Finite Group Databasebeta

← #32992908

Subgroups — #32992908

Order 18688.

1454 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556506C212yesmaximal
2C2×#17988447C211yesmaximal, characteristic, complemented
3C2×#17988354C212yesmaximal, complemented
4#22608154C211yesmaximal, characteristic, complemented
5C2×#386×C73C211yesmaximal, characteristic
6C22×C4⋊Dic73—21no—
7C22×C22⋊Dic73C2212yes—
8C22×C22⋊Dic73C2212yes—
9C2×#14556506—24no—
10C2×#14556506—24no—
11C2×#14556506—24no—
12#17988447—24no—
13C2×#14556498—21no—
14C2×#14556498—22no—
15#17988354—24no—
16C23×D4×C73C2211yescharacteristic
17C24×C4×C73C2211yescharacteristic
18C22×C22⋊C4×C73C412yescomplemented
19C22×C22⋊C4×C73C2211yescharacteristic
20#386×C73—21no—
21#386×C73—22no—
22#386×C73—21no—
23C2×#95×C73C412yescomplemented
24C23×Dic73—22no—
25C23×Dic73—22no—
26C2×C4⋊Dic73—24no—
27C2×C4⋊Dic73—44no—
28C2×C22⋊Dic73—22no—
29C2×C22⋊Dic73—22no—
30C2×C22⋊Dic73—22no—
31C2×C22⋊Dic73—22no—
32C2×C22⋊Dic73—22no—
33C2×C22⋊Dic73—22no—
34C2×C22⋊Dic73—22no—
35C2×C22⋊Dic73—22no—
36C2×C22⋊Dic73—22no—
37C2×C22⋊Dic73—22no—
38C2×C22⋊Dic73D414yes—
39C2×C22⋊Dic73D414yes—
40#14556506—216no—
41#14556498—24no—
42#14556498—44no—
43C25×C73C2×C411yescharacteristic
44C25×C73C2311yescharacteristic
45C22×D4×C73—21no—
46C22×D4×C73—21no—
47C22×D4×C73—22no—
48C22×D4×C73—22no—
49C22×D4×C73—21no—
50C22×D4×C73—21no—
51C22×D4×C73—22no—
52C22×D4×C73—22no—
53C22×D4×C73D412yes—
54C22×D4×C73Q812yes—
55C23×C4×C73—22no—
56C23×C4×C73—22no—
57C23×C4×C73—44no—
58C23×C4×C73C2×C411yescharacteristic
59C23×C4×C73C2×C412yes—
60C23×C4×C73C2×C412yes—
61C23×C4×C73D411yescharacteristic
62C23×C4×C73D412yes—
63C23×C4×C73D411yescharacteristic
64C2×C22⋊C4×C73—22no—
65C2×C22⋊C4×C73—21no—
66C2×C22⋊C4×C73—21no—
67C2×C22⋊C4×C73—22no—
68C2×C22⋊C4×C73—22no—
69C2×C22⋊C4×C73—22no—
70C2×C22⋊C4×C73—44no—
71#95×C73—22no—
72#95×C73—22no—
73C22×Dic73—24no—
74C22×Dic73—24no—
75C22×Dic73—44no—
76C22×Dic73—44no—
77C22×Dic73—44no—
78C22×Dic73—44no—
79C22×Dic73—42no—
80C22×Dic73—42no—
81C22×Dic73—42no—
82C22×Dic73—42no—
83C4⋊Dic73—48no—
84C22⋊Dic73—24no—
85C22⋊Dic73—24no—
86C22⋊Dic73—24no—
87C22⋊Dic73—24no—
88C22⋊Dic73—42no—
89C22⋊Dic73—42no—
90C22⋊Dic73—42no—
91C22⋊Dic73—42no—
92C24×C73—21no—
93C24×C73—21no—
94C24×C73—22no—
95C24×C73—22no—
96C24×C73—42no—
97C24×C73—42no—
98C24×C73—42no—
99C24×C73—42no—
100C24×C73C4⋊C412yescomplemented
101C24×C73C22×C411yescharacteristic
102C24×C73C2×D412yes—
103C24×C73C2×D412yes—
104C24×C73C2×D411yescharacteristic
105C24×C73C2×D411yescharacteristic
106C24×C73C2×D411yescharacteristic
107C24×C73C2×Q811yescharacteristic
108C24×C73#4112yes—
109C24×C73#4112yes—
110C24×C73#4111yescharacteristic
111C24×C73#4111yescharacteristic
112C2×D4×C73—24no—
113C2×D4×C73—22no—
114C2×D4×C73—22no—
115C2×D4×C73—24no—
116C2×D4×C73—24no—
117C2×D4×C73—22no—
118C2×D4×C73—22no—
119C2×D4×C73—24no—
120C2×D4×C73—41no—
121C2×D4×C73—42no—
122C2×D4×C73—42no—
123C2×D4×C73—42no—
124C2×D4×C73—41no—
125C2×D4×C73—42no—
126C2×D4×C73—42no—
127C2×D4×C73—41no—
128C2×D4×C73—42no—
129C2×D4×C73—41no—
130C22×C4×C73—21no—
131C22×C4×C73—21no—
132C22×C4×C73—24no—
133C22×C4×C73—21no—
134C22×C4×C73—21no—
