Finite Group Databasebeta

← D73⋊#1922 #34021828

Subgroups — D73⋊#1922 #34021828

Order 18688.

854 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D73⋊#424C211yesmaximal, characteristic
2#22626491C211yesmaximal, characteristic
3#22625999C212yesmaximal, complemented
4#22625998C212yesmaximal, complemented
5#22625997C212yesmaximal, complemented
6#22625996C212yesmaximal, complemented
7#22625623C211yesmaximal, characteristic
8#22625607C211yesmaximal, characteristic
9#22625607C211yesmaximal, characteristic
10C2×#17989452C211yesmaximal, characteristic
11#427×D73C211yesmaximal, characteristic
12C2×D73⋊M16C2211yescharacteristic
13C2×D73⋊M16C2211yescharacteristic
14C22×#11924036C2211yescharacteristic
15C22×C4×#64408C2211yescharacteristic
16#17989594C2212yes—
17#17989594C2212yes—
18#17989593—22no—
19#17989588—21no—
20#17989588—21no—
21#17989552C2212yes—
22#17989552C2212yes—
23#17989551—22no—
24#17989546—21no—
25C4×#11924036—21no—
26#17989463C2212yes—
27#17989463C2212yes—
28#17989457C2212yes—
29#17989457C2212yes—
30#17989457C2212yes—
31#17989457C2212yes—
32#17989452C2212yes—
33#17989452C2212yes—
34C22×C8×D73C2211yescharacteristic
35#117×D73C2211yescharacteristic
36#117×D73C2211yescharacteristic
37#17988625C411yescharacteristic, complemented
38#17988624C2211yescharacteristic
39#17988624C2211yescharacteristic
40#17988623C411yescharacteristic, complemented
41#17988623C411yescharacteristic, complemented
42#17988622C2211yescharacteristic
43#17988622C2211yescharacteristic
44#107×D73C411yescharacteristic, complemented
45#107×D73C411yescharacteristic, complemented
46#106×D73C411yescharacteristic, complemented
47#106×D73C411yescharacteristic, complemented
48#427×C73C411yescharacteristic, complemented
49C23×#64408—21no—
50C2×#11924038C2312yes—
51C2×#11924038C2312yes—
52D73⋊M16—22no—
53D73⋊M16—22no—
54D73⋊M16—22no—
55D73⋊M16Q814yes—
56C2×#11924037—21no—
57C2×#11924037—21no—
58C2×#11924036—21no—
59C2×#11924036—21no—
60C2×#11924036—22no—
61C2×#11924036—22no—
62C2×#11924036D411yescharacteristic
63C2×#11924036D411yescharacteristic
64C2×#11924036C2312yes—
65C22×#10596833D412yes—
66C2×C4×#64408—22no—
67C2×C4×#64408—22no—
68C2×C4×#64408—21no—
69C2×C4×#64408C2312yes—
70#14556658—22no—
71#14556658—22no—
72C4⋊#10596833—22no—
73C4⋊#10596833—22no—
74#14556646—22no—
75#14556646—22no—
76C4×#10596833—22no—
77C4×#10596833—22no—
78C22×C4×D73C2311yescharacteristic
79C22×#10596831C2×C411yescharacteristic
80C2×C8×D73—22no—
81C2×C8×D73—22no—
82C2×C8×D73C2×C411yescharacteristic
83C2×C8×D73C2×C411yescharacteristic
84C2×C8×D73C2311yescharacteristic
85C2×C8×D73C2311yescharacteristic
86#14556550C2×C411yescharacteristic
87#14556550C2×C411yescharacteristic
88#14556549C2311yescharacteristic
89#14556549C2311yescharacteristic
90#14556549C2311yescharacteristic
91#14556549C2311yescharacteristic
92#14556548—21no—
93#14556548—21no—
94#14556547—21no—
95#14556547—21no—
96C4⋊C4×D73C2×C411yescharacteristic
97C4⋊C4×D73C2×C411yescharacteristic
98C4⋊C4×D73C2×C411yescharacteristic
99C4⋊C4×D73C2×C411yescharacteristic
100C22⋊C4×D73—21no—
101C22⋊C4×D73—21no—
102C42×D73—21no—
103C42×D73—21no—
104#14556525C2×C411yescharacteristic, complemented
105#14556525C2×C411yescharacteristic, complemented
106#14556524C2×C411yescharacteristic, complemented
107#14556524C2×C411yescharacteristic, complemented
108#14556524C2×C411yescharacteristic, complemented
109#14556524C2×C411yescharacteristic, complemented
110#14556523C2×C411yescharacteristic, complemented
111#14556523C2×C411yescharacteristic, complemented
112#14556522C2×C411yescharacteristic, complemented
