Finite Group Databasebeta

← #33089465

Subgroups — #33089465

Order 18688.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988628C211yesmaximal, characteristic
2C2×#17988626C211yesmaximal, characteristic
3C2×#17988609C211yesmaximal, characteristic
4#382×D73C211yesmaximal, characteristic
5C4×#14556549C211yesmaximal, characteristic
6#22610702C211yesmaximal, characteristic, complemented
7#22610701C211yesmaximal, characteristic, complemented
8#22610700C211yesmaximal, characteristic, complemented
9#22610699C211yesmaximal, characteristic, complemented
10#22610698C211yesmaximal, characteristic, complemented
11#22610697C211yesmaximal, characteristic, complemented
12#22610696C211yesmaximal, characteristic, complemented
13#22609649C211yesmaximal, characteristic
14#22609649C211yesmaximal, characteristic
15C73×#1949C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C2×#14556549C2211yescharacteristic
19C2×#14556549C2211yescharacteristic
20C2×C4⋊C4×D73C2211yescharacteristic
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C42×D73C2211yescharacteristic
23#17988628—24no—
24#17988626—24no—
25C2×#14556525C2211yescharacteristic
26C2×#14556524C2211yescharacteristic
27C2×#14556524C2211yescharacteristic
28C2×#14556523C2211yescharacteristic
29C2×#14556522C2211yescharacteristic
30C2×#14556522C2211yescharacteristic
31#17988609C418yescomplemented
32C2×C4⋊#10596831C2211yescharacteristic
33C2×#14556520C2211yescharacteristic
34C2×#14556520C2211yescharacteristic
35#17988453C2211yescharacteristic
36#17988452C2211yescharacteristic
37#17988452C2211yescharacteristic
38#17988451—21no—
39#17988451—21no—
40C4⋊C4×Dic73C2211yescharacteristic
41C4⋊C4×Dic73C2211yescharacteristic
42C4×C4⋊Dic73C2211yescharacteristic
43C4×#11924005—21no—
44#17988434—21no—
45#17988432—21no—
46#95×D73—21no—
47#95×D73—21no—
48C42×Dic73—21no—
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C2×#107×C73C2211yescharacteristic
56C2×#106×C73C2211yescharacteristic
57C2×C4⋊C8×C73C2211yescharacteristic
58#382×C73C2211yescharacteristic
59C4×C4⋊C4×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×C4×D73—21no—
63C22×C4×D73—21no—
64C22×C4×D73D411yescharacteristic
65C22×C4×D73D411yescharacteristic
66C22×C4×D73C2311yescharacteristic
67C2×#11924011—22no—
68C2×#11924011—22no—
69C2×#11924011—22no—
70C2×#11924011—22no—
71C2×#11924011C2×C414yes—
72C2×#11924011C2×C414yes—
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75#14556549—22no—
76#14556549—22no—
77#14556549D414yes—
78#14556549Q814yes—
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×#11924007—21no—
84C2×#11924007—21no—
85C4⋊C4×D73—22no—
86C4⋊C4×D73—22no—
87C4⋊C4×D73—22no—
88C4⋊C4×D73—22no—
89C2×#11924005—21no—
90C2×#11924005—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73—21no—
94C2×C4×Dic73—21no—
95C2×C4×Dic73—21no—
96C2×C4×Dic73D411yescharacteristic
97C2×C4×Dic73D411yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C42×D73C2×C414yes—
100C42×D73Q814yes—
101#14556525—22no—
102#14556524—22no—
103#14556524—22no—
104#14556523—22no—
105#14556522—22no—
106#14556522—22no—
107C4⋊#10596831C2×C414yescomplemented
108#14556520C2×C414yescomplemented
109#14556520C2×C414yescomplemented
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115#14556498—21no—
116#14556498—21no—
117#14556498—21no—
118#14556498—21no—
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C42×C73—21no—
