Finite Group Databasebeta

← C4×#17989028 #33239313

Subgroups — C4×#17989028 #33239313

Order 18688.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989028C211yesmaximal, characteristic
2C4×#14556613C211yesmaximal, characteristic
3#22611800C212yesmaximal, complemented
4#22611793C212yesmaximal, complemented
5C4×#14556537C212yesmaximal, complemented
6C4×#14556534C212yesmaximal, complemented
7#22611717C211yesmaximal, characteristic, complemented
8#22611651C211yesmaximal, characteristic, complemented
9#22611641C211yesmaximal, characteristic
10C4×#14556531C211yesmaximal, characteristic, complemented
11C2×C4×Q16×C73C211yesmaximal, characteristic, complemented
12C2×#14556613C2211yescharacteristic
13C4×#11924028—21no—
14#17989028C418yesdirect product factor
15C2×#14556537C2212yes—
16C2×#14556534C2212yes—
17C2×#14556531C2211yescharacteristic
18C2×#14556531C2211yescharacteristic
19C4×Dic292C2211yescharacteristic
20C4×Dic292C2211yescharacteristic
21C4×#11924017—21no—
22C4×#11924017—21no—
23C4×D584C2211yescharacteristic
24C4×D584C2211yescharacteristic
25#17988625C2211yescharacteristic
26#17988584—21no—
27#17988414C2212yes—
28#17988412C2212yes—
29#17988391C2212yes—
30#17988391C2212yes—
31#17988390C2212yes—
32#17988387C2212yes—
33#17988363C2212yes—
34C4×#11924003C2212yes—
35C22×Q16×C73C2211yescharacteristic
36C2×C4×Q8×C73—21no—
37C4×Q16×C73—21no—
38C4×Q16×C73—21no—
39C4×Q16×C73C2212yes—
40C4×Q16×C73C2212yes—
41C2×#107×C73C2211yescharacteristic
42C2×#103×C73—21no—
43C2×C4×C8×C73C2211yescharacteristic
44C2×#11924028—21no—
45#14556613—22no—
46#14556613C2×C414yes—
47C2×Dic292C2311yescharacteristic
48C2×#11924017—21no—
49C2×D584C2311yescharacteristic
50C4×Dic146—21no—
51C4×Dic146—21no—
52C4×D292—21no—
53C4×D292—21no—
54C4×C22⋊D73—41no—
55C4×C22⋊D73—41no—
56#14556550—21no—
57#14556548—41no—
58C42×D73—41no—
59#14556537C2×C418yescomplemented
60#14556534C2×C418yescomplemented
61#14556531—22no—
62#14556531C2×C414yescomplemented
63C2×#11924003C2312yes—
64C2×#11924003C2312yes—
65#14556525C2311yescharacteristic
66#14556525C2311yescharacteristic
67#14556523—21no—
68#14556516—21no—
69#14556516—21no—
70#14556513—21no—
71#14556513—21no—
72C22×Q8×C73—21no—
73C2×Q16×C73—21no—
74C2×Q16×C73—22no—
75C2×Q16×C73C2×C414yescomplemented
76C2×Q16×C73C2312yes—
77C22×C8×C73D411yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C4×Q8×C73—22no—
80C4×Q8×C73—22no—
81C4×Q8×C73—41no—
82C4×Q8×C73—41no—
83C2×C4⋊C4×C73—21no—
84C2×C4⋊C4×C73—41no—
85C2×C42×C73—41no—
86C2×C42×C73D411yescharacteristic
87#107×C73—21no—
88#107×C73C2312yes—
89#103×C73—22no—
90#103×C73—22no—
91C4×C8×C73D411yescharacteristic
92C4×C8×C73D411yescharacteristic
93C4×C8×C73C2311yescharacteristic
94C4×C8×C73C2311yescharacteristic
95#11924028—24no—
96#11924028—42no—
97C2×Dic146—21no—
98C2×D292—21no—
99C2×C22⋊D73—41no—
100C2×C4×D73—41no—
101C2×C4×D73—41no—
102C2×C4×D73—41no—
103Dic292—21no—
104Dic292C22×C412yes—
105#11924017—24no—
106D584—21no—
107D584C22×C412yes—
108C4⋊Dic73—21no—
109C4⋊Dic73—21no—
110#11924007—41no—
111#11924007—41no—
112C22⋊Dic73—41no—
113#11924005—41no—
114#11924005—41no—
115C4×Dic73—41no—
116C4×Dic73—41no—
117C4×Dic73—41no—
118#11924003—22no—
119#11924003C22×C414yes—
120C2×Q8×C73—24no—
121C2×Q8×C73—22no—
122C2×Q8×C73—41no—
123C2×Q8×C73—42no—
124C22×C4×C73—41no—
125C22×C4×C73—41no—
126C22×C4×C73D811yescharacteristic
127C22×C4×C73D811yescharacteristic
128C22×C4×C73C2×D411yescharacteristic
129Q16×C73—24no—
130Q16×C73—22no—
131Q16×C73C22×C414yes—
132C2×C8×C73—22no—
