Finite Group Databasebeta

← #33007184

Subgroups — #33007184

Order 18688.

2110 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556556C211yesmaximal, characteristic
2C2×#17988491C212yesmaximal
3C2×#17988438C211yesmaximal, characteristic
4C2×C42×Dic73C211yesmaximal, characteristic
5#22608166C211yesmaximal, characteristic
6#22608164C211yesmaximal, characteristic
7#22608163C211yesmaximal, characteristic
8#22608159C212yesmaximal
9#95×Dic73C212yesmaximal
10#95×Dic73C212yesmaximal
11C73×#1436C211yesmaximal, characteristic
12C23×Dic146C2211yescharacteristic
13C2×#14556556—24no—
14C2×#14556556—24no—
15C2×#14556556C418yescomplemented
16C22×#11924007C2211yescharacteristic
17C22×#11924007C2212yes—
18C22×#11924007C2211yescharacteristic
19C22×C4×Dic73C2212yes—
20C22×C4×Dic73C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22C22×C4×Dic73C2211yescharacteristic
23C22×C4×Dic73C2212yes—
24C22×C4×Dic73C2212yes—
25C22×C4×Dic73C2211yescharacteristic
26#17988491C4116yescomplemented
27#17988438—24no—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C42×Dic73—24no—
36C22×C4⋊C4×C73C2211yescharacteristic
37C22×C42×C73C2211yescharacteristic
38C2×#95×C73C2212yes—
39C2×#95×C73C2211yescharacteristic
40C2×#95×C73C2212yes—
41C22×Dic146—22no—
42C22×Dic146—22no—
43C22×Dic146—24no—
44C22×Dic146C2×C418yes—
45C22×Dic146C2×C414yes—
46C23×Dic73C2312yes—
47C23×Dic73C2311yescharacteristic
48C23×Dic73C2311yescharacteristic
49C23×Dic73C2312yes—
50C23×Dic73C2311yescharacteristic
51C23×Dic73C2311yescharacteristic
52#14556556—232no—
53C2×#11924007—24no—
54C2×#11924007—22no—
55C2×#11924007—22no—
56C2×#11924007—24no—
57C2×#11924007—22no—
58C2×#11924007—22no—
59C2×#11924007C2×C418yes—
60C2×#11924007C2×C414yes—
61C2×#11924007C2×C414yes—
62C2×C4×Dic73—24no—
63C2×C4×Dic73—24no—
64C2×C4×Dic73—22no—
65C2×C4×Dic73—22no—
66C2×C4×Dic73—22no—
67C2×C4×Dic73—22no—
68C2×C4×Dic73—24no—
69C2×C4×Dic73—24no—
70C2×C4×Dic73—24no—
71C2×C4×Dic73—24no—
72C2×C4×Dic73—24no—
73C2×C4×Dic73—24no—
74C2×C4×Dic73—22no—
75C2×C4×Dic73C2×C418yes—
76C2×C4×Dic73C2×C414yes—
77C2×C4×Dic73C2×C414yes—
78C2×C4×Dic73C2×C414yes—
79C2×C4×Dic73D414yes—
80C2×C4×Dic73D414yes—
81C2×C4×Dic73Q818yescomplemented
82#14556498—24no—
83#14556498—24no—
84#14556498—22no—
85#14556498—24no—
86#14556498C2×C418yes—
87#14556498C2×C418yes—
88#14556498C2×C418yes—
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2312yes—
91C23×C4×C73C2311yescharacteristic
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2312yes—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73C2×C414yes—
97C2×C42×C73—22no—
98C2×C42×C73—24no—
99#95×C73—22no—
100#95×C73—24no—
101#95×C73C2×C418yes—
102C2×Dic146—28no—
103C2×Dic146—28no—
104C2×Dic146—216no—
105C2×Dic146—216no—
106C2×Dic146C42116yescomplemented
107C22×Dic73—22no—
108C22×Dic73—21no—
109C22×Dic73—21no—
110C22×Dic73—22no—
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—22no—
120C22×Dic73—22no—
121C22×Dic73—22no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73C22×C414yes—
125C22×Dic73C22×C412yes—
126C22×Dic73C22×C414yes—
127C22×Dic73C22×C412yes—
128C22×Dic73C22×C414yes—