126C2×C42×C73C2311yescharacteristic
127#107×C73—22no—
128#106×C73—22no—
129C4⋊C8×C73C2×C414yescomplemented
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133C23×D73C2×D411yescharacteristic
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73C2×D411yescharacteristic
139C22×Dic73C2×D411yescharacteristic
140C22×Dic73C2×D411yescharacteristic
141C2×C4×D73—41no—
142C2×C4×D73—41no—
143C2×C4×D73—41no—
144C2×C4×D73—41no—
145C2×C4×D73—42no—
146C2×C4×D73—42no—
147C2×C4×D73—42no—
148C2×C4×D73—42no—
149C2×C4×D73—42no—
150C2×C4×D73—42no—
151C2×C4×D73C4⋊C414yes—
152C2×C4×D73C4⋊C414yes—
153C2×C4×D73C22×C412yes—
154C2×C4×D73C2×D412yes—
155C2×C4×D73C2×Q812yes—
156C2×C4×D73C2×Q812yes—
157C2×C4×D73#4112yes—
158C2×C4×D73#4112yes—
159#11924011—28no—
160#11924011—28no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831C22×C412yes—
166C2×#10596831C22×C412yes—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73C2×D412yes—
174C4⋊Dic73C2×Q812yes—
175#11924007—42no—
176#11924007—42no—
177#11924005—24no—
178#11924005—24no—
179C4×Dic73—24no—
180C4×Dic73—24no—
181C4×Dic73—42no—
182C4×Dic73—42no—
183C4×Dic73—42no—
184C4×Dic73C4⋊C414yes—
185C4×Dic73C4⋊C414yes—
186C4×Dic73C22×C412yes—
187C4×Dic73C2×Q812yes—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2411yescharacteristic
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73C22×C412yes—
200C2×C8×C73C22×C412yes—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73C2×D412yes—
208C4⋊C4×C73C2×Q812yes—
209C42×C73—42no—
210C42×C73C22×C412yes—
211C42×C73C2×Q812yes—
212C23×C73C22×D411yescharacteristic
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—21no—
217C22×D73C2×C4⋊C412yes—
218C22×D73#12112yes—
219C22×D73C22⋊Q812yes—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—22no—
225C2×C4×C73—22no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73C2×C4⋊C412yes—
237C2×C4×C73C2×C4⋊C412yes—
238C2×C4×C73C23×C411yescharacteristic
239C2×C4×C73C22×D411yescharacteristic
240C2×C4×C73C22×Q811yescharacteristic
241C2×C4×C73C22×Q811yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—22no—
249C2×Dic73—22no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73—41no—
259C2×Dic73—41no—
260C2×Dic73C2×C4⋊C412yes—
261C2×Dic73C2×C4⋊C412yes—
262C2×Dic73C2×C4⋊C412yes—
263C2×Dic73#12112yes—
264C2×Dic73C22⋊Q812yes—
265C4×D73—44no—
266C4×D73—44no—
267C4×D73—84no—
268C4×D73—84no—
269C4×D73C4×D414yes—
270C4×D73C4×Q814yes—
271C4×D73#12514yes—
272C4×D73C4⋊Q814yes—
273C8×C73—22no—
274C8×C73—22no—
275#10596831—22no—
276#10596831—22no—
277C22×C73C22×C4⋊C411yescharacteristic
278C22×C73C2×#12111yescharacteristic
279C22×C73C2×C22⋊Q811yescharacteristic
280C22×C73#57511yescharacteristic
281C22×C73#57511yescharacteristic
282C22×C73#57511yescharacteristic
283C22×C73#57511yescharacteristic
284C2×D73—22no—
285C2×D73—22no—
286C2×D73—22no—
287C2×D73—22no—
288C2×D73—22no—
289C2×D73—22no—
290C2×D73#38914yes—
291C4×C73—22no—
292C4×C73—22no—
293C4×C73—42no—
294C4×C73—42no—
295C4×C73—81no—
296C4×C73—81no—
297C4×C73C2×C4×D411yescharacteristic
298C4×C73C2×C4×Q811yescharacteristic
299C4×C73C2×#12511yescharacteristic
300C4×C73C2×C4⋊Q811yescharacteristic
301Dic73—22no—
302Dic73—22no—
303Dic73—42no—
304Dic73—42no—
305Dic73—81no—
306Dic73—81no—
307Dic73#38914yes—
308#21172—731nomaximal, Sylow
309C2×C73C2×#38911yescharacteristic
310C2×C73#291111yescharacteristic
