Finite Group Databasebeta

← #33095528

Subgroups — #33095528

Order 18688.

970 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989214C211yesmaximal, characteristic
2C2×#17988646C211yesmaximal, characteristic
3#22612539C211yesmaximal, characteristic
4#22610905C211yesmaximal, characteristic, complemented
5#22610899C211yesmaximal, characteristic, complemented
6#22610896C211yesmaximal, characteristic, complemented
7#22610887C211yesmaximal, characteristic, complemented
8#22610885C211yesmaximal, characteristic, complemented
9#22610881C211yesmaximal, characteristic, complemented
10#22610877C211yesmaximal, characteristic, complemented
11#22610025C211yesmaximal, characteristic
12#22610024C211yesmaximal, characteristic
13#22610020C211yesmaximal, characteristic
14#22610016C211yesmaximal, characteristic
15C73×#1990C211yesmaximal, characteristic, complemented
16#17989214—24no—
17#17989214C418yescomplemented
18C2×#14556590C2211yescharacteristic
19C2×#14556589—21no—
20C2×#14556583C2211yescharacteristic
21C2×#14556582C2211yescharacteristic
22C2×#14556581—21no—
23C2×#14556569—21no—
24C2×#14556567—21no—
25C2×#14556549C2211yescharacteristic
26C2×#14556548C2211yescharacteristic
27C2×C4⋊C4×D73C2211yescharacteristic
28#17988646—24no—
29C2×#14556520C2211yescharacteristic
30C2×#14556520C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556502C2211yescharacteristic
34#17988477—21no—
35#17988477—21no—
36#17988468—21no—
37#17988468—21no—
38#17988453C2211yescharacteristic
39#17988444C2211yescharacteristic
40#17988444C2211yescharacteristic
41C4⋊C4×Dic73C2211yescharacteristic
42C4⋊C4×Dic73C2211yescharacteristic
43#17988350C2211yescharacteristic
44#17988350C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C2×C4⋊Q8×C73C2211yescharacteristic
56C2×C4×C8×C73C2211yescharacteristic
57#384×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×Dic146—21no—
63C22×C4×D73—21no—
64C22×C4×D73C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67#14556590—22no—
68#14556590C2×C414yes—
69#14556589—28no—
70#14556583—22no—
71#14556583C2×C414yes—
72#14556582—22no—
73#14556582C2×C414yes—
74#14556581—28no—
75#14556569—28no—
76#14556567—28no—
77#14556549—22no—
78#14556549C2×C414yes—
79#14556548C2×C414yes—
80#14556548D414yes—
81C2×C4⋊Dic73—21no—
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×#11924007—21no—
89C2×#11924007—21no—
90C2×#11924007—21no—
91C2×#11924007D411yescharacteristic
92C2×#11924007D411yescharacteristic
93C4⋊C4×D73—22no—
94C4⋊C4×D73C2×C414yes—
95C2×#11924005—21no—
96C2×#11924005—21no—
97C2×#11924005—21no—
98C2×#11924005D411yescharacteristic
99C2×#11924005D411yescharacteristic
100C2×C4×Dic73—21no—
101C2×C4×Dic73—21no—
102C2×C4×Dic73—21no—
103C2×C4×Dic73C2311yescharacteristic
104#14556520—22no—
105#14556520—22no—
106#14556503—22no—
107#14556503—22no—
108#14556502—22no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498—21no—
114#14556498—21no—
115C22×Q8×C73—21no—
116C22×C8×C73C2311yescharacteristic
117C22×C8×C73C2311yescharacteristic
118C4⋊Q8×C73—22no—
119C4⋊Q8×C73C2×C414yes—
120C2×C4⋊C4×C73—21no—
121C2×C4⋊C4×C73—21no—
122C2×C4⋊C4×C73—21no—
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C4×C8×C73—22no—
