Finite Group Databasebeta

← C2×#22626022 #34021922

Subgroups — C2×#22626022 #34021922

Order 18688.

1206 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556654C211yesmaximal, characteristic
2C22×#14556645C211yesmaximal, characteristic
3C2×(C2×#64408)⋊Q8C211yesmaximal, characteristic
4C2×#17989538C211yesmaximal, characteristic
5#22626022C218yesmaximal, direct product factor
6C2×#17989461C211yesmaximal, characteristic
7C2×#17989460C211yesmaximal, characteristic
8C2×#103×D73C211yesmaximal, characteristic
9C22×#11924036C2211yescharacteristic
10C22×C4⋊#64408—21no—
11C22×C4⋊#64408C2211yescharacteristic
12C22×C4⋊#64408C2211yescharacteristic
13C22×C4×#64408C2211yescharacteristic
14C2×#14556654—24no—
15C2×#14556654C2214yes—
16C2×#14556645—24no—
17C2×#14556645C2214yes—
18(C2×#64408)⋊Q8—22no—
19(C2×#64408)⋊Q8C2214yes—
20#17989538—22no—
21#17989538C2214yes—
22C2×(C2×#64408)⋊C4—21no—
23C2×(C2×#64408)⋊C4—21no—
24C2×(C2×#64408)⋊C4—21no—
25#17989461C2214yes—
26#17989460C2214yes—
27C22×Q8×D73C2211yescharacteristic
28C22×C8×D73C2211yescharacteristic
29C2×C4⋊C4×D73C2211yescharacteristic
30C2×#14556516C411yescharacteristic, complemented
31C2×#14556515C411yescharacteristic, complemented
32C2×#14556514C411yescharacteristic, complemented
33#103×D73C414yescomplemented
34#103×D73C2214yes—
35C2×#103×C73C411yescharacteristic, complemented
36C23×#64408—21no—
37C23×#64408—21no—
38C23×#64408D411yescharacteristic
39C23×#64408D411yescharacteristic
40C2×#11924036—22no—
41C2×#11924036—21no—
42C2×#11924036D414yes—
43C2×#11924036C2312yes—
44C22×#10596833—21no—
45C2×C4⋊#64408—24no—
46C2×C4⋊#64408—22no—
47C2×C4⋊#64408—21no—
48C2×C4⋊#64408—21no—
49C2×C4⋊#64408—22no—
50C2×C4⋊#64408—22no—
51C2×C4⋊#64408—22no—
52C2×C4⋊#64408—44no—
53C2×C4⋊#64408C2312yes—
54C2×C4⋊#64408C2312yes—
55C2×C4×#64408—22no—
56C2×C4×#64408—22no—
57C2×C4×#64408D412yes—
58C2×C4×#64408C2312yes—
59#14556654—28no—
60#14556645—28no—
61(C2×#64408)⋊C4—24no—
62(C2×#64408)⋊C4—24no—
63(C2×#64408)⋊C4—24no—
64C22×Dic146—21no—
65C22×Dic146C2×C411yescharacteristic
66C2×Q8×D73—21no—
67C2×Q8×D73—21no—
68C2×Q8×D73—22no—
69C2×Q8×D73—22no—
70C2×Q8×D73—22no—
71C2×Q8×D73—22no—
72C2×Q8×D73C2×C412yes—
73C2×Q8×D73C2312yes—
74C22×C4×D73—21no—
75C22×C4×D73—21no—
76C22×C4×D73C2311yescharacteristic
77C22×#10596831C2×C411yescharacteristic
78C2×C8×D73—22no—
79C2×C8×D73—22no—
80C2×C8×D73C2×C412yes—
81C2×C8×D73C2312yes—
82C2×C4⋊Dic73C2×C411yescharacteristic
83C2×#11924007—21no—
84C4⋊C4×D73—21no—
85C4⋊C4×D73—21no—
86C4⋊C4×D73C2×C412yes—
87C4⋊C4×D73C2312yes—
88#14556516C2×C414yescomplemented
89#14556515C2×C414yescomplemented
90#14556514C2×C414yescomplemented
