Finite Group Databasebeta

← #33012643

Subgroups — #33012643

Order 18688.

1414 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556581C211yesmaximal, characteristic
2C2×#17988454C211yesmaximal, characteristic
3C2×C4×#11924007C211yesmaximal, characteristic
4#22608197C212yesmaximal
5#22608197C212yesmaximal
6#22608183C212yesmaximal
7#22608182C212yesmaximal
8#22608166C211yesmaximal, characteristic
9#22608164C211yesmaximal, characteristic
10#22608163C211yesmaximal, characteristic
11C73×#1436C211yesmaximal, characteristic
12C2×#14556581—24no—
13C2×#14556581—24no—
14C2×#14556581C418yescomplemented
15C22×C4⋊Dic73C2211yescharacteristic
16C22×#11924007C2212yes—
17C22×#11924007C2211yescharacteristic
18C22×#11924007C2211yescharacteristic
19C22×#11924007C2211yescharacteristic
20C22×#11924007C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22C22×C4×Dic73C2211yescharacteristic
23#17988454—24no—
24C4×#11924007—24no—
25C2×#14556498C2211yescharacteristic
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C22×C4⋊C4×C73C2211yescharacteristic
36C22×C42×C73C2211yescharacteristic
37C2×#95×C73C2211yescharacteristic
38C2×#95×C73C2212yes—
39C2×#95×C73C2212yes—
40C23×Dic73C2312yes—
41C23×Dic73C2311yescharacteristic
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2312yes—
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2311yescharacteristic
46#14556581—232no—
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73C2×C414yes—
50C2×#11924007—24no—
51C2×#11924007—22no—
52C2×#11924007—22no—
53C2×#11924007—22no—
54C2×#11924007—22no—
55C2×#11924007—22no—
56C2×#11924007—22no—
57C2×#11924007—24no—
58C2×#11924007—22no—
59C2×#11924007—22no—
60C2×#11924007—24no—
61C2×#11924007C2×C414yes—
62C2×#11924007C2×C414yes—
63C2×#11924007C2×C414yes—
64C2×#11924007C2×C414yes—
65C2×C4×Dic73—22no—
66C2×C4×Dic73—42no—
67C2×C4×Dic73C2×C414yes—
68C2×C4×Dic73D414yes—
69C2×C4×Dic73D414yes—
70#14556498—24no—
71#14556498—24no—
72#14556498—24no—
73#14556498—24no—
74#14556498—24no—
75#14556498—22no—
76#14556498—24no—
77#14556498—42no—
78#14556498—42no—
79#14556498—42no—
80C23×C4×C73C2312yes—
81C23×C4×C73C2311yescharacteristic
82C23×C4×C73C2311yescharacteristic
83C23×C4×C73C2312yes—
84C23×C4×C73C2311yescharacteristic
85C2×C4⋊C4×C73—22no—
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73C2×C414yes—
88C2×C42×C73—22no—
89C2×C42×C73—42no—
90#95×C73—22no—
91#95×C73—24no—
92#95×C73—42no—
93C22×Dic73—22no—
94C22×Dic73—22no—
95C22×Dic73—22no—
96C22×Dic73—22no—
97C22×Dic73—22no—
98C22×Dic73—21no—
99C22×Dic73—21no—
100C22×Dic73—21no—
101C22×Dic73—21no—
102C22×Dic73—22no—
103C22×Dic73—22no—
104C22×Dic73—22no—
105C22×Dic73—22no—
106C22×Dic73—22no—
107C22×Dic73—22no—
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×Dic73C22×C412yes—
