Finite Group Databasebeta

← #33102606

Subgroups — #33102606

Order 18688.

1110 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989293C211yesmaximal, characteristic
2C2×#17988715C211yesmaximal, characteristic, complemented
3#22612843C211yesmaximal, characteristic, complemented
4#22610898C211yesmaximal, characteristic, complemented
5#22610890C211yesmaximal, characteristic, complemented
6#22610889C211yesmaximal, characteristic, complemented
7#22610885C211yesmaximal, characteristic, complemented
8#22610877C211yesmaximal, characteristic, complemented
9#22609930C211yesmaximal, characteristic
10#22609930C211yesmaximal, characteristic
11#22609928C211yesmaximal, characteristic
12#22609757C211yesmaximal, characteristic
13#22609755C211yesmaximal, characteristic
14#22609745C211yesmaximal, characteristic
15C73×#1992C211yesmaximal, characteristic, complemented
16#17989293—24no—
17#17989293C418yescomplemented
18C2×#14556590C2211yescharacteristic
19C2×#14556582C2211yescharacteristic
20C2×#14556571—21no—
21C2×#14556569—21no—
22C2×#14556569—21no—
23C2×C4×Dic146C2211yescharacteristic
24C2×#14556556—21no—
25C2×C4×D292C2211yescharacteristic
26C2×#14556553C2211yescharacteristic
27C2×#14556553C2211yescharacteristic
28C2×C4⋊C4×D73—21no—
29#17988715—24no—
30C2×C4⋊#10596831C2211yescharacteristic
31C2×#14556520C2211yescharacteristic
32C2×#14556520C2211yescharacteristic
33C2×#14556513C2211yescharacteristic
34C2×#14556513C2211yescharacteristic
35C2×#14556511C2211yescharacteristic
36C2×#14556511C2211yescharacteristic
37C2×#14556501C2211yescharacteristic
38C2×C8×Dic73C2211yescharacteristic
39#17988483—21no—
40#17988482—21no—
41#17988482—21no—
42#17988456C2211yescharacteristic
43#17988456C2211yescharacteristic
44C4⋊C4×Dic73C2211yescharacteristic
45C4⋊C4×Dic73C2211yescharacteristic
46C4×C4⋊Dic73C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C2×#125×C73C2211yescharacteristic
56C2×#97×C73C2211yescharacteristic
57#384×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×Dic146—21no—
63C22×Dic146D411yescharacteristic
64C22×D292C2311yescharacteristic
65C22×C4×D73—21no—
66C22×C4×D73—21no—
67C22×C4×D73—21no—
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70#14556590—22no—
71#14556590C2×C414yes—
72#14556582—22no—
73#14556582C2×C414yes—
74#14556571—28no—
75#14556569—28no—
76#14556569—28no—
77C4×Dic146C2×C414yes—
78C4×Dic146D414yes—
79#14556556—44no—
80C4×D292—22no—
81C4×D292C2×C414yes—
82#14556553—22no—
83#14556553—22no—
84#14556553C2×C414yes—
85#14556553C2×C414yes—
86C2×C4⋊Dic73—21no—
87C2×C4⋊Dic73D411yescharacteristic
88C2×C4⋊Dic73C2311yescharacteristic
89C2×C4⋊Dic73C2311yescharacteristic
90C2×C4⋊Dic73C2311yescharacteristic
91C2×#11924007—21no—
92C2×#11924007—21no—
93C2×#11924007—21no—
94C2×#11924007—21no—
95C2×#11924007—21no—
96C2×#11924007—21no—
97C2×#11924007D411yescharacteristic
98C2×#11924007D411yescharacteristic
99C4⋊C4×D73—28no—
100C2×#11924005—21no—
101C2×#11924005—21no—
102C2×#11924005—21no—
103C2×C4×Dic73—21no—
104C2×C4×Dic73—21no—
105C2×C4×Dic73—21no—
106C2×C4×Dic73C2311yescharacteristic
107C2×C4×Dic73C2311yescharacteristic
108C4⋊#10596831—22no—
109#14556520—22no—
110#14556520—22no—
111#14556513—22no—
112#14556513Q814yescomplemented
113#14556511—22no—
114#14556511—22no—
115#14556501—22no—
116C8×Dic73—22no—
117#14556498—21no—
118#14556498—21no—
119#14556498—21no—
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122#125×C73—22no—
123#125×C73C2×C414yes—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73—21no—