311C2×C73#291111yescharacteristic
312C2×C73#304011yescharacteristic
313C2×C73#304011yescharacteristic
314C2×C73#308011yescharacteristic
315C2×C73#308011yescharacteristic
316D73—24no—
317C2×#428—731no—
318C2×#428—731no—
319C2×#423—731no—
320C2×#382—731no—
321C4×#117—731no—
322#1949—731no—
323#1949—731no—
324#1949—731no—
325#1949—731no—
326#1949—731no—
327#1949—731no—
328#1949—731no—
329#1949D7311yescharacteristic, complemented
330#1736—731no—
331#1736—731no—
332C73#2117211yescharacteristic, complemented, Sylow
333C22×M16—731no—
334C22×M16—731no—
335C2×#117—731no—
336C2×#117—731no—
337C22×C4⋊C4—731no—
338C22×C4⋊C4—731no—
339C22×C42—731no—
340#428—1464no—
341#428—1464no—
342C2×#107—731no—
343C2×#107—731no—
344C2×#107—731no—
345C2×#107C2×D7311yescharacteristic
346C2×#106—731no—
347C2×#106—731no—
348C2×#106—731no—
349C2×#106C2×D7311yescharacteristic
350#423—738no—
351C2×C4⋊C8—731no—
352C2×C4⋊C8—731no—
353C2×C4⋊C8—731no—
354C2×C4⋊C8C2×D7311yescharacteristic
355#382—731no—
356#382—731no—
357#382—731no—
358#382—1461no—
359#382—1461no—
360#382C2×D7311yescharacteristic
361C4×C4⋊C4—731no—
362C4×C4⋊C4—731no—
363C4×C4⋊C4—731no—
364C4×C4⋊C4C2×D7311yescharacteristic
365C4×C22⋊C4—1461no—
366C4×C22⋊C4—1461no—
367#376—1461no—
368C2×#95—1461no—
369C2×#95—1461no—
370C43—1461no—
371#340—731no—
372#340—731no—
373#340—731no—
374#340—731no—
375#340—731no—
376#340—731no—
377#340C2×D7311yescharacteristic
378#340C2×D7311yescharacteristic
379C23×C4—731no—
380C23×C4—731no—
381C23×C4—731no—
382C23×C4—1461no—
383C23×C4—1461no—
384C2×M16—734no—
385C2×M16—734no—
386C2×M16—1462no—
387C2×M16—1462no—
388C2×M16—1462no—
389C2×M16—1462no—
390C22×C8—731no—
391C22×C8—731no—
392C22×C8C22×D7311yescharacteristic
393C22×C8C22×D7311yescharacteristic
394#117—734no—
395#117—734no—
396#117—1462no—
397#117—1462no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—1462no—
403C2×C4⋊C4—1462no—
404C2×C4⋊C4—1462no—
405C2×C4⋊C4—1462no—
406C2×C4⋊C4—1461no—
407C2×C4⋊C4—1461no—
408C2×C4⋊C4C22×D7311yescharacteristic
409C2×C4⋊C4C22×D7311yescharacteristic
410C2×C4⋊C4C22×D7311yescharacteristic
411C2×C4⋊C4C22×D7311yescharacteristic
412C2×C22⋊C4—1461no—
413C2×C22⋊C4—1461no—
414C2×C42—21no—
415C2×C42—731no—
416C2×C42—731no—
417C2×C42—731no—
418C2×C42—734no—
419C2×C42—734no—
420C2×C42—1461no—
421C2×C42—1461no—
422C2×C42—1461no—
423C2×C42—1461no—
424C2×C42—1461no—
425C2×C42C22×D7311yescharacteristic
426#107—22no—
427#107—1462no—
428#107—1462no—
429#107—1462no—
430#106—22no—
431#106—1462no—
432#106—1462no—
433#106—1462no—
434C4⋊C8—734no—
435C4⋊C8—734no—
436C4⋊C8—734no—
437C4⋊C8C4×D7314yescomplemented
438#95—21no—
439#95—21no—
440#95—21no—
441#95—1461no—
442#95—1461no—
443#95—1461no—
444#95—1461no—
445#95—1461no—
446#95—1461no—
447#95—1461no—
448#95—1461no—
449#95—1461no—
450C24—731no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—2921no—
456C22×C4—2921no—
457C22×C4—2921no—
458C22×C4—2921no—
459C22×C4—2922no—
460C22×C4—2922no—
461C22×C4—2922no—
462C22×C4—2922no—
463C22×C4—2922no—
464C22×C4—2922no—
465C22×C4—734no—
466C22×C4—734no—
467C22×C4—731no—
468C22×C4—732no—
469C22×C4—732no—
470C22×C4—732no—
471C22×C4—732no—
472C22×C4—732no—
473C22×C4—732no—
474C22×C4—731no—
475C22×C4—731no—
476C22×C4—1461no—
477C22×C4—1461no—
478C22×C4—1461no—
479C22×C4—1461no—
480C22×C4D4×D7311yescharacteristic
481C22×C4D4×D7311yescharacteristic