119C22×Dic73C22×C412yes—
120C22×Dic73C22×C412yes—
121C22×Dic73C22×C412yes—
122C22×Dic73C2×D412yes—
123C22×Dic73C2×D412yes—
124C22×Dic73C2×D412yes—
125C22×Dic73C2×D412yes—
126C22×Dic73#4114yes—
127C4⋊Dic73—28no—
128#11924007—216no—
129#11924007—28no—
130#11924007—28no—
131#11924007—28no—
132#11924007—28no—
133C4×Dic73—44no—
134C4×Dic73C22⋊C4116yes—
135C24×C73C2411yescharacteristic
136C22×C4×C73—22no—
137C22×C4×C73—22no—
138C22×C4×C73—22no—
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×C73—22no—
158C22×C4×C73—22no—
159C22×C4×C73C22×C412yes—
160C22×C4×C73C22×C412yes—
161C22×C4×C73C22×C412yes—
162C22×C4×C73C2×D412yes—
163C22×C4×C73C2×D412yes—
164C22×C4×C73#4114yes—
165C4⋊C4×C73—28no—
166C42×C73—44no—
167C23×C73C23×C411yescharacteristic
168C23×C73C22×D411yescharacteristic
169C23×C73C22×D411yescharacteristic
170C23×C73C2×#4112yes—
171C23×C73C2×#4112yes—
172C23×C73H(5,𝔽2)12yes—
173C23×C732−1+412yes—
174C23×C732−1+412yes—
175C23×C732−1+412yes—
176C2×C4×C73—24no—
177C2×C4×C73—22no—
178C2×C4×C73—22no—
179C2×C4×C73—24no—
180C2×C4×C73—22no—
181C2×C4×C73—22no—
182C2×C4×C73—22no—
183C2×C4×C73—22no—
184C2×C4×C73—24no—
185C2×C4×C73—24no—
186C2×C4×C73—24no—
187C2×C4×C73—24no—
188C2×C4×C73—42no—
189C2×C4×C73—42no—
190C2×C4×C73—42no—
191C2×C4×C73—41no—
192C2×C4×C73—41no—
193C2×C4×C73—42no—
194C2×C4×C73—42no—
195C2×C4×C73—42no—
196C2×C4×C73—42no—
197C2×C4×C73—42no—
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×C73C2×C22⋊C414yes—
205C2×Dic73—22no—
206C2×Dic73—22no—
207C2×Dic73—24no—
208C2×Dic73—24no—
209C2×Dic73—24no—
210C2×Dic73—22no—
211C2×Dic73—24no—
212C2×Dic73—22no—
213C2×Dic73—22no—
214C2×Dic73—22no—
215C2×Dic73—22no—
216C2×Dic73—22no—
217C2×Dic73—24no—
218C2×Dic73—24no—
219C2×Dic73—24no—
220C2×Dic73—24no—
221C2×Dic73—42no—
222C2×Dic73—42no—
223C2×Dic73—42no—
224C2×Dic73—41no—
225C2×Dic73—41no—
226C2×Dic73—42no—
227C2×Dic73—42no—
228C2×Dic73—42no—
229C2×Dic73—42no—
230C2×Dic73—42no—
231C2×Dic73—42no—
232C2×Dic73—42no—
233C2×Dic73—42no—
234C2×Dic73—42no—
235C2×Dic73—42no—
236C2×Dic73—42no—
237C2×Dic73C2×C22⋊C414yes—
238C2×Dic73C2×C22⋊C414yes—
239C22×C73C22×C22⋊C411yescharacteristic
240C22×C73C4×#4111yescharacteristic
241C22×C73C4×#4111yescharacteristic
242C22×C73#51912yes—
243C22×C73#52012yes—
244C22×C73#52512yes—
245C22×C73#53212yes—
246C22×C73#53511yescharacteristic
247C22×C73#53611yescharacteristic
248C22×C73#53611yescharacteristic
249C22×C73#53612yes—
250C22×C73#53611yescharacteristic
251C22×C73#53712yes—
252C22×C73#53912yes—
253C22×C73#53912yes—
254C22×C73#53912yes—
255C22×C73#53912yes—
256C22×C73#54112yes—
257C22×C73#54112yes—
258C22×C73#54112yes—
259C22×C73#54112yes—
260C4×C73—24no—
261C4×C73—42no—
262C4×C73—44no—
263C4×C73—42no—
264C4×C73—82no—