129C23×D73C2×D411yescharacteristic
130C2×Dic146—24no—
131C2×Dic146—81no—
132C2×Dic146—81no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73C2×D411yescharacteristic
138C22×Dic73C2×D411yescharacteristic
139C22×Dic73C2×D411yescharacteristic
140C2×C4×D73—21no—
141C2×C4×D73—21no—
142C2×C4×D73—21no—
143C2×C4×D73—21no—
144C2×C4×D73—24no—
145C2×C4×D73—81no—
146C2×C4×D73—81no—
147C2×C4×D73C22×C412yes—
148C2×C4×D73C2×D412yes—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73—24no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73C22×C412yes—
163C4⋊Dic73C22×C412yes—
164#11924007—24no—
165#11924007—24no—
166#11924007—24no—
167#11924007—24no—
168#11924007—24no—
169#11924007C22⋊C414yes—
170#11924007C22⋊C414yes—
171#11924005—24no—
172#11924005—81no—
173#11924005—81no—
174#11924005C22⋊C414yes—
175#11924005C22⋊C414yes—
176C4×Dic73—24no—
177C4×Dic73—81no—
178C4×Dic73—81no—
179C4×Dic73C22×C412yes—
180C4×Dic73C2×D412yes—
181C2×Q8×C73—24no—
182C2×Q8×C73—81no—
183C2×Q8×C73—81no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73C2411yescharacteristic
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C4⋊C4×C73—24no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—81no—
205C4⋊C4×C73—81no—
206C4⋊C4×C73C22×C412yes—
207C4⋊C4×C73C22×C412yes—
208C42×C73C22×C412yes—
209C42×C73C2×D412yes—
210C23×C73C22×D411yescharacteristic
211C22×D73—21no—
212C22×D73—21no—
213C22×D73—21no—
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—21no—
217C22×D73C2×C22⋊C412yes—
218Q8×C73—84no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—22no—
224C2×C4×C73—22no—
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×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73C2×C22⋊C412yes—
236C2×C4×C73C2×C22⋊C412yes—
237C2×C4×C73C23×C411yescharacteristic
238C2×C4×C73C22×D411yescharacteristic
239C2×C4×C732−1+411yescharacteristic
240C2×C4×C732−1+411yescharacteristic
241C2×C4×C732−1+411yescharacteristic
242C2×C4×C732−1+411yescharacteristic
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—22no—
250C2×Dic73—22no—
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×Dic73—41no—
261C2×Dic73C2×C22⋊C412yes—
262C2×Dic73C2×C22⋊C412yes—
263C2×Dic73C2×C22⋊C412yes—
264C4×D73—22no—
265C4×D73—22no—
266C4×D73—22no—
267C4×D73—22no—
268C4×D73—84no—
269Dic146—84no—
270C8×C73—41no—
271C8×C73—41no—
272#10596831—41no—
273#10596831—41no—
274C22×C73C22×C22⋊C411yescharacteristic
275C22×C73#53611yescharacteristic
276C22×C73#53611yescharacteristic
277C22×C73#57611yescharacteristic
278C22×C73#57711yescharacteristic
279C22×C73#57711yescharacteristic
280C22×C73#57811yescharacteristic
281C2×D73—22no—
282C2×D73—22no—
283C2×D73—22no—
284C2×D73—41no—
285C2×D73—41no—
286C2×D73—41no—
287C2×D73—41no—
288C4×C73—22no—
289C4×C73—22no—
290C4×C73—42no—
291C4×C73—42no—
292C4×C73—81no—
293C4×C73—81no—
294C4×C73#51911yescharacteristic
295C4×C73#51911yescharacteristic
296C4×C73#53611yescharacteristic
297C4×C73#53611yescharacteristic
298Dic73—22no—
299Dic73—22no—
300Dic73—22no—
301Dic73—42no—
302Dic73—42no—
303Dic73—81no—
304Dic73—81no—
305#21843—731nomaximal, Sylow
306C2×C73#231011yescharacteristic
