Finite Group Databasebeta

← C2×#22625834 #34021069

Subgroups — C2×#22625834 #34021069

Order 18688.

1878 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989555C211yesmaximal, characteristic
2C2×#17989529C211yesmaximal, characteristic
3#22625834C218yesmaximal, direct product factor
4C2×#17989460C214yesmaximal, complemented
5C22×C4⋊C4×D73C211yesmaximal, characteristic
6C22×#11924036C2212yes—
7C22×C4⋊#64408C2212yes—
8C22×C22⋊#64408—21no—
9C2×#14556648—21no—
10#17989555—22no—
11#17989555C2214yes—
12C2×C22⋊#10596833—21no—
13#17989529—22no—
14#17989529C2214yes—
15C2×(C2×#64408)⋊C4—21no—
16#17989460C22116yescomplemented
17C23×C4×D73—21no—
18C23×C4×D73C2211yescharacteristic
19C22×C4⋊Dic73C411yescharacteristic, complemented
20C22×#11924007—21no—
21C2×C4⋊C4×D73—21no—
22C2×C4⋊C4×D73—22no—
23C2×C4⋊C4×D73—22no—
24C2×C4⋊C4×D73—21no—
25C2×C4⋊C4×D73C412yescomplemented
26C2×C4⋊C4×D73C414yescomplemented
27C2×C4⋊C4×D73C2212yes—
28C2×C4⋊C4×D73C2214yes—
29C22×C4⋊C4×C73C411yescharacteristic, complemented
30C23×#64408—22no—
31C2×#11924036—22no—
32C2×#11924036—28no—
33C2×#11924036C2314yes—
34C22×#10596833—22no—
35C2×C4⋊#64408—22no—
36C2×C4⋊#64408—28no—
37C2×C4⋊#64408C2314yes—
38C2×C22⋊#64408—24no—
39C2×C22⋊#64408—44no—
40#14556648—24no—
41C22⋊#10596833—24no—
42(C2×#64408)⋊C4—24no—
43C24×D73D411yescharacteristic
44C23×Dic73—21no—
45C23×Dic73D411yescharacteristic
46C22×C4×D73—28no—
47C22×C4×D73—22no—
48C22×C4×D73—24no—
49C22×C4×D73—22no—
50C22×C4×D73—24no—
51C22×C4×D73—44no—
52C22×C4×D73—44no—
53C22×C4×D73C2×C412yes—
54C22×C4×D73C2×C411yescharacteristic
55C22×C4×D73D411yescharacteristic
56C22×C4×D73D412yes—
57C22×C4×D73D412yes—
58C22×C4×D73D411yescharacteristic
59C22×C4×D73C2312yes—
60C22×C4×D73C2311yescharacteristic
61C2×C4⋊Dic73—22no—
62C2×C4⋊Dic73—21no—
63C2×C4⋊Dic73C2×C412yes—
64C2×C4⋊Dic73C2×C414yescomplemented
65C2×#11924007—22no—
66C2×#11924007—24no—
67C2×#11924007—22no—
68C2×#11924007—24no—
69C4⋊C4×D73—24no—
70C4⋊C4×D73—24no—
71C4⋊C4×D73—24no—
72C4⋊C4×D73—22no—
73C4⋊C4×D73—22no—
74C4⋊C4×D73—24no—
75C4⋊C4×D73—24no—
76C4⋊C4×D73C2×C414yes—
77C4⋊C4×D73C2×C418yescomplemented
78C4⋊C4×D73C2314yes—
79C23×C4×C73—21no—
80C23×C4×C73C2×C411yescharacteristic
81C2×C4⋊C4×C73—22no—
82C2×C4⋊C4×C73—21no—
83C2×C4⋊C4×C73C2×C412yes—
84C2×C4⋊C4×C73C2×C414yescomplemented
85C22×#64408—24no—
86C22×#64408—44no—
87C22×#64408—44no—
88C22×#64408—44no—
89#11924036—28no—
90#11924036—44no—
91C2×#10596833—24no—
92C2×#10596833—44no—
93C4⋊#64408—28no—
94C4⋊#64408—44no—
95C22⋊#64408—48no—
96C23×D73—24no—
97C23×D73—24no—
98C23×D73C22⋊C412yes—
99C23×D73C22⋊C411yescharacteristic
100C23×D73D814yes—
101C23×D73SD1614yes—
102C23×D73C2×D412yes—
103C23×D73C2×D411yescharacteristic
104C22×Dic73—24no—
105C22×Dic73—22no—
106C22×Dic73—24no—
107C22×Dic73—44no—
108C22×Dic73C22⋊C412yes—
109C22×Dic73C22⋊C411yescharacteristic
110C22×Dic73C2×D412yes—
111C22×Dic73C2×D411yescharacteristic
112C2×C4×D73—24no—
113C2×C4×D73—24no—
114C2×C4×D73—24no—
115C2×C4×D73—28no—