113#14556522C2×C411yescharacteristic, complemented
114#14556522C2×C411yescharacteristic, complemented
115#14556522C2×C411yescharacteristic, complemented
116C22×C8×C73C2×C411yescharacteristic
117#117×C73C2×C411yescharacteristic
118#117×C73C2×C411yescharacteristic
119#107×C73C2×C411yescharacteristic, complemented
120#107×C73C2×C411yescharacteristic, complemented
121#106×C73C2×C411yescharacteristic, complemented
122#106×C73C2×C411yescharacteristic, complemented
123C22×#64408—24no—
124C22×#64408—22no—
125C22×#64408—42no—
126C22×#64408—42no—
127#11924038—22no—
128#11924038—22no—
129#11924038—22no—
130#11924038C2×Q814yes—
131#11924037—24no—
132#11924037—42no—
133#11924036—24no—
134#11924036—22no—
135#11924036—22no—
136#11924036—22no—
137#11924036—22no—
138#11924036—42no—
139C2×#10596833—24no—
140C2×#10596833—22no—
141C2×#10596833—22no—
142C2×#10596833C2×D412yes—
143C2×#10596833C2×D412yes—
144C4×#64408—22no—
145C4×#64408—22no—
146C4×#64408—42no—
147C23×D73#4111yescharacteristic
148C22×Dic73C2×D411yescharacteristic
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73C22×C411yescharacteristic
154C2×C4×D73C2×D411yescharacteristic
155C2×C4×D73C2×Q812yes—
156C2×C4×D73#4112yes—
157C2×C4×D73#4112yes—
158C2×C4×D73#4112yes—
159C2×C4×D73#4111yescharacteristic
160C2×C4×D73C2411yescharacteristic
161C2×#10596831—22no—
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C8×D73—22no—
165C8×D73—22no—
166C8×D73—21no—
167C8×D73—21no—
168C8×D73—21no—
169C8×D73—21no—
170C4⋊Dic73C22×C411yescharacteristic
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174#11924007—21no—
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178C22⋊Dic73—21no—
179C22⋊Dic73—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183#11924005—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C22×C4×C73C22×C411yescharacteristic
191C2×C8×C73—22no—
192C2×C8×C73C22×C411yescharacteristic
193C2×C8×C73C22×C411yescharacteristic
194C4⋊C4×C73C22×C411yescharacteristic
195C4⋊C4×C73C22×C411yescharacteristic
196C4⋊C4×C73C22×C411yescharacteristic
197C4⋊C4×C73C22×C411yescharacteristic
198C22⋊C4×C73—21no—
199C22⋊C4×C73—21no—
200C42×C73—21no—
201C42×C73—21no—
202C23×C73C4×D411yescharacteristic
203C22×D73—22no—
204C22×D73—22no—
205C22×D73C4×D411yescharacteristic
206C22×D73#12512yes—
207C22×D73#12612yes—
208C22×D73C2×#4111yescharacteristic
209C2×#64408—24no—
210C2×#64408—42no—
211C2×#64408—48no—
212C2×#64408—42no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73#11712yes—
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×Q812yes—
220C2×C4×C73C23×C411yescharacteristic
221C2×Dic73—21no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73C4×D411yescharacteristic
226C2×Dic73C22⋊Q812yes—
227C2×Dic73#12312yes—
228C2×Dic73C22×D411yescharacteristic
229C4×D73—42no—
230C4×D73—42no—
231C4×D73—42no—
232C4×D73—42no—
233C4×D73#11712yes—
234C4×D73C4×Q812yes—
235C4×D73C22⋊Q812yes—
236C4×D73#12312yes—
237C4×D73#12512yes—
238C4×D73#12612yes—
239C4×D73C22×Q811yescharacteristic
240C4×D73C2×#4111yescharacteristic
241C4×D73C2×#4111yescharacteristic
242C4×D73C2×#4111yescharacteristic
243#10596833—24no—
244#10596833—22no—
245#10596833—22no—
246#10596833—42no—
247C8×C73—21no—
248C8×C73—21no—
249#10596831—21no—
250#10596831—21no—
251C22×C73—21no—
252C22×C73—21no—
253C22×C73#38712yes—
254C22×C73C2×C4×D411yescharacteristic
255C2×D73—21no—
256C2×D73—21no—
257C2×D73—24no—
258C2×D73—24no—
259C2×D73#38712yes—
260C2×D73#44312yes—
261C2×D73#44412yes—
262C2×D73C2×#12511yescharacteristic
263C2×D73C2×#12611yescharacteristic
264#64408—44no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73#38712yes—