135C22×C4×C73—24no—
136C22×C4×C73—22no—
137C22×C4×C73—22no—
138C22×C4×C73—21no—
139C22×C4×C73—24no—
140C22×C4×C73—21no—
141C22×C4×C73—24no—
142C22×C4×C73—24no—
143C22×C4×C73—22no—
144C22×C4×C73—24no—
145C22×C4×C73—42no—
146C22×C4×C73—42no—
147C22×C4×C73—42no—
148C22×C4×C73—48no—
149C22×C4×C73—48no—
150C22×C4×C73—42no—
151C22×C4×C73—42no—
152C22×C4×C73C22⋊C412yes—
153C22×C4×C73C22⋊C412yes—
154C22×C4×C73C4⋊C412yescomplemented
155C22⋊C4×C73—44no—
156C22⋊C4×C73—42no—
157C22⋊C4×C73—41no—
158C22⋊C4×C73—41no—
159C22⋊C4×C73—44no—
160C23×C73—22no—
161C23×C73—22no—
162C23×C73—22no—
163C23×C73—22no—
164C23×C73—22no—
165C23×C73—22no—
166C23×C73—22no—
167C23×C73—24no—
168C23×C73—42no—
169C23×C73—42no—
170C23×C73—42no—
171C23×C73—44no—
172C23×C73—42no—
173C23×C73—42no—
174C23×C73—42no—
175C23×C73—44no—
176C23×C73—42no—
177C23×C73—42no—
178C23×C73—44no—
179C23×C73—44no—
180C23×C73—41no—
181C23×C73—42no—
182C23×C73—41no—
183C23×C73—42no—
184C23×C73—42no—
185C23×C73—82no—
186C23×C73—82no—
187C23×C73—84no—
188C23×C73C2×C22⋊C411yescharacteristic
189C23×C73C2×C4⋊C411yescharacteristic
190C23×C73#11711yescharacteristic
191C23×C73C4×D412yes—
192C23×C73C4×D412yes—
193C23×C73#12011yescharacteristic
194C23×C73#12012yes—
195C23×C73#12112yes—
196C23×C73#12112yes—
197C23×C73#12112yes—
198C23×C73#12111yescharacteristic
199C23×C73#12111yescharacteristic
200C23×C73C22⋊Q812yes—
201C23×C73C22⋊Q812yes—
202C23×C73C22⋊Q811yescharacteristic
203C23×C73C22⋊Q811yescharacteristic
204C23×C73#12311yescharacteristic
205C23×C73#12312yes—
206C23×C73#12312yes—
207C23×C73#12412yes—
208C23×C73#12411yescharacteristic
209C23×C73#12612yes—
210C23×C73#12711yescharacteristic
211D4×C73—42no—
212D4×C73—42no—
213D4×C73—44no—
214D4×C73—44no—
215D4×C73—42no—
216D4×C73—42no—
217C2×C4×C73—24no—
218C2×C4×C73—24no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—22no—
222C2×C4×C73—24no—
223C2×C4×C73—22no—
224C2×C4×C73—22no—
225C2×C4×C73—22no—
226C2×C4×C73—48no—
227C2×C4×C73—48no—
228C2×C4×C73—42no—
229C2×C4×C73—42no—
230C2×C4×C73—41no—
231C2×C4×C73—42no—
232C2×C4×C73—41no—
233C2×C4×C73—42no—
234C2×C4×C73—42no—
235C2×C4×C73—42no—
236C2×C4×C73—84no—
237C2×C4×C73#9914yescomplemented
238C2×Dic73—44no—
239C2×Dic73—44no—
240C2×Dic73—48no—
241C2×Dic73—44no—
242C2×Dic73—44no—
243C2×Dic73—84no—
244C2×Dic73—84no—
245C2×Dic73—82no—
246C2×Dic73—82no—
247C2×Dic73—84no—
248C22×C73—22no—
249C22×C73—22no—
250C22×C73—22no—
251C22×C73—22no—
252C22×C73—22no—
253C22×C73—22no—
254C22×C73—21no—
255C22×C73—22no—
256C22×C73—21no—
257C22×C73—22no—
258C22×C73—21no—
259C22×C73—22no—
260C22×C73—22no—
261C22×C73—21no—
262C22×C73—24no—
263C22×C73—22no—
264C22×C73—24no—
265C22×C73—22no—
266C22×C73—42no—
267C22×C73—42no—
268C22×C73—42no—
269C22×C73—42no—
270C22×C73—42no—
271C22×C73—42no—
272C22×C73—42no—
273C22×C73—42no—
274C22×C73—44no—
275C22×C73—42no—
276C22×C73—84no—
277C22×C73—84no—
278C22×C73—81no—
279C22×C73—81no—
280C22×C73—82no—
281C22×C73#38011yescharacteristic
282C22×C73#38512yes—
283C22×C73#38611yescharacteristic
284C22×C73#38812yes—
285C22×C73#39011yescharacteristic
286C22×C73#39211yescharacteristic
287C22×C73#39311yescharacteristic