116C2×C4×D73—28no—
117C2×C4×D73—28no—
118C2×C4×D73—28no—
119C2×C4×D73—24no—
120C2×C4×D73—28no—
121C2×C4×D73—24no—
122C2×C4×D73—48no—
123C2×C4×D73—416no—
124C2×C4×D73—48no—
125C2×C4×D73—44no—
126C2×C4×D73—48no—
127C2×C4×D73—44no—
128C2×C4×D73C22⋊C412yes—
129C2×C4×D73C22⋊C412yes—
130C2×C4×D73C22⋊C412yes—
131C2×C4×D73C22×C412yes—
132C2×C4×D73C22×C411yescharacteristic
133C2×C4×D73C2×D412yes—
134C2×C4×D73C2×D412yes—
135C2×C4×D73C2×D411yescharacteristic
136C2×C4×D73C2×D411yescharacteristic
137C2×C4×D73#4118yes—
138C2×C4×D73C2411yescharacteristic
139C4⋊Dic73—22no—
140C4⋊Dic73—24no—
141C4⋊Dic73C22×C414yes—
142#11924007—24no—
143#11924007—28no—
144#11924007—24no—
145C24×C73C22⋊C411yescharacteristic
146C22×C4×C73—24no—
147C22×C4×C73—22no—
148C22×C4×C73—24no—
149C22×C4×C73—44no—
150C22×C4×C73C22⋊C412yes—
151C22×C4×C73C22⋊C411yescharacteristic
152C22×C4×C73C22×C412yes—
153C22×C4×C73C22×C411yescharacteristic
154C4⋊C4×C73—22no—
155C4⋊C4×C73—24no—
156C4⋊C4×C73C22×C414yes—
157C23×C73—22no—
158C23×C73—22no—
159C23×C73#10214yes—
160C23×C73C2×C22⋊C412yes—
161C23×C73C2×C22⋊C411yescharacteristic
162C22×D73—22no—
163C22×D73—22no—
164C22×D73—24no—
165C22×D73—24no—
166C22×D73—24no—
167C22×D73—24no—
168C22×D73—216no—
169C22×D73—216no—
170C22×D73#10214yes—
171C22×D73#10218yes—
172C22×D73C2×C22⋊C412yes—
173C22×D73C2×C22⋊C411yescharacteristic
174C22×D73#12314yes—
175C22×D73C2×D814yes—
176C22×D73C2×D812yes—
177C22×D73C2×SD1614yes—
178C22×D73C2×SD1612yes—
179C22×D73#13714yes—
180C22×D73C22×D411yescharacteristic
181C2×#64408—44no—
182C2×#64408—44no—
183C2×#64408—44no—
184C2×#64408—88no—
185C2×C4×C73—22no—
186C2×C4×C73—24no—
187C2×C4×C73—24no—
188C2×C4×C73—24no—
189C2×C4×C73—48no—
190C2×C4×C73—44no—
191C2×C4×C73C2×C22⋊C412yes—
192C2×C4×C73C2×C22⋊C411yescharacteristic
193C2×C4×C73#11714yes—
194C2×C4×C73C23×C411yescharacteristic
195C2×Dic73—22no—
196C2×Dic73—24no—
197C2×Dic73—24no—
198C2×Dic73—24no—
199C2×Dic73—48no—
200C2×Dic73—44no—
201C2×Dic73C2×C22⋊C412yes—
202C2×Dic73C2×C22⋊C411yescharacteristic
203C2×Dic73#12314yes—
204C2×Dic73C22×D411yescharacteristic
205C4×D73—24no—
206C4×D73—24no—
207C4×D73—24no—
208C4×D73—24no—
209C4×D73—24no—
210C4×D73—24no—
211C4×D73—44no—
212C4×D73—44no—
213C4×D73—416no—
214C4×D73—48no—
215C4×D73#11714yes—
216C4×D73#12314yes—
217C4×D73#12314yes—
218C4×D73C2×#4114yes—
219#10596833—44no—
220C22×C73—28no—
221C22×C73—22no—
222C22×C73—22no—
223C22×C73#38112yes—
224C22×C73C2×#10214yes—
225C22×C73C2×#10212yes—
226C22×C73#41912yes—
227C22×C73C22×C22⋊C411yescharacteristic
228C2×D73—28no—
229C2×D73—22no—
230C2×D73—22no—
231C2×D73—28no—
232C2×D73—28no—
233C2×D73—216no—
234C2×D73#38112yes—
235C2×D73C2×#10214yes—
236C2×D73C2×#10212yes—
237C2×D73#41912yes—
238C2×D73#48018yes—
239C2×D73#48318yes—
240C2×D73C2×#12312yes—
241C2×D73C22×D811yescharacteristic
242C2×D73C22×SD1611yescharacteristic
243C2×D73C2×#13712yes—
244#64408—84no—
245C4×C73—22no—
246C4×C73—44no—
247C4×C73#38112yes—
248C4×C73C2×#11712yes—
249Dic73—22no—
250Dic73—44no—
