Finite Group Databasebeta

← #32991581

Subgroups — #32991581

Order 18688.

1164 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989353C211yesmaximal, characteristic
2C2×#17988605C211yesmaximal, characteristic
3C2×#17988603C211yesmaximal, characteristic
4#22609669C211yesmaximal, characteristic, complemented
5C2×#17988345C211yesmaximal, characteristic, complemented
6C2×#17988343C211yesmaximal, characteristic, complemented
7C73×#1742C211yesmaximal, characteristic, complemented
8C22×#11924028C2211yescharacteristic
9#17989353—22no—
10#17989353—22no—
11#17989353—22no—
12#17989353—22no—
13C2×#14556599C414yescomplemented
14C2×#14556597—22no—
15C22×#11924012C2211yescharacteristic
16C22×#11924012C2211yescharacteristic
17C2×M16×D73—22no—
18C2×#14556550C2211yescharacteristic
19#17988605—22no—
20#17988605—22no—
21#17988603—22no—
22#17988603—22no—
23C2×#14556519C414yescomplemented
24C2×#14556517C414yescomplemented
25#17988355—22no—
26#17988345—22no—
27#17988343—22no—
28C22×M16×C73C2211yescharacteristic
29C22×M16×C73C2211yescharacteristic
30C2×#117×C73C2211yescharacteristic
31#343×C73—22no—
32C2×#11924028—21no—
33C2×#11924028—21no—
34C2×#11924028—21no—
35C2×#11924028—21no—
36C2×#11924028—21no—
37C2×#11924028—21no—
38C2×#11924028C2×C412yes—
39C2×#11924028C2×C412yes—
40C2×#11924028C2×C412yes—
41C2×#11924028D412yes—
42C2×#11924028D412yes—
43C2×#11924028D412yes—
44C22×Dic146Q811yescharacteristic
45C22×D292Q811yescharacteristic
46C22×C22⋊D73—21no—
47C22×C4×D73—21no—
48#14556599—28no—
49#14556599—28no—
50#14556597—28no—
51#14556597—28no—
52C2×#11924012—21no—
53C2×#11924012—21no—
54C2×#11924012—21no—
55C2×#11924012—21no—
56C2×#11924012—21no—
57C2×#11924012—21no—
58C2×#11924012—21no—
59C2×#11924012—21no—
60C2×#11924012—21no—
61C2×#11924012C2×C412yes—
62C2×#11924012D412yes—
63C2×#11924012D412yes—
64C2×#11924011—24no—
65M16×D73—28no—
66M16×D73—28no—
67C22×#10596831—21no—
68C22×#10596831C2×C412yes—
69C2×C8×D73—24no—
70#14556550—21no—
71#14556550—21no—
72#14556550—21no—
73#14556550—21no—
74C2×C4⋊Dic73—21no—
75C2×C22⋊Dic73—21no—
76C2×C4×Dic73C2×C412yes—
77#14556519—28no—
78#14556517—28no—
79C23×C4×C73C2311yescharacteristic
80C2×M16×C73—21no—
81C2×M16×C73—21no—
82C2×M16×C73—21no—
83C2×M16×C73—21no—
84C2×M16×C73—21no—
85C2×M16×C73—21no—
86C2×M16×C73—21no—
87C2×M16×C73—21no—
88C2×M16×C73C2×C412yes—
89C2×M16×C73C2×C412yes—
90C2×M16×C73D412yes—
91C2×M16×C73D412yes—
92C22×C8×C73—21no—
93C22×C8×C73—21no—
94#117×C73—21no—
95#117×C73—21no—
96#117×C73—21no—
97#117×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C22⋊C4×C73—21no—
100C2×C42×C73C2×C412yes—
101C23×D73—21no—
102#11924028—22no—
103#11924028—22no—
104#11924028—22no—
105#11924028—22no—
106#11924028—22no—
107#11924028—22no—
108#11924028—22no—
109#11924028—22no—
110#11924028—22no—
111#11924028—22no—