270C4×C73C2×#11711yescharacteristic
271C4×C73C2×C4×Q811yescharacteristic
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276Dic73#38712yes—
277Dic73C2×C22⋊Q811yescharacteristic
278Dic73C2×#12311yescharacteristic
279C2×#1922—731nomaximal, Sylow
280C2×C73—22no—
281C2×C73C2×#38711yescharacteristic
282C2×C73C2×#44311yescharacteristic
283C2×C73C2×#44411yescharacteristic
284D73—21no—
285D73—21no—
286D73#192214yescomplemented
287C2×#427—731no—
288C2×#424—731no—
289C2×#405—731no—
290#1922—732no—
291#1922—732no—
292#1922—732no—
293#1922—732no—
294C2×#341—731no—
295C2×#339—731no—
296C2×#339—731no—
297C2×#336—731no—
298C73C2×#192211yescharacteristic, complemented, Sylow
299C22×M16—731no—
300C22×M16—731no—
301C23×C8—731no—
302C23×C8—731no—
303C2×#117—731no—
304C2×#117—731no—
305C22×C42—731no—
306#427—731no—
307#427—731no—
308#427—731no—
309#427—731no—
310#427—731no—
311#427—731no—
312#427—731no—
313#427#6440811yescharacteristic, complemented
314C2×#107—731no—
315C2×#107—731no—
316C2×#106—731no—
317C2×#106—731no—
318#424—732no—
319#424—732no—
320#424—1462no—
321C2×C4⋊C8—1461no—
322C2×C4⋊C8—1461no—
323#405—732no—
324#405—732no—
325#405—1462no—
326C2×#97—1461no—
327C2×C4×C8—1461no—
328#341—732no—
329#341—732no—
330#339—732no—
331#339—732no—
332#339—732no—
333#339—732no—
334#336—732no—
335#336—732no—
336C23×C4—731no—
337C23×C4—1461no—
338C2×M16—734no—
339C2×M16—732no—
340C2×M16—732no—
341C2×M16—1462no—
342C2×M16—1462no—
343C2×M16—1461no—
344C2×M16—1461no—
345C2×M16—1462no—
346C22×C8—732no—
347C22×C8—731no—
348C22×C8—731no—
349C22×C8—732no—
350C22×C8—731no—
351C22×C8—731no—
352C22×C8—731no—
353C22×C8—731no—
354C22×C8—731no—
355C22×C8—1462no—
356C22×C8—1462no—
357C22×C8—1461no—
358C22×C8—1462no—
359C22×C8—1462no—
360C22×C8—1461no—
361C22×C8C2×#6440811yescharacteristic
362#117—731no—
363#117—731no—
364#117—731no—
365#117—731no—
366#117—731no—
367#117—731no—
368#117—1461no—
369#117—1461no—
370#117—1461no—
371#117—1461no—
372#117C2×#6440811yescharacteristic
373#117C2×#6440811yescharacteristic
374C2×C4⋊C4—731no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—731no—
378C2×C22⋊C4—1461no—
379C2×C22⋊C4—1461no—
380C2×C42—732no—
381C2×C42—1461no—
382C2×C42—1461no—
383C2×C42—1461no—
384C2×C42—1462no—
385C2×C42—1462no—
386#107—731no—
387#107—731no—
388#107—731no—
389#107—731no—
390#107—731no—
391#107—731no—
392#107C2×#6440811yescharacteristic, complemented
393#107C2×#6440811yescharacteristic, complemented
394#106—731no—
395#106—731no—
396#106—731no—
397#106—731no—
398#106—731no—
399#106—731no—
400#106C2×#6440811yescharacteristic, complemented
401#106C2×#6440811yescharacteristic, complemented
402C4⋊C8—1462no—
403C4⋊C8—1462no—
404C4⋊C8—1462no—
405C4⋊C8—1462no—
406#97—1462no—
407#97—1462no—
408C4×C8—1462no—
409C4×C8—1462no—
410C24—731no—
411C22×C4—2922no—
412C22×C4—2922no—
413C22×C4—731no—
414C22×C4—732no—
415C22×C4—732no—
416C22×C4—731no—
417C22×C4—731no—
418C22×C4—732no—
419C22×C4—732no—
420C22×C4—731no—
421C22×C4—731no—
422C22×C4—1461no—
423C22×C4—1461no—
424C22×C4—1461no—
425C22×C4—1461no—
426C22×C4—1462no—
427C22×C4—1464no—
428C22×C4C22×#6440811yescharacteristic
429M16—2922no—
430M16—734no—
431M16—1462no—
432M16—1462no—
433M16—1464no—
434M16—1462no—
435C2×C8—22no—
436C2×C8—2922no—
437C2×C8—732no—
438C2×C8—732no—
439C2×C8—731no—
440C2×C8—731no—
441C2×C8—1461no—
442C2×C8—1461no—
443C2×C8—1461no—
444C2×C8—1461no—
445C2×C8—1462no—
446C2×C8—1462no—
447C2×C8—1462no—
448C2×C8—1462no—
449C2×C8—1464no—
450C2×C8—1462no—
451C2×C8—1462no—
452C2×C8—1462no—
453C2×C8—1462no—
454C2×C8—1464no—
