Finite Group Databasebeta

← C4×#17989026 #33239308

Subgroups — C4×#17989026 #33239308

Order 18688.

674 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989026C211yesmaximal, characteristic
2C4×#14556610C211yesmaximal, characteristic
3C4×Q16×D73C211yesmaximal, characteristic, complemented
4#22611801C211yesmaximal, characteristic, complemented
5#22611799C211yesmaximal, characteristic, complemented
6#22611796C211yesmaximal, characteristic, complemented
7#22611792C211yesmaximal, characteristic, complemented
8C4×Dic584C211yesmaximal, characteristic, complemented
9C4×#14556537C211yesmaximal, characteristic, complemented
10C4×#14556535C211yesmaximal, characteristic, complemented
11#22611718C211yesmaximal, characteristic, complemented
12#22611649C211yesmaximal, characteristic, complemented
13#22611640C211yesmaximal, characteristic
14C4×#14556530C211yesmaximal, characteristic, complemented
15C4×SD32×C73C211yesmaximal, characteristic, complemented
16C2×#14556610C2211yescharacteristic
17C2×Q16×D73C2211yescharacteristic
18C4×#11924027—21no—
19C4×Q8×D73—21no—
20#17989026C418yesdirect product factor
21C2×Dic584C2211yescharacteristic
22C2×#14556537C2211yescharacteristic
23C2×#14556535C2211yescharacteristic
24C2×#14556530C2211yescharacteristic
25C2×#14556530C2211yescharacteristic
26C4×Dic292C2211yescharacteristic
27C4×Dic292C2211yescharacteristic
28Q16×Dic73C2211yescharacteristic
29#17988681C2211yescharacteristic
30#17988681C2211yescharacteristic
31C4×#11924018—21no—
32#17988679—21no—
33#17988678—21no—
34C4×#11924016—21no—
35D8×Dic73C2211yescharacteristic
36#17988624C2211yescharacteristic
37#107×D73C2211yescharacteristic
38#17988580—21no—
39#103×D73—21no—
40C4×C8×D73C2211yescharacteristic
41#17988414C2211yescharacteristic
42#17988413C2211yescharacteristic
43#17988412C2211yescharacteristic
44#17988392C2211yescharacteristic
45#17988392C2211yescharacteristic
46#17988391C2211yescharacteristic
47#17988390C2211yescharacteristic
48#17988390C2211yescharacteristic
49#17988388C2211yescharacteristic
50#17988362C2211yescharacteristic
51#17988362C2211yescharacteristic
52C4×#11924003C2211yescharacteristic
53C2×SD32×C73C2211yescharacteristic
54C4×Q16×C73C2211yescharacteristic
55C4×D8×C73C2211yescharacteristic
56#367×C73C2211yescharacteristic
57#358×C73C2211yescharacteristic
58#357×C73C2211yescharacteristic
59C4×C16×C73C2211yescharacteristic
60C2×#11924027—21no—
61C2×Q8×D73—21no—
62#14556610—22no—
63#14556610C2×C414yes—
64C2×Dic292C2311yescharacteristic
65C2×Dic292C2311yescharacteristic
66C2×#11924018—21no—
67Q16×D73—22no—
68Q16×D73C2×C414yescomplemented
69C2×#11924016—21no—
70C2×C8×D73D411yescharacteristic
71C2×C8×D73C2311yescharacteristic
72Q8×Dic73—21no—
73C4×Dic146—21no—
74C4×Dic146—21no—
75C4×Dic146—41no—
76#14556556—21no—
77#14556556—21no—
78#14556556—41no—
79D4×Dic73—21no—
80C4×C22⋊D73—41no—
81#14556551—41no—
82#14556549—21no—
83#14556547—41no—
84C4⋊C4×D73—21no—
85C4⋊C4×D73—41no—
86C2×C4×Dic73—41no—
87C42×D73—41no—
88C42×D73D411yescharacteristic
89Dic584C2×C414yescomplemented
90#14556537C2×C414yescomplemented
91#14556535C2×C414yescomplemented
92#14556530—22no—
93#14556530C2×C414yescomplemented