91C22×Q8×C73C2×C411yescharacteristic
92C22×C8×C73C2×C411yescharacteristic
93C2×C4⋊C4×C73C2×C411yescharacteristic
94#103×C73C2×C414yescomplemented
95C22×#64408—22no—
96C22×#64408—22no—
97C22×#64408—22no—
98C22×#64408—22no—
99C22×#64408—22no—
100C22×#64408—22no—
101C22×#64408—22no—
102C22×#64408—22no—
103C22×#64408—42no—
104C22×#64408—42no—
105C22×#64408—42no—
106C22×#64408—42no—
107C22×#64408—42no—
108C22×#64408—42no—
109C22×#64408C2×D412yes—
110C22×#64408C2×D412yes—
111#11924036—24no—
112#11924036—22no—
113#11924036C2×D414yes—
114C2×#10596833—24no—
115C2×#10596833—22no—
116C4⋊#64408—22no—
117C4⋊#64408—22no—
118C4⋊#64408—22no—
119C4⋊#64408—22no—
120C4⋊#64408—48no—
121C4⋊#64408—42no—
122C4⋊#64408—42no—
123C4×#64408—24no—
124C4×#64408—22no—
125C4×#64408—22no—
126C23×D73C2×D411yescharacteristic
127C2×Dic146—22no—
128C2×Dic146—22no—
129C2×Dic146—21no—
130C2×Dic146—22no—
131C2×Dic146—22no—
132C2×Dic146—42no—
133C2×Dic146—42no—
134C2×Dic146C22×C412yes—
135Q8×D73—24no—
136Q8×D73—24no—
137Q8×D73—22no—
138Q8×D73—22no—
139Q8×D73—22no—
140Q8×D73—22no—
141Q8×D73—42no—
142Q8×D73—42no—
143Q8×D73—42no—
144Q8×D73—42no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73#4111yescharacteristic
148C2×C4×D73—22no—
149C2×C4×D73—22no—
150C2×C4×D73—22no—
151C2×C4×D73—22no—
152C2×C4×D73—42no—
153C2×C4×D73—42no—
154C2×C4×D73—42no—
155C2×C4×D73—42no—
156C2×C4×D73C22×C411yescharacteristic
157C2×C4×D73C2×D412yes—
158C2×C4×D73C2×D411yescharacteristic
159C2×C4×D73#4112yes—
160C2×C4×D73#4112yes—
161C2×C4×D73#4112yes—
162C2×C4×D73#4111yescharacteristic
163C2×C4×D73C2411yescharacteristic
164C2×#10596831—22no—
165C2×#10596831C22×C412yes—
166C8×D73—24no—
167C8×D73—22no—
168C8×D73—22no—
169C4⋊Dic73—21no—
170C4⋊Dic73C22×C412yes—
171#11924007—22no—
172#11924007—22no—
173C2×Q8×C73—21no—
174C2×Q8×C73—22no—
175C2×Q8×C73—22no—
176C2×Q8×C73C22×C412yes—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73C22×C411yescharacteristic
180C2×C8×C73—22no—
181C2×C8×C73C22×C412yes—
182C4⋊C4×C73—21no—
183C4⋊C4×C73C22×C412yes—
184C23×C73C4×D411yescharacteristic
185C22×D73C4×D411yescharacteristic
186C22×D73#12112yes—
187C22×D73#12412yes—
188C22×D73AGL(1,ℤ/8)12yes—
189C22×D73#13712yes—
190C22×D73#13712yes—
191C22×D73#13712yes—
192C22×D73C22×D411yescharacteristic
193C2×#64408—22no—
194C2×#64408—22no—
195C2×#64408—22no—
196C2×#64408—22no—
197C2×#64408—22no—
198C2×#64408—22no—
199C2×#64408—44no—
200C2×#64408—44no—
201C2×#64408—42no—
202C2×#64408—42no—
203C2×#64408—42no—
204C2×#64408—42no—
205C2×#64408—42no—
206C2×#64408—42no—
207C2×#64408—84no—
208C2×#64408—84no—
209Q8×C73—22no—
210Q8×C73—22no—
211Q8×C73—42no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—42no—
