Finite Group Databasebeta

← #33087778

Subgroups — #33087778

Order 18688.

1994 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989098C211yesmaximal, characteristic
2C2×#17988560C212yesmaximal, complemented
3#22612314C211yesmaximal, characteristic, complemented
4#22610389C214yesmaximal, complemented
5#22610384C214yesmaximal, complemented
6#22609663C212yesmaximal, complemented
7C22×#117×C73C211yesmaximal, characteristic, complemented
8C22×#11924028C2211yescharacteristic
9#17989098—22no—
10#17989098—22no—
11#17989098—21no—
12#17989098—21no—
13#17989098—21no—
14#17989098—21no—
15C2×#14556574C2212yes—
16C2×#14556570C412yescomplemented
17C2×#14556565C412yescomplemented
18C2×#14556560C2212yes—
19C2×C4×C22⋊D73C414yescomplemented
20C2×#14556550C2212yes—
21C2×#14556550C2211yescharacteristic
22#17988560—28no—
23C2×#14556505C2218yes—
24#17988450C2212yes—
25#17988447—22no—
26#17988443C2212yes—
27C4×C22⋊Dic73—22no—
28#17988353C2218yes—
29C24×C4×C73C2211yescharacteristic
30C2×#117×C73—21no—
31C2×#117×C73—21no—
32C2×#117×C73—28no—
33C2×#117×C73C2212yes—
34C2×#117×C73C2212yes—
35C22×C4⋊C4×C73—21no—
36C22×C22⋊C4×C73C2212yes—
37C22×C42×C73—21no—
38C2×#11924028—24no—
39C2×#11924028—21no—
40C2×#11924028—21no—
41C2×#11924028—21no—
42C2×#11924028—21no—
43C2×#11924028—24no—
44C22×Dic146C2×C411yescharacteristic, complemented
45C22×D292C2×C411yescharacteristic, complemented
46C22×C22⋊D73C2×C414yes—
47C22×C22⋊D73C2312yes—
48C22×C4×D73C2×C412yescomplemented
49#14556574—22no—
50#14556574—22no—
51#14556574—24no—
52#14556570—22no—
53#14556570—22no—
54#14556570—22no—
55#14556570—22no—
56#14556565—22no—
57#14556565—22no—
58#14556565—22no—
59#14556565—22no—
60#14556560—22no—
61#14556560—22no—
62#14556560—24no—
63C4×C22⋊D73—24no—
64C4×C22⋊D73—24no—
65C4×C22⋊D73—24no—
66C4×C22⋊D73—24no—
67#14556550—21no—
68#14556550—21no—
69#14556550—21no—
70#14556550—21no—
71#14556550—24no—
72#14556550—24no—
73C2×C4⋊Dic73—22no—
74C2×C4⋊Dic73C2×C412yescomplemented
75C2×#11924007C2×C414yescomplemented
76C2×C22⋊Dic73—24no—
77C2×C22⋊Dic73C2×C414yes—
78C2×C22⋊Dic73C2314yes—
79C2×C22⋊Dic73C2312yes—
80C2×#11924005C2×C414yescomplemented
81C2×C4×Dic73—22no—
82C2×C4×Dic73C2×C412yescomplemented
83#14556505—216no—
84#14556498—24no—
85C25×C73C2311yescharacteristic
86C23×C4×C73—24no—
87C23×C4×C73—24no—
88C23×C4×C73—22no—
89C23×C4×C73C2×C412yes—
90C23×C4×C73C2×C412yes—
91C23×C4×C73D412yes—
92C23×C4×C73D412yes—
93C23×C4×C73D411yescharacteristic
94C23×C4×C73D411yescharacteristic
95C23×C4×C73D411yescharacteristic
96C23×C4×C73D411yescharacteristic
97C23×C4×C73C2311yescharacteristic
98C23×C4×C73C2311yescharacteristic
99#117×C73—28no—
100#117×C73—28no—
101#117×C73—24no—
102#117×C73—28no—
103#117×C73D418yescomplemented
104C2×C4⋊C4×C73—28no—
105C2×C4⋊C4×C73—22no—
106C2×C4⋊C4×C73—22no—
107C2×C22⋊C4×C73—22no—
108C2×C22⋊C4×C73—28no—
109C2×C22⋊C4×C73C2314yes—