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C4⋊C4×C73C2311yescharacteristic
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C4⋊C4×C73C2311yescharacteristic
132C2×C42×C73C2311yescharacteristic
133#97×C73—22no—
134C23×D73—21no—
135C2×Dic146—22no—
136C2×Dic146—22no—
137C2×Dic146—24no—
138C2×Dic146—81no—
139C2×Dic146—81no—
140C2×Dic146C22⋊C414yes—
141C2×D292—21no—
142C2×D292—21no—
143C2×D292—21no—
144C2×D292C22×C412yes—
145C2×D292C2×Q812yes—
146C2×D292#4112yes—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73C2×D411yescharacteristic
151C22×Dic73C2×D411yescharacteristic
152C22×Dic73C2×D411yescharacteristic
153C22×Dic73C2×D411yescharacteristic
154C2×C4×D73—24no—
155C2×C4×D73—24no—
156C2×C4×D73—24no—
157C2×C4×D73—42no—
158C2×C4×D73—42no—
159C2×C4×D73—81no—
160C2×C4×D73—81no—
161C2×C4×D73—81no—
162C2×C4×D73—81no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—24no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73C22⋊C414yes—
175C4⋊Dic73C22×C412yes—
176C4⋊Dic73C2×Q812yes—
177#11924007—24no—
178#11924007—24no—
179#11924007—42no—
180#11924007—42no—
181#11924007—81no—
182#11924007—81no—
183#11924007C22⋊C414yes—
184#11924007C22⋊C414yes—
185#11924005—24no—
186#11924005—24no—
187#11924005—24no—
188C4×Dic73—42no—
189C4×Dic73—42no—
190C4×Dic73—42no—
191C4×Dic73C22×C412yes—
192C4×Dic73C22×C412yes—
193C4×Dic73C2×D412yes—
194C4×Dic73C2×D412yes—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2411yescharacteristic
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73C2×Q812yes—
208C4⋊C4×C73—24no—
209C4⋊C4×C73—24no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73—81no—
218C4⋊C4×C73C22×C412yes—
219C4⋊C4×C73C22×C412yes—
220C42×C73C22×C412yes—
221C42×C73C2×D412yes—
222C23×C73C22×D411yescharacteristic
223C22×D73—22no—
224C22×D73—22no—
225C22×D73—22no—
226C22×D73—41no—
227C22×D73—41no—
228C22×D73—41no—
229C22×D73—41no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—22no—
235C2×C4×C73—22no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73C2×C22⋊C412yes—
247C2×C4×C73C2×C22⋊C412yes—
248C2×C4×C73C23×C411yescharacteristic
249C2×C4×C73C22×D411yescharacteristic
250C2×C4×C73C22×Q811yescharacteristic
251C2×C4×C73C2×#4111yescharacteristic
252C2×C4×C732−1+411yescharacteristic
253C2×C4×C732−1+411yescharacteristic
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—22no—
261C2×Dic73—22no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73—41no—
268C2×Dic73—41no—
269C2×Dic73C2×C22⋊C412yes—
270C2×Dic73C2×C22⋊C412yes—
271C2×Dic73C2×C22⋊C412yes—
272C2×Dic73C2×C22⋊C412yes—
273C2×Dic73AGL(1,ℤ/8)12yes—
274C2×Dic73#13712yes—
275D292—22no—
276D292—22no—
277D292—22no—
278D292C4×Q814yescomplemented
279C4×D73—48no—
280C4×D73—84no—
281C4×D73—84no—
282Dic146—28no—
283Dic146—84no—
284C8×C73—22no—
285C8×C73—41no—
286#10596831—41no—
287#10596831—41no—
288C22×C73C22×C22⋊C411yescharacteristic
289C22×C73#54811yescharacteristic
290C22×C73D4×Q811yescharacteristic
291C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C73C2×#13711yescharacteristic
293C22×C73#57611yescharacteristic
294C22×C73#57711yescharacteristic
295C2×D73—24no—
296C2×D73—42no—
297C2×D73—42no—
298C2×D73—42no—
299C2×D73—42no—
300C2×D73—42no—
301C2×D73—42no—
302C4×C73—22no—
303C4×C73—22no—
304C4×C73—42no—
305C4×C73—42no—
306C4×C73—81no—
307C4×C73—81no—
308C4×C73C2×C4×Q811yescharacteristic
309C4×C73#51911yescharacteristic
310C4×C73#54811yescharacteristic
311C4×C73D4×Q811yescharacteristic
312Dic73—22no—
313Dic73—22no—