129C22×Dic73C22×C412yes—
130C22×Dic73C22×C414yes—
131C22×Dic73C22×C412yes—
132C22×Dic73C2×D412yes—
133C22×Dic73C2×D412yes—
134C22×Dic73C2×D412yes—
135C22×Dic73C2×D412yes—
136C22×Dic73C2×Q814yes—
137C22×Dic73C2×Q814yes—
138C22×Dic73#4114yes—
139C22×Dic73#4114yes—
140C22×Dic73#4114yes—
141#11924007—28no—
142#11924007—28no—
143#11924007—216no—
144C4×Dic73—28no—
145C4×Dic73—28no—
146C4×Dic73—28no—
147C4×Dic73—216no—
148C4×Dic73—216no—
149C4×Dic73—48no—
150C4×Dic73C22⋊C4116yes—
151C24×C73C2411yescharacteristic
152C22×C4×C73—22no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—22no—
156C22×C4×C73—22no—
157C22×C4×C73—22no—
158C22×C4×C73—22no—
159C22×C4×C73—22no—
160C22×C4×C73—22no—
161C22×C4×C73—22no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
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×C73C22×C414yes—
172C22×C4×C73C22×C412yes—
173C22×C4×C73C22×C414yes—
174C22×C4×C73C22×C412yes—
175C22×C4×C73C22×C412yes—
176C22×C4×C73C22×C414yes—
177C22×C4×C73C2×D412yes—
178C22×C4×C73C2×D412yes—
179C22×C4×C73C2×Q814yes—
180C22×C4×C73#4114yes—
181C4⋊C4×C73—28no—
182C42×C73—28no—
183C23×C73C23×C411yescharacteristic
184C23×C73C23×C412yes—
185C23×C73C22×D411yescharacteristic
186C23×C73C22×D411yescharacteristic
187C23×C73C22×Q812yes—
188C23×C73C2×#4112yes—
189C23×C73C2×#4112yes—
190C23×C73C2×#4112yes—
191C23×C73C2×#4112yes—
192C2×C4×C73—22no—
193C2×C4×C73—22no—
194C2×C4×C73—24no—
195C2×C4×C73—24no—
196C2×C4×C73—24no—
197C2×C4×C73—24no—
198C2×C4×C73—24no—
199C2×C4×C73—24no—
200C2×C4×C73—22no—
201C2×C4×C73—24no—
202C2×C4×C73—22no—
203C2×C4×C73—24no—
204C2×C4×C73—24no—
205C2×C4×C73—24no—
206C2×C4×C73—22no—
207C2×C4×C73—24no—
208C2×C4×C73—24no—
209C2×C4×C73—24no—
210C2×C4×C73—24no—
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×C73C2×C4214yes—
219C2×C4×C73C2×C22⋊C414yes—
220C2×C4×C73C4×Q818yescomplemented
221C2×Dic73—22no—
222C2×Dic73—22no—
223C2×Dic73—24no—
224C2×Dic73—24no—
225C2×Dic73—24no—
226C2×Dic73—24no—
227C2×Dic73—24no—
228C2×Dic73—24no—
229C2×Dic73—24no—
230C2×Dic73—24no—
231C2×Dic73—22no—
232C2×Dic73—24no—
233C2×Dic73—24no—
234C2×Dic73—24no—
235C2×Dic73—24no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—42no—
239C2×Dic73—42no—
240C2×Dic73—42no—
241C2×Dic73—42no—
242C2×Dic73—42no—
243C2×Dic73C2×C4214yes—
244C2×Dic73C2×C4214yes—
245C2×Dic73C2×C22⋊C414yes—
246C2×Dic73C2×C22⋊C414yes—
247C2×Dic73#11714yes—
248C2×Dic73C4×D418yes—
249C2×Dic73C4×D418yes—
250C2×Dic73C4×Q818yes—
251C2×Dic73C4×Q818yescomplemented
252C2×Dic73C22⋊Q818yes—
253C2×Dic73#12414yes—
254C2×Dic73C4⋊Q814yes—
255Dic146—232no—
256C22×C73C22×C4211yescharacteristic
257C22×C73C22×C22⋊C411yescharacteristic
258C22×C73C2×#11711yescharacteristic
259C22×C73C2×C4×D412yes—
260C22×C73C2×C4×D412yes—
261C22×C73C2×C4×Q812yes—
262C22×C73C2×C4×Q812yes—
263C22×C73C2×C4×Q812yes—
264C22×C73C4×#4112yes—
265C22×C73C4×#4112yes—
266C22×C73C4×#4112yes—
267C22×C73C2×C22⋊Q812yes—
268C22×C73#52511yescharacteristic
269C22×C73#52511yescharacteristic
270C22×C73C2×#12411yescharacteristic
271C22×C73#52912yes—
272C22×C73#52912yes—
273C22×C73C2×C4⋊Q811yescharacteristic
274C22×C73#53212yes—
