73—21no—
144C22×C4×C73—22no—
145C22×C4×C73—22no—
146C22×C4×C73—22no—
147C22×C4×C73—21no—
148C22×C4×C73—22no—
149C22×C4×C73—22no—
150C22×C4×C73—21no—
151C22×C4×C73—22no—
152C22×C4×C73—21no—
153C22×C4×C73—22no—
154C22×C4×C73—22no—
155C22×C4×C73—21no—
156C22×C4×C73—22no—
157C22×C4×C73—22no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—22no—
162C22×C4×C73—22no—
163C22×C4×C73C2×D412yes—
164C22×C4×C73C2×D412yes—
165C22×C4×C73C2×D414yes—
166C22×C4×C73C2×D412yes—
167C22×C4×C73C2×Q814yes—
168C22×C4×C73#4112yes—
169C4⋊C4×C73—28no—
170C4⋊C4×C73—48no—
171C4⋊C4×C73—44no—
172C23×C73C22×D411yescharacteristic
173C23×C73C22×D411yescharacteristic
174C23×C73C22×D411yescharacteristic
175C23×C73C22×Q812yes—
176C23×C73C2×#4111yescharacteristic
177C23×C73C2×#4112yes—
178C23×C73C2×#4112yes—
179C23×C73C2×#4111yescharacteristic
180C23×C73H(5,𝔽2)11yescharacteristic
181C23×C732−1+411yescharacteristic
182C23×C732−1+412yes—
183C2×C4×C73—22no—
184C2×C4×C73—22no—
185C2×C4×C73—24no—
186C2×C4×C73—24no—
187C2×C4×C73—24no—
188C2×C4×C73—22no—
189C2×C4×C73—24no—
190C2×C4×C73—22no—
191C2×C4×C73—24no—
192C2×C4×C73—24no—
193C2×C4×C73—22no—
194C2×C4×C73—24no—
195C2×C4×C73—24no—
196C2×C4×C73—41no—
197C2×C4×C73—42no—
198C2×C4×C73—42no—
199C2×C4×C73—42no—
200C2×C4×C73—41no—
201C2×C4×C73—42no—
202C2×C4×C73—42no—
203C2×C4×C73—41no—
204C2×C4×C73—42no—
205C2×C4×C73—42no—
206C2×C4×C73—42no—
207C2×C4×C73—41no—
208C2×C4×C73—41no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—42no—
212C2×C4×C73—42no—
213C2×C4×C73#12114yes—
214C2×Dic73—22no—
215C2×Dic73—24no—
216C2×Dic73—22no—
217C2×Dic73—24no—
218C2×Dic73—22no—
219C2×Dic73—22no—
220C2×Dic73—22no—
221C2×Dic73—22no—
222C2×Dic73—24no—
223C2×Dic73—24no—
224C2×Dic73—24no—
225C2×Dic73—24no—
226C2×Dic73—42no—
227C2×Dic73—41no—
228C2×Dic73—42no—
229C2×Dic73—42no—
230C2×Dic73—41no—
231C2×Dic73—42no—
232C2×Dic73—42no—
233C2×Dic73—42no—
234C2×Dic73—42no—
235C2×Dic73—41no—
236C2×Dic73—42no—
237C2×Dic73—42no—
238C2×Dic73—42no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—42no—
244C2×Dic73—42no—
245C2×Dic73#12114yes—
246C2×Dic73C22⋊Q818yes—
247C2×Dic73#12314yes—
248C2×Dic73#12518yes—
249C2×Dic73C4⋊Q814yes—
250C22×C73C2×#12111yescharacteristic
251C22×C73C2×#12111yescharacteristic
252C22×C73C2×C22⋊Q812yes—
253C22×C73C2×#12311yescharacteristic
254C22×C73#52511yescharacteristic
255C22×C73C2×#12512yes—
256C22×C73#52912yes—
257C22×C73C2×C4⋊Q811yescharacteristic
258C22×C73#53212yes—
259C22×C73#53611yescharacteristic
260C22×C73#53711yescharacteristic
261C22×C73#54112yes—
262C22×C73#54212yes—
263C22×C73D4211yescharacteristic
264C22×C73#54711yescharacteristic
265C22×C73#54711yescharacteristic
266C22×C73#54812yes—
267C22×C73D4×Q812yes—
268C22×C73#55212yes—
269C22×C73#55412yes—
270C22×C73#55511yescharacteristic
271C22×C73#55712yes—
272C22×C73#55712yes—
273C4×C73—24no—
274C4×C73—44no—
275C4×C73—44no—
276C4×C73—42no—
277C4×C73—81no—
278Dic73—42no—
