Finite Group Databasebeta

← #33115086

Subgroups — #33115086

Order 18688.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988626C211yesmaximal, characteristic
2C2×#17988612C211yesmaximal, characteristic
3#22612553C211yesmaximal, characteristic
4#22612546C211yesmaximal, characteristic
5#22611434C211yesmaximal, characteristic, complemented
6#22611433C211yesmaximal, characteristic, complemented
7#22611430C211yesmaximal, characteristic, complemented
8#22611428C211yesmaximal, characteristic, complemented
9#22611424C211yesmaximal, characteristic, complemented
10#22611422C211yesmaximal, characteristic, complemented
11#22611421C211yesmaximal, characteristic, complemented
12#22609649C211yesmaximal, characteristic
13#22609646C211yesmaximal, characteristic
14#340×D73C211yesmaximal, characteristic
15C73×#2088C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556549C2211yescharacteristic
19C2×#14556549C2211yescharacteristic
20C2×#14556548C2211yescharacteristic
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C4⋊C4×D73C2211yescharacteristic
23#17988626—24no—
24C2×#14556525C2211yescharacteristic
25C2×#14556524C2211yescharacteristic
26C2×#14556522C2211yescharacteristic
27#17988612—24no—
28C2×C4⋊#10596831C2211yescharacteristic
29C2×#14556520C2211yescharacteristic
30C2×#14556520C2211yescharacteristic
31#17988486C2211yescharacteristic
32#17988486C2211yescharacteristic
33#17988485C2211yescharacteristic
34#17988485C2211yescharacteristic
35#17988484—21no—
36#17988483C2211yescharacteristic
37#17988483C2211yescharacteristic
38#17988482—21no—
39#17988461—21no—
40#17988458—21no—
41#17988456—21no—
42#17988451—21no—
43#17988446—21no—
44#17988444—21no—
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54C2×#106×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic
56#389×C73C2211yescharacteristic
57#389×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61C22×C4×D73—21no—
62C22×C4×D73—21no—
63C22×C4×D73C2311yescharacteristic
64C2×#11924011—22no—
65C2×#11924011—22no—
66C2×#11924011D414yes—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C2×C8×D73—22no—
70C2×C8×D73—22no—
71C2×C8×D73—22no—
72#14556549—22no—
73#14556549—22no—
74#14556549—22no—
75#14556549Q814yes—
76#14556548—22no—
77#14556548—22no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×#11924007—21no—
89C2×#11924007—21no—
90C2×#11924007D411yescharacteristic
91C2×#11924007D411yescharacteristic
92C4⋊C4×D73—22no—
93C4⋊C4×D73—22no—
94C4⋊C4×D73—22no—
95C4⋊C4×D73Q814yes—
96C2×#11924005—21no—
97C2×#11924005—21no—
98C2×#11924005D411yescharacteristic
99C2×#11924005D411yescharacteristic
100C2×C4×Dic73—21no—
101C2×C4×Dic73—21no—
102C2×C4×Dic73C2311yescharacteristic
103#14556525—22no—
104#14556524—22no—
105#14556522—22no—
106C4⋊#10596831—22no—
107#14556520—22no—
108#14556520—22no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115C22×C8×C73C2311yescharacteristic
116C22×C8×C73C2311yescharacteristic
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73—21no—
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C42×C73C2311yescharacteristic
124#106×C73—22no—
125C4⋊C8×C73—22no—
126#95×C73—21no—
127#95×C73—21no—
128C23×D73C2×D411yescharacteristic
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73C2×D411yescharacteristic
134C22×Dic73C2×D411yescharacteristic
135C22×Dic73C2×D411yescharacteristic
136C2×C4×D73—24no—
137C2×C4×D73—42no—
138C2×C4×D73—81no—
139C2×C4×D73—81no—
140C2×C4×D73—81no—
141C2×C4×D73—81no—
142C2×C4×D73C2×D412yes—
143C2×C4×D73C2×Q812yes—
144C2×C4×D73C2×Q812yes—
145C2×C4×D73#4112yes—
146C2×C4×D73#4112yes—
147C2×C4×D73#4112yes—
148#11924011—28no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831C2×D412yes—
155C8×D73—44no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—81no—
163C4⋊Dic73—81no—
164C4⋊Dic73C2×Q812yes—
165C4⋊Dic73C2×Q812yes—
166#11924007—22no—
167#11924007—22no—
168#11924007—24no—
169#11924007—42no—
170#11924007—81no—
171#11924007—81no—
172#11924007—81no—
173#11924007—81no—
174#11924005—22no—
175#11924005—22no—
176#11924005—24no—
177#11924005—42no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—24no—