275C22×C73#53312yes—
276C22×C73#53312yes—
277C4×C73—24no—
278C4×C73—24no—
279C4×C73—28no—
280C4×C73—42no—
281C4×C73—44no—
282Dic73—24no—
283Dic73—28no—
284Dic73—42no—
285Dic73—44no—
286Dic73C4×C22⋊C418yes—
287Dic73#39118yescomplemented
288C4×#391—731nomaximal, Sylow
289C2×C73C2×C4×C22⋊C411yescharacteristic
290C2×C73C42×Q812yes—
291C2×C73C2×#39111yescharacteristic
292C2×C73#229512yes—
293C2×C73#229711yescharacteristic
294C2×C73C4×C22⋊Q812yes—
295C2×C73C4×C22⋊Q812yes—
296C2×C73C4×#12412yes—
297C2×C73C4×C4⋊Q812yes—
298C22×C4×Q8—731no—
299C2×#391—732no—
300C2×C4×C4⋊C4—731no—
301C2×C43—731no—
302#1436—731no—
303#1436—731no—
304#1436—731no—
305#1436D7311yescharacteristic
306C4⋊#95—732no—
307C4×#95—732no—
308C4×#95—732no—
309C73C4×#39111yescharacteristic, complemented, Sylow
310C23×Q8—731no—
311C2×C4×Q8—738no—
312C2×C4×Q8—1464no—
313C2×C4×Q8—1464no—
314C22×C4⋊C4—731no—
315C22×C4⋊C4—731no—
316C22×C4⋊C4—732no—
317C22×C4⋊C4C2×D7311yescharacteristic
318C22×C42—731no—
319C22×C42—731no—
320C22×C42—731no—
321C22×C42—732no—
322C22×C42—732no—
323C22×C42—732no—
324C22×C42—731no—
325C22×C42C2×D7311yescharacteristic
326#391—7316no—
327C4×C4⋊C4—1464no—
328C2×#95—732no—
329C2×#95—732no—
330C2×#95—732no—
331C2×#95—732no—
332C2×#95—732no—
333C2×#95—732no—
334C2×#95—731no—
335C2×#95C2×D7312yes—
336C2×#95C2×D7311yescharacteristic
337C2×#95C2×D7312yes—
338C43—1464no—
339C22×Q8—734no—
340C22×Q8—738no—
341C22×Q8—1462no—
342C22×Q8—1462no—
343C22×Q8—1464no—
344C23×C4—731no—
345C23×C4—731no—
346C23×C4—731no—
347C23×C4—732no—
348C23×C4—731no—
349C23×C4—732no—
350C23×C4C22×D7311yescharacteristic
351C23×C4C22×D7312yes—
352C23×C4C22×D7311yescharacteristic
353C23×C4C22×D7311yescharacteristic
354C23×C4C22×D7312yes—
355C4×Q8—14632no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—734no—
359C2×C4⋊C4—734no—
360C2×C4⋊C4—738no—
361C2×C4⋊C4—1462no—
362C2×C4⋊C4—1462no—
363C2×C4⋊C4—1464no—
364C2×C4⋊C4—1464no—
365C2×C4⋊C4—1462no—
366C2×C4⋊C4—1462no—
367C2×C4⋊C4C4×D7314yes—
368C2×C42—22no—
369C2×C42—24no—
370C2×C42—734no—
371C2×C42—734no—
372C2×C42—734no—
373C2×C42—734no—
374C2×C42—734no—
375C2×C42—738no—
376C2×C42—738no—
377C2×C42—1464no—
378C2×C42—1464no—
379C2×C42—1464no—
380C2×C42—1462no—
381C2×C42—1462no—
382C2×C42—1462no—
383C2×C42—1462no—
384C2×C42—1464no—
385C2×C42—1464no—
386C2×C42—1464no—
387C2×C42—1464no—
388C2×C42—1464no—
389C2×C42—1462no—
390#95—22no—
391#95—24no—
392#95—738no—
393#95—738no—
394#95—738no—
395#95—1464no—
396#95—1464no—
397#95—1462no—
398#95—1464no—
399#95C4×D7318yes—
400C24C23×D7311yescharacteristic
401C2×Q8—7316no—
402C2×Q8—1468no—
403C2×Q8—1468no—
404C2×Q8—14616no—
405C2×Q8—14616no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—732no—
426C22×C4—732no—
427C22×C4—734no—
428C22×C4—732no—
429C22×C4—732no—
430C22×C4—732no—
431C22×C4—732no—
432C22×C4—734no—
433C22×C4—734no—
434C22×C4—734no—
435C22×C4—734no—
436C22×C4—734no—
437C22×C4—732no—
438C22×C4—734no—
439C22×C4—734no—
440C22×C4—734no—
441C22×C4—732no—
442C22×C4—1462no—
443C22×C4—1461no—
444C22×C4—1461no—
445C22×C4—1462no—
446C22×C4—1462no—