279Dic73—44no—
280Dic73—44no—
281Dic73—42no—
282Dic73—81no—
283Dic73#39818yescomplemented
284#15149—731nomaximal, Sylow
285C2×C73C2×#39811yescharacteristic
286C2×C73#245212yes—
287C2×C73#245312yes—
288C2×C73#250612yes—
289C2×C73#250812yes—
290C2×C73#253611yescharacteristic
291C2×C73#253711yescharacteristic
292C2×C73#254611yescharacteristic
293C2×C73#258411yescharacteristic
294C2×C73#262511yescharacteristic
295C2×C73#285411yescharacteristic
296C2×#398—731no—
297C2×#398D7311yescharacteristic
298C2×#389—732no—
299C2×#389—731no—
300C2×C4×C4⋊C4—731no—
301#1442—732no—
302#1442—732no—
303#1441—731no—
304#1441—731no—
305C4⋊#95—731no—
306C4⋊#95—732no—
307C73#1514911yescharacteristic, complemented, Sylow
308C22×C4⋊C4—732no—
309C22×C4⋊C4—732no—
310C22×C4⋊C4—731no—
311C22×C4⋊C4—731no—
312C22×C4⋊C4—731no—
313C22×C4⋊C4—731no—
314C22×C4⋊C4C2×D7311yescharacteristic
315C22×C4⋊C4C2×D7312yes—
316C22×C4⋊C4C2×D7311yescharacteristic
317C22×C42—731no—
318C22×C42—732no—
319#398—24no—
320#398—1464no—
321#389—1464no—
322#389—1468no—
323C4×C4⋊C4—1464no—
324C2×#95—732no—
325C2×#95—731no—
326C2×#95—732no—
327C2×#95—732no—
328C2×#95—732no—
329C2×#95—732no—
330C2×#95—732no—
331C2×#95—732no—
332C2×#95—731no—
333C2×#95—731no—
334C2×#95C2×D7311yescharacteristic
335C2×#95C2×D7312yes—
336C23×C4—731no—
337C23×C4—731no—
338C23×C4—732no—
339C23×C4—732no—
340C23×C4—731no—
341C23×C4—731no—
342C23×C4C22×D7311yescharacteristic
343C23×C4C22×D7311yescharacteristic
344C23×C4C22×D7312yes—
345C23×C4C22×D7312yes—
346C23×C4C22×D7311yescharacteristic
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—2922no—
356C2×C4⋊C4—734no—
357C2×C4⋊C4—738no—
358C2×C4⋊C4—1464no—
359C2×C4⋊C4—1464no—
360C2×C4⋊C4—1462no—
361C2×C4⋊C4—1462no—
362C2×C4⋊C4—1464no—
363C2×C4⋊C4—1462no—
364C2×C4⋊C4—1462no—
365C2×C4⋊C4—1462no—
366C2×C4⋊C4—1464no—
367C2×C4⋊C4—1462no—
368C2×C4⋊C4—1464no—
369C2×C4⋊C4—1464no—
370C2×C4⋊C4—1462no—
371C2×C4⋊C4C22⋊D7314yes—
372C2×C42—734no—
373C2×C42—1464no—
374C2×C42—1464no—
375C2×C42—1464no—
376C2×C42—1464no—
377#95—22no—
378#95—24no—
379#95—2922no—
380#95—1464no—
381#95—1464no—
382#95—1464no—
383#95—1462no—
384#95—1464no—
385#95—1462no—
386#95—1464no—
387#95—1464no—
388#95—1462no—
389C24C23×D7311yescharacteristic
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—732no—
416C22×C4—732no—
417C22×C4—734no—
418C22×C4—732no—
419C22×C4—734no—
420C22×C4—732no—
421C22×C4—732no—
422C22×C4—734no—
423C22×C4—734no—
424C22×C4—1461no—
425C22×C4—1461no—
426C22×C4—1462no—
427C22×C4—1462no—
428C22×C4—1461no—
429C22×C4—1462no—
430C22×C4—1462no—
431C22×C4—1461no—
432C22×C4—1462no—
433C22×C4—1462no—
434C22×C4—1461no—
435C22×C4—1462no—
436C22×C4—1462no—
437C22×C4—1462no—
438C22×C4—1462no—
439C22×C4—1461no—
440C22×C4—1462no—
441C22×C4—1461no—
442C22×C4—1461no—
443C22×C4—1462no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4—1462no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4D4×D7312yes—