314Dic73—22no—
315Dic73—42no—
316Dic73—42no—
317Dic73—81no—
318Dic73#41714yes—
319#22522—731nomaximal, Sylow
320C2×C73Q8×C22⋊C411yescharacteristic
321C2×C73C2×#41711yescharacteristic
322C2×C73#289711yescharacteristic
323C2×C73#336611yescharacteristic
324C2×C73#337211yescharacteristic
325C2×C73#338411yescharacteristic
326C2×C73#338511yescharacteristic
327D73—44no—
328C2×#554—731no—
329C2×#446—731no—
330Q8×C4⋊C4—731no—
331#1992—731no—
332#1992D7311yescharacteristic, complemented
333#1990—731no—
334#1989—731no—
335#1989—731no—
336#1987—731no—
337#1802—731no—
338#1802—731no—
339#1802—731no—
340#1762—731no—
341#1762—731no—
342C4×#102—731no—
343C73#2252211yescharacteristic, complemented, Sylow
344#554—738no—
345#554—1464no—
346C2×C4⋊Q8—731no—
347C2×#125—731no—
348C2×#125C2×D7311yescharacteristic
349C2×C22⋊Q8—1461no—
350C2×C22⋊Q8—1461no—
351C2×C22⋊Q8—1461no—
352C2×C4×Q8—731no—
353C2×C4×Q8—1461no—
354C2×C4×D4—731no—
355C2×C4×D4—731no—
356C2×C4×D4—731no—
357C22×C4⋊C4—1461no—
358#446—1464no—
359C2×C4⋊C8—731no—
360C2×C4⋊C8—731no—
361C2×C4⋊C8—731no—
362C2×#102—731no—
363C2×#102—731no—
364C2×#102—731no—
365C2×#102—731no—
366C2×#97—731no—
367C2×#97C2×D7311yescharacteristic
368C2×C4×C8—731no—
369#389—1461no—
370#389—1461no—
371#389—1461no—
372#384—731no—
373#384—731no—
374#384C2×D7311yescharacteristic
375C4×C4⋊C4—731no—
376C4×C4⋊C4—731no—
377C4×C4⋊C4—731no—
378#340—731no—
379#340—731no—
380#340—731no—
381#340—731no—
382#340—731no—
383#340—731no—
384#340—731no—
385#340—731no—
386#340C2×D7311yescharacteristic
387#340C2×D7311yescharacteristic
388#340C2×D7311yescharacteristic
389#340C2×D7311yescharacteristic
390C22×Q8—731no—
391C22×Q8—1461no—
392C22×D4—731no—
393C23×C4—1461no—
394C23×C4—1461no—
395C23×C4—1461no—
396C22×C8—731no—
397C22×C8—731no—
398C22×C8C22×D7311yescharacteristic
399C22×C8C22×D7311yescharacteristic
400C4⋊Q8—734no—
401C4⋊Q8—1462no—
402#125—22no—
403#125—734no—
404#125—1462no—
405#125C4×D7314yes—
406C22⋊Q8—1468no—
407C22⋊Q8—1468no—
408C22⋊Q8—1468no—
409C4×Q8—2924no—
410C4×Q8—734no—
411C4×Q8—734no—
412C4×D4—734no—
413C4×D4—734no—
414C4×D4—734no—
415C4×D4—1462no—
416C4×D4—1462no—
417C4×D4—1462no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—731no—
423C2×C4⋊C4—731no—
424C2×C4⋊C4—731no—
425C2×C4⋊C4—731no—
426C2×C4⋊C4—731no—
427C2×C4⋊C4—731no—
428C2×C4⋊C4—1468no—
429C2×C4⋊C4—1461no—
430C2×C4⋊C4—1461no—
431C2×C4⋊C4—1461no—
432C2×C4⋊C4—1461no—
433C2×C4⋊C4—1461no—
434C2×C4⋊C4—1461no—
435C2×C4⋊C4—1461no—
436C2×C4⋊C4C22×D7311yescharacteristic
437C2×C4⋊C4C22×D7311yescharacteristic
438C2×C4⋊C4C22×D7311yescharacteristic
439C2×C4⋊C4C22×D7311yescharacteristic
440C2×C22⋊C4—1461no—
441C2×C22⋊C4—1461no—
442C2×C22⋊C4—1461no—
443C2×C42—731no—
444C2×C42—731no—
445C2×C42—1461no—
446C2×C42—1461no—
447C2×C42—1461no—
448C2×C42C22×D7311yescharacteristic
449C4⋊C8—1462no—
450C4⋊C8—1462no—
451C4⋊C8—1462no—
452#102—734no—
453#102—1462no—
454#102—1462no—
455#102—1462no—
456#97—22no—
457#97—1462no—
458C4×C8—1462no—
459#95—1461no—
460#95—1461no—
461#95—1461no—
462C24—1461no—
463C2×Q8—5841no—
464C2×Q8—5841no—
465C2×Q8—734no—
466C2×Q8—1464no—
467C2×Q8—1462no—
468C2×Q8—1462no—
469C2×D4—732no—
470C2×D4—732no—
471C2×D4—732no—
472C2×D4—1461no—
473C2×D4—1461no—
474C2×D4—1461no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—2922no—
480C22×C4—2922no—
481C22×C4—5841no—
482C22×C4—5841no—
483C22×C4—5841no—
484C22×C4—5841no—
485C22×C4—731no—
486C22×C4—731no—
487C22×C4—731no—
488C22×C4—731no—
489C22×C4—1464no—