112#11924028—22no—
113#11924028—22no—
114#11924028C4214yes—
115#11924028C22⋊C414yes—
116#11924028C22⋊C414yes—
117#11924028C22⋊C414yes—
118C2×Dic146—21no—
119C2×Dic146—21no—
120C2×Dic146—21no—
121C2×Dic146C4⋊C412yes—
122C2×Dic146C4⋊C412yes—
123C2×Dic146C4⋊C412yes—
124C2×D292—21no—
125C2×D292—21no—
126C2×D292—21no—
127C2×D292C4⋊C412yes—
128C2×D292C4⋊C412yes—
129C2×D292C4⋊C412yes—
130C2×C22⋊D73—22no—
131C2×C22⋊D73—22no—
132C2×C22⋊D73—22no—
133C2×C22⋊D73—22no—
134C2×C22⋊D73—22no—
135C2×C22⋊D73—22no—
136C22×Dic73—21no—
137C22×Dic73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—22no—
143C2×C4×D73—22no—
144#11924012—22no—
145#11924012—22no—
146#11924012—22no—
147#11924012—22no—
148#11924012—22no—
149#11924012—22no—
150#11924012—41no—
151#11924012—41no—
152#11924011—216no—
153C2×#10596831—22no—
154C2×#10596831—22no—
155C2×#10596831—22no—
156C2×#10596831—41no—
157C2×#10596831—41no—
158C2×#10596831C22⋊C414yes—
159C8×D73—216no—
160C4⋊Dic73—41no—
161C4⋊Dic73—41no—
162C22⋊Dic73—41no—
163C22⋊Dic73—41no—
164C4×Dic73—22no—
165C4×Dic73—22no—
166C24×C73#4111yescharacteristic
167C22×C4×C73—22no—
168C22×C4×C73C22×C411yescharacteristic
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×Q811yescharacteristic
179C22×C4×C73#4111yescharacteristic
180C22×C4×C73#4111yescharacteristic
181C22×C4×C73#4111yescharacteristic
182M16×C73—22no—
183M16×C73—22no—
184M16×C73—22no—
185M16×C73—22no—
186M16×C73—22no—
187M16×C73—41no—
188M16×C73—41no—
189M16×C73C22⋊C414yes—
190C2×C8×C73—22no—
191C2×C8×C73—22no—
192C2×C8×C73—22no—
193C2×C8×C73—22no—
194C2×C8×C73—41no—
195C2×C8×C73—41no—
196C4⋊C4×C73—41no—
197C4⋊C4×C73—41no—
198C22⋊C4×C73—41no—
199C22⋊C4×C73—41no—
200C42×C73—22no—
201C42×C73—22no—
202C23×C73—81no—
203C23×C73#11711yescharacteristic
204C23×C73C4×D411yescharacteristic
205C23×C73C4×D411yescharacteristic
206C23×C73#12111yescharacteristic
207C23×C73C22⋊Q811yescharacteristic
208C23×C73#12311yescharacteristic
209C23×C73#12311yescharacteristic
210C22×D73—22no—
211C22×D73—22no—
212C22×D73—22no—
213C22×D73—82no—
214C2×C4×C73—42no—
215C2×C4×C73—82no—
216C2×C4×C73C2×C4211yescharacteristic
217C2×C4×C73C2×C22⋊C411yescharacteristic
218C2×C4×C73C2×C22⋊C411yescharacteristic
219C2×C4×C73C2×C22⋊C411yescharacteristic
220C2×C4×C73C2×C22⋊C411yescharacteristic
221C2×C4×C73C2×C22⋊C411yescharacteristic
222C2×C4×C73C2×C4⋊C411yescharacteristic
223C2×C4×C73C2×C4⋊C411yescharacteristic
224C2×C4×C73C2×C4⋊C411yescharacteristic
225C2×C4×C73#11711yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C4×D411yescharacteristic
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C4×D411yescharacteristic
232C2×C4×C73#12011yescharacteristic
233C2×C4×C73#12011yescharacteristic
234C2×C4×C73#12011yescharacteristic
235C2×C4×C73#12011yescharacteristic
236C2×C4×C73#12111yescharacteristic
