Finite Group Databasebeta

← #33091141

Subgroups — #33091141

Order 18688.

1086 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989200C211yesmaximal, characteristic
2C2×#17988647C211yesmaximal, characteristic
3#22612285C211yesmaximal, characteristic
4#22610889C211yesmaximal, characteristic, complemented
5#22610854C211yesmaximal, characteristic, complemented
6#22610853C211yesmaximal, characteristic, complemented
7#22610242C211yesmaximal, characteristic
8#22610242C211yesmaximal, characteristic
9#22610237C211yesmaximal, characteristic
10#22610237C211yesmaximal, characteristic
11#22609760C211yesmaximal, characteristic, complemented
12#22609760C211yesmaximal, characteristic, complemented
13#22609750C211yesmaximal, characteristic, complemented
14#22609750C211yesmaximal, characteristic, complemented
15C73×#1989C211yesmaximal, characteristic, complemented
16#17989200—24no—
17#17989200C418yescomplemented
18C2×#14556591C2211yescharacteristic
19C2×#14556586—21no—
20C2×#14556586—21no—
21C2×#14556582—21no—
22C2×#14556582—21no—
23C2×#14556571C2211yescharacteristic
24C2×#14556571C2211yescharacteristic
25C2×#14556556C2211yescharacteristic
26C2×#14556556C2211yescharacteristic
27C2×#14556549C2211yescharacteristic
28C2×#14556548C2211yescharacteristic
29C2×C4⋊C4×D73C2211yescharacteristic
30#17988647—24no—
31C2×C4⋊#10596831C2211yescharacteristic
32C2×#14556516C2211yescharacteristic
33C2×#14556516C2211yescharacteristic
34C2×#14556516C2211yescharacteristic
35C2×#14556516C2211yescharacteristic
36C2×#14556514C2211yescharacteristic
37C2×#14556514C2211yescharacteristic
38C2×#14556514C2211yescharacteristic
39C2×#14556514C2211yescharacteristic
40C2×#14556503C2211yescharacteristic
41C2×#14556503C2211yescharacteristic
42C2×#14556501C2211yescharacteristic
43C2×C8×Dic73C2211yescharacteristic
44C4⋊C4×Dic73C2211yescharacteristic
45C4⋊C4×Dic73C2211yescharacteristic
46C4×#11924007—21no—
47C4×C4⋊Dic73C2211yescharacteristic
48#17988438—21no—
49C4×#11924005—21no—
50#17988434—21no—
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C2×#125×C73C2211yescharacteristic
56C2×C4⋊C8×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×Dic146C2311yescharacteristic
63C22×Dic146C2311yescharacteristic
64C22×C4×D73—21no—
65C22×C4×D73C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68#14556591—22no—
69#14556591C2×C414yescomplemented
70#14556586—28no—
71#14556586—28no—
72#14556582—28no—
73#14556582—28no—
74#14556571—22no—
75#14556571—22no—
76#14556571C2×C414yes—
77#14556571C2×C414yes—
78#14556556—22no—
79#14556556—22no—
80#14556556C2×C414yescomplemented
81#14556556C2×C414yescomplemented
82#14556549—22no—
83#14556549—22no—
84#14556548C2×C414yes—
85#14556548D414yes—
86C2×C4⋊Dic73—21no—
87C2×C4⋊Dic73—21no—
88C2×C4⋊Dic73—21no—
89C2×C4⋊Dic73—21no—
90C2×C4⋊Dic73C2311yescharacteristic
91C2×C4⋊Dic73C2311yescharacteristic
92C2×#11924007—21no—
93C2×#11924007—21no—
94C2×#11924007—21no—
95C2×#11924007D411yescharacteristic