288C22×C73#39412yes—
289C22×C73#39612yes—
290C22×C73#39711yescharacteristic
291C22×C73#39911yescharacteristic
292C22×C73C2×#9912yes—
293C22×C73#41012yes—
294C4×C73—24no—
295C4×C73—42no—
296C4×C73—42no—
297C4×C73—82no—
298Dic73—84no—
299Dic73—84no—
300#11043—731nomaximal, Sylow
301C2×C73—21no—
302C2×C73—22no—
303C2×C73—22no—
304C2×C73—22no—
305C2×C73—21no—
306C2×C73—22no—
307C2×C73—21no—
308C2×C73—21no—
309C2×C73—82no—
310C2×C73#143911yescharacteristic
311C2×C73#179912yes—
312C2×C73#189811yescharacteristic
313C2×C73#189911yescharacteristic
314C2×C73#196412yes—
315C22×#99—732no—
316C2×#386D7311yescharacteristic
317C2×#380—731no—
318C2×#342—732no—
319C22⋊#95—731no—
320C73#1104311yescharacteristic, complemented, Sylow
321C23×D4C2×D7311yescharacteristic
322C24×C4C2×D7311yescharacteristic
323C22×C4⋊C4—1461no—
324C22×C22⋊C4—732no—
325C22×C22⋊C4—732no—
326C22×C22⋊C4Dic7312yescomplemented
327C22×C22⋊C4C2×D7311yescharacteristic
328C2×#99—1464no—
329C2×#99—1464no—
330C2×#99—1464no—
331#386—21no—
332#386—22no—
333#386—21no—
334#380—1464no—
335C2×#95—1462no—
336C2×#95—1461no—
337C2×#95Dic7312yescomplemented
338#342—1464no—
339C25C2×Dic7311yescharacteristic
340C25C22×D7311yescharacteristic
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4Dic14612yes—
350C22×D4D29212yes—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—44no—
354C23×C4—1462no—
355C23×C4—1462no—
356C23×C4C2×Dic7311yescharacteristic
357C23×C4C2×Dic7312yes—
358C23×C4C2×Dic7312yes—
359C23×C4C22⋊D7311yescharacteristic
360C23×C4C22⋊D7312yes—
361C23×C4C22⋊D7311yescharacteristic
362C2×C4⋊C4—2924no—
363C2×C4⋊C4—1464no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—734no—
372C2×C22⋊C4—734no—
373C2×C22⋊C4—1462no—
374C2×C22⋊C4—1462no—
375C2×C22⋊C4—1462no—
376C2×C22⋊C4—1462no—
377C2×C22⋊C4—1462no—
378C2×C22⋊C4—1462no—
379C2×C22⋊C4—1462no—
380C2×C22⋊C4—1462no—
381C2×C22⋊C4—1462no—
382C2×C22⋊C4—1462no—
383#99—14616no—
384#95—22no—
385#95—22no—
386#95—2924no—
387#95—1464no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24C4⋊Dic7312yescomplemented
397C24C22×Dic7311yescharacteristic
398C24D4×D7312yes—
399C24D4×D7312yes—
400C24C2×C22⋊D7311yescharacteristic
401C24C2×C22⋊D7311yescharacteristic
402C24C2×D29211yescharacteristic
403C24C2×Dic14611yescharacteristic
404C24#1192402712yes—
405C24#1192402712yes—
406C24#1192402811yescharacteristic
407C24#1192402811yescharacteristic
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—24no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—41no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—48no—
445C22×C4—48no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—2924no—
449C22×C4—2924no—
450C22×C4—2924no—
451C22×C4—2924no—
452C22×C4—2922no—
453C22×C4—2922no—
454C22×C4—2922no—
455C22×C4—2922no—
456C22×C4—1464no—
457C22×C4—1464no—
458C22×C4C22⋊Dic7312yes—
459C22×C4C22⋊Dic7312yes—
460C22×C4C4⋊Dic7312yescomplemented
461C4⋊C4—2928no—
462C22⋊C4—44no—
463C22⋊C4—42no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—44no—
467C22⋊C4—2922no—
468C22⋊C4—2922no—
469C22⋊C4—2922no—
470C22⋊C4—2922no—
471C22⋊C4—1464no—
472C22⋊C4—1464no—
473C22⋊C4—1464no—