110C2×C42×C73—28no—
111C2×C42×C73—22no—
112C2×C42×C73—22no—
113C23×D73C22×C412yes—
114#11924028—42no—
115#11924028—42no—
116#11924028—44no—
117#11924028—44no—
118#11924028—42no—
119#11924028—42no—
120C2×Dic146—21no—
121C2×Dic146—21no—
122C2×Dic146—24no—
123C2×D292—21no—
124C2×D292—21no—
125C2×D292—24no—
126C2×C22⋊D73—24no—
127C2×C22⋊D73—24no—
128C2×C22⋊D73—24no—
129C2×C22⋊D73—22no—
130C2×C22⋊D73—22no—
131C2×C22⋊D73—24no—
132C2×C22⋊D73—48no—
133C22×Dic73—24no—
134C22×Dic73C22×C412yes—
135C22×Dic73C22×C414yes—
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—28no—
139C4⋊Dic73—22no—
140C4⋊Dic73—22no—
141C4⋊Dic73—44no—
142#11924007—24no—
143#11924007—24no—
144C22⋊Dic73—24no—
145C22⋊Dic73—24no—
146C22⋊Dic73—22no—
147C22⋊Dic73—22no—
148C22⋊Dic73—24no—
149C22⋊Dic73—24no—
150C22⋊Dic73—48no—
151#11924005—24no—
152#11924005—24no—
153C4×Dic73—22no—
154C4×Dic73—22no—
155C4×Dic73—44no—
156C24×C73—22no—
157C24×C73—22no—
158C24×C73—44no—
159C24×C73C22×C412yes—
160C24×C73C2×D411yescharacteristic
161C24×C73C2×D411yescharacteristic
162C24×C73C2×D412yes—
163C24×C73C2411yescharacteristic
164C22×C4×C73—22no—
165C22×C4×C73—22no—
166C22×C4×C73—28no—
167C22×C4×C73—28no—
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73—22no—
172C22×C4×C73—28no—
173C22×C4×C73—28no—
174C22×C4×C73—22no—
175C22×C4×C73—22no—
176C22×C4×C73—22no—
177C22×C4×C73—22no—
178C22×C4×C73—28no—
179C22×C4×C73—24no—
180C22×C4×C73—48no—
181C22×C4×C73C22⋊C412yes—
182C22×C4×C73C22⋊C412yes—
183C22×C4×C73C22⋊C412yes—
184C22×C4×C73C22⋊C412yes—
185C22×C4×C73C22⋊C412yes—
186C22×C4×C73C22⋊C412yes—
187C22×C4×C73C22⋊C412yes—
188C22×C4×C73C22⋊C412yes—
189C22×C4×C73C22×C412yes—
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D414yes—
197C22×C4×C73C2×D412yes—
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73#4114yes—
201C4⋊C4×C73—28no—
202C4⋊C4×C73—28no—
203C22⋊C4×C73—28no—
204C22⋊C4×C73—24no—
205C22⋊C4×C73C2×D418yes—
206C42×C73—28no—
207C42×C73—28no—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73—24no—
211C23×C73—24no—
212C23×C73—21no—
213C23×C73—24no—
214C23×C73—21no—
215C23×C73—24no—
216C23×C73—24no—
217C23×C73—42no—
218C23×C73—42no—
219C23×C73—42no—
220C23×C73—42no—
221C23×C73—48no—
222C23×C73—48no—
223C23×C73C2×C22⋊C412yes—
224C23×C73C2×C22⋊C412yes—
225C23×C73C23×C411yescharacteristic
226C23×C73C22×D411yescharacteristic
227C23×C73C22×D412yes—
228C23×C73C22×D411yescharacteristic
229C23×C73C2×#4112yes—
230C22×D73—22no—
231C22×D73—24no—
232C22×D73—44no—
233C2×C4×C73—24no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—24no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—24no—
240C2×C4×C73—24no—
241C2×C4×C73—24no—
242C2×C4×C73—24no—
243C2×C4×C73—24no—
244C2×C4×C73—24no—
245C2×C4×C73—24no—
246C2×C4×C73—24no—
247C2×C4×C73—28no—
248C2×C4×C73—416no—
249C2×C4×C73—48no—
250C2×C4×C73C2×C22⋊C412yes—
251C2×C4×C73C2×C22⋊C412yes—
