Finite Group Databasebeta

← #33022755

Subgroups — #33022755

Order 18688.

1494 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988520C212yesmaximal
2C2×#17988517C211yesmaximal, characteristic
3C2×#17988482C212yesmaximal
4C2×#17988456C211yesmaximal, characteristic
5C2×C4⋊C4×Dic73C211yesmaximal, characteristic
6#22608200C211yesmaximal, characteristic
7#22608199C211yesmaximal, characteristic
8#22608197C212yesmaximal
9#22608159C212yesmaximal
10#22608159C211yesmaximal, characteristic
11C2×#398×C73C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×#11924007C2212yes—
15C22×#11924007C2212yes—
16C22×#11924007C2212yes—
17C22×#11924007C2212yes—
18C22×C4×Dic73C2211yescharacteristic
19C22×C4×Dic73C2211yescharacteristic
20C22×C4×Dic73C2211yescharacteristic
21#17988520—28no—
22#17988517—24no—
23#17988482—28no—
24#17988456—24no—
25C4⋊C4×Dic73—24no—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2211yescharacteristic
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C22×C4⋊C4×C73C2211yescharacteristic
36C22×C4⋊C4×C73C2212yes—
37C22×C4⋊C4×C73C2211yescharacteristic
38#398×C73—24no—
39C2×#95×C73C2212yes—
40C2×#95×C73C2211yescharacteristic
41C23×Dic73C2312yes—
42C23×Dic73C2311yescharacteristic
43C23×Dic73C2311yescharacteristic
44C23×Dic73C2312yes—
45C23×Dic73C2311yescharacteristic
46C23×Dic73C2311yescharacteristic
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—22no—
51C2×C4⋊Dic73—22no—
52C2×C4⋊Dic73D414yes—
53C2×#11924007—24no—
54C2×#11924007—24no—
55C2×#11924007—24no—
56C2×#11924007—24no—
57C2×#11924007—24no—
58C2×#11924007—24no—
59C2×#11924007—24no—
60C2×#11924007—24no—
61C2×#11924007—24no—
62C2×#11924007—24no—
63C2×#11924007—24no—
64C2×#11924007Q818yes—
65C2×C4×Dic73—22no—
66C2×C4×Dic73—22no—
67C2×C4×Dic73—24no—
68C2×C4×Dic73—22no—
69C2×C4×Dic73—24no—
70C2×C4×Dic73D414yes—
71C2×C4×Dic73D414yes—
72#14556498—22no—
73#14556498—24no—
74#14556498—24no—
75#14556498—24no—
76#14556498—24no—
77#14556498—24no—
78#14556498—22no—
79#14556498—24no—
80#14556498—22no—
81C23×C4×C73C2312yes—
82C23×C4×C73C2311yescharacteristic
83C23×C4×C73C2312yes—
84C23×C4×C73C2311yescharacteristic
85C23×C4×C73C2311yescharacteristic
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—24no—
90C2×C4⋊C4×C73—22no—
91C2×C4⋊C4×C73—24no—
92C2×C4⋊C4×C73—24no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73D414yes—
95#95×C73—22no—
96#95×C73—24no—
97C22×Dic73—22no—
98C22×Dic73—22no—
99C22×Dic73—21no—
100C22×Dic73—22no—
101C22×Dic73—22no—
102C22×Dic73—21no—
103C22×Dic73—22no—
104C22×Dic73—21no—
105C22×Dic73—22no—
106C22×Dic73—22no—
107C22×Dic73—21no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73—22no—
120C22×Dic73C2×D412yes—
121C22×Dic73C2×D412yes—
122C22×Dic73C2×D412yes—
123C22×Dic73C2×D412yes—
124C22×Dic73C2×D412yes—
125C22×Dic73C2×D412yes—
126C22×Dic73C2×Q814yes—
127C22×Dic73C2×Q814yes—
128C22×Dic73#4112yes—
129C22×Dic73#4112yes—