94C2×#11924003C2311yescharacteristic
95C2×#11924003C2311yescharacteristic
96#14556525C2311yescharacteristic
97#14556525C2311yescharacteristic
98#14556524—21no—
99#14556522—21no—
100#14556516—21no—
101#14556516—21no—
102#14556515—21no—
103#14556514—21no—
104#14556514—21no—
105#14556512—21no—
106C4×#10596831D411yescharacteristic
107C8×Dic73D411yescharacteristic
108C8×Dic73C2311yescharacteristic
109C2×Q16×C73C2311yescharacteristic
110C2×D8×C73C2311yescharacteristic
111C4×Q8×C73—21no—
112C4×D4×C73—21no—
113SD32×C73C2×C414yescomplemented
114C2×C16×C73C2311yescharacteristic
115C2×C16×C73C2311yescharacteristic
116#107×C73C2311yescharacteristic
117#107×C73C2311yescharacteristic
118#103×C73—21no—
119#102×C73—21no—
120C4×C8×C73C2311yescharacteristic
121#11924027—24no—
122#11924027—42no—
123C2×Dic146—21no—
124C2×Dic146—21no—
125C2×Dic146—41no—
126Q8×D73—24no—
127Q8×D73—42no—
128C2×C22⋊D73—41no—
129C22×Dic73—41no—
130C22×Dic73—41no—
131C2×C4×D73—41no—
132C2×C4×D73—41no—
133C2×C4×D73D811yescharacteristic
134C2×C4×D73D811yescharacteristic
135C2×C4×D73C2×D411yescharacteristic
136Dic292—21no—
137Dic292—21no—
138Dic292C22×C412yes—
139Dic292C22×C412yes—
140#11924018—24no—
141#11924016—24no—
142C2×#10596831C2×D411yescharacteristic
143C2×#10596831C2×D411yescharacteristic
144C8×D73—22no—
145C8×D73C22×C412yes—
146C8×D73#4112yes—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—41no—
150#11924007—41no—
151#11924007—41no—
152#11924007—41no—
153#11924007—41no—
154#11924007—41no—
155C22⋊Dic73—41no—
156#11924005—41no—
157C4×Dic73—41no—
158C4×Dic73—41no—
159C4×Dic73—41no—
160C4×Dic73—41no—
161C4×Dic73—41no—
162C4×Dic73—41no—
163C4×Dic73D811yescharacteristic
164C4×Dic73D811yescharacteristic
165C4×Dic73C2×D411yescharacteristic
166#11924003—21no—
167#11924003C22×C412yes—
168C2×Q8×C73—21no—
169C2×D4×C73—21no—
170C22×C4×C73—41no—
171Q16×C73—21no—
172Q16×C73C22×C412yes—
173D8×C73—21no—
174D8×C73C22×C412yes—
175C2×C8×C73C2×D411yescharacteristic
176C2×C8×C73C2411yescharacteristic
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—41no—
180C22⋊C4×C73—41no—
181C42×C73—41no—
182C42×C73C2×D411yescharacteristic
183C16×C73—21no—
184C16×C73C22×C412yes—
185C23×C73—41no—
186C22×D73C2×D811yescharacteristic
187Q8×C73—22no—
188Q8×C73—41no—
189D4×C73—22no—
190D4×C73—41no—
191C2×C4×C73—41no—
192C2×C4×C73—41no—
193C2×C4×C73—41no—
194C2×C4×C73—82no—
195C2×C4×C73C2×D811yescharacteristic
196C2×C4×C73C2×D811yescharacteristic
197C2×C4×C73C22×D411yescharacteristic
198C22⋊D73—44no—
199C2×Dic73—41no—
200C2×Dic73—41no—
201C2×Dic73—44no—
202C2×Dic73—41no—
203C2×Dic73—41no—
204C2×Dic73—82no—
205C2×Dic73C2×D811yescharacteristic
206C2×Dic73C2×D811yescharacteristic
207C2×Dic73C2×D811yescharacteristic
208C4×D73—22no—
209C4×D73—41no—
210C4×D73—44no—
211C4×D73—82no—
212C4×D73C4×D412yes—
213C4×D73#13512yes—
214Dic146—22no—
215Dic146—22no—
216Dic146—41no—
217Dic146—41no—
218Dic146—44no—
219C8×C73—21no—
220C8×C73C23×C411yescharacteristic
221C8×C73C2×#4111yescharacteristic
222#10596831—21no—
223#10596831C4×D412yes—
224C22×C73—42no—
225C22×C73—81no—
226C22×C73—81no—
227C22×C73C22×D811yescharacteristic
228C2×D73—21no—