96C2×#11924007D411yescharacteristic
97C4⋊C4×D73—22no—
98C4⋊C4×D73—22no—
99C2×#11924005—21no—
100C2×#11924005—21no—
101C2×#11924005—21no—
102C2×#11924005D411yescharacteristic
103C2×#11924005D411yescharacteristic
104C2×C4×Dic73—21no—
105C2×C4×Dic73—21no—
106C2×C4×Dic73—21no—
107C2×C4×Dic73—21no—
108C2×C4×Dic73—21no—
109C2×C4×Dic73—21no—
110C2×C4×Dic73C2311yescharacteristic
111C4⋊#10596831—22no—
112#14556516—22no—
113#14556516—22no—
114#14556516—22no—
115#14556516—22no—
116#14556514—22no—
117#14556514—22no—
118#14556514—22no—
119#14556514—22no—
120#14556503—22no—
121#14556503—22no—
122#14556501—22no—
123C8×Dic73—22no—
124#14556498—21no—
125#14556498—21no—
126#14556498—21no—
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129#125×C73—22no—
130#125×C73C2×C414yescomplemented
131C2×C4⋊C4×C73—21no—
132C2×C4⋊C4×C73—21no—
133C2×C4⋊C4×C73C2311yescharacteristic
134C2×C4⋊C4×C73C2311yescharacteristic
135C2×C4⋊C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73C2311yescharacteristic
137C2×C42×C73—21no—
138C2×C42×C73C2311yescharacteristic
139C4⋊C8×C73—22no—
140#95×C73—21no—
141C23×D73C2×D411yescharacteristic
142C2×Dic146—21no—
143C2×Dic146—21no—
144C2×Dic146—21no—
145C2×Dic146—21no—
146C2×Dic146—21no—
147C2×Dic146—21no—
148C2×Dic146—21no—
149C2×Dic146—21no—
150C2×Dic146—21no—
151C2×Dic146—21no—
152C2×Dic146C22×C412yes—
153C2×Dic146C22×C412yes—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73C2×D411yescharacteristic
159C22×Dic73C2×D411yescharacteristic
160C22×Dic73C2×D411yescharacteristic
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—24no—
166C2×C4×D73—81no—
167C2×C4×D73—81no—
168C2×C4×D73C22×C412yes—
169C2×C4×D73C2×D412yes—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C4⋊Dic73—24no—
177C4⋊Dic73—24no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—24no—
181C4⋊Dic73—24no—
182C4⋊Dic73#4112yes—
183C4⋊Dic73#4112yes—
184#11924007—24no—
185#11924007—24no—
186#11924007—24no—
187#11924007C22⋊C414yes—
188#11924007C22⋊C414yes—
189#11924005—24no—
190#11924005—24no—
191#11924005—24no—
192#11924005C22⋊C414yes—
193#11924005C22⋊C414yes—
194C4×Dic73—24no—
195C4×Dic73—24no—
196C4×Dic73—24no—
197C4×Dic73—81no—
198C4×Dic73—81no—
199C4×Dic73—81no—
200C4×Dic73C22×C412yes—
201C4×Dic73C2×D412yes—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2411yescharacteristic
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C4⋊C4×C73—24no—
216C4⋊C4×C73—24no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73C22×C412yes—
222C4⋊C4×C73C22×C412yes—
223C4⋊C4×C73#4112yes—
224C4⋊C4×C73#4112yes—
225C42×C73—81no—
226C42×C73C22×C412yes—
227C42×C73C2×D412yes—
228C23×C73C22×D411yescharacteristic
229C22×D73—21no—
230C22×D73—21no—
231C22×D73—21no—
232C22×D73—21no—
233C22×D73—21no—
234C22×D73—21no—
235C22×D73C2×C22⋊C412yes—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—22no—
241C2×C4×C73—22no—
242C2×C4×C73—22no—
243C2×C4×C73—22no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73C2×C22⋊C412yes—