482C22×C4C23×D7311yescharacteristic
483M16—1468no—
484M16—1468no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—732no—
490C2×C8—732no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8—1461no—
494C2×C8—1461no—
495C2×C8C2×C4×D7312yes—
496C2×C8C2×C4×D7312yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—2922no—
504C4⋊C4—2922no—
505C4⋊C4—732no—
506C4⋊C4—732no—
507C4⋊C4—1461no—
508C4⋊C4—1461no—
509C4⋊C4—1461no—
510C4⋊C4—1461no—
511C4⋊C4—1461no—
512C4⋊C4—1461no—
513C4⋊C4D4×D7312yes—
514C4⋊C4Q8×D7312yes—
515C22⋊C4—1464no—
516C22⋊C4—1464no—
517C42—42no—
518C42—2922no—
519C42—2922no—
520C42—2922no—
521C42—734no—
522C42—734no—
523C42—732no—
524C42—732no—
525C42—1464no—
526C42—1464no—
527C42C2×C4×D7312yes—
528C42Q8×D7312yes—
529C23—732no—
530C23—732no—
531C23—732no—
532C23—1461no—
533C23—1461no—
534C23—1461no—
535C23—1461no—
536C23C2×D4×D7311yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—2924no—
554C2×C4—2924no—
555C2×C4—2921no—
556C2×C4—2921no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—5844no—
566C2×C4—5844no—
567C2×C4—732no—
568C2×C4—732no—
569C2×C4—732no—
570C2×C4—734no—
571C2×C4—734no—
572C2×C4—734no—
573C2×C4—734no—
574C2×C4—732no—
575C2×C4—732no—
576C2×C4—1462no—
577C2×C4—1462no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1461no—
581C2×C4—1461no—
582C2×C4C4⋊C4×D7312yes—
583C2×C4C4⋊C4×D7312yes—
584C2×C4C22×C4×D7311yescharacteristic
585C2×C4C2×D4×D7311yescharacteristic
586C2×C4C2×Q8×D7311yescharacteristic
587C2×C4C2×Q8×D7311yescharacteristic
588C2×C4#41×D7311yescharacteristic
589C2×C4#41×D7311yescharacteristic
590C8—22no—
591C8—22no—
592C8—1462no—
593C8—1462no—
594C22—734no—
595C22—1462no—
596C22—1462no—
597C22—1462no—
598C22—1462no—
599C22—1462no—
600C22—1462no—
601C22C2×C4⋊C4×D7311yescharacteristic
602C22#121×D7311yescharacteristic
603C22C22⋊Q8×D7311yescharacteristic
604C22#1798938311yescharacteristic
605C22#1798938411yescharacteristic
606C22#1798938411yescharacteristic
607C22#1798938611yescharacteristic
608C4—22no—
609C4—22no—
610C4—42no—
611C4—42no—
612C4—81no—
613C4—81no—
614C4—2922no—
615C4—2922no—
616C4—5841no—
617C4—5841no—
618C4—734no—
619C4—1462no—
620C4—1462no—
621C4C4×D4×D7311yescharacteristic
622C4C4×Q8×D7311yescharacteristic
623C4#125×D7311yescharacteristic
624C4C4⋊Q8×D7311yescharacteristic
625C2—1464no—
626C2#389×D7311yescharacteristic
627C2#2261851811yescharacteristic
628C2#2261851911yescharacteristic
629C2#2261942011yescharacteristic
630C2#2261942211yescharacteristic
631C2#2261974811yescharacteristic
632C2#2261975011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1949C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1949D73
hypocenterC73#21172
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
6. #22610702C2semidirect
7. #22610701C2semidirect
8. #22610700C2semidirect
9. #22610699C2semidirect
10. #22610698C2semidirect
11. #22610697C2semidirect
12. #22610696C2semidirect
15. C73×#1949C2semidirect
31. #17988609C4semidirect
107. C4⋊#10596831C2×C4semidirect
108. #14556520C2×C4semidirect
109. #14556520C2×C4semidirect
129. C4⋊C8×C73C2×C4semidirect
329. #1949D73semidirect
332. C73#21172semidirect
437. C4⋊C8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886282
C2×#179886262
C2×#179886092
#382×D732
C4×#145565492
#226107022
#226107012
#226107002
#226106992
#226106982
#226106972
#226106962
#226096492
C73×#19492
#2117273