307C2×C73#289711yescharacteristic
308C2×C73#289811yescharacteristic
309C2×C73#324111yescharacteristic
310C2×C73#324211yescharacteristic
311C2×C73#324311yescharacteristic
312C2×C73#324411yescharacteristic
313D73—42no—
314C2×#544—731no—
315C2×#433—731no—
316#2314—731no—
317#1993—731no—
318#1992—731no—
319#1991—731no—
320#1990D7311yescharacteristic, complemented
321#1989—731no—
322#1989—731no—
323#1988—731no—
324#1987—731no—
325#1825—731no—
326#1825—731no—
327#1824—731no—
328#1823—731no—
329C73#2184311yescharacteristic, complemented, Sylow
330#544—738no—
331#544—1464no—
332C2×C4⋊Q8—731no—
333C2×C4⋊Q8—1461no—
334C2×C4⋊Q8C2×D7311yescharacteristic
335C2×#125—731no—
336C2×#125—731no—
337C2×#125—1461no—
338C2×C22⋊Q8—1461no—
339C2×C22⋊Q8—1461no—
340C2×#117—731no—
341C2×#117—731no—
342C22×C4⋊C4—731no—
343#433—1464no—
344C2×C4⋊C8—731no—
345C2×C4⋊C8—731no—
346C2×C22⋊C8—731no—
347C2×C22⋊C8—731no—
348C2×#97—731no—
349C2×C4×C8C2×D7311yescharacteristic
350#388—1461no—
351#388—1461no—
352#387—1461no—
353#387—1461no—
354#384C2×D7311yescharacteristic
355#382—731no—
356#380—731no—
357#380—731no—
358C4×C4⋊C4—731no—
359C4×C4⋊C4—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#340—731no—
369#340—731no—
370#340—731no—
371#340—731no—
372#340C2×D7311yescharacteristic
373#340C2×D7311yescharacteristic
374#340C2×D7311yescharacteristic
375#340C2×D7311yescharacteristic
376C22×Q8—21no—
377C22×Q8—1461no—
378C23×C4—731no—
379C23×C4—1461no—
380C22×C8—731no—
381C22×C8—731no—
382C22×C8C22×D7311yescharacteristic
383C22×C8C22×D7311yescharacteristic
384C4⋊Q8—22no—
385C4⋊Q8—734no—
386C4⋊Q8—1462no—
387C4⋊Q8—1468no—
388C4⋊Q8C4×D7314yes—
389#125—734no—
390#125—734no—
391#125—1462no—
392#125—1468no—
393#125—1462no—
394C22⋊Q8—1468no—
395C22⋊Q8—1468no—
396#117—734no—
397#117—734no—
398#117—734no—
399#117—1462no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4—731no—
405C2×C4⋊C4—731no—
406C2×C4⋊C4—731no—
407C2×C4⋊C4—734no—
408C2×C4⋊C4—731no—
409C2×C4⋊C4—731no—
410C2×C4⋊C4—1462no—
411C2×C4⋊C4—1461no—
412C2×C4⋊C4—1461no—
413C2×C4⋊C4—1461no—
414C2×C4⋊C4—1461no—
415C2×C4⋊C4—1461no—
416C2×C4⋊C4—1461no—
417C2×C4⋊C4C22×D7311yescharacteristic
418C2×C4⋊C4C22×D7311yescharacteristic
419C2×C4⋊C4C22×D7311yescharacteristic
420C2×C4⋊C4C22×D7311yescharacteristic
421C2×C22⋊C4—731no—
422C2×C22⋊C4—731no—
423C2×C22⋊C4—1461no—
424C2×C22⋊C4—1461no—
425C2×C22⋊C4—1461no—
426C2×C42—731no—
427C2×C42—1461no—
428C2×C42—1461no—
429C2×C42—1461no—
430C2×C42C22×D7311yescharacteristic
431C4⋊C8—1462no—
432C4⋊C8—1462no—
433C22⋊C8—1462no—
434C22⋊C8—1462no—
435#97—1462no—
436C4×C8—22no—
437#95—1461no—
438#95—1461no—
439#95—1461no—
440#95—1461no—
441#95—1461no—
442#95—1461no—
443C24—731no—
444C2×Q8—24no—
445C2×Q8—81no—
446C2×Q8—81no—
447C2×Q8—5841no—
448C2×Q8—5841no—
449C2×Q8—1464no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—5841no—
455C22×C4—5841no—
456C22×C4—731no—
457C22×C4—731no—
458C22×C4—731no—
459C22×C4—732no—
460C22×C4—732no—
461C22×C4—1464no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4—1461no—
465C22×C4—1461no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1461no—
469C22×C4—1461no—
470C22×C4D4×D7311yescharacteristic