237C2×C4×C73#12111yescharacteristic
238C2×C4×C73#12111yescharacteristic
239C2×C4×C73C22⋊Q811yescharacteristic
240C2×C4×C73C22⋊Q811yescharacteristic
241C2×C4×C73C22⋊Q811yescharacteristic
242C2×C4×C73#12311yescharacteristic
243C2×C4×C73#12311yescharacteristic
244C22⋊D73—24no—
245C22⋊D73—24no—
246C22⋊D73—24no—
247C22⋊D73—24no—
248C2×Dic73—22no—
249C2×Dic73—22no—
250C2×Dic73—22no—
251C2×Dic73—42no—
252C2×Dic73—82no—
253D292—22no—
254D292—22no—
255D292—22no—
256D292#9514yes—
257C4×D73—24no—
258C4×D73—24no—
259C4×D73—24no—
260C4×D73—24no—
261Dic146—22no—
262Dic146—22no—
263Dic146—22no—
264Dic146#9514yes—
265C8×C73—24no—
266C8×C73—42no—
267#10596831—24no—
268#10596831—42no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73C4×C22⋊C411yescharacteristic
277C22×C73#38011yescharacteristic
278C22×C73#38111yescharacteristic
279C22×C73#38511yescharacteristic
280C22×C73#38511yescharacteristic
281C22×C73#38611yescharacteristic
282C22×C73#38611yescharacteristic
283C2×D73—24no—
284C2×D73—44no—
285C2×D73—82no—
286C2×D73—82no—
287C4×C73—82no—
288C4×C73C2×#9511yescharacteristic
289C4×C73C4×C22⋊C411yescharacteristic
290C4×C73#37911yescharacteristic
291C4×C73#38011yescharacteristic
292C4×C73#38511yescharacteristic
293C4×C73#38511yescharacteristic
294C4×C73#38611yescharacteristic
295C4×C73#38611yescharacteristic
296Dic73—24no—
297Dic73—82no—
298#10794—731nomaximal, Sylow
299C2×C73—21no—
300C2×C73—21no—
301C2×C73—21no—
302C2×C73—21no—
303C2×C73—21no—
304C2×C73—21no—
305C2×C73—21no—
306C2×C73C22⋊#9511yescharacteristic
307D73—44no—
308C2×#568—731no—
309C2×#421—731no—
310C2×#421—731no—
311#1742—731no—
312#1742D7311yescharacteristic, complemented
313C2×#338—731no—
314C2×H(3,ℤ/4)—731no—
315C73#1079411yescharacteristic, complemented, Sylow
316C22×#41—731no—
317#568—1462no—
318#568—1462no—
319#568—1462no—
320#568—1462no—
321C2×#131—734no—
322C2×#131—1462no—
323C22×M16—731no—
324C22×M16—731no—
325C22×M16—1462no—
326C22×M16C2×D7311yescharacteristic
327C22×M16C2×D7311yescharacteristic
328C2×#117—731no—
329C2×#117C2×D7311yescharacteristic
330#421—1462no—
331#421—1462no—
332#421—1462no—
333#421—1462no—
334C2×#104—734no—
335C2×#104—734no—
336#343—22no—
337#343—1462no—
338#338—1462no—
339H(3,ℤ/4)—1462no—
340C2×#41—732no—
341C2×#41—732no—
342C2×#41—732no—
343C2×#41—732no—
344C2×#41—732no—
345C2×#41—732no—
346C2×#41—1461no—
347C2×#41—1461no—
348C2×#41—1461no—
349C2×#41—1461no—
350C2×#41—1461no—
351C2×#41—1461no—
352C22×Q8—731no—
353C22×D4—731no—
354C22×D4—1461no—
355C23×C4—1461no—
356C23×C4C22×D7311yescharacteristic
357#131—1468no—
358#131—1468no—
359#131—1468no—
360#131—1468no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—732no—
370C2×M16—732no—
371C2×M16—732no—
372C2×M16—1464no—
373C2×M16—1461no—
374C2×M16—1461no—
375C2×M16—1461no—
376C2×M16—1461no—
377C2×M16—1468no—
378C2×M16—1468no—