265Dic73—24no—
266Dic73—24no—
267Dic73—42no—
268Dic73—44no—
269Dic73—42no—
270Dic73—82no—
271#14289—731nomaximal, Sylow
272C2×C73#229711yescharacteristic
273C2×C73#231011yescharacteristic
274C2×C73#231111yescharacteristic
275C2×C73#233612yes—
276C2×C73#233612yes—
277C2×C73#263312yes—
278C2×C73#263412yes—
279C2×C73#266412yes—
280C2×C73#266412yes—
281C22×#125—731no—
282C2×#383—731no—
283C2×C4×C4⋊C4—731no—
284#1445—732no—
285#1445—732no—
286#1441—732no—
287#1441—732no—
288#1436—731no—
289#1436—731no—
290#1436—731no—
291#1436D7311yescharacteristic
292C73#1428911yescharacteristic, complemented, Sylow
293C2×#125—738no—
294C2×#125—1464no—
295C2×#125—1464no—
296C22×C4⋊C4—731no—
297C22×C4⋊C4—731no—
298C22×C4⋊C4—731no—
299C22×C4⋊C4—731no—
300C22×C4⋊C4—731no—
301C22×C4⋊C4—732no—
302C22×C4⋊C4C2×D7311yescharacteristic
303C22×C42—731no—
304C22×C42—731no—
305C22×C42C2×D7311yescharacteristic
306#383—1464no—
307C4×C4⋊C4—1464no—
308C2×#95—732no—
309C2×#95—732no—
310C2×#95—732no—
311C2×#95—731no—
312C2×#95—732no—
313C2×#95—732no—
314C2×#95—732no—
315C2×#95—732no—
316C2×#95—732no—
317C2×#95—732no—
318C2×#95C2×D7311yescharacteristic
319C2×#95C2×D7312yes—
320C2×#95C2×D7312yes—
321C23×C4—731no—
322C23×C4—731no—
323C23×C4—731no—
324C23×C4—731no—
325C23×C4—732no—
326C23×C4—732no—
327C23×C4C22×D7312yes—
328C23×C4C22×D7311yescharacteristic
329C23×C4C22×D7311yescharacteristic
330C23×C4C22×D7312yes—
331C23×C4C22×D7311yescharacteristic
332#125—14632no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—734no—
336C2×C4⋊C4—734no—
337C2×C4⋊C4—734no—
338C2×C4⋊C4—734no—
339C2×C4⋊C4—734no—
340C2×C4⋊C4—1462no—
341C2×C4⋊C4—1462no—
342C2×C4⋊C4—1462no—
343C2×C4⋊C4—1462no—
344C2×C4⋊C4—1462no—
345C2×C4⋊C4—1462no—
346C2×C4⋊C4—1462no—
347C2×C4⋊C4—1462no—
348C2×C4⋊C4—1464no—
349C2×C4⋊C4—1464no—
350C2×C4⋊C4—1462no—
351C2×C4⋊C4—1462no—
352C2×C4⋊C4—1464no—
353C2×C4⋊C4C4×D7314yes—
354C2×C42—22no—
355C2×C42—42no—
356C2×C42—2922no—
357C2×C42—734no—
358C2×C42—734no—
359C2×C42—734no—
360C2×C42—1462no—
361#95—22no—
362#95—24no—
363#95—42no—
364#95—2922no—
365#95—2922no—
366#95—2922no—
367#95—1464no—
368#95—1464no—
369#95—1464no—
370#95—1464no—
371#95—1464no—
372#95—1462no—
373#95—1464no—
374C24C23×D7311yescharacteristic
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—732no—
399C22×C4—732no—
400C22×C4—732no—
401C22×C4—732no—
402C22×C4—732no—
403C22×C4—732no—
404C22×C4—732no—
405C22×C4—732no—
406C22×C4—734no—
407C22×C4—1462no—
408C22×C4—1462no—
409C22×C4—1462no—
410C22×C4—1462no—
411C22×C4—1462no—
412C22×C4—1462no—
413C22×C4—1462no—
414C22×C4—1462no—
415C22×C4—1461no—
416C22×C4—1461no—
417C22×C4—1461no—
418C22×C4—1461no—
419C22×C4—1462no—
420C22×C4—1462no—
421C22×C4—1462no—
422C22×C4—1462no—
423C22×C4—1462no—