471C22×C4D4×D7311yescharacteristic
472C22×C4C23×D7311yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—734no—
495C4⋊C4—734no—
496C4⋊C4—732no—
497C4⋊C4—732no—
498C4⋊C4—1464no—
499C4⋊C4—1464no—
500C4⋊C4—1464no—
501C4⋊C4—1464no—
502C4⋊C4—1461no—
503C4⋊C4—1461no—
504C4⋊C4—1461no—
505C4⋊C4—1461no—
506C4⋊C4—1464no—
507C4⋊C4—1464no—
508C4⋊C4—1461no—
509C4⋊C4—1461no—
510C4⋊C4C2×C4×D7312yes—
511C4⋊C4C2×C4×D7312yes—
512C22⋊C4—5841no—
513C22⋊C4—5841no—
514C22⋊C4—734no—
515C22⋊C4—734no—
516C22⋊C4—1464no—
517C42—5841no—
518C42—5841no—
519C42—732no—
520C42—732no—
521C42—1464no—
522C42C2×C4×D7312yes—
523C42D4×D7312yes—
524C23—732no—
525C23—1461no—
526C23—1461no—
527C23—1461no—
528C23—1461no—
529C23—1461no—
530C23—1461no—
531C23C2×D4×D7311yescharacteristic
532Q8—84no—
533Q8—5844no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—2921no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—2921no—
555C2×C4—2921no—
556C2×C4—2921no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—5844no—
561C2×C4—732no—
562C2×C4—732no—
563C2×C4—732no—
564C2×C4—1462no—
565C2×C4—1462no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4—1462no—
573C2×C4—1462no—
574C2×C4—1462no—
575C2×C4—1462no—
576C2×C4C22⋊C4×D7312yes—
577C2×C4C22⋊C4×D7312yes—
578C2×C4C22×C4×D7311yescharacteristic
579C2×C4C2×D4×D7311yescharacteristic
580C2×C4#1455663811yescharacteristic
581C2×C4#1455663811yescharacteristic
582C2×C4#1455663911yescharacteristic
583C2×C4#1455663911yescharacteristic
584C8—41no—
585C8—41no—
586C8—2921no—
587C8—2921no—
588C22—2921no—
589C22—2921no—
590C22—2921no—
591C22—2921no—
592C22—1462no—
593C22—1462no—
594C22—1462no—
595C22C2×C22⋊C4×D7311yescharacteristic
596C22#1798915711yescharacteristic
597C22#1798916211yescharacteristic
598C22#1798938811yescharacteristic
599C22#1798939311yescharacteristic
600C22#1798939311yescharacteristic
601C22#1798940011yescharacteristic
602C4—22no—
603C4—22no—
604C4—42no—
605C4—42no—
606C4—81no—
607C4—81no—
608C4—2922no—
609C4—2922no—
610C4—5841no—
611C4—5841no—
612C4—1462no—
613C4—1462no—
614C4—1462no—
615C4#1798906311yescharacteristic
616C4#1798906311yescharacteristic
617C4#1798916011yescharacteristic
618C4#1798916011yescharacteristic
619C2—2922no—
620C2#2261251411yescharacteristic
621C2#2261845211yescharacteristic
622C2#2261845911yescharacteristic
623C2#2262117711yescharacteristic
624C2#2262119211yescharacteristic
625C2#2262121711yescharacteristic
626C2#2262123211yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1990C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1990D73
hypocenterC73#21843
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #22610905C2semidirect
5. #22610899C2semidirect
6. #22610896C2semidirect
7. #22610887C2semidirect
8. #22610885C2semidirect
9. #22610881C2semidirect
10. #22610877C2semidirect
15. C73×#1990C2semidirect
17. #17989214C4semidirect
320. #1990D73semidirect
329. C73#21843semidirect

Maximal subgroups

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

subgroupindex
C2×#179892142
C2×#179886462
#226125392
#226109052
#226108992
#226108962
#226108872
#226108852
#226108812
#226108772
#226100252
#226100242
#226100202
#226100162
C73×#19902
#2184373