133C2×C8×C73C22×C412yes—
134C2×C8×C73C2×D411yescharacteristic
135C2×C8×C73C2×D411yescharacteristic
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73#4112yes—
138C2×C8×C73C2411yescharacteristic
139C4⋊C4×C73—22no—
140C4⋊C4×C73—41no—
141C4⋊C4×C73—42no—
142C4⋊C4×C73—42no—
143C42×C73—42no—
144C42×C73—42no—
145C42×C73D811yescharacteristic
146C42×C73D811yescharacteristic
147C42×C73C2×D411yescharacteristic
148C42×C73C2×D411yescharacteristic
149C23×C73C2×D811yescharacteristic
150C22×D73—41no—
151Q8×C73—24no—
152Q8×C73—42no—
153Q8×C73—44no—
154C2×C4×C73—22no—
155C2×C4×C73—41no—
156C2×C4×C73—42no—
157C2×C4×C73—44no—
158C2×C4×C73—42no—
159C2×C4×C73—82no—
160C2×C4×C73C4×D412yes—
161C2×C4×C73C2×D811yescharacteristic
162C2×C4×C73C2×D811yescharacteristic
163C2×C4×C73C2×D811yescharacteristic
164C2×C4×C73C2×D811yescharacteristic
165C2×C4×C73C2×D811yescharacteristic
166C2×C4×C73#13512yes—
167C2×C4×C73C22×D411yescharacteristic
168C22⋊D73—44no—
169C2×Dic73—41no—
170C2×Dic73—41no—
171C2×Dic73—41no—
172D292—22no—
173D292—41no—
174C4×D73—44no—
175C4×D73—82no—
176C4×D73—82no—
177Dic146—22no—
178Dic146—41no—
179C8×C73—21no—
180C8×C73—21no—
181C8×C73C4×D412yes—
182C8×C73C23×C411yescharacteristic
183C8×C73C2×#4111yescharacteristic
184C22×C73—21no—
185C22×C73—21no—
186C22×C73C4×D812yes—
187C22×C73C22×D811yescharacteristic
188C2×D73—42no—
189C2×D73—81no—
190C2×D73—81no—
191C4×C73—21no—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—44no—
195C4×C73—82no—
196C4×C73C4×D812yes—
197C4×C73#51012yescomplemented
198C4×C73C2×C4×D411yescharacteristic
199C4×C73C2×#13511yescharacteristic
200Dic73—42no—
201Dic73—81no—
202Dic73—81no—
203C4×#510—731nomaximal, Sylow
204C2×C73—22no—
205C2×C73C2×C4×D811yescharacteristic
206C2×C73C2×#51011yescharacteristic
207C2×C73#341411yescharacteristic
208D73—82no—
209C2×#510—731no—
210C4×#135—731no—
211C2×C4×Q16D7311yescharacteristic, complemented
212#2176—732no—
213#2175—732no—
214C4×Q32—732no—
215C4×SD32—732no—
216#2159—731no—
217#2141—731no—
218#2139—731no—
219C4×M32—731no—
220C73C4×#51011yescharacteristic, complemented, Sylow
221C2×#135—731no—
222C22×Q16C2×D7311yescharacteristic
223C4×#41—1461no—
224C2×C4×Q8—21no—
225#510—738no—
226C2×Q32—732no—
227C2×SD32—732no—
228C2×M32—731no—
229C2×M32—731no—
230C4×Q16—21no—
231C4×Q16—21no—
232C4×Q16—731no—
233C4×Q16—731no—
234C4×Q16C2×D7312yes—
235C4×Q16C2×D7312yes—
236C4×SD16—1461no—
237C4×SD16—1461no—
238C4×D8—731no—
239C4×D8—731no—
240#427—731no—
241C2×#107C2×D7311yescharacteristic
242#416—1461no—
243C2×#103—21no—
244C2×C4×C8C2×D7311yescharacteristic
245#367—732no—
246#366—732no—
247#358—732no—
248#358—732no—
249#358—732no—
250#357—732no—
251#346—732no—
252C4×C16—732no—
253C2×#41—1461no—
254C22×Q8—21no—
255#135—734no—
256#135—1462no—
257C2×Q16—21no—
258C2×Q16—22no—
259C2×Q16—731no—
260C2×Q16C4×D7314yescomplemented
261C2×Q16C22×D7312yes—
262C2×SD16—1461no—
263C2×D8—731no—
264C22×C8C22⋊D7311yescharacteristic
265C22×C8C22×D7311yescharacteristic
266C4×Q8—22no—
267C4×Q8—22no—
268C4×Q8—41no—
269C4×Q8—41no—
270C4×Q8—1461no—
271C4×Q8—1461no—
272C4×D4—2921no—
273C4×D4—2921no—
274C4×D4—1461no—
275C4×D4—1461no—
276#117—2921no—
277#117—1461no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—41no—
280C2×C42—41no—
281C2×C42—2921no—
282C2×C42C22⋊D7311yescharacteristic
283Q32—738no—
284SD32—738no—
285M32—734no—
286M32—1462no—
287C2×C16—732no—
288C2×C16—732no—
289#107—21no—
290#107—731no—
291#107—731no—
292#107C22×D7312yes—
293#106—1461no—
294#103—22no—
295#103—22no—
296#103—1461no—