229C2×D73—21no—
230C2×D73C4×D812yes—
231C4×C73—21no—
232C4×C73—42no—
233C4×C73—81no—
234C4×C73—81no—
235C4×C73#51012yescomplemented
236C4×C73C2×C4×D411yescharacteristic
237C4×C73C2×#13511yescharacteristic
238Dic73—21no—
239Dic73—21no—
240Dic73—42no—
241Dic73—42no—
242Dic73—81no—
243Dic73—81no—
244Dic73C4×D812yes—
245C4×#510—731nomaximal, Sylow
246C2×C73—82no—
247C2×C73C2×C4×D811yescharacteristic
248C2×C73C2×#51011yescharacteristic
249C2×C73#341411yescharacteristic
250D73—22no—
251C2×#510—731no—
252C4×#135—731no—
253C2×C4×Q16—731no—
254#2176—731no—
255#2176—731no—
256#2175—731no—
257#2175—731no—
258C4×Q32—731no—
259C4×Q32—731no—
260C4×SD32—731no—
261C4×SD32D7311yescharacteristic, complemented
262#2159—731no—
263#2141—731no—
264#2139—731no—
265C4×M32—731no—
266C73C4×#51011yescharacteristic, complemented, Sylow
267C2×#135—731no—
268C22×Q16—731no—
269C4×#41—1461no—
270C2×C4×Q8—1461no—
271#510—738no—
272C2×Q32—731no—
273C2×Q32—731no—
274C2×SD32—731no—
275C2×SD32C2×D7311yescharacteristic
276C2×M32—731no—
277C2×M32—731no—
278C4×Q16—731no—
279C4×Q16—731no—
280C4×Q16—731no—
281C4×Q16—731no—
282C4×Q16—731no—
283C4×Q16—1461no—
284C4×Q16—1461no—
285C4×Q16C2×D7311yescharacteristic
286C4×SD16—1461no—
287C4×SD16—1461no—
288C4×D8—731no—
289C4×D8C2×D7311yescharacteristic
290#427—731no—
291C2×#107—731no—
292#416—1461no—
293C2×#103—1461no—
294C2×C4×C8—731no—
295#367—731no—
296#367C2×D7311yescharacteristic
297#366—731no—
298#366—731no—
299#358—731no—
300#358—731no—
301#358—731no—
302#358—731no—
303#358—731no—
304#358C2×D7311yescharacteristic
305#357—731no—
306#357C2×D7311yescharacteristic
307#346—731no—
308#346—731no—
309C4×C16—731no—
310C4×C16C2×D7311yescharacteristic
311C2×#41—1461no—
312C22×Q8—1461no—
313#135—734no—
314#135—1462no—
315C2×Q16—734no—
316C2×Q16—731no—
317C2×Q16—731no—
318C2×Q16—1462no—
319C2×Q16—1461no—
320C2×Q16C22×D7311yescharacteristic
321C2×SD16—1461no—
322C2×D8C22×D7311yescharacteristic
323C22×C8—731no—
324C22×C8—731no—
325C4×Q8—21no—
326C4×Q8—2921no—
327C4×Q8—2921no—
328C4×Q8—1461no—
329C4×Q8—1461no—
330C4×Q8—1461no—
331C4×Q8—1461no—
332C4×Q8—1461no—
333C4×D4—21no—
334C4×D4—2921no—
335C4×D4—2921no—
336C4×D4—1461no—
337#117—2921no—
338#117—1461no—
339C2×C4⋊C4—2921no—
340C2×C4⋊C4—1461no—
341C2×C42—2921no—
342C2×C42—2921no—
343C2×C42—731no—
344Q32—734no—
345Q32—734no—
346SD32—734no—
347SD32C4×D7314yescomplemented
348M32—734no—
349M32—1462no—
350C2×C16—731no—
351C2×C16—731no—
352C2×C16C22×D7311yescharacteristic
353C2×C16C22×D7311yescharacteristic
354#107—731no—
355#107—731no—
356#107—1461no—
357#107C22×D7311yescharacteristic
358#107C22×D7311yescharacteristic
359#106—1461no—
360#103—21no—
361#103—1461no—
362#103—1461no—
363#103—1461no—
364#103—1461no—
365#103—1461no—
366#102—21no—
367#102—1461no—
368C4×C8—731no—
369C4×C8—731no—
370C4×C8—731no—
371C4×C8C22×D7311yescharacteristic
372#41—2922no—
373#41—1464no—
374C2×Q8—21no—
375C2×Q8—2921no—
376C2×Q8—2922no—
377C2×Q8—1464no—
378C2×Q8—1461no—
379C2×Q8—1461no—
380C2×D4—21no—
381C2×D4—2921no—
382C22×C4—41no—
383C22×C4—2921no—
384C22×C4—2921no—
385C22×C4—2921no—
386C22×C4—2921no—
387C22×C4—731no—
388C22×C4—731no—
389C22×C4—731no—