251Dic73#38112yes—
252Dic73C2×#12312yes—
253C2×#1823—731nomaximal, Sylow
254C2×C73—24no—
255C2×C73#182314yescomplemented
256C2×C73C2×#38111yescharacteristic
257C2×C73C22×#10211yescharacteristic
258C2×C73C2×#41911yescharacteristic
259D73—24no—
260D73#182314yescomplemented
261D73C2×#48012yes—
262D73C2×#48312yes—
263C23×C4⋊C4—731no—
264C22×C22⋊C8—731no—
265C2×#380—731no—
266#1823—738no—
267C2×#340—734no—
268C73C2×#182311yescharacteristic, complemented, Sylow
269C24×C4—731no—
270C24×C4—1461no—
271C23×C8—732no—
272C22×C4⋊C4—731no—
273C22×C4⋊C4—732no—
274C22×C4⋊C4—732no—
275C22×C4⋊C4—734no—
276C22×C4⋊C4—734no—
277C22×C4⋊C4—732no—
278C22×C4⋊C4—1461no—
279C22×C4⋊C4—1462no—
280C22×C4⋊C4—1462no—
281C22×C4⋊C4—1461no—
282C22×C4⋊C4—1461no—
283C22×C4⋊C4#6440811yescharacteristic, complemented
284C22×C22⋊C4—1461no—
285C2×C22⋊C8—734no—
286C2×C22⋊C8—1461no—
287C2×C22⋊C8—1462no—
288C2×C22⋊C8—1461no—
289#380—734no—
290#380—1462no—
291C2×#95—1461no—
292#340—7316no—
293C25—731no—
294C23×C4—21no—
295C23×C4—2924no—
296C23×C4—2924no—
297C23×C4—731no—
298C23×C4—731no—
299C23×C4—731no—
300C23×C4—732no—
301C23×C4—731no—
302C23×C4—732no—
303C23×C4—732no—
304C23×C4—732no—
305C23×C4—731no—
306C23×C4—1464no—
307C23×C4—1464no—
308C23×C4—1462no—
309C23×C4—1462no—
310C23×C4—1468no—
311C23×C4—1462no—
312C23×C4—1461no—
313C23×C4C2×#6440811yescharacteristic
314C22×C8—734no—
315C22×C8—1462no—
316C22×C8—1468no—
317C22×C8—1462no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—732no—
321C2×C4⋊C4—734no—
322C2×C4⋊C4—734no—
323C2×C4⋊C4—734no—
324C2×C4⋊C4—738no—
325C2×C4⋊C4—734no—
326C2×C4⋊C4—1462no—
327C2×C4⋊C4—1462no—
328C2×C4⋊C4—1464no—
329C2×C4⋊C4—1464no—
330C2×C4⋊C4—1464no—
331C2×C4⋊C4—1464no—
332C2×C4⋊C4—1464no—
333C2×C4⋊C4—1462no—
334C2×C4⋊C4—1468no—
335C2×C4⋊C4—1464no—
336C2×C4⋊C4—1464no—
337C2×C4⋊C4—1462no—
338C2×C4⋊C4—1462no—
339C2×C4⋊C4—1462no—
340C2×C4⋊C4—1461no—
341C2×C4⋊C4C2×#6440812yes—
342C2×C4⋊C4C2×#6440814yescomplemented
343C2×C22⋊C4—2924no—
344C2×C22⋊C4—1464no—
345C22⋊C8—1464no—
346C22⋊C8—1464no—
347#95—1464no—
348C24—731no—
349C24—734no—
350C24—734no—
351C24—732no—
352C24—732no—
353C24—731no—
354C24—1464no—
355C24—1464no—
356C24C22⋊#6440811yescharacteristic
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—44no—
361C22×C4—2924no—
362C22×C4—2924no—
363C22×C4—2928no—
364C22×C4—29216no—
365C22×C4—2928no—
366C22×C4—2928no—
367C22×C4—2924no—
368C22×C4—2924no—
369C22×C4—2924no—
370C22×C4—2924no—
371C22×C4—731no—
372C22×C4—731no—
373C22×C4—731no—
374C22×C4—731no—
375C22×C4—731no—
376C22×C4—738no—
377C22×C4—732no—
378C22×C4—732no—
379C22×C4—731no—
380C22×C4—732no—
381C22×C4—732no—
382C22×C4—732no—
383C22×C4—732no—
384C22×C4—732no—
385C22×C4—732no—
386C22×C4—1464no—
387C22×C4—1464no—
388C22×C4—1468no—
389C22×C4—1464no—
390C22×C4—1468no—
391C22×C4—1468no—
392C22×C4—1468no—
393C22×C4—1468no—
394C22×C4—1464no—
395C22×C4—1464no—
396C22×C4—1464no—
397C22×C4—1462no—
398C22×C4—1464no—
399C22×C4—1464no—
400C22×C4C22⋊#6440812yes—