215C2×C4×C73—42no—
216C2×C4×C73#11712yes—
217C2×C4×C73C4×D412yes—
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C23×C411yescharacteristic
220C2×Dic73—22no—
221C2×Dic73—22no—
222C2×Dic73—42no—
223C2×Dic73—42no—
224C2×Dic73C4×D411yescharacteristic
225C2×Dic73#12312yes—
226C2×Dic73#12612yes—
227C2×Dic73C2×#4111yescharacteristic
228C4×D73—42no—
229C4×D73—42no—
230C4×D73—42no—
231C4×D73—42no—
232C4×D73—44no—
233C4×D73—44no—
234C4×D73#11712yes—
235C4×D73C4×D412yes—
236C4×D73#12112yes—
237C4×D73#12312yes—
238C4×D73#12412yes—
239C4×D73#12612yes—
240C4×D73C22×D411yescharacteristic
241C4×D73C2×#4111yescharacteristic
242C4×D73C2×#4111yescharacteristic
243C4×D73C2×#4111yescharacteristic
244Dic146—22no—
245Dic146—22no—
246Dic146—42no—
247Dic146—42no—
248Dic146—42no—
249Dic146—44no—
250#10596833—24no—
251C8×C73—22no—
252#10596831—22no—
253C22×C73#38812yes—
254C22×C73#44012yes—
255C22×C73#44112yes—
256C22×C73C2×C4×D411yescharacteristic
257C2×D73#38812yes—
258C2×D73#44012yes—
259C2×D73#44112yes—
260C2×D73#46814yes—
261C2×D73#47014yes—
262C2×D73#48914yes—
263C2×D73#49114yes—
264C2×D73C2×#12111yescharacteristic
265C2×D73C2×#12411yescharacteristic
266C2×D73C2×AGL(1,ℤ/8)11yescharacteristic
267C2×D73C2×#13711yescharacteristic
268C2×D73C2×#13711yescharacteristic
269C2×D73C2×#13711yescharacteristic
270#64408—42no—
271#64408—42no—
272#64408—82no—
273#64408—82no—
274C4×C73—42no—
275C4×C73—42no—
276C4×C73#38812yes—
277C4×C73C2×#11711yescharacteristic
278C4×C73C2×C4×D411yescharacteristic
279Dic73—42no—
280Dic73—42no—
281Dic73#38812yes—
282Dic73C2×#12311yescharacteristic
283Dic73C2×#12611yescharacteristic
284C2×#1935—731nomaximal, Sylow
285C2×C73#193514yescomplemented
286C2×C73C2×#38811yescharacteristic
287C2×C73C2×#44011yescharacteristic
288C2×C73C2×#44111yescharacteristic
289D73#193514yescomplemented
290D73C2×#46811yescharacteristic
291D73C2×#47011yescharacteristic
292D73C2×#48911yescharacteristic
293D73C2×#49111yescharacteristic
294C22×#103—731no—
295C22×#103—731no—
296C22×#97—731no—
297C2×#391—731no—
298C2×#389—731no—
299#1935—738no—
300C2×#340—731no—
301C2×#340—731no—
302C73C2×#193511yescharacteristic, complemented, Sylow
303C23×Q8—731no—
304C23×C8—731no—
305C23×C8—731no—
306C22×C4⋊C4—731no—
307C22×C4⋊C4—731no—
308C22×C4⋊C4—731no—
309C22×C4⋊C4—1461no—
310C22×C42—731no—
311C2×#103—731no—
312C2×#103—731no—
313C2×#103—731no—
314C2×#103—734no—
315C2×#103—734no—
316C2×#103—734no—
317C2×#103—1464no—
318C2×#103#6440811yescharacteristic, complemented
319C2×#97—734no—
320C2×#97—1464no—
321#391—734no—
322#391—1462no—
323#389—734no—
324#389—1462no—
325C2×#95—1461no—