181C4×Dic73—42no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2411yescharacteristic
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73C2×D412yes—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—81no—
202C4⋊C4×C73—81no—
203C4⋊C4×C73C2×Q812yes—
204C4⋊C4×C73C2×Q812yes—
205C42×C73—21no—
206C42×C73—21no—
207C23×C73C22×D411yescharacteristic
208C22×D73—21no—
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73#12112yes—
213C22×D73C22⋊Q812yes—
214C22×D73C22⋊Q812yes—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
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×C73C22×D411yescharacteristic
234C2×C4×C73C22×Q811yescharacteristic
235C2×C4×C73C22×Q811yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C2×C4×C73C2×#4111yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—22no—
242C2×Dic73—22no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73#12112yes—
258C2×Dic73C22⋊Q812yes—
259C2×Dic73C22⋊Q812yes—
260C4×D73—84no—
261C4×D73—84no—
262C4×D73#12314yes—
263C4×D73#12514yes—
264C4×D73#12514yes—
265C4×D73C4⋊Q814yes—
266C8×C73—22no—
267C8×C73—41no—
268#10596831—22no—
269#10596831—41no—
270C22×C73C2×#12111yescharacteristic
271C22×C73C2×C22⋊Q811yescharacteristic
272C22×C73C2×C22⋊Q811yescharacteristic
273C22×C73#57611yescharacteristic
274C22×C73#57711yescharacteristic
275C22×C73#57711yescharacteristic
276C22×C73#57811yescharacteristic
277C2×D73—22no—
278C2×D73—22no—
279C2×D73—22no—
280C2×D73—22no—
281C2×D73—22no—
282C2×D73—22no—
283C2×D73#39814yes—
284C4×C73—42no—
285C4×C73—42no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73—81no—
289C4×C73—81no—
290C4×C73C2×#12311yescharacteristic
291C4×C73C2×#12511yescharacteristic
292C4×C73C2×#12511yescharacteristic
293C4×C73C2×C4⋊Q811yescharacteristic
294Dic73—42no—
295Dic73—42no—
296Dic73—41no—
297Dic73—41no—
298Dic73—81no—
299Dic73—81no—
300Dic73#39814yes—
301#23671—731nomaximal, Sylow
302C2×C73C2×#39811yescharacteristic
303C2×C73#306211yescharacteristic
304C2×C73#306311yescharacteristic
305C2×C73#308111yescharacteristic
306C2×C73#308211yescharacteristic
307C2×C73#308311yescharacteristic
308C2×C73#308411yescharacteristic
309D73—24no—
310C2×#428—731no—
311C2×#424—731no—
312#2317—731no—
313#2316—731no—
314#2088—731no—
315#2088—731no—
316#2088—731no—
317#2088D7311yescharacteristic, complemented
318#2087—731no—
319#2087—731no—
320#2086—731no—
321#2086—731no—
322#1736—731no—
323#1735—731no—
324C2×#340—731no—
325C73#2367111yescharacteristic, complemented, Sylow
326C22×M16—731no—
327C23×C8—731no—
328C2×#117—731no—
329C2×#117—731no—
330C2×#117—731no—
331C22×C4⋊C4—731no—
332C22×C4⋊C4—731no—
333#428—1464no—
334C2×#107—731no—
335C2×#107—731no—
336C2×#106—731no—
337C2×#106C2×D7311yescharacteristic
338#424—1464no—
339C2×C4⋊C8—731no—
340C2×C4⋊C8—731no—
341C2×C4⋊C8—731no—
342C2×C4⋊C8C2×D7311yescharacteristic
343#389—731no—
344#389—731no—
345#389—731no—
346#389—731no—
347#389—731no—
348#389—731no—
349#389—1461no—
350#389—1461no—
351#389C2×D7311yescharacteristic
352#389C2×D7311yescharacteristic
353#385—1461no—
354#385—1461no—
355#384—1461no—
356#382—1461no—
357#380—1461no—
358#380—1461no—
359#340—731no—
360#340—731no—
361#340—731no—
362#340—731no—
363#340—731no—
364#340—731no—
365#340—731no—
366#340—731no—
367#340—731no—
368#340C2×D7311yescharacteristic
369#340C2×D7311yescharacteristic
370#340C2×D7311yescharacteristic
371C23×C4—731no—
372C23×C4—1461no—
373C23×C4—1461no—
374C2×M16—734no—
375C2×M16—1462no—
376C2×M16—1462no—
377C22×C8—731no—
378C22×C8—731no—
379C22×C8—1462no—
380C22×C8—1462no—
381C22×C8—1462no—
382C22×C8C22×D7311yescharacteristic
383C22×C8C22×D7311yescharacteristic
384#117—734no—
385#117—1462no—
386#117—1462no—
387#117—1462no—
388#117—1462no—
389#117—1462no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—731no—
393C2×C4⋊C4—731no—
394C2×C4⋊C4—734no—
395C2×C4⋊C4—731no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—731no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—1462no—
400C2×C4⋊C4—1462no—
401C2×C4⋊C4—1462no—
402C2×C4⋊C4—1461no—
403C2×C4⋊C4—1461no—
404C2×C4⋊C4—1461no—
405C2×C4⋊C4—1461no—
406C2×C4⋊C4—1461no—
407C2×C4⋊C4—1461no—
408C2×C4⋊C4—1461no—