452C22×C4D4×D7312yes—
453C22×C4C2×C22⋊D7314yes—
454C22×C4C2×C22⋊D7312yes—
455C22×C4Q8×D7314yes—
456C22×C4#1192402712yes—
457C4⋊C4—28no—
458C4⋊C4—48no—
459C4⋊C4—44no—
460C4⋊C4—2928no—
461C4⋊C4—2924no—
462C4⋊C4—2924no—
463C4⋊C4—1468no—
464C4⋊C4—14616no—
465C4⋊C4—1468no—
466C42—2928no—
467C42—1468no—
468C23C2×D4×D7311yescharacteristic
469C23C2×D4×D7311yescharacteristic
470C23C22×C22⋊D7311yescharacteristic
471C23C2×Q8×D7312yes—
472C23#41×D7312yes—
473C23#41×D7312yes—
474C23#41×D7311yescharacteristic
475C23C2×#1192402711yescharacteristic
476C23#1455663611yescharacteristic
477C23#1455663811yescharacteristic
478C23#1455663912yes—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—2922no—
510C2×C4—2922no—
511C2×C4—2921no—
512C2×C4—2922no—
513C2×C4—2922no—
514C2×C4—2922no—
515C2×C4—2922no—
516C2×C4—2921no—
517C2×C4—2922no—
518C2×C4—2922no—
519C2×C4—2922no—
520C2×C4—2921no—
521C2×C4—2922no—
522C2×C4—2921no—
523C2×C4—2922no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—2921no—
527C2×C4—2922no—
528C2×C4—734no—
529C2×C4—734no—
530C2×C4—738no—
531C2×C4—734no—
532C2×C4—738no—
533C2×C4—1462no—
534C2×C4—1462no—
535C2×C4—1462no—
536C2×C4—1462no—
537C2×C4—1464no—
538C2×C4—1464no—
539C2×C4—1464no—
540C2×C4—1464no—
541C2×C4—1462no—
542C2×C4—1464no—
543C2×C4—1462no—
544C2×C4—1464no—
545C2×C4#1455656314yes—
546C22#121×D7311yescharacteristic
547C22C2×#1455656311yescharacteristic
548C22C22⋊Q8×D7312yes—
549C22#123×D7311yescharacteristic
550C22#1798909511yescharacteristic
551C22#125×D7312yes—
552C22#1798911412yes—
553C22C4⋊Q8×D7311yescharacteristic
554C22#1798913312yes—
555C22#1798916211yescharacteristic
556C22#1798916611yescharacteristic
557C22#1798919612yes—
558C22#1798920712yes—
559C22D4×C22⋊D7311yescharacteristic
560C22#1798923611yescharacteristic
561C22#1798923711yescharacteristic
562C22#1798924712yes—
563C22Q8×C22⋊D7312yes—
564C22#1798926912yes—
565C22#1798929112yes—
566C22#1798930111yescharacteristic
567C22#1798931212yes—
568C22#1798931412yes—
569C4—24no—
570C4—44no—
571C4—42no—
572C4—44no—
573C4—81no—
574C4—2924no—
575C4—2924no—
576C4—2922no—
577C4—2922no—
578C4—5841no—
579C4—738no—
580C2#398×D7311yescharacteristic
581C2#2261378012yes—
582C2#2261378712yes—
583C2#2261444612yes—
584C2#2261446412yes—
585C2#2261483711yescharacteristic
586C2#2261484511yescharacteristic
587C2#2261491711yescharacteristic
588C2#2261531511yescharacteristic
589C2#2261573411yescharacteristic
590C2#2261826011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, prime radical, cosocleC24×C73C24
FittingC2×#398×C73C2
hypercenterC2×#398D73
hypocenterC73#15149
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
283. Dic73#398semidirect
307. C73#15149semidirect

Maximal subgroups

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

subgroupindex
C2×#179885182
C2×#179884822
C2×C4⋊C4×Dic732
#226081902
#226081892
#226081852
#226081842
#226081592
C2×#398×C732
#1514973