326C2×#95—1461no—
327C2×#95—1461no—
328#340—734no—
329#340—734no—
330C22×Q8—732no—
331C22×Q8—732no—
332C22×Q8—731no—
333C22×Q8—1461no—
334C22×Q8—1462no—
335C22×Q8—1462no—
336C22×Q8—1462no—
337C22×Q8—1462no—
338C22×Q8—1461no—
339C22×Q8—1461no—
340C22×Q8C2×#6440811yescharacteristic
341C23×C4—731no—
342C23×C4—731no—
343C23×C4—731no—
344C23×C4—1461no—
345C23×C4—1461no—
346C23×C4—1461no—
347C23×C4—1461no—
348C22×C8—734no—
349C22×C8—732no—
350C22×C8—731no—
351C22×C8—732no—
352C22×C8—732no—
353C22×C8—1462no—
354C22×C8—1462no—
355C22×C8—1461no—
356C22×C8—1462no—
357C22×C8—1461no—
358C22×C8C2×#6440811yescharacteristic
359C2×C4⋊C4—2924no—
360C2×C4⋊C4—731no—
361C2×C4⋊C4—732no—
362C2×C4⋊C4—732no—
363C2×C4⋊C4—732no—
364C2×C4⋊C4—732no—
365C2×C4⋊C4—1461no—
366C2×C4⋊C4—1461no—
367C2×C4⋊C4—1461no—
368C2×C4⋊C4—1461no—
369C2×C4⋊C4—1464no—
370C2×C4⋊C4—1462no—
371C2×C4⋊C4—1462no—
372C2×C4⋊C4—1462no—
373C2×C4⋊C4—1462no—
374C2×C4⋊C4—1461no—
375C2×C4⋊C4C2×#6440811yescharacteristic
376C2×C42—732no—
377C2×C42—732no—
378C2×C42—1462no—
379C2×C42—1462no—
380#103—734no—
381#103—734no—
382#103—734no—
383#103—1468no—
384#103C2×#6440814yescomplemented
385#97—1468no—
386#95—1464no—
387#95—1464no—
388#95—1464no—
389C24—731no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—2922no—
394C2×Q8—2922no—
395C2×Q8—2922no—
396C2×Q8—2922no—
397C2×Q8—2922no—
398C2×Q8—2922no—
399C2×Q8—732no—
400C2×Q8—1462no—
401C2×Q8—1462no—
402C2×Q8—1462no—
403C2×Q8—1462no—
404C2×Q8—1462no—
405C2×Q8—1464no—
406C2×Q8—1462no—
407C2×Q8—1464no—
408C2×Q8—1462no—
409C2×Q8—1462no—
410C2×Q8—1461no—
411C2×Q8C22×#6440812yes—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—2922no—
415C22×C4—2922no—
416C22×C4—2922no—
417C22×C4—2922no—
418C22×C4—2922no—
419C22×C4—2922no—
420C22×C4—2922no—
421C22×C4—2922no—
422C22×C4—2922no—
423C22×C4—2922no—
424C22×C4—731no—
425C22×C4—731no—
426C22×C4—731no—
427C22×C4—732no—
428C22×C4—732no—
429C22×C4—731no—
430C22×C4—732no—
431C22×C4—731no—
432C22×C4—732no—
433C22×C4—732no—
434C22×C4—732no—
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—1461no—
448C22×C4—1461no—
449C22×C4C22×#6440811yescharacteristic
450C2×C8—22no—
451C2×C8—734no—
452C2×C8—732no—
453C2×C8—1462no—
454C2×C8—1462no—
455C2×C8—1464no—
456C2×C8—1462no—
457C2×C8—1464no—
458C2×C8—1462no—
459C2×C8—1464no—
460C2×C8—1462no—
461C2×C8C22×#6440812yes—
462C4⋊C4—21no—
463C4⋊C4—2922no—
464C4⋊C4—2922no—
465C4⋊C4—2928no—
466C4⋊C4—732no—
467C4⋊C4—1462no—
468C4⋊C4—1462no—
469C4⋊C4—1462no—
470C4⋊C4—1462no—
471C4⋊C4—1462no—
472C4⋊C4—1462no—
473C4⋊C4—1461no—
474C4⋊C4C22×#6440812yes—
475C42—1462no—
476C42—1462no—
477C42—1464no—
478C23—731no—
479C23—731no—
480C23—732no—