253C2×C4×C73C2×C22⋊C412yes—
254C2×C4×C73C23×C411yescharacteristic
255C2×C4×C73C22×D411yescharacteristic
256C2×C4×C73C2×#4111yescharacteristic
257C2×C4×C73C2×#4111yescharacteristic
258C2×C4×C73C2×#4111yescharacteristic
259C2×C4×C73C2×#4111yescharacteristic
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—22no—
267C2×Dic73—22no—
268C2×Dic73—22no—
269C2×Dic73—22no—
270C2×Dic73—41no—
271C2×Dic73—41no—
272C2×Dic73—41no—
273C2×Dic73—41no—
274C2×Dic73—41no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73C2×C22⋊C412yes—
279C2×Dic73C2×C22⋊C412yes—
280C2×Dic73C2×C22⋊C412yes—
281C4×D73—22no—
282C4×D73—22no—
283C4×D73—22no—
284C4×D73—22no—
285C4×D73—84no—
286Dic146—22no—
287Dic146—22no—
288Dic146—22no—
289Dic146—22no—
290Dic146—41no—
291Dic146—41no—
292Dic146—41no—
293Dic146—41no—
294C8×C73—41no—
295C8×C73—41no—
296#10596831—41no—
297#10596831—41no—
298C22×C73C22×C22⋊C411yescharacteristic
299C22×C73#52511yescharacteristic
300C22×C73#52511yescharacteristic
301C22×C73#57711yescharacteristic
302C22×C73#57711yescharacteristic
303C22×C73#57811yescharacteristic
304C22×C73#57811yescharacteristic
305C2×D73—22no—
306C2×D73—22no—
307C2×D73—22no—
308C2×D73—41no—
309C2×D73—41no—
310C2×D73—41no—
311C2×D73—41no—
312C4×C73—22no—
313C4×C73—22no—
314C4×C73—42no—
315C4×C73—42no—
316C4×C73—42no—
317C4×C73—42no—
318C4×C73C4×#4111yescharacteristic
319C4×C73C4×#4111yescharacteristic
320C4×C73#53211yescharacteristic
321C4×C73#53211yescharacteristic
322Dic73—22no—
323Dic73—22no—
324Dic73—22no—
325Dic73—42no—
326Dic73—42no—
327Dic73—42no—
328Dic73—42no—
329#21398—731nomaximal, Sylow
330C2×C73#229711yescharacteristic
331C2×C73#289811yescharacteristic
332C2×C73#289811yescharacteristic
333C2×C73#312011yescharacteristic
334C2×C73#312011yescharacteristic
335C2×C73#312311yescharacteristic
336C2×C73#312711yescharacteristic
337D73—42no—
338C2×#541—731no—
339C2×#433—731no—
340#2274—731no—
341#1989—731no—
342#1989D7311yescharacteristic, complemented
343#1981—731no—
344#1981—731no—
345#1873—731no—
346#1873—731no—
347#1872—731no—
348#1872—731no—
349#1763—731no—
350#1763—731no—
351C4×#103—731no—
352C4×#103—731no—
353C73#2139811yescharacteristic, complemented, Sylow
354#541—738no—
355#541—1464no—
356C2×C4⋊Q8—731no—
357C2×#126—1461no—
358C2×#126—1461no—
359C2×#125—1461no—
360C2×#125—1461no—
361C2×#125C2×D7311yescharacteristic
362C2×C22⋊Q8—731no—
363C2×C22⋊Q8—731no—
364C2×C4×Q8—731no—
365C2×C4×Q8—731no—
366C2×#117—731no—
367C2×#117—731no—
368C22×C4⋊C4—731no—
369#433—1464no—
370C2×C4⋊C8—731no—
371C2×C4⋊C8C2×D7311yescharacteristic
372C2×#103—731no—
373C2×#103—731no—
374C2×#103—731no—
375C2×#103—731no—
376C2×#103—731no—
377C2×#103—731no—
378C2×#103—731no—
379C2×#103—731no—
380C2×C22⋊C8—731no—
381C2×C22⋊C8—731no—
382C2×#97—731no—
383C2×C4×C8—731no—
384C4×C4⋊C4—731no—
385C4×C4⋊C4—731no—
386C4×C4⋊C4—731no—
387C4×C4⋊C4—1461no—
388C4×C4⋊C4—1461no—
389C4×C4⋊C4C2×D7311yescharacteristic
390C4×C22⋊C4—1461no—
391C4×C22⋊C4—1461no—
