Finite Group Databasebeta

← #33008658

Subgroups — #33008658

Order 18688.

1630 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988484C212yesmaximal
2C2×#17988482C212yesmaximal
3C2×#17988451C211yesmaximal, characteristic
4C2×C4×#11924007C211yesmaximal, characteristic
5C2×#17988438C211yesmaximal, characteristic
6#22608195C212yesmaximal
7#22608194C212yesmaximal
8#22608161C211yesmaximal, characteristic
9#22608159C211yesmaximal, characteristic
10#22608159C211yesmaximal, characteristic
11C73×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic73C2212yes—
13C22×#11924007C2212yes—
14C22×#11924007C2212yes—
15C22×#11924007C2212yes—
16C22×#11924007C2212yes—
17C22×#11924007C2211yescharacteristic
18C22×#11924007C2211yescharacteristic
19C22×C4×Dic73C2212yes—
20C22×C4×Dic73C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22#17988484—28no—
23#17988482—28no—
24#17988451—24no—
25C4×#11924007C418yescomplemented
26#17988438—24no—
27C2×#14556498C2211yescharacteristic
28C2×#14556498C2211yescharacteristic
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2211yescharacteristic
35C22×C4⋊C4×C73C2212yes—
36C22×C42×C73C2211yescharacteristic
37C2×#95×C73C2211yescharacteristic
38C2×#95×C73C2211yescharacteristic
39C2×#95×C73C2212yes—
40C23×Dic73C2312yes—
41C23×Dic73C2312yes—
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2311yescharacteristic
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2311yescharacteristic
46C2×C4⋊Dic73—24no—
47C2×C4⋊Dic73—24no—
48C2×C4⋊Dic73—42no—
49C2×#11924007—24no—
50C2×#11924007—24no—
51C2×#11924007—24no—
52C2×#11924007—24no—
53C2×#11924007—24no—
54C2×#11924007—24no—
55C2×#11924007—24no—
56C2×#11924007—24no—
57C2×#11924007—24no—
58C2×#11924007—24no—
59C2×#11924007—42no—
60C2×#11924007—42no—
61C2×#11924007C2×C414yes—
62C2×#11924007C2×C414yes—
63C2×#11924007D414yes—
64C2×#11924007D414yes—
65C2×#11924007Q814yes—
66C2×#11924007Q814yes—
67C2×C4×Dic73—24no—
68C2×C4×Dic73—24no—
69C2×C4×Dic73—24no—
70C2×C4×Dic73—42no—
71C2×C4×Dic73C2×C414yes—
72C2×C4×Dic73C2×C414yes—
73C2×C4×Dic73D414yes—
74C2×C4×Dic73Q814yes—
75#14556498—24no—
76#14556498—24no—
77#14556498—24no—
78#14556498—22no—
79#14556498—22no—
80#14556498—24no—
81#14556498C2×C414yes—
82#14556498C2×C414yes—
83C23×C4×C73C2312yes—
84C23×C4×C73C2312yes—
85C23×C4×C73C2311yescharacteristic
86C23×C4×C73C2311yescharacteristic
87C23×C4×C73C2311yescharacteristic
88C2×C4⋊C4×C73—24no—
89C2×C4⋊C4×C73—24no—
90C2×C4⋊C4×C73—42no—
91C2×C42×C73—42no—
92C2×C42×C73C2×C414yes—
93#95×C73—22no—
94#95×C73—22no—
95#95×C73—24no—
96C22×Dic73—22no—