424C22×C4—1462no—
425C22×C4—1462no—
426C22×C4—1462no—
427C22×C4—1462no—
428C22×C4—1462no—
429C22×C4—1462no—
430C22×C4—1462no—
431C22×C4—1462no—
432C22×C4C2×C4×D7312yes—
433C22×C4C2×C4×D7312yes—
434C22×C4C2×C4×D7312yes—
435C22×C4D4×D7312yes—
436C22×C4D4×D7312yes—
437C22×C4#1192402814yes—
438C4⋊C4—28no—
439C4⋊C4—1468no—
440C4⋊C4—1468no—
441C4⋊C4—1468no—
442C4⋊C4—1468no—
443C4⋊C4—14616no—
444C4⋊C4—1468no—
445C42—44no—
446C42—2924no—
447C42—7316no—
448C23C22×C4×D7311yescharacteristic
449C23C2×D4×D7311yescharacteristic
450C23C2×D4×D7311yescharacteristic
451C23#41×D7312yes—
452C23C2×#1192402812yes—
453C23#1455663612yes—
454C23#1455663812yes—
455C23#1455663812yes—
456C23#1455663912yes—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—2922no—
486C2×C4—2922no—
487C2×C4—2921no—
488C2×C4—2921no—
489C2×C4—2922no—
490C2×C4—2922no—
491C2×C4—2922no—
492C2×C4—2922no—
493C2×C4—2922no—
494C2×C4—2922no—
495C2×C4—2922no—
496C2×C4—2922no—
497C2×C4—2922no—
498C2×C4—2922no—
499C2×C4—2922no—
500C2×C4—2922no—
501C2×C4—734no—
502C2×C4—734no—
503C2×C4—1464no—
504C2×C4—1464no—
505C2×C4—1462no—
506C2×C4—1462no—
507C2×C4—1462no—
508C2×C4—1462no—
509C2×C4—1464no—
510C2×C4—1464no—
511C2×C4—1464no—
512C2×C4—1462no—
513C2×C4—1464no—
514C2×C4—1462no—
515C2×C4—1462no—
516C2×C4—1462no—
517C2×C4—1464no—
518C2×C4—1464no—
519C2×C4C22⋊C4×D7314yes—
520C22C2×C22⋊C4×D7311yescharacteristic
521C22#1798905511yescharacteristic
522C22C4×#1192402811yescharacteristic
523C22#1798906312yes—
524C22#1798906612yes—
525C22#1798909612yes—
526C22#1798913412yes—
527C22#1798915211yescharacteristic
528C22#1798915711yescharacteristic
529C22#1798915911yescharacteristic
530C22#1798916012yes—
531C22#1798916211yescharacteristic
532C22#1798916412yes—
533C22#1798917912yes—
534C22#1798918012yes—
535C22#1798918312yes—
536C22#1798918412yes—
537C22#1798919412yes—
538C22#1798919512yes—
539C22#1798919612yes—
540C22#1798919912yes—
541C4—24no—
542C4—42no—
543C4—42no—
544C4—44no—
545C4—82no—
546C4—2922no—
547C4—2922no—
548C4—2924no—
549C4—5842no—
550C4—1464no—
551C4—1464no—
552C2#2261241711yescharacteristic
553C2#2261251411yescharacteristic
554C2#2261251811yescharacteristic
555C2#2261273012yes—
556C2#2261273312yes—
557C2#2261580312yes—
558C2#2261581112yes—
559C2#2261609412yes—
560C2#2261609612yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1436C2
socle, prime radical, cosocleC24×C73C24
hypercenter#1436D73
hypocenterC73#14289
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
14. C2×#14556581C4semidirect
292. C73#14289semidirect

Maximal subgroups

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

subgroupindex
C22×#145565812
C2×#179884542
C2×C4×#119240072
#226081972
#226081832
#226081822
#226081662
#226081642
#226081632
C73×#14362
#1428973