130C22×Dic73#4114yes—
131C4⋊Dic73—28no—
132C4⋊Dic73—44no—
133#11924007—216no—
134#11924007—48no—
135#11924007—48no—
136#11924007—48no—
137C4×Dic73—28no—
138C4×Dic73—28no—
139C4×Dic73—44no—
140C24×C73C2411yescharacteristic
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—21no—
144C22×C4×C73—22no—
145C22×C4×C73—21no—
146C22×C4×C73—22no—
147C22×C4×C73—22no—
148C22×C4×C73—22no—
149C22×C4×C73—21no—
150C22×C4×C73—22no—
151C22×C4×C73—21no—
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×C73—22no—
163C22×C4×C73—22no—
164C22×C4×C73C2×D412yes—
165C22×C4×C73C2×D412yes—
166C22×C4×C73C2×D412yes—
167C22×C4×C73C2×D412yes—
168C22×C4×C73C2×D412yes—
169C22×C4×C73C2×D412yes—
170C22×C4×C73C2×Q814yes—
171C22×C4×C73#4112yes—
172C4⋊C4×C73—28no—
173C4⋊C4×C73—44no—
174C4⋊C4×C73—48no—
175C23×C73C22×D411yescharacteristic
176C23×C73C22×D411yescharacteristic
177C23×C73C22×D411yescharacteristic
178C23×C73C22×D411yescharacteristic
179C23×C73C22×Q812yes—
180C23×C73C2×#4111yescharacteristic
181C23×C73C2×#4111yescharacteristic
182C23×C73C2×#4112yes—
183C23×C73C2×#4111yescharacteristic
184C23×C732−1+412yes—
185C23×C732−1+412yes—
186C2×C4×C73—22no—
187C2×C4×C73—22no—
188C2×C4×C73—22no—
189C2×C4×C73—22no—
190C2×C4×C73—22no—
191C2×C4×C73—22no—
192C2×C4×C73—22no—
193C2×C4×C73—22no—
194C2×C4×C73—24no—
195C2×C4×C73—24no—
196C2×C4×C73—22no—
197C2×C4×C73—24no—
198C2×C4×C73—24no—
199C2×C4×C73—24no—
200C2×C4×C73—24no—
201C2×C4×C73—41no—
202C2×C4×C73—42no—
203C2×C4×C73—41no—
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×C73—42no—
212C2×C4×C73—42no—
213C2×C4×C73—42no—
214C2×C4×C73—42no—
215C2×C4×C73#12114yes—
216C2×C4×C73#12714yes—
217C2×Dic73—22no—
218C2×Dic73—22no—
219C2×Dic73—24no—
220C2×Dic73—24no—
221C2×Dic73—22no—
222C2×Dic73—22no—
223C2×Dic73—24no—
224C2×Dic73—24no—
225C2×Dic73—24no—
226C2×Dic73—24no—
227C2×Dic73—24no—
228C2×Dic73—41no—
229C2×Dic73—42no—
230C2×Dic73—41no—
231C2×Dic73—42no—
232C2×Dic73—41no—
233C2×Dic73—41no—
234C2×Dic73—42no—
235C2×Dic73—42no—
236C2×Dic73—42no—
237C2×Dic73—42no—
238C2×Dic73—42no—
239C2×Dic73—42no—
240C2×Dic73—42no—
241C2×Dic73—42no—
242C2×Dic73—42no—
243C2×Dic73—42no—
244C2×Dic73—42no—
245C2×Dic73#12114yes—
246C2×Dic73#12114yes—
247C2×Dic73C22⋊Q818yes—
248C2×Dic73#12314yes—
249C2×Dic73#12518yes—
250C2×Dic73C4⋊Q814yes—
251C22×C73C2×#12111yescharacteristic
252C22×C73C2×#12111yescharacteristic
253C22×C73C2×#12111yescharacteristic
254C22×C73C2×C22⋊Q812yes—
255C22×C73C2×#12311yescharacteristic
256C22×C73C2×#12512yes—
257C22×C73C2×#12711yescharacteristic
258C22×C73C2×C4⋊Q811yescharacteristic
259C22×C73#53211yescharacteristic
260C22×C73#53211yescharacteristic
261C22×C73#53211yescharacteristic
262C22×C73#53611yescharacteristic
263C22×C73#53612yes—
264C22×C73#53611yescharacteristic
265C22×C73#54112yes—
266C22×C73#54712yes—
267C22×C73#54712yes—
268C22×C73D4×Q812yes—
269C22×C73D4×Q812yes—
270C22×C73#55212yes—
271C22×C73#55212yes—