97C22×Dic73—22no—
98C22×Dic73—22no—
99C22×Dic73—22no—
100C22×Dic73—22no—
101C22×Dic73—22no—
102C22×Dic73—22no—
103C22×Dic73—22no—
104C22×Dic73—22no—
105C22×Dic73—22no—
106C22×Dic73—22no—
107C22×Dic73—22no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73C22×C412yes—
116C22×Dic73C22×C412yes—
117C22×Dic73C22×C412yes—
118C22×Dic73C22×C412yes—
119C22×Dic73C2×D412yes—
120C22×Dic73C2×D412yes—
121C22×Dic73C2×D412yes—
122C22×Dic73C2×D412yes—
123C22×Dic73C2×D412yes—
124C22×Dic73C2×D412yes—
125C22×Dic73C2×Q812yes—
126C22×Dic73C2×Q812yes—
127C22×Dic73C2×Q812yes—
128C22×Dic73C2×Q812yes—
129C22×Dic73C2×Q812yes—
130C22×Dic73C2×Q812yes—
131C22×Dic73#4114yes—
132C4⋊Dic73—48no—
133#11924007—216no—
134#11924007—48no—
135#11924007—48no—
136#11924007—48no—
137#11924007C4⋊C4116yescomplemented
138#11924007C4⋊C4116yescomplemented
139C4×Dic73—44no—
140C4×Dic73—48no—
141C4×Dic73C4⋊C4116yescomplemented
142C24×C73C2411yescharacteristic
143C22×C4×C73—22no—
144C22×C4×C73—22no—
145C22×C4×C73—22no—
146C22×C4×C73—22no—
147C22×C4×C73—22no—
148C22×C4×C73—22no—
149C22×C4×C73—22no—
150C22×C4×C73—22no—
151C22×C4×C73—22no—
152C22×C4×C73—22no—
153C22×C4×C73—22no—
154C22×C4×C73—22no—
155C22×C4×C73—22no—
156C22×C4×C73—22no—
157C22×C4×C73—22no—
158C22×C4×C73—22no—
159C22×C4×C73—22no—
160C22×C4×C73—22no—
161C22×C4×C73—22no—
162C22×C4×C73C22×C412yes—
163C22×C4×C73C22×C412yes—
164C22×C4×C73C22×C412yes—
165C22×C4×C73C2×D412yes—
166C22×C4×C73C2×D412yes—
167C22×C4×C73C2×D412yes—
168C22×C4×C73C2×Q812yes—
169C22×C4×C73C2×Q812yes—
170C22×C4×C73C2×Q812yes—
171C22×C4×C73#4114yes—
172C4⋊C4×C73—48no—
173C42×C73—44no—
174C23×C73C23×C411yescharacteristic
175C23×C73C22×D411yescharacteristic
176C23×C73C22×D411yescharacteristic
177C23×C73C22×D411yescharacteristic
178C23×C73C22×Q811yescharacteristic
179C23×C73C22×Q811yescharacteristic
180C23×C73C22×Q811yescharacteristic
181C23×C73C2×#4112yes—
182C23×C73C2×#4112yes—
183C23×C73H(5,𝔽2)12yes—
184C23×C732−1+412yes—
185C2×C4×C73—22no—
186C2×C4×C73—22no—
187C2×C4×C73—22no—
188C2×C4×C73—22no—
189C2×C4×C73—22no—
190C2×C4×C73—22no—
191C2×C4×C73—24no—
192C2×C4×C73—24no—
193C2×C4×C73—24no—
194C2×C4×C73—24no—
195C2×C4×C73—24no—
196C2×C4×C73—24no—
197C2×C4×C73—24no—
198C2×C4×C73—24no—
199C2×C4×C73—24no—
200C2×C4×C73—42no—
201C2×C4×C73—42no—
202C2×C4×C73—42no—
203C2×C4×C73—42no—
204C2×C4×C73—42no—
205C2×C4×C73—42no—
206C2×C4×C73—42no—
207C2×C4×C73—42no—
208C2×C4×C73—42no—
209C2×C4×C73—42no—
210C2×C4×C73—42no—
211C2×C4×C73C2×C4⋊C414yes—
212C2×C4×C73C2×C4⋊C414yes—
213C2×C4×C73C2×C4⋊C414yes—
214C2×Dic73—22no—
215C2×Dic73—22no—