379C2×M16—1461no—
380C2×M16—1461no—
381C2×M16—1461no—
382C2×M16—1461no—
383C2×M16—1461no—
384C2×M16C4×D7312yes—
385C2×M16C4×D7312yes—
386C2×M16D29212yes—
387C2×M16C22⋊D7312yes—
388C22×C8—21no—
389C22×C8—21no—
390C22×C8—732no—
391C22×C8—1464no—
392C22×C8—1461no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—1461no—
398#117—1461no—
399#117—1461no—
400#117—1461no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—1461no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—1461no—
405C2×C42—732no—
406C2×C42C4×D7312yes—
407#104—1468no—
408#104—1468no—
409C24—1461no—
410C24#1192402811yescharacteristic
411#41—734no—
412#41—734no—
413#41—734no—
414#41—734no—
415#41—1462no—
416#41—1462no—
417#41—1462no—
418#41—1462no—
419#41—1462no—
420#41—1462no—
421#41—1462no—
422#41—1462no—
423#41—1462no—
424#41—1462no—
425#41—1462no—
426#41—1462no—
427C2×Q8—732no—
428C2×Q8—732no—
429C2×Q8—732no—
430C2×Q8—1461no—
431C2×Q8—1461no—
432C2×Q8—1461no—
433C2×D4—732no—
434C2×D4—732no—
435C2×D4—732no—
436C2×D4—1462no—
437C2×D4—1462no—
438C2×D4—1462no—
439C2×D4—1462no—
440C2×D4—1462no—
441C2×D4—1462no—
442C2×D4—1461no—
443C2×D4—1461no—
444C2×D4—1461no—
445C22×C4—22no—
446C22×C4—1462no—
447C22×C4—1461no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4C2×C4×D7311yescharacteristic
455C22×C4C2×C4×D7311yescharacteristic
456C22×C4C2×C4×D7311yescharacteristic
457C22×C4D4×D7311yescharacteristic
458C22×C4D4×D7311yescharacteristic
459C22×C4D4×D7311yescharacteristic
460C22×C4D4×D7311yescharacteristic
461C22×C4D4×D7311yescharacteristic
462C22×C4C2×C22⋊D7311yescharacteristic
463C22×C4C2×D29211yescharacteristic
464C22×C4Q8×D7311yescharacteristic
465C22×C4#1192402711yescharacteristic
466C22×C4#1192402811yescharacteristic
467C22×C4#1192402911yescharacteristic
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—41no—
474M16—41no—
475M16—2921no—
476M16—2921no—
477M16—14616no—
478M16—1462no—
479M16—1462no—
480M16—1462no—
481M16—1462no—
482M16—1462no—
483M16—1462no—
484M16#1192400514yes—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—2921no—
492C2×C8—2921no—
493C2×C8—734no—
494C2×C8—14616no—
495C2×C8—1462no—
496C2×C8—1462no—
497C2×C8—1462no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—2921no—
501C4⋊C4—2921no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—2921no—
505C22⋊C4—2921no—
506C42—22no—
507C42—22no—
508C42—1462no—
509C42—1462no—
510C23—81no—
511C23—5842no—
512C23—1462no—
513C23—1462no—
514C23—1462no—
515C23#1455654811yescharacteristic
516C23C4×C22⋊D7311yescharacteristic
517C23C4×D29211yescharacteristic
518C23#1455656411yescharacteristic
519C23#1455656911yescharacteristic
520C23#1455657311yescharacteristic
521C23#1455657611yescharacteristic
522Q8—734no—
523Q8—1462no—
524Q8—1462no—
525Q8—1462no—
526D4—734no—
527D4—1464no—
528D4—1464no—
529D4—1464no—