490C22×C4—1464no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4—1464no—
495C22×C4D4×D7311yescharacteristic
496C22×C4D4×D7311yescharacteristic
497C22×C4C23×D7311yescharacteristic
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8Q8×D7312yes—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—81no—
520C4⋊C4—2922no—
521C4⋊C4—2922no—
522C4⋊C4—5841no—
523C4⋊C4—5841no—
524C4⋊C4—734no—
525C4⋊C4—734no—
526C4⋊C4—734no—
527C4⋊C4—732no—
528C4⋊C4—732no—
529C4⋊C4—1464no—
530C4⋊C4—1464no—
531C4⋊C4—1464no—
532C4⋊C4—1461no—
533C4⋊C4—1461no—
534C4⋊C4—1461no—
535C4⋊C4—1461no—
536C4⋊C4C2×C4×D7312yes—
537C4⋊C4C2×C4×D7312yes—
538C22⋊C4—1464no—
539C22⋊C4—1464no—
540C22⋊C4—1464no—
541C42—2922no—
542C42—2922no—
543C42—2922no—
544C42—732no—
545C42—732no—
546C42—732no—
547C42—732no—
548C42C2×C4×D7312yes—
549C42D4×D7312yes—
550C23—2921no—
551C23—2921no—
552C23—2921no—
553C23—2921no—
554C23—1462no—
555C23—1462no—
556C23—1462no—
557C23C2×D4×D7311yescharacteristic
558Q8—5844no—
559Q8—1468no—
560D4—734no—
561D4—1462no—
562D4—1462no—
563D4—1462no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—2928no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—2921no—
584C2×C4—2921no—
585C2×C4—2921no—
586C2×C4—2921no—
587C2×C4—2921no—
588C2×C4—5844no—
589C2×C4—5844no—
590C2×C4—732no—
591C2×C4—732no—
592C2×C4—732no—
593C2×C4—732no—
594C2×C4—732no—
595C2×C4—732no—
596C2×C4—1462no—
597C2×C4—1462no—
598C2×C4—1461no—
599C2×C4—1461no—
600C2×C4—1461no—
601C2×C4—1461no—
602C2×C4—1461no—
603C2×C4—1461no—
604C2×C4C22⋊C4×D7312yes—
605C2×C4C22⋊C4×D7312yes—
606C2×C4C22×C4×D7311yescharacteristic
607C2×C4C2×D4×D7311yescharacteristic
608C2×C4C2×Q8×D7311yescharacteristic
609C2×C4#41×D7311yescharacteristic
610C2×C4#1455663811yescharacteristic
611C2×C4#1455663911yescharacteristic
612C8—22no—
613C8—41no—
614C8—2921no—
615C8—2921no—
616C22—2922no—
617C22—2922no—
618C22—2922no—
619C22—2922no—
620C22—2922no—
621C22—2922no—
622C22—1464no—
623C22C2×C22⋊C4×D7311yescharacteristic
624C22#1798924511yescharacteristic
625C22#1798925211yescharacteristic
626C22AGL(1,ℤ/8)×D7311yescharacteristic
627C22#137×D7311yescharacteristic
628C22#1798939111yescharacteristic
629C22#1798939611yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—2922no—
637C4—2922no—
638C4—5841no—
639C4—734no—
640C4—1462no—
641C4—1462no—
642C4—1462no—
643C4C4×Q8×D7311yescharacteristic
644C4#1798906311yescharacteristic
645C4#1798924711yescharacteristic
646C4#1798925011yescharacteristic
647C2—2924no—
648C2#2261276511yescharacteristic
649C2#417×D7311yescharacteristic
650C2#2261845511yescharacteristic
651C2#2262263511yescharacteristic
652C2#2262270911yescharacteristic
653C2#2262282711yescharacteristic
654C2#2262283811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1992C2
socleC23×C73C22×D4
prime radicalC22×D292C23
cosocleC22×C4×C73C24
hypercenter#1992D73
hypocenterC73#22522
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
2. C2×#17988715C2semidirect
3. #22612843C2semidirect
4. #22610898C2semidirect
5. #22610890C2semidirect
6. #22610889C2semidirect
7. #22610885C2semidirect
8. #22610877C2semidirect
15. C73×#1992C2semidirect
17. #17989293C4semidirect
112. #14556513Q8semidirect
278. D292C4×Q8semidirect
332. #1992D73semidirect
343. C73#22522semidirect

Maximal subgroups

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

subgroupindex
C2×#179892932
C2×#179887152
#226128432
#226108982
#226108902
#226108892
#226108852
#226108772
#226099302
#226099282
#226097572
#226097552
#226097452
C73×#19922
#2252273