216C2×Dic73—22no—
217C2×Dic73—22no—
218C2×Dic73—22no—
219C2×Dic73—22no—
220C2×Dic73—24no—
221C2×Dic73—24no—
222C2×Dic73—24no—
223C2×Dic73—24no—
224C2×Dic73—24no—
225C2×Dic73—24no—
226C2×Dic73—24no—
227C2×Dic73—24no—
228C2×Dic73—24no—
229C2×Dic73—42no—
230C2×Dic73—42no—
231C2×Dic73—42no—
232C2×Dic73—42no—
233C2×Dic73—42no—
234C2×Dic73—42no—
235C2×Dic73—42no—
236C2×Dic73—42no—
237C2×Dic73—42no—
238C2×Dic73—42no—
239C2×Dic73—42no—
240C2×Dic73C2×C4⋊C414yes—
241C2×Dic73C2×C4⋊C414yes—
242C2×Dic73C2×C4⋊C414yes—
243C2×Dic73C2×C4⋊C414yes—
244C2×Dic73C2×C4⋊C414yes—
245C2×Dic73C2×C4⋊C414yes—
246C2×Dic73#12714yes—
247C2×Dic73C4⋊Q814yes—
248C2×Dic73C4⋊Q814yes—
249C2×Dic73C4⋊Q814yes—
250C22×C73C22×C4⋊C411yescharacteristic
251C22×C73C22×C4⋊C411yescharacteristic
252C22×C73C22×C4⋊C411yescharacteristic
253C22×C73C4×#4111yescharacteristic
254C22×C73C4×#4111yescharacteristic
255C22×C73#51811yescharacteristic
256C22×C73#51911yescharacteristic
257C22×C73#52512yes—
258C22×C73C2×#12711yescharacteristic
259C22×C73C2×C4⋊Q811yescharacteristic
260C22×C73C2×C4⋊Q811yescharacteristic
261C22×C73C2×C4⋊Q811yescharacteristic
262C22×C73#53312yes—
263C22×C73#53712yes—
264C22×C73#54412yes—
265C22×C73#54612yes—
266C22×C73#54612yes—
267C22×C73#54812yes—
268C22×C73#54812yes—
269C22×C73#55412yes—
270C22×C73#55412yes—
271C22×C73#55712yes—
272C22×C73#55712yes—
273C4×C73—24no—
274C4×C73—24no—
275C4×C73—24no—
276C4×C73—44no—
277C4×C73—82no—
278Dic73—24no—
279Dic73—24no—
280Dic73—24no—
281Dic73—44no—
282Dic73—82no—
283Dic73#38418yes—
284#13954—731nomaximal, Sylow
285C2×C73C2×#38411yescharacteristic
286C2×C73#229611yescharacteristic
287C2×C73#231611yescharacteristic
288C2×C73#234911yescharacteristic
289C2×C73#234911yescharacteristic
290C2×C73#235111yescharacteristic
291C2×C73#235111yescharacteristic
292C2×C73#254012yes—
293C2×C73#255012yes—
294C2×C73#255012yes—
295C2×C73#258412yes—
296C2×#389—732no—
297C2×#389—732no—
298C2×#382—731no—
299C2×C4×C4⋊C4—731no—
300C2×C4×C4⋊C4—731no—
301#1444—732no—
302#1444—732no—
303C4⋊#95—731no—
304C4⋊#95—731no—
305C4⋊#95—731no—
306C4⋊#95D7311yescharacteristic
307C73#1395411yescharacteristic, complemented, Sylow
308C22×C4⋊C4—732no—
309C22×C4⋊C4—732no—
310C22×C4⋊C4—732no—
311C22×C4⋊C4—731no—
312C22×C4⋊C4—731no—
313C22×C4⋊C4—732no—
314C22×C4⋊C4—732no—
315C22×C4⋊C4C2×D7312yes—
316C22×C42—731no—
317C22×C42—731no—
318C22×C42—732no—
319C22×C42C2×D7311yescharacteristic
320#389—1468no—
321#389—1468no—
322#382—1464no—
323C4×C4⋊C4—738no—
324C4×C4⋊C4—1464no—
325C2×#95—731no—
326C2×#95—731no—
327C2×#95—731no—
328C2×#95—731no—