455C2×C8—1462no—
456C2×C8C22×#6440811yescharacteristic
457C2×C8C22×#6440811yescharacteristic
458C4⋊C4—731no—
459C4⋊C4—731no—
460C4⋊C4—731no—
461C4⋊C4—731no—
462C4⋊C4—1461no—
463C4⋊C4—1461no—
464C4⋊C4—1461no—
465C4⋊C4—1461no—
466C4⋊C4C22×#6440811yescharacteristic
467C4⋊C4C22×#6440811yescharacteristic
468C4⋊C4C22×#6440811yescharacteristic
469C4⋊C4C22×#6440811yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—1461no—
473C22⋊C4—1461no—
474C22⋊C4—1461no—
475C22⋊C4—1461no—
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C42—21no—
479C42—21no—
480C42—2922no—
481C42—1461no—
482C42—1461no—
483C42—1461no—
484C42—1461no—
485C42—1462no—
486C42—1462no—
487C42—1461no—
488C42—1461no—
489C23—731no—
490C23—731no—
491C23—732no—
492C23—732no—
493C23—1462no—
494C23—1462no—
495C23D4×#6440811yescharacteristic
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—2922no—
501C2×C4—2922no—
502C2×C4—2922no—
503C2×C4—2922no—
504C2×C4—2922no—
505C2×C4—2928no—
506C2×C4—2922no—
507C2×C4—731no—
508C2×C4—731no—
509C2×C4—732no—
510C2×C4—732no—
511C2×C4—731no—
512C2×C4—731no—
513C2×C4—732no—
514C2×C4—731no—
515C2×C4—731no—
516C2×C4—732no—
517C2×C4—732no—
518C2×C4—732no—
519C2×C4—732no—
520C2×C4—732no—
521C2×C4—1464no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4#1455667012yes—
527C2×C4D4×#6440811yescharacteristic
528C2×C4Q8×#6440812yes—
529C2×C4C23×#6440811yescharacteristic
530C8—21no—
531C8—21no—
532C8—2922no—
533C8—1462no—
534C8—1462no—
535C8—1464no—
536C8—1461no—
537C8—1461no—
538C22—21no—
539C22—21no—
540C22—732no—
541C22—732no—
542C22—732no—
543C22—731no—
544C22—731no—
545C22—1464no—
546C22—1464no—
547C22—1461no—
548C22—1461no—
549C22#1798953612yes—
550C22C2×D4×#6440811yescharacteristic
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—2924no—
556C4—2921no—
557C4—2921no—
558C4—2921no—
559C4—2921no—
560C4—731no—
561C4—731no—
562C4—732no—
563C4#1798953612yes—
564C4C2×#1455667011yescharacteristic
565C4C2×Q8×#6440811yescharacteristic
566C2—22no—
567C2—734no—
568C2—1461no—
569C2—1461no—
570C2C2×#1798953611yescharacteristic
571C2D73⋊#44311yescharacteristic
572C2D73⋊#44411yescharacteristic
subgroupG/H
centerC2×C4D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#427×C73C4
socleC22×C73C2×C4×D4
prime radicalC23×D73#41
cosocleC2×C4×D73C24
hypercenter#427#64408
hypocenterC73C2×#1922
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
3. #22625999C2semidirect
4. #22625998C2semidirect
5. #22625997C2semidirect
6. #22625996C2semidirect
37. #17988625C4semidirect
40. #17988623C4semidirect
41. #17988623C4semidirect
44. #107×D73C4semidirect
45. #107×D73C4semidirect
46. #106×D73C4semidirect
47. #106×D73C4semidirect
48. #427×C73C4semidirect
104. #14556525C2×C4semidirect
105. #14556525C2×C4semidirect
106. #14556524C2×C4semidirect
107. #14556524C2×C4semidirect
108. #14556524C2×C4semidirect
109. #14556524C2×C4semidirect
110. #14556523C2×C4semidirect
111. #14556523C2×C4semidirect
112. #14556522C2×C4semidirect
113. #14556522C2×C4semidirect
114. #14556522C2×C4semidirect
115. #14556522C2×C4semidirect
119. #107×C73C2×C4semidirect
120. #107×C73C2×C4semidirect
121. #106×C73C2×C4semidirect
122. #106×C73C2×C4semidirect
286. D73#1922semidirect
298. C73C2×#1922semidirect
313. #427#64408semidirect
392. #107C2×#64408semidirect
393. #107C2×#64408semidirect
400. #106C2×#64408semidirect
401. #106C2×#64408semidirect

Maximal subgroups

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

subgroupindex
D73⋊#4242
#226264912
#226259992
#226259982
#226259972
#226259962
#226256232
#226256072
C2×#179894522
#427×D732
C2×#192273