272C22×C73#55712yes—
273C22×C73#55712yes—
274C4×C73—24no—
275C4×C73—24no—
276C4×C73—42no—
277C4×C73—44no—
278C4×C73—82no—
279Dic73—24no—
280Dic73—42no—
281Dic73—42no—
282Dic73—44no—
283Dic73—82no—
284Dic73#39818yescomplemented
285#15151—731nomaximal, Sylow
286C2×C73C2×#39811yescharacteristic
287C2×C73#248611yescharacteristic
288C2×C73#248611yescharacteristic
289C2×C73#250612yes—
290C2×C73#250612yes—
291C2×C73#254212yes—
292C2×C73#254611yescharacteristic
293C2×C73#254611yescharacteristic
294C2×C73#256512yes—
295C2×C73#262111yescharacteristic
296C2×C73#285611yescharacteristic
297C2×#398—731no—
298C2×#398—732no—
299C2×#398D7311yescharacteristic
300C2×#389—732no—
301C2×#384—731no—
302C2×C4×C4⋊C4—731no—
303#1445—732no—
304#1445—731no—
305#1445—731no—
306C4⋊#95—731no—
307C4⋊#95—732no—
308C73#1515111yescharacteristic, complemented, Sylow
309C22×C4⋊C4—731no—
310C22×C4⋊C4—732no—
311C22×C4⋊C4—732no—
312C22×C4⋊C4—732no—
313C22×C4⋊C4—731no—
314C22×C4⋊C4—732no—
315C22×C4⋊C4C2×D7312yes—
316C22×C4⋊C4C2×D7311yescharacteristic
317C22×C4⋊C4C2×D7311yescharacteristic
318C22×C42—731no—
319C22×C42—731no—
320C22×C42—731no—
321#398—24no—
322#398—1468no—
323#398—1464no—
324#389—1468no—
325#384—1464no—
326C4×C4⋊C4—1464no—
327C2×#95—732no—
328C2×#95—732no—
329C2×#95—732no—
330C2×#95—731no—
331C2×#95—732no—
332C2×#95—731no—
333C2×#95—731no—
334C2×#95—732no—
335C2×#95—732no—
336C2×#95C2×D7312yes—
337C2×#95C2×D7311yescharacteristic
338C23×C4—731no—
339C23×C4—731no—
340C23×C4—732no—
341C23×C4—731no—
342C23×C4—731no—
343C23×C4—732no—
344C23×C4C22×D7312yes—
345C23×C4C22×D7311yescharacteristic
346C23×C4C22×D7312yes—
347C23×C4C22×D7311yescharacteristic
348C23×C4C22×D7311yescharacteristic
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—734no—
358C2×C4⋊C4—738no—
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—1462no—
366C2×C4⋊C4—1464no—
367C2×C4⋊C4—1464no—
368C2×C4⋊C4—1464no—
369C2×C4⋊C4—1462no—
370C2×C4⋊C4—1462no—
371C2×C4⋊C4—1462no—
372C2×C4⋊C4—1464no—
373C2×C4⋊C4—1464no—
374C2×C4⋊C4—1462no—
375C2×C4⋊C4C22⋊D7314yes—
376C2×C42—734no—
377C2×C42—734no—
378C2×C42—1462no—
379C2×C42—1464no—
380C2×C42—1462no—
381C2×C42—1464no—
382C2×C42—1462no—
383#95—22no—
384#95—24no—
385#95—1462no—
386#95—1464no—
387#95—1464no—
388#95—1464no—
389#95—1464no—
390#95—1464no—
391#95—1462no—
392#95—1464no—
393#95—1462no—
394C24C23×D7311yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—732no—
419C22×C4—732no—
420C22×C4—734no—
421C22×C4—734no—
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—1461no—
437C22×C4—1462no—
438C22×C4—1461no—
439C22×C4—1462no—
440C22×C4—1462no—
441C22×C4—1461no—
442C22×C4—1462no—
443C22×C4—1462no—
444C22×C4—1461no—
445C22×C4—1462no—
446C22×C4—1462no—
447C22×C4—1462no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4D4×D7312yes—
453C22×C4D4×D7312yes—
454C22×C4D4×D7312yes—
455C22×C4C2×C22⋊D7312yes—
456C22×C4C2×C22⋊D7312yes—