329C2×#95—732no—
330C2×#95—732no—
331C2×#95—732no—
332C2×#95—732no—
333C2×#95C2×D7311yescharacteristic
334C2×#95C2×D7311yescharacteristic
335C2×#95C2×D7312yes—
336C23×C4—731no—
337C23×C4—731no—
338C23×C4—731no—
339C23×C4—731no—
340C23×C4—732no—
341C23×C4—732no—
342C23×C4C22×D7312yes—
343C23×C4C22×D7312yes—
344C23×C4C22×D7311yescharacteristic
345C23×C4C22×D7311yescharacteristic
346C23×C4C22×D7311yescharacteristic
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—2922no—
351C2×C4⋊C4—2922no—
352C2×C4⋊C4—2922no—
353C2×C4⋊C4—734no—
354C2×C4⋊C4—734no—
355C2×C4⋊C4—734no—
356C2×C4⋊C4—734no—
357C2×C4⋊C4—734no—
358C2×C4⋊C4—734no—
359C2×C4⋊C4—1464no—
360C2×C4⋊C4—1464no—
361C2×C4⋊C4—1464no—
362C2×C4⋊C4—1464no—
363C2×C4⋊C4—1464no—
364C2×C4⋊C4—1464no—
365C2×C4⋊C4—1464no—
366C2×C4⋊C4—1464no—
367C2×C4⋊C4—1464no—
368C2×C4⋊C4—1464no—
369C2×C4⋊C4—1464no—
370C2×C4⋊C4—1464no—
371C2×C42—42no—
372C2×C42—2922no—
373C2×C42—734no—
374C2×C42—734no—
375C2×C42—734no—
376C2×C42—734no—
377C2×C42—1464no—
378C2×C42—1464no—
379C2×C42—1464no—
380C2×C42C4×D7314yes—
381#95—22no—
382#95—22no—
383#95—24no—
384#95—734no—
385#95—734no—
386#95—1464no—
387#95—1464no—
388#95—1464no—
389#95—1462no—
390#95—1462no—
391#95—1464no—
392C24C23×D7311yescharacteristic
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—732no—
413C22×C4—732no—
414C22×C4—732no—
415C22×C4—732no—
416C22×C4—732no—
417C22×C4—732no—
418C22×C4—732no—
419C22×C4—732no—
420C22×C4—732no—
421C22×C4—732no—
422C22×C4—732no—
423C22×C4—732no—
424C22×C4—732no—
425C22×C4—732no—
426C22×C4—732no—
427C22×C4—732no—
428C22×C4—734no—
429C22×C4—1462no—
430C22×C4—1462no—
431C22×C4—1462no—
432C22×C4—1462no—
433C22×C4—1462no—
434C22×C4—1462no—
435C22×C4—1462no—
436C22×C4—1462no—
437C22×C4—1462no—
438C22×C4—1462no—
439C22×C4—1462no—
440C22×C4—1462no—
441C22×C4—1462no—
442C22×C4—1462no—
443C22×C4—1462no—
444C22×C4—1462no—
445C22×C4—1462no—
446C22×C4—1462no—
447C22×C4—1462no—
448C22×C4C2×C4×D7312yes—
449C22×C4C2×C4×D7312yes—
450C22×C4C2×C4×D7312yes—
451C22×C4D4×D7312yes—
452C22×C4D4×D7312yes—
453C22×C4D4×D7312yes—
454C22×C4Q8×D7312yes—
455C22×C4Q8×D7312yes—
456C22×C4Q8×D7312yes—
457C22×C4#1192402814yes—
458C4⋊C4—48no—
459C4⋊C4—2928no—
460C4⋊C4—2928no—
461C4⋊C4—2928no—
462C4⋊C4—2928no—
463C4⋊C4—7316no—
464C4⋊C4—7316no—
465C4⋊C4—14616no—
466C42—44no—
467C42—2924no—
468C42—2928no—
469C42—7316no—
470C23C22×C4×D7311yescharacteristic
471C23C2×D4×D7311yescharacteristic
472C23C2×D4×D7311yescharacteristic
473C23C2×D4×D7311yescharacteristic
474C23C2×Q8×D7311yescharacteristic
475C23C2×Q8×D7311yescharacteristic