401C22×C4C22⋊#6440811yescharacteristic
402C22×C4C22×#6440812yes—
403C22×C4C22×#6440811yescharacteristic
404C2×C8—2924no—
405C2×C8—2924no—
406C2×C8—1464no—
407C2×C8—1468no—
408C4⋊C4—22no—
409C4⋊C4—24no—
410C4⋊C4—2924no—
411C4⋊C4—734no—
412C4⋊C4—1464no—
413C4⋊C4—1464no—
414C4⋊C4—1468no—
415C4⋊C4—1468no—
416C4⋊C4—1464no—
417C4⋊C4—1462no—
418C4⋊C4C22×#6440814yes—
419C22⋊C4—2928no—
420C23—22no—
421C23—22no—
422C23—731no—
423C23—731no—
424C23—734no—
425C23—732no—
426C23—732no—
427C23—734no—
428C23—732no—
429C23—734no—
430C23—738no—
431C23—734no—
432C23—734no—
433C23—1464no—
434C23—1464no—
435C23—14616no—
436C23—14616no—
437C23—1464no—
438C23—1464no—
439C23—1462no—
440C23—1462no—
441C23#1455665314yes—
442C23C2×C22⋊#6440812yes—
443C23C2×C22⋊#6440811yescharacteristic
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—48no—
449C2×C4—44no—
450C2×C4—2924no—
451C2×C4—2924no—
452C2×C4—2928no—
453C2×C4—29216no—
454C2×C4—2928no—
455C2×C4—2924no—
456C2×C4—2924no—
457C2×C4—2924no—
458C2×C4—2924no—
459C2×C4—5848no—
460C2×C4—731no—
461C2×C4—731no—
462C2×C4—734no—
463C2×C4—734no—
464C2×C4—734no—
465C2×C4—734no—
466C2×C4—734no—
467C2×C4—732no—
468C2×C4—1464no—
469C2×C4—1464no—
470C2×C4—1464no—
471C2×C4—1464no—
472C2×C4—1464no—
473C2×C4—1464no—
474C2×C4—1464no—
475C2×C4—1462no—
476C2×C4—1464no—
477C2×C4—1464no—
478C2×C4C2×C22⋊#6440812yes—
479C2×C4C2×C22⋊#6440811yescharacteristic
480C2×C4#1455667014yes—
481C2×C4C23×#6440811yescharacteristic
482C8—2924no—
483C22—28no—
484C22—22no—
485C22—22no—
486C22—738no—
487C22—738no—
488C22—732no—
489C22—732no—
490C22—731no—
491C22—731no—
492C22—732no—
493C22—732no—
494C22—732no—
495C22—734no—
496C22—1468no—
497C22—1468no—
498C22—14616no—
499C22—1468no—
500C22—1462no—
501C22—1462no—
502C22#1798953012yes—
503C22C2×#1455665314yes—
504C22C2×#1455665312yes—
505C22#1798958012yes—
506C22C22×C22⋊#6440811yescharacteristic
507C4—22no—
508C4—44no—
509C4—2924no—
510C4—5844no—
511C4—732no—
512C4—732no—
513C4—1462no—
514C4#1798953012yes—
515C4C2×#1455667012yes—
516C2—24no—
517C2—732no—
518C2—732no—
519C2—734no—
520C2—1464no—
521C2#2262583414yesdirect product factor
522C2C2×#1798953011yescharacteristic
523C2C22×#1455665311yescharacteristic
524C2C2×#1798958011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×D73D4
cosocleC2×C4×D73C24
hypercenterC22×C4⋊C4#64408
hypocenterC73C2×#1823
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22625834C2direct (N × H)
4. C2×#17989460C2semidirect
16. #17989460C22semidirect
19. C22×C4⋊Dic73C4semidirect
25. C2×C4⋊C4×D73C4semidirect
26. C2×C4⋊C4×D73C4semidirect
29. C22×C4⋊C4×C73C4semidirect
64. C2×C4⋊Dic73C2×C4semidirect
77. C4⋊C4×D73C2×C4semidirect
84. C2×C4⋊C4×C73C2×C4semidirect
255. C2×C73#1823semidirect
260. D73#1823semidirect
268. C73C2×#1823semidirect
283. C22×C4⋊C4#64408semidirect
342. C2×C4⋊C4C2×#64408semidirect
521. C2#22625834direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179895552
C2×#179895292
#226258342
C2×#179894602
C22×C4⋊C4×D732
C2×#182373