474C22⋊C4—1464no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—44no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—44no—
494C23—44no—
495C23—41no—
496C23—42no—
497C23—41no—
498C23—42no—
499C23—42no—
500C23—84no—
501C23—82no—
502C23—82no—
503C23C2×C22⋊Dic7311yescharacteristic
504C23C2×C4⋊Dic7311yescharacteristic
505C23#1455655011yescharacteristic
506C23D4×Dic7312yes—
507C23D4×Dic7312yes—
508C23#1455655911yescharacteristic
509C23#1455656112yes—
510C23#1455656212yes—
511C23#1455656312yes—
512C23#1455656412yes—
513C23#1455656511yescharacteristic
514C23#1455656511yescharacteristic
515C23#1455656812yes—
516C23#1455656812yes—
517C23#1455657011yescharacteristic
518C23#1455657011yescharacteristic
519C23#1455657211yescharacteristic
520C23#1455657312yes—
521C23#1455657512yes—
522C23#1455657712yes—
523C23#1455657811yescharacteristic
524C23#1455658412yes—
525C23#1455658711yescharacteristic
526D4—42no—
527D4—42no—
528D4—44no—
529D4—44no—
530D4—42no—
531D4—42no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—48no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—84no—
552C2×C4—2924no—
553C2×C4—2928no—
554C2×C4—2924no—
555C2×C4—2924no—
556C2×C4—2924no—
557C2×C4—5844no—
558C2×C4—5842no—
559C2×C4—5842no—
560C2×C4—5844no—
561C2×C4—5844no—
562C2×C4#1455650614yescomplemented
563C22—24no—
564C22—24no—
565C22—22no—
566C22—22no—
567C22—21no—
568C22—21no—
569C22—22no—
570C22—22no—
571C22—21no—
572C22—22no—
573C22—22no—
574C22—21no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—44no—
591C22—84no—
592C22—84no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22#1798844711yescharacteristic
597C22#1798846212yes—
598C22#1798846711yescharacteristic
599C22#1798848012yes—
600C22#1798849011yescharacteristic
601C22#1798849611yescharacteristic
602C22#1798849911yescharacteristic
603C22#1798850312yes—
604C22#1798851012yes—
605C22#1798851211yescharacteristic
606C22#1798852311yescharacteristic
607C22C2×#1455650612yes—
608C22#1798856112yes—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—82no—
613C4—5844no—
614C4—5844no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—22no—
619C2—21no—
620C2—22no—
621C2—21no—
622C2—21no—
623C2—82no—
624C2#2260817611yescharacteristic
625C2#2260991912yes—
626C2#2261038511yescharacteristic
627C2#2261039011yescharacteristic
628C2#2261076812yes—
subgroupG/H
centerC23C2×C22⋊Dic73
commutatorC24×C73C22×C4
FrattiniC25C22×D73
FittingC2×#386×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC23×D4×C73C22
cosocleC25×C73C23
hypercenterC2×#386D73
hypocenterC73#11043
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#17988447C2semidirect
3. C2×#17988354C2semidirect
4. #22608154C2semidirect
18. C22×C22⋊C4×C73C4semidirect
23. C2×#95×C73C4semidirect
100. C24×C73C4⋊C4semidirect
154. C22×C4×C73C4⋊C4semidirect
237. C2×C4×C73#99semidirect
320. C73#11043semidirect
326. C22×C22⋊C4Dic73semidirect
337. C2×#95Dic73semidirect
396. C24C4⋊Dic73semidirect
460. C22×C4C4⋊Dic73semidirect
562. C2×C4#14556506semidirect

Maximal subgroups

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

subgroupindex
C22×#145565062
C2×#179884472
C2×#179883542
#226081542
C2×#386×C732
#1104373