252C2×C4×C73C2×C22⋊C411yescharacteristic
253C2×C4×C73C2×C22⋊C411yescharacteristic
254C2×C4×C73C2×C22⋊C411yescharacteristic
255C2×C4×C73C2×C22⋊C411yescharacteristic
256C2×C4×C73C4×D414yes—
257C2×C4×C73C4×D414yes—
258C2×C4×C73#12012yes—
259C2×C4×C73#12012yes—
260C2×C4×C73#12114yes—
261C2×C4×C73#12114yes—
262C2×C4×C73#12312yes—
263C2×C4×C73#12312yes—
264C22⋊D73—48no—
265C22⋊D73—42no—
266C22⋊D73—44no—
267C22⋊D73—42no—
268C22⋊D73—48no—
269C2×Dic73—24no—
270C2×Dic73—22no—
271C2×Dic73—24no—
272C2×Dic73—44no—
273C2×Dic73—48no—
274C2×Dic73—44no—
275D292—42no—
276D292—42no—
277C4×D73—44no—
278C4×D73—44no—
279Dic146—42no—
280Dic146—42no—
281C22×C73—24no—
282C22×C73—24no—
283C22×C73—22no—
284C22×C73—22no—
285C22×C73—22no—
286C22×C73—22no—
287C22×C73—22no—
288C22×C73—22no—
289C22×C73—22no—
290C22×C73—22no—
291C22×C73—42no—
292C22×C73—42no—
293C22×C73—48no—
294C22×C73—48no—
295C22×C73—42no—
296C22×C73—42no—
297C22×C73#41014yescomplemented
298C22×C73C22×C22⋊C411yescharacteristic
299C22×C73C2×C4×D412yes—
300C22×C73C2×#12011yescharacteristic
301C22×C73C2×#12112yes—
302C22×C73C2×#12311yescharacteristic
303C2×D73—44no—
304C2×D73—42no—
305C2×D73—84no—
306C4×C73—22no—
307C4×C73—22no—
308C4×C73—48no—
309C4×C73#38612yes—
310C4×C73#38612yes—
311C4×C73#38612yes—
312C4×C73#38612yes—
313Dic73—44no—
314Dic73—42no—
315Dic73—84no—
316#20983—731nomaximal, Sylow
317C2×C73—22no—
318C2×C73—21no—
319C2×C73—22no—
320C2×C73—21no—
321C2×C73—24no—
322C2×C73—42no—
323C2×C73C2×#38611yescharacteristic
324C2×C73C2×#41012yes—
325D73—82no—
326C2×#525—731no—
327C22×#117D7311yescharacteristic, complemented
328C2×#410—732no—
329#2280—731no—
330#1899—734no—
331#1898—734no—
332#1740—732no—
333C73#2098311yescharacteristic, complemented, Sylow
334C22×#41—731no—
335C24×C4C2×D7311yescharacteristic
336#525—1462no—
337#525—1462no—
338#525—1461no—
339#525—1461no—
340#525—1461no—
341#525—1461no—
342C2×#123—732no—
343C2×C22⋊Q8—732no—
344C2×#121—732no—
345C2×#120—732no—
346C2×C4×D4—734no—
347C2×#117—21no—
348C2×#117—21no—
349C2×#117—28no—
350C2×#117—731no—
351C2×#117—732no—
352C2×#117C2×D7312yes—
353C2×#117C2×D7312yes—
354C22×C4⋊C4—21no—
355C22×C22⋊C4C2×D7312yes—
356C22×C42—21no—
357#410—1468no—
358C2×#99—738no—
359#381—732no—
360#380—1462no—
361#379—732no—
362C4×C22⋊C4—1462no—
363#342—738no—
364C25C22×D7311yescharacteristic
365C2×#41—1461no—
366C2×#41—1461no—
367C2×#41—1464no—
368C2×#41—1461no—
369C2×#41—1461no—
370C2×#41—1464no—
371C22×Q8—731no—
372C22×D4—734no—
373C22×D4—732no—
374C22×D4—731no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—22no—
378C23×C4—732no—
379C23×C4C4×D7312yes—
380C23×C4C4×D7312yes—
381C23×C4D29212yes—
382C23×C4D29212yes—
383C23×C4C22⋊D7311yescharacteristic
384C23×C4C22⋊D7311yescharacteristic
385C23×C4C22⋊D7311yescharacteristic
386C23×C4C22⋊D7311yescharacteristic
387C23×C4C22×D7311yescharacteristic