481C23—732no—
482C23—732no—
483C23—732no—
484C23—732no—
485C23—732no—
486C23D4×#6440811yescharacteristic
487Q8—22no—
488Q8—22no—
489Q8—42no—
490Q8—2922no—
491Q8—2922no—
492Q8—2924no—
493Q8—2922no—
494Q8—1462no—
495Q8—1462no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—2922no—
501C2×C4—2922no—
502C2×C4—2922no—
503C2×C4—2924no—
504C2×C4—2922no—
505C2×C4—2924no—
506C2×C4—2924no—
507C2×C4—2924no—
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—5844no—
517C2×C4—5844no—
518C2×C4—731no—
519C2×C4—731no—
520C2×C4—732no—
521C2×C4—732no—
522C2×C4—731no—
523C2×C4—731no—
524C2×C4—732no—
525C2×C4—731no—
526C2×C4—731no—
527C2×C4—732no—
528C2×C4—732no—
529C2×C4—732no—
530C2×C4—732no—
531C2×C4—732no—
532C2×C4—1462no—
533C2×C4—1462no—
534C2×C4—1462no—
535C2×C4—1462no—
536C2×C4—1462no—
537C2×C4—1462no—
538C2×C4—1462no—
539C2×C4—1462no—
540C2×C4#1455667012yes—
541C2×C4D4×#6440812yes—
542C2×C4D4×#6440811yescharacteristic
543C2×C4C23×#6440811yescharacteristic
544C8—22no—
545C8—1464no—
546C8—1462no—
547C22—731no—
548C22—731no—
549C22—732no—
550C22—731no—
551C22—731no—
552C22—732no—
553C22—731no—
554C22—731no—
555C22—732no—
556C22—734no—
557C22—734no—
558C22—734no—
559C22—734no—
560C22#1798953712yes—
561C22#1798962612yes—
562C22#1798962712yes—
563C22C2×D4×#6440811yescharacteristic
564C4—42no—
565C4—42no—
566C4—2922no—
567C4—2922no—
568C4—2922no—
569C4—2922no—
570C4—5842no—
571C4—5842no—
572C4—731no—
573C4—731no—
574C4—732no—
575C4#1798953712yes—
576C4C2×#1455667011yescharacteristic
577C4C2×D4×#6440811yescharacteristic
578C2—731no—
579C2—731no—
580C2—731no—
581C2—731no—
582C2—734no—
583C2#2262602214yesdirect product factor
584C2C2×#1798953711yescharacteristic
585C2C2×#1798962611yescharacteristic
586C2C2×#1798962711yescharacteristic
subgroupG/H
centerC23D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC2×#103×C73C4
socleC23×C73C4×D4
prime radicalC23×D73C2×D4
cosocleC2×C4×D73C24
hypercenterC2×#103#64408
hypocenterC73C2×#1935
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
5. #22626022C2direct (N × H)
30. C2×#14556516C4semidirect
31. C2×#14556515C4semidirect
32. C2×#14556514C4semidirect
33. #103×D73C4semidirect
35. C2×#103×C73C4semidirect
88. #14556516C2×C4semidirect
89. #14556515C2×C4semidirect
90. #14556514C2×C4semidirect
94. #103×C73C2×C4semidirect
285. C2×C73#1935semidirect
289. D73#1935semidirect
302. C73C2×#1935semidirect
318. C2×#103#64408semidirect
384. #103C2×#64408semidirect
583. C2#22626022direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566542
C22×#145566452
C2×(C2×#64408)⋊Q82
C2×#179895382
#226260222
C2×#179894612
C2×#179894602
C2×#103×D732
C2×#193573