297#103—1461no—
298#102—1461no—
299#102—1461no—
300C4×C8C22⋊D7311yescharacteristic
301C4×C8C22⋊D7311yescharacteristic
302C4×C8C22×D7311yescharacteristic
303C4×C8C22×D7311yescharacteristic
304#41—2922no—
305#41—1464no—
306C2×Q8—24no—
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—42no—
310C2×Q8—1461no—
311C2×D4—2921no—
312C2×D4—1461no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—2921no—
316C22×C4—2921no—
317C22×C4—2921no—
318C22×C4#1192401311yescharacteristic
319C22×C4#1192401311yescharacteristic
320C22×C4C2×C22⋊D7311yescharacteristic
321Q16—24no—
322Q16—22no—
323Q16—732no—
324Q16—1461no—
325Q16C2×C4×D7314yes—
326SD16—1464no—
327D8—732no—
328D8—1461no—
329C2×C8—22no—
330C2×C8C2×C4×D7312yes—
331C2×C8C2×C22⋊D7311yescharacteristic
332C2×C8C2×C22⋊D7311yescharacteristic
333C2×C8C2×C22⋊D7311yescharacteristic
334C2×C8#1192402812yes—
335C2×C8C23×D7311yescharacteristic
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—2921no—
341C4⋊C4—2921no—
342C4⋊C4—1461no—
343C4⋊C4—1461no—
344C22⋊C4—2921no—
345C22⋊C4—2921no—
346C22⋊C4—2921no—
347C42—42no—
348C42—42no—
349C42—2921no—
350C42—2921no—
351C42—2921no—
352C42#1192401311yescharacteristic
353C42#1192401311yescharacteristic
354C42C2×C22⋊D7311yescharacteristic
355C42C2×C22⋊D7311yescharacteristic
356C16—734no—
357C16—1462no—
358C23—2921no—
359C23C2×#1192401311yescharacteristic
360Q8—24no—
361Q8—44no—
362Q8—42no—
363Q8—2921no—
364Q8—1462no—
365D4—2924no—
366D4—2921no—
367D4—1462no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—82no—
374C2×C4—2921no—
375C2×C4—2924no—
376C2×C4—2921no—
377C2×C4—2921no—
378C2×C4—5842no—
379C2×C4—5842no—
380C2×C4C4×C22⋊D7312yes—
381C2×C4C2×#1192401311yescharacteristic
382C2×C4C2×#1192401311yescharacteristic
383C2×C4C2×#1192401311yescharacteristic
384C2×C4C2×#1192401311yescharacteristic
385C2×C4C2×#1192401311yescharacteristic
386C2×C4#1455661112yes—
387C2×C4C22×C22⋊D7311yescharacteristic
388C8—21no—
389C8—21no—
390C8C4×C22⋊D7312yes—
391C8C22×C4×D7311yescharacteristic
392C8C2×#1192402811yescharacteristic
393C22—21no—
394C22—21no—
395C22—2922no—
396C22—5841no—
397C22—5841no—
398C22C4×#1192401312yes—
399C22C22×#1192401311yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—82no—
405C4—2922no—
406C4—5841no—
407C4—5841no—
408C4C4×#1192401312yes—
409C4#1798902812yesdirect product factor
410C4C2×C4×C22⋊D7311yescharacteristic
411C4C2×#1455661111yescharacteristic
412C2—22no—
413C2—5842no—
414C2C2×C4×#1192401311yescharacteristic
415C2C2×#1798902811yescharacteristic
416C2#2262306511yescharacteristic
subgroupG/H
centerC2×C4C2×#11924013
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC2×C4×Q16×C73C2
socleC22×C73C22×D8
prime radicalC2×#14556613C22
cosocleC2×C8×C73C24
hypercenterC2×C4×Q16D73
hypocenterC73C4×#510
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #22611800C2semidirect
4. #22611793C2semidirect
5. C4×#14556537C2semidirect
6. C4×#14556534C2semidirect
7. #22611717C2semidirect
8. #22611651C2semidirect
10. C4×#14556531C2semidirect
11. C2×C4×Q16×C73C2semidirect
14. #17989028C4direct (N × H)
59. #14556537C2×C4semidirect
60. #14556534C2×C4semidirect
62. #14556531C2×C4semidirect
75. C2×Q16×C73C2×C4semidirect
197. C4×C73#510semidirect
211. C2×C4×Q16D73semidirect
220. C73C4×#510semidirect
260. C2×Q16C4×D73semidirect
409. C4#17989028direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890282
C4×#145566132
#226118002
#226117932
C4×#145565372
C4×#145565342
#226117172
#226116512
#226116412
C4×#145565312
C2×C4×Q16×C732
C4×#51073