390Q16—21no—
391Q16—732no—
392Q16—732no—
393Q16—1464no—
394Q16—1461no—
395Q16—1461no—
396Q16C2×C4×D7312yes—
397SD16—1464no—
398D8—21no—
399D8C2×C4×D7312yes—
400C2×C8—731no—
401C2×C8—732no—
402C2×C8—732no—
403C2×C8—731no—
404C2×C8—1462no—
405C2×C8D4×D7311yescharacteristic
406C2×C8C23×D7311yescharacteristic
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—41no—
410C4⋊C4—2921no—
411C4⋊C4—2921no—
412C4⋊C4—2921no—
413C4⋊C4—2921no—
414C4⋊C4—2921no—
415C4⋊C4—2921no—
416C4⋊C4—1461no—
417C4⋊C4—1461no—
418C22⋊C4—41no—
419C22⋊C4—2921no—
420C22⋊C4—2921no—
421C42—41no—
422C42—2921no—
423C42—2921no—
424C42—2921no—
425C42—2921no—
426C42—2921no—
427C42—2921no—
428C42—731no—
429C42—731no—
430C42—731no—
431C42D4×D7311yescharacteristic
432C16—21no—
433C16—732no—
434C16—1461no—
435C16C2×C4×D7312yes—
436C23—41no—
437C23—731no—
438Q8—22no—
439Q8—41no—
440Q8—2924no—
441Q8—2921no—
442Q8—2921no—
443Q8—1462no—
444Q8—1462no—
445D4—22no—
446D4—41no—
447D4—2924no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—82no—
452C2×C4—2921no—
453C2×C4—2924no—
454C2×C4—2921no—
455C2×C4—2921no—
456C2×C4—2924no—
457C2×C4—2921no—
458C2×C4—2921no—
459C2×C4—5842no—
460C2×C4—5842no—
461C2×C4—731no—
462C2×C4—732no—
463C2×C4—732no—
464C2×C4—731no—
465C2×C4—731no—
466C2×C4—1462no—
467C2×C4D8×D7311yescharacteristic
468C2×C4D8×D7311yescharacteristic
469C2×C4C2×D4×D7311yescharacteristic
470C8—21no—
471C8—732no—
472C8—1461no—
473C8C22×C4×D7311yescharacteristic
474C8#41×D7311yescharacteristic
475C22—42no—
476C22—81no—
477C22—81no—
478C22—732no—
479C22—1461no—
480C22—1461no—
481C22C2×D8×D7311yescharacteristic
482C4—21no—
483C4—42no—
484C4—81no—
485C4—81no—
486C4—2922no—
487C4—2922no—
488C4—5841no—
489C4—5841no—
490C4—732no—
491C4—1461no—
492C4—1461no—
493C4#1798902612yesdirect product factor
494C4C4×D4×D7311yescharacteristic
495C4#135×D7311yescharacteristic
496C2—82no—
497C2—1462no—
498C2C4×D8×D7311yescharacteristic
499C2C2×#1798902611yescharacteristic
500C2#2262306411yescharacteristic
subgroupG/H
centerC2×C4D8×D73
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC4×SD32×C73C2
socleC22×C73C22×D8
prime radicalC2×#14556610C22
cosocleC2×C8×C73C24
hypercenterC4×SD32D73
hypocenterC73C4×#510
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
3. C4×Q16×D73C2semidirect
4. #22611801C2semidirect
5. #22611799C2semidirect
6. #22611796C2semidirect
7. #22611792C2semidirect
8. C4×Dic584C2semidirect
9. C4×#14556537C2semidirect
10. C4×#14556535C2semidirect
11. #22611718C2semidirect
12. #22611649C2semidirect
14. C4×#14556530C2semidirect
15. C4×SD32×C73C2semidirect
20. #17989026C4direct (N × H)
68. Q16×D73C2×C4semidirect
89. Dic584C2×C4semidirect
90. #14556537C2×C4semidirect
91. #14556535C2×C4semidirect
93. #14556530C2×C4semidirect
113. SD32×C73C2×C4semidirect
235. C4×C73#510semidirect
261. C4×SD32D73semidirect
266. C73C4×#510semidirect
347. SD32C4×D73semidirect
493. C4#17989026direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890262
C4×#145566102
C4×Q16×D732
#226118012
#226117992
#226117962
#226117922
C4×Dic5842
C4×#145565372
C4×#145565352
#226117182
#226116492
#226116402
C4×#145565302
C4×SD32×C732
C4×#51073