392#340—731no—
393#340—731no—
394#340—731no—
395#340—731no—
396#340C2×D7311yescharacteristic
397#340C2×D7311yescharacteristic
398#340C2×D7311yescharacteristic
399#340C2×D7311yescharacteristic
400C22×Q8—731no—
401C22×Q8—731no—
402C23×C4—731no—
403C23×C4—1461no—
404C22×C8—731no—
405C22×C8—731no—
406C22×C8C22×D7311yescharacteristic
407C22×C8C22×D7311yescharacteristic
408C4⋊Q8—734no—
409C4⋊Q8—1462no—
410#126—1468no—
411#126—1468no—
412#125—22no—
413#125—1468no—
414#125—1468no—
415#125C4×D7314yescomplemented
416C22⋊Q8—734no—
417C22⋊Q8—734no—
418C22⋊Q8—1462no—
419C22⋊Q8—1462no—
420C4×Q8—734no—
421C4×Q8—734no—
422C4×Q8—1462no—
423C4×Q8—1462no—
424#117—734no—
425#117—734no—
426#117—1462no—
427#117—1462no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—731no—
431C2×C4⋊C4—731no—
432C2×C4⋊C4—731no—
433C2×C4⋊C4—731no—
434C2×C4⋊C4—1462no—
435C2×C4⋊C4—1461no—
436C2×C4⋊C4—1461no—
437C2×C4⋊C4—1461no—
438C2×C4⋊C4—1461no—
439C2×C4⋊C4—1461no—
440C2×C4⋊C4—1461no—
441C2×C4⋊C4—1461no—
442C2×C4⋊C4—1462no—
443C2×C4⋊C4C22×D7311yescharacteristic
444C2×C4⋊C4C22×D7311yescharacteristic
445C2×C4⋊C4C22×D7311yescharacteristic
446C2×C4⋊C4C22×D7311yescharacteristic
447C2×C22⋊C4—731no—
448C2×C22⋊C4—731no—
449C2×C22⋊C4—1461no—
450C2×C22⋊C4—1461no—
451C2×C22⋊C4—1461no—
452C2×C42—21no—
453C2×C42—731no—
454C2×C42—1461no—
455C2×C42—1461no—
456C2×C42—1461no—
457C2×C42—1461no—
458C2×C42—1461no—
459C2×C42—1461no—
460C2×C42C22×D7311yescharacteristic
461C4⋊C8—22no—
462C4⋊C8—1462no—
463#103—1462no—
464#103—1462no—
465#103—1462no—
466#103—1462no—
467#103—1462no—
468#103—1462no—
469#103—1462no—
470#103—1462no—
471C22⋊C8—1462no—
472C22⋊C8—1462no—
473#97—1462no—
474C4×C8—1462no—
475#95—21no—
476#95—1461no—
477#95—1461no—
478#95—1461no—
479C24—731no—
480C2×Q8—732no—
481C2×Q8—732no—
482C2×Q8—1461no—
483C2×Q8—1461no—
484C2×Q8—1461no—
485C2×Q8—1461no—
486C2×Q8—1461no—
487C2×Q8—1461no—
488C2×Q8—1461no—
489C2×Q8—1461no—
490C2×Q8—1461no—
491C2×Q8—1461no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—5841no—
497C22×C4—5841no—
498C22×C4—731no—
499C22×C4—731no—
500C22×C4—731no—
501C22×C4—732no—
502C22×C4—732no—
503C22×C4—1464no—
504C22×C4—1461no—
505C22×C4—1461no—
506C22×C4—1461no—
507C22×C4—1461no—
508C22×C4—1461no—
509C22×C4—1461no—
510C22×C4—1461no—
511C22×C4—1461no—
512C22×C4D4×D7311yescharacteristic
513C22×C4D4×D7311yescharacteristic
514C22×C4C23×D7311yescharacteristic
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—1461no—
522C2×C8—1461no—
523C2×C8—1461no—
524C2×C8—1461no—
525C2×C8—1461no—
526C2×C8—1461no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—734no—
534C4⋊C4—734no—
535C4⋊C4—732no—
536C4⋊C4—732no—
537C4⋊C4—1464no—
538C4⋊C4—1464no—
539C4⋊C4—1464no—
540C4⋊C4—1464no—
541C4⋊C4—1464no—
542C4⋊C4—1464no—
543C4⋊C4—1464no—
544C4⋊C4—1461no—
545C4⋊C4—1461no—
546C4⋊C4C2×C4×D7312yes—
547C4⋊C4C2×C4×D7312yes—
548C4⋊C4#1192402912yes—
549C4⋊C4#1192402912yes—
550C22⋊C4—734no—
551C22⋊C4—734no—
552C22⋊C4—1464no—
553C22⋊C4—1464no—