409C2×C4⋊C4—1461no—
410C2×C4⋊C4C22×D7311yescharacteristic
411C2×C4⋊C4C22×D7311yescharacteristic
412C2×C4⋊C4C22×D7311yescharacteristic
413C2×C4⋊C4C22×D7311yescharacteristic
414C2×C22⋊C4—731no—
415C2×C22⋊C4—731no—
416C2×C22⋊C4—1461no—
417C2×C22⋊C4—1461no—
418C2×C42—731no—
419C2×C42—1461no—
420C2×C42—1461no—
421C2×C42C22×D7311yescharacteristic
422#107—1462no—
423#107—1462no—
424#106—22no—
425#106—1462no—
426C4⋊C8—22no—
427C4⋊C8—1462no—
428C4⋊C8—1462no—
429C4⋊C8—1462no—
430#95—21no—
431#95—21no—
432#95—1461no—
433#95—1461no—
434#95—1461no—
435#95—1461no—
436#95—1461no—
437#95—1461no—
438C24—731no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—2922no—
444C22×C4—5841no—
445C22×C4—5841no—
446C22×C4—5841no—
447C22×C4—5841no—
448C22×C4—731no—
449C22×C4—732no—
450C22×C4—732no—
451C22×C4—732no—
452C22×C4—732no—
453C22×C4—732no—
454C22×C4—732no—
455C22×C4—731no—
456C22×C4—731no—
457C22×C4—1464no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4D4×D7311yescharacteristic
463C22×C4D4×D7311yescharacteristic
464C22×C4C23×D7311yescharacteristic
465M16—1468no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—2924no—
472C2×C8—732no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8D4×D7312yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—2922no—
488C4⋊C4—5841no—
489C4⋊C4—5841no—
490C4⋊C4—5841no—
491C4⋊C4—5841no—
492C4⋊C4—5841no—
493C4⋊C4—5841no—
494C4⋊C4—732no—
495C4⋊C4—732no—
496C4⋊C4—1464no—
497C4⋊C4—1462no—
498C4⋊C4—1462no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4—1461no—
503C4⋊C4—1461no—
504C4⋊C4—1461no—
505C4⋊C4Q8×D7312yes—
506C4⋊C4Q8×D7312yes—
507C22⋊C4—2922no—
508C22⋊C4—1462no—
509C22⋊C4—1462no—
510C22⋊C4—1464no—
511C42—21no—
512C42—21no—
513C42—2922no—
514C42—1464no—
515C42—1461no—
516C42—1461no—
517C23—732no—
518C23—732no—
519C23—732no—
520C23—1461no—
521C23—1461no—
522C23—1461no—
523C23—1461no—
524C23C2×D4×D7311yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—5844no—
554C2×C4—5844no—
555C2×C4—732no—
556C2×C4—732no—
557C2×C4—732no—
558C2×C4—734no—
559C2×C4—734no—
560C2×C4—734no—
561C2×C4—734no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1462no—
569C2×C4—1462no—
570C2×C4C2×D4×D7311yescharacteristic
571C2×C4C2×Q8×D7311yescharacteristic
572C2×C4C2×Q8×D7311yescharacteristic
573C2×C4#41×D7311yescharacteristic
574C2×C4#41×D7311yescharacteristic
575C2×C4#41×D7311yescharacteristic
576C8—22no—
577C8—41no—
578C8—2921no—
579C8—1462no—
580C22—734no—
581C22—1462no—
582C22—1462no—
583C22—1462no—
584C22—1462no—
585C22—1462no—
586C22—1462no—
587C22#121×D7311yescharacteristic
588C22C22⋊Q8×D7311yescharacteristic
589C22C22⋊Q8×D7311yescharacteristic
590C22#1798939111yescharacteristic
591C22#1798939311yescharacteristic
592C22#1798939611yescharacteristic
593C22#1798940111yescharacteristic
594C4—42no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—2922no—
601C4—2922no—
602C4—2921no—
603C4—2921no—
604C4—5841no—
605C4—5841no—
606C4—734no—
607C4#123×D7311yescharacteristic
608C4#125×D7311yescharacteristic
609C4#125×D7311yescharacteristic
610C4C4⋊Q8×D7311yescharacteristic
611C2—1464no—
612C2#398×D7311yescharacteristic
613C2#2261960611yescharacteristic
614C2#2261961511yescharacteristic
615C2#2261975711yescharacteristic
616C2#2261977211yescharacteristic
617C2#2261978311yescharacteristic
618C2#2261979011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2088C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenter#2088D73
hypocenterC73#23671
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2088

Complements

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

NH ≅ G/Ntype
5. #22611434C2semidirect
6. #22611433C2semidirect
7. #22611430C2semidirect
8. #22611428C2semidirect
9. #22611424C2semidirect
10. #22611422C2semidirect
11. #22611421C2semidirect
15. C73×#2088C2semidirect
317. #2088D73semidirect
325. C73#23671semidirect

Maximal subgroups

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

subgroupindex
C2×#179886262
C2×#179886122
#226125532
#226125462
#226114342
#226114332
#226114302
#226114282
#226114242
#226114222
#226114212
#226096492
#226096462
#340×D732
C73×#20882
#2367173