530D4—1464no—
531D4—1462no—
532D4—1462no—
533D4—1462no—
534C2×C4—42no—
535C2×C4—82no—
536C2×C4—2922no—
537C2×C4—5842no—
538C2×C4—1462no—
539C2×C4—1462no—
540C2×C4—1462no—
541C2×C4—1464no—
542C2×C4—1464no—
543C2×C4—1464no—
544C2×C4—1464no—
545C2×C4C42×D7311yescharacteristic
546C2×C4C22⋊C4×D7311yescharacteristic
547C2×C4C22⋊C4×D7311yescharacteristic
548C2×C4C22⋊C4×D7311yescharacteristic
549C2×C4C22⋊C4×D7311yescharacteristic
550C2×C4C2×#1192400511yescharacteristic
551C2×C4C4⋊C4×D7311yescharacteristic
552C2×C4C4⋊C4×D7311yescharacteristic
553C2×C4C4⋊C4×D7311yescharacteristic
554C2×C4#1455654911yescharacteristic
555C2×C4#1455655111yescharacteristic
556C2×C4#1455655111yescharacteristic
557C2×C4C4×C22⋊D7311yescharacteristic
558C2×C4#1455655311yescharacteristic
559C2×C4#1455655311yescharacteristic
560C2×C4C4×D29211yescharacteristic
561C2×C4#1455655911yescharacteristic
562C2×C4#1455655911yescharacteristic
563C2×C4#1455656111yescharacteristic
564C2×C4#1455656111yescharacteristic
565C2×C4#1455656211yescharacteristic
566C2×C4#1455656411yescharacteristic
567C2×C4#1455656611yescharacteristic
568C2×C4#1455656711yescharacteristic
569C2×C4#1455656911yescharacteristic
570C2×C4#1455657111yescharacteristic
571C2×C4#1455657311yescharacteristic
572C2×C4#1455657611yescharacteristic
573C8—24no—
574C8—42no—
575C8—2922no—
576C8—1464no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—2924no—
585C22—5842no—
586C22—5842no—
587C22—1464no—
588C22C4×#1192400511yescharacteristic
589C22#1798844611yescharacteristic
590C22#1798844911yescharacteristic
591C22#1798845811yescharacteristic
592C22#1798846111yescharacteristic
593C22#1798846311yescharacteristic
594C22#1798846511yescharacteristic
595C4—82no—
596C4—5842no—
597C4—1464no—
598C4#95×D7311yescharacteristic
599C4#1798843411yescharacteristic
600C4#1798844211yescharacteristic
601C4#1798844411yescharacteristic
602C4#1798845811yescharacteristic
603C4#1798846111yescharacteristic
604C4#1798846311yescharacteristic
605C4#1798846511yescharacteristic
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—2924no—
614C2#2260815211yescharacteristic
subgroupG/H
centerC4#17988434
commutatorC2×C4×C73C2×C42
FrattiniC23×C4C22×D73
FittingC73×#1742C2
socleC2×C73C22⋊#95
prime radicalC22×#11924028C22
cosocleC23×C4×C73C23
hypercenter#1742D73
hypocenterC73#10794
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
4. #22609669C2semidirect
5. C2×#17988345C2semidirect
6. C2×#17988343C2semidirect
7. C73×#1742C2semidirect
13. C2×#14556599C4semidirect
23. C2×#14556519C4semidirect
24. C2×#14556517C4semidirect
312. #1742D73semidirect
315. C73#10794semidirect

Maximal subgroups

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

subgroupindex
C2×#179893532
C2×#179886052
C2×#179886032
#226096692
C2×#179883452
C2×#179883432
C73×#17422
#1079473