476C23C2×Q8×D7311yescharacteristic
477C23#41×D7312yes—
478C23C2×#1192402812yes—
479C23#1455663612yes—
480C23#1455663812yes—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—2922no—
508C2×C4—2922no—
509C2×C4—2922no—
510C2×C4—2922no—
511C2×C4—2922no—
512C2×C4—2922no—
513C2×C4—2922no—
514C2×C4—2922no—
515C2×C4—2922no—
516C2×C4—2922no—
517C2×C4—2922no—
518C2×C4—734no—
519C2×C4—734no—
520C2×C4—734no—
521C2×C4—734no—
522C2×C4—734no—
523C2×C4—734no—
524C2×C4—734no—
525C2×C4—734no—
526C2×C4—734no—
527C2×C4—734no—
528C2×C4—1464no—
529C2×C4—1464no—
530C2×C4—1464no—
531C2×C4—1464no—
532C2×C4—1464no—
533C2×C4—1464no—
534C2×C4—1464no—
535C2×C4—1464no—
536C2×C4—1462no—
537C2×C4—1462no—
538C2×C4—1462no—
539C2×C4—1462no—
540C2×C4—1462no—
541C2×C4—1462no—
542C2×C4—1464no—
543C2×C4C4⋊C4×D7314yes—
544C2×C4C4⋊C4×D7314yes—
545C2×C4C4⋊C4×D7314yes—
546C22C2×C4⋊C4×D7311yescharacteristic
547C22C2×C4⋊C4×D7311yescharacteristic
548C22C2×C4⋊C4×D7311yescharacteristic
549C22#1798905511yescharacteristic
550C22C4×#1192402811yescharacteristic
551C22#1798906011yescharacteristic
552C22#1798906411yescharacteristic
553C22#1798909612yes—
554C22#127×D7311yescharacteristic
555C22C4⋊Q8×D7311yescharacteristic
556C22C4⋊Q8×D7311yescharacteristic
557C22C4⋊Q8×D7311yescharacteristic
558C22#1798914112yes—
559C22#1798916412yes—
560C22#1798921612yes—
561C22#1798922612yes—
562C22#1798922712yes—
563C22#1798924512yes—
564C22#1798924612yes—
565C22#1798929112yes—
566C22#1798929212yes—
567C22#1798931412yes—
568C22#1798931512yes—
569C4—24no—
570C4—24no—
571C4—24no—
572C4—44no—
573C4—82no—
574C4—2924no—
575C4—5842no—
576C4—738no—
577C4—1464no—
578C4—1464no—
579C4—1464no—
580C2#384×D7311yescharacteristic
581C2#2261241111yescharacteristic
582C2#2261254811yescharacteristic
583C2#2261283511yescharacteristic
584C2#2261283811yescharacteristic
585C2#2261284811yescharacteristic
586C2#2261285111yescharacteristic
587C2#2261486812yes—
588C2#2261494912yes—
589C2#2261495112yes—
590C2#2261531712yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×C4⋊#95C2
socle, prime radical, cosocleC24×C73C24
hypercenterC4⋊#95D73
hypocenterC73#13954
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
25. C4×#11924007C4semidirect
137. #11924007C4⋊C4semidirect
138. #11924007C4⋊C4semidirect
141. C4×Dic73C4⋊C4semidirect
307. C73#13954semidirect

Maximal subgroups

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

subgroupindex
C2×#179884842
C2×#179884822
C2×#179884512
C2×C4×#119240072
C2×#179884382
#226081952
#226081942
#226081612
#226081592
C73×C4⋊#952
#1395473