388C23×C4C22×D7311yescharacteristic
389#123—1462no—
390#123—1462no—
391#123—1464no—
392C22⋊Q8—1462no—
393C22⋊Q8—1462no—
394C22⋊Q8—1462no—
395C22⋊Q8—1462no—
396#121—1462no—
397#121—1462no—
398#121—1462no—
399#121—1462no—
400#120—1462no—
401#120—1462no—
402#120—1464no—
403C4×D4—1464no—
404C4×D4—1464no—
405C4×D4—1464no—
406C4×D4—1464no—
407#117—28no—
408#117—28no—
409#117—24no—
410#117—28no—
411#117—1464no—
412#117—1464no—
413#117—1461no—
414#117—1461no—
415#117—1461no—
416#117—1461no—
417#117C22⋊D7318yescomplemented
418C2×C4⋊C4—28no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—732no—
422C2×C4⋊C4—734no—
423C2×C4⋊C4—1462no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—734no—
427C2×C22⋊C4—732no—
428C2×C22⋊C4—734no—
429C2×C22⋊C4—734no—
430C2×C22⋊C4—1464no—
431C2×C22⋊C4C22×D7314yes—
432C2×C42—28no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—732no—
436C2×C42—1462no—
437#99—14616no—
438#95—1464no—
439C24—22no—
440C24—22no—
441C24—44no—
442C24—732no—
443C24C2×C4×D7312yes—
444C24C2×C22⋊D7311yescharacteristic
445C24C2×C22⋊D7311yescharacteristic
446C24C2×D29212yes—
447C24C23×D7311yescharacteristic
448#41—2922no—
449#41—2922no—
450#41—2924no—
451#41—2924no—
452#41—2922no—
453#41—2922no—
454C2×Q8—1461no—
455C2×Q8—1461no—
456C2×Q8—1464no—
457C2×D4—2928no—
458C2×D4—1464no—
459C2×D4—1464no—
460C2×D4—1464no—
461C2×D4—1462no—
462C2×D4—1462no—
463C2×D4—1464no—
464C2×D4—1461no—
465C2×D4—1461no—
466C2×D4—1464no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—24no—
483C22×C4—48no—
484C22×C4—734no—
485C22×C4—732no—
486C22×C4—1464no—
487C22×C4—1462no—
488C22×C4—1462no—
489C22×C4—1468no—
490C22×C4#1192400512yes—
491C22×C4#1192400512yes—
492C22×C4#1192400512yes—
493C22×C4#1192400512yes—
494C22×C4#1192400512yes—
495C22×C4#1192400512yes—
496C22×C4#1192400512yes—
497C22×C4#1192400512yes—
498C22×C4C2×C4×D7312yes—
499C22×C4C2×C4×D7311yescharacteristic
500C22×C4C2×C4×D7311yescharacteristic
501C22×C4C2×C22⋊D7311yescharacteristic
502C22×C4C2×C22⋊D7311yescharacteristic
503C22×C4C2×C22⋊D7311yescharacteristic
504C22×C4C2×C22⋊D7311yescharacteristic
505C22×C4C2×C22⋊D7314yes—
506C22×C4C2×D29212yes—
507C22×C4C2×D29211yescharacteristic
508C22×C4C2×D29211yescharacteristic
509C22×C4#1192402814yes—
510C4⋊C4—28no—
511C4⋊C4—28no—
512C4⋊C4—2924no—
513C4⋊C4—1464no—
514C4⋊C4—1464no—
515C4⋊C4—1462no—
516C4⋊C4—1462no—
517C22⋊C4—28no—
518C22⋊C4—24no—
519C22⋊C4—2928no—
520C22⋊C4—1464no—
521C22⋊C4—1464no—
522C22⋊C4—1464no—
523C22⋊C4—1464no—
524C22⋊C4—1462no—
525C22⋊C4—1462no—
526C22⋊C4—1464no—
527C22⋊C4—1464no—
528C22⋊C4C2×C22⋊D7318yes—
529C42—28no—
530C42—28no—
531C42—2924no—
532C42—1462no—
533C42—1462no—
534C23—24no—
535C23—21no—
536C23—21no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—21no—
541C23—24no—
542C23—21no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—48no—
548C23—48no—
549C23—2924no—