554C22⋊C4—1464no—
555C42—81no—
556C42—5841no—
557C42—5841no—
558C42—5841no—
559C42—732no—
560C42—732no—
561C42—1464no—
562C42—1464no—
563C42—1464no—
564C42C2×C4×D7312yes—
565C42D4×D7312yes—
566C23—732no—
567C23—1461no—
568C23—1461no—
569C23—1461no—
570C23—1461no—
571C23—1461no—
572C23—1461no—
573C23C2×D4×D7311yescharacteristic
574Q8—2921no—
575Q8—2921no—
576Q8—2921no—
577Q8—2921no—
578Q8—1462no—
579Q8—1462no—
580Q8—1462no—
581Q8—1462no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—2921no—
599C2×C4—2921no—
600C2×C4—2921no—
601C2×C4—2921no—
602C2×C4—2921no—
603C2×C4—2921no—
604C2×C4—2921no—
605C2×C4—2921no—
606C2×C4—5844no—
607C2×C4—732no—
608C2×C4—732no—
609C2×C4—732no—
610C2×C4—1462no—
611C2×C4—1462no—
612C2×C4—1462no—
613C2×C4—1462no—
614C2×C4—1461no—
615C2×C4—1461no—
616C2×C4—1461no—
617C2×C4—1461no—
618C2×C4—1461no—
619C2×C4—1461no—
620C2×C4—1462no—
621C2×C4—1462no—
622C2×C4—1462no—
623C2×C4—1462no—
624C2×C4C22⋊C4×D7312yes—
625C2×C4C22⋊C4×D7312yes—
626C2×C4C22×C4×D7311yescharacteristic
627C2×C4C2×D4×D7311yescharacteristic
628C2×C4#41×D7311yescharacteristic
629C2×C4#41×D7311yescharacteristic
630C2×C4C2×#1192402911yescharacteristic
631C2×C4C2×#1192402911yescharacteristic
632C8—41no—
633C8—41no—
634C8—2921no—
635C8—2921no—
636C22—2921no—
637C22—2921no—
638C22—2921no—
639C22—2921no—
640C22—1462no—
641C22—1462no—
642C22—1462no—
643C22C2×C22⋊C4×D7311yescharacteristic
644C22#1798910011yescharacteristic
645C22#1798910011yescharacteristic
646C22#1798939411yescharacteristic
647C22#1798939711yescharacteristic
648C22#1798940111yescharacteristic
649C22#1798940311yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—42no—
654C4—42no—
655C4—42no—
656C4—2922no—
657C4—2922no—
658C4—2922no—
659C4—2922no—
660C4—1462no—
661C4—1462no—
662C4—1462no—
663C4C4×#1192402911yescharacteristic
664C4C4×#1192402911yescharacteristic
665C4#1798913611yescharacteristic
666C4#1798913811yescharacteristic
667C2—2922no—
668C2#2261242011yescharacteristic
669C2#2261846011yescharacteristic
670C2#2261846211yescharacteristic
671C2#2262015011yescharacteristic
672C2#2262015211yescharacteristic
673C2#2262018511yescharacteristic
674C2#2262023311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1989C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1989D73
hypocenterC73#21398
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
4. #22610889C2semidirect
5. #22610854C2semidirect
6. #22610853C2semidirect
11. #22609760C2semidirect
12. #22609760C2semidirect
13. #22609750C2semidirect
14. #22609750C2semidirect
15. C73×#1989C2semidirect
17. #17989200C4semidirect
69. #14556591C2×C4semidirect
80. #14556556C2×C4semidirect
81. #14556556C2×C4semidirect
130. #125×C73C2×C4semidirect
342. #1989D73semidirect
353. C73#21398semidirect
415. #125C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179892002
C2×#179886472
#226122852
#226108892
#226108542
#226108532
#226102422
#226102372
#226097602
#226097502
C73×#19892
#2139873