447C22×C4—1462no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1462no—
456C22×C4—1462no—
457C22×C4—1462no—
458C22×C4—1462no—
459C22×C4C2×C4×D7314yes—
460C22×C4C2×C4×D7312yes—
461C22×C4C2×C4×D7314yes—
462C22×C4C2×C4×D7312yes—
463C22×C4C2×C4×D7312yes—
464C22×C4C2×C4×D7314yes—
465C22×C4D4×D7312yes—
466C22×C4D4×D7312yes—
467C22×C4Q8×D7314yes—
468C22×C4#1192402714yes—
469C4⋊C4—28no—
470C4⋊C4—14616no—
471C4⋊C4—1468no—
472C4⋊C4—1468no—
473C42—28no—
474C42—2928no—
475C42—7316no—
476C42—14616no—
477C42—14616no—
478C42—1468no—
479C42—1468no—
480C42—1468no—
481C23C22×C4×D7311yescharacteristic
482C23C22×C4×D7312yes—
483C23C2×D4×D7311yescharacteristic
484C23C2×D4×D7311yescharacteristic
485C23C2×Q8×D7312yes—
486C23#41×D7312yes—
487C23#41×D7312yes—
488C23#41×D7312yes—
489C23C2×#1192402712yes—
490Q8—14632no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—2922no—
518C2×C4—2922no—
519C2×C4—2922no—
520C2×C4—2921no—
521C2×C4—2921no—
522C2×C4—2922no—
523C2×C4—2922no—
524C2×C4—734no—
525C2×C4—734no—
526C2×C4—734no—
527C2×C4—734no—
528C2×C4—734no—
529C2×C4—738no—
530C2×C4—738no—
531C2×C4—738no—
532C2×C4—738no—
533C2×C4—734no—
534C2×C4—734no—
535C2×C4—738no—
536C2×C4—1462no—
537C2×C4—1464no—
538C2×C4—1464no—
539C2×C4—1464no—
540C2×C4—1464no—
541C2×C4—1464no—
542C2×C4—1464no—
543C2×C4—1462no—
544C2×C4—1462no—
545C2×C4—1464no—
546C2×C4—1464no—
547C2×C4—1464no—
548C2×C4—1464no—
549C2×C4—1464no—
550C2×C4—1464no—
551C2×C4C42×D7314yes—
552C2×C4C22⋊C4×D7314yes—
553C2×C4#1455655618yescomplemented
554C22C2×C42×D7311yescharacteristic
555C22C2×C22⋊C4×D7311yescharacteristic
556C22#117×D7311yescharacteristic
557C22C4×D4×D7312yes—
558C22C4×D4×D7312yes—
559C22C4×Q8×D7312yes—
560C22C4×Q8×D7312yes—
561C22C2×#1455655612yes—
562C22C4×#1192402712yes—
563C22C4×#1192402712yes—
564C22#1798905512yes—
565C22C22⋊Q8×D7312yes—
566C22#1798909311yescharacteristic
567C22#1798909511yescharacteristic
568C22#124×D7311yescharacteristic
569C22#1798911412yes—
570C22#1798912012yes—
571C22C4⋊Q8×D7311yescharacteristic
572C22#1798913212yes—
573C22#1798913912yes—
574C22#1798914312yes—
575C4—24no—
576C4—24no—
577C4—28no—
578C4—42no—
579C4—44no—
580C4—2922no—
581C4—2924no—
582C4—738no—
583C4—738no—
584C4—1464no—
585C4—1468no—
586C2C4×C22⋊C4×D7311yescharacteristic
587C2C4×#1455655612yes—
588C2#391×D7311yescharacteristic
589C2#2261240412yes—
590C2#2261241611yescharacteristic
591C2#2261246312yes—
592C2#2261246512yes—
593C2#2261247212yes—
594C2#2261250212yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC73×#1436C2
socle, prime radical, cosocleC24×C73C24
hypercenter#1436D73
hypocenterC73C4×#391
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
15. C2×#14556556C4semidirect
26. #17988491C4semidirect
81. C2×C4×Dic73Q8semidirect
106. C2×Dic146C42semidirect
220. C2×C4×C73C4×Q8semidirect
251. C2×Dic73C4×Q8semidirect
287. Dic73#391semidirect
309. C73C4×#391semidirect
553. C2×C4#14556556semidirect

Maximal subgroups

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

subgroupindex
C22×#145565562
C2×#179884912
C2×#179884382
C2×C42×Dic732
#226081662
#226081642
#226081632
#226081592
#95×Dic732
C73×#14362
C4×#39173