550C23—1462no—
551C23—1464no—
552C23C2×#1192400512yes—
553C23C2×#1192400512yes—
554C23C22×C4×D7311yescharacteristic
555C23C22×C22⋊D7311yescharacteristic
556C23C22×C22⋊D7312yes—
557C23C22×D29211yescharacteristic
558C23C2×#1192402812yes—
559Q8—2922no—
560Q8—2922no—
561D4—2928no—
562D4—2928no—
563D4—2922no—
564D4—2924no—
565D4—2922no—
566D4—2922no—
567D4—2922no—
568C2×C4—24no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—24no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—28no—
583C2×C4—416no—
584C2×C4—48no—
585C2×C4—2924no—
586C2×C4—2924no—
587C2×C4—2924no—
588C2×C4—2928no—
589C2×C4—2924no—
590C2×C4—1464no—
591C2×C4—1462no—
592C2×C4—1464no—
593C2×C4C2×#1192400512yes—
594C2×C4C2×#1192400512yes—
595C2×C4C2×#1192400511yescharacteristic
596C2×C4C2×#1192400511yescharacteristic
597C2×C4C2×#1192400511yescharacteristic
598C2×C4C2×#1192400511yescharacteristic
599C2×C4C4×C22⋊D7314yes—
600C2×C4C4×C22⋊D7314yes—
601C2×C4#1455656012yes—
602C2×C4#1455656012yes—
603C2×C4#1455656514yes—
604C2×C4#1455656514yes—
605C2×C4#1455657412yes—
606C2×C4#1455657412yes—
607C22—24no—
608C22—24no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—42no—
618C22—42no—
619C22—48no—
620C22—48no—
621C22—42no—
622C22—42no—
623C22—2924no—
624C22—2922no—
625C22—5844no—
626C22#1798856014yescomplemented
627C22C22×#1192400511yescharacteristic
628C22C2×C4×C22⋊D7312yes—
629C22C2×#1455656011yescharacteristic
630C22C2×#1455656512yes—
631C22C2×#1455657411yescharacteristic
632C4—22no—
633C4—22no—
634C4—48no—
635C4—2924no—
636C4—2922no—
637C4—5844no—
638C4#1798846612yes—
639C4#1798846612yes—
640C4#1798846612yes—
641C4#1798846612yes—
642C2—21no—
643C2—22no—
644C2—24no—
645C2—21no—
646C2—22no—
647C2—42no—
648C2—5842no—
649C2C2×#1798846611yescharacteristic
650C2C2×#1798856012yes—
subgroupG/H
centerC2×C4C2×#11924005
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC22×#117×C73C2
socleC22×C73C22×C22⋊C4
prime radicalC2×#17989098C2
cosocleC24×C73C24
hypercenterC22×#117D73
hypocenterC73#20983
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#17988560C2semidirect
3. #22612314C2semidirect
4. #22610389C2semidirect
5. #22610384C2semidirect
6. #22609663C2semidirect
7. C22×#117×C73C2semidirect
16. C2×#14556570C4semidirect
17. C2×#14556565C4semidirect
19. C2×C4×C22⋊D73C4semidirect
44. C22×Dic146C2×C4semidirect
45. C22×D292C2×C4semidirect
48. C22×C4×D73C2×C4semidirect
74. C2×C4⋊Dic73C2×C4semidirect
75. C2×#11924007C2×C4semidirect
80. C2×#11924005C2×C4semidirect
82. C2×C4×Dic73C2×C4semidirect
103. #117×C73D4semidirect
297. C22×C73#410semidirect
327. C22×#117D73semidirect
333. C73#20983semidirect
417. #117C22⋊D73semidirect
626. C22#17988560semidirect

Maximal subgroups

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

subgroupindex
C2×#179890982
C2×#179885602
#226123142
#226103892
#226103842
#226096632
C22×#117×C732
#2098373