457C22×C4C2×C22⋊D7312yes—
458C22×C4Q8×D7314yes—
459C22×C4#1192402712yes—
460C4⋊C4—28no—
461C4⋊C4—44no—
462C4⋊C4—48no—
463C4⋊C4—2928no—
464C4⋊C4—2928no—
465C4⋊C4—2924no—
466C4⋊C4—2928no—
467C4⋊C4—14616no—
468C4⋊C4—1468no—
469C42—2924no—
470C42—1468no—
471C42—1468no—
472C23C2×D4×D7311yescharacteristic
473C23C2×D4×D7311yescharacteristic
474C23C2×D4×D7311yescharacteristic
475C23C22×C22⋊D7311yescharacteristic
476C23C2×Q8×D7312yes—
477C23#41×D7311yescharacteristic
478C23#41×D7311yescharacteristic
479C23#41×D7312yes—
480C23C2×#1192402711yescharacteristic
481C23#1455663812yes—
482C23#1455663912yes—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—2922no—
513C2×C4—2921no—
514C2×C4—2922no—
515C2×C4—2921no—
516C2×C4—2921no—
517C2×C4—2922no—
518C2×C4—2922no—
519C2×C4—2922no—
520C2×C4—2922no—
521C2×C4—2921no—
522C2×C4—2922no—
523C2×C4—2922no—
524C2×C4—2922no—
525C2×C4—2922no—
526C2×C4—2922no—
527C2×C4—2922no—
528C2×C4—2922no—
529C2×C4—734no—
530C2×C4—734no—
531C2×C4—738no—
532C2×C4—734no—
533C2×C4—738no—
534C2×C4—734no—
535C2×C4—1464no—
536C2×C4—1464no—
537C2×C4—1464no—
538C2×C4—1464no—
539C2×C4—1462no—
540C2×C4—1462no—
541C2×C4—1464no—
542C2×C4—1462no—
543C2×C4—1464no—
544C2×C4—1464no—
545C2×C4—1462no—
546C2×C4#1455656314yes—
547C2×C4#1455658714yes—
548C22#121×D7311yescharacteristic
549C22#121×D7311yescharacteristic
550C22C2×#1455656311yescharacteristic
551C22C22⋊Q8×D7312yes—
552C22#123×D7311yescharacteristic
553C22#125×D7312yes—
554C22C2×#1455658711yescharacteristic
555C22C4⋊Q8×D7311yescharacteristic
556C22#1798913211yescharacteristic
557C22#1798913211yescharacteristic
558C22#1798913311yescharacteristic
559C22#1798915911yescharacteristic
560C22#1798916012yes—
561C22#1798916211yescharacteristic
562C22#1798919612yes—
563C22#1798923612yes—
564C22#1798923912yes—
565C22#1798925012yes—
566C22Q8×C22⋊D7312yes—
567C22#1798926912yes—
568C22#1798927412yes—
569C22#1798931212yes—
570C22#1798931412yes—
571C4—24no—
572C4—24no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—2924no—
577C4—2922no—
578C4—2922no—
579C4—5842no—
580C4—738no—
581C4—1464no—
582C2#398×D7311yescharacteristic
583C2#2261423411yescharacteristic
584C2#2261423611yescharacteristic
585C2#2261444012yes—
586C2#2261444612yes—
587C2#2261488112yes—
588C2#2261491511yescharacteristic
589C2#2261491711yescharacteristic
590C2#2261511712yes—
591C2#2261569911yescharacteristic
592C2#2261827411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutator, socle, prime radical, cosocleC24×C73C24
FittingC2×#398×C73C2
hypercenterC2×#398D73
hypocenterC73#15151
LCSG ▷ C24×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
284. Dic73#398semidirect
308. C73#15151semidirect

Maximal subgroups

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

subgroupindex
C2×#179885202
C2×#179885172
C2×#179884822
C2×#179884562
C2×C4⋊C4×Dic732
#226082002
#226081992
#226081972
#226081592
C2×#398×C732
#1515173