Finite Group Databasebeta

← C4×#17988859 #33092869

Subgroups — C4×#17988859 #33092869

Order 18688.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988859C211yesmaximal, characteristic
2C4×#14556622C212yesmaximal
3C4×#14556597C211yesmaximal, characteristic
4#22610847C211yesmaximal, characteristic, complemented
5#22610714C211yesmaximal, characteristic, complemented
6#22610583C212yesmaximal, complemented
7#22610449C212yesmaximal
8#22609996C211yesmaximal, characteristic
9C4×#14556527C211yesmaximal, characteristic, complemented
10C4×#14556510C212yesmaximal, complemented
11C2×C4×Q16×C73C211yesmaximal, characteristic, complemented
12C2×#14556622C2212yes—
13C2×#14556597C2211yescharacteristic
14C2×#14556597C2211yescharacteristic
15C4×#11924028C2211yescharacteristic
16#17988859C418yesdirect product factor
17#17988692—22no—
18#17988685—22no—
19C4×#11924018—22no—
20C4×#11924015—22no—
21C2×#14556527C2211yescharacteristic
22C2×#14556527C2211yescharacteristic
23#17988627C2212yes—
24#17988596C2212yes—
25#17988586C2212yes—
26C2×#14556510C2212yes—
27C2×#14556510C2212yes—
28#17988542C2211yescharacteristic
29#17988542C2211yescharacteristic
30#17988541—21no—
31#17988541—21no—
32C4×#11924012C2211yescharacteristic
33C4×#11924012C2212yes—
34C4×#11924011—21no—
35C4×C8×D73—21no—
36#17988356C2212yes—
37#17988356C2212yes—
38#17988352C2212yes—
39C22×Q16×C73C2211yescharacteristic
40C2×C4×Q8×C73C2212yes—
41C4×Q16×C73—21no—
42C4×Q16×C73—21no—
43C4×Q16×C73—21no—
44C4×Q16×C73—21no—
45C2×#107×C73C2211yescharacteristic
46C2×#103×C73C2212yes—
47C2×C4×C8×C73C2211yescharacteristic
48C2×#11924028C2311yescharacteristic
49#14556622—24no—
50#14556622C2×C418yes—
51C2×#11924018—22no—
52C2×#11924015—22no—
53#14556597—22no—
54#14556597—22no—
55#14556597—22no—
56#14556597C2×C414yes—
57C2×#11924012C2312yes—
58C2×#11924012C2312yes—
59C2×#11924012C2311yescharacteristic
60C2×#11924012C2311yescharacteristic
61C2×#11924011—21no—
62C2×#11924011—21no—
63C2×C8×D73—21no—
64C2×C8×D73—21no—
65C4×Dic146D411yescharacteristic
66C4×Dic146D411yescharacteristic
67C4×D292D411yescharacteristic
68C4×D292D411yescharacteristic
69C4×C22⋊D73—21no—
70C4×C22⋊D73—21no—
71#14556550C2311yescharacteristic
72#14556548—21no—
73C42×D73—21no—
74#14556527—22no—
75#14556527C2×C414yescomplemented
76#14556524—22no—
77#14556522—22no—
78#14556515—22no—
79#14556515—22no—
80#14556514—22no—
81#14556511—22no—
82#14556510—24no—
83#14556510C2×C418yescomplemented
84#14556502—22no—
85#14556502—21no—
86#14556501—21no—
87#14556501—21no—
88C4×#10596831—22no—
89C4×#10596831—21no—
90C8×Dic73—21no—
91C8×Dic73—21no—
92C22×Q8×C73C2312yes—
93C2×Q16×C73—21no—
94C2×Q16×C73—21no—
95C2×Q16×C73—22no—
96C2×Q16×C73C2×C414yescomplemented
97C22×C8×C73C2311yescharacteristic
98C22×C8×C73C2311yescharacteristic
99C4×Q8×C73—22no—
100C4×Q8×C73—22no—
101C4×Q8×C73—22no—
102C4×Q8×C73—22no—
103C2×C4⋊C4×C73—22no—
104C2×C4⋊C4×C73C2312yes—
105C2×C42×C73—22no—
106C2×C42×C73C2311yescharacteristic
107#107×C73—21no—
108#107×C73—21no—
109#103×C73—22no—
110#103×C73—22no—
111C4×C8×C73D411yescharacteristic
112C4×C8×C73D411yescharacteristic
113C4×C8×C73D411yescharacteristic
114C4×C8×C73D411yescharacteristic
115#11924028—21no—
116#11924028—21no—
117#11924028C22×C412yes—
118#11924028#4112yes—
119C2×Dic146C2×D411yescharacteristic
120C2×D292C2×D411yescharacteristic
121C2×C22⋊D73—21no—
122C2×C4×D73—21no—
123C2×C4×D73—21no—
124C2×C4×D73—21no—
125#11924018—28no—
126#11924015—28no—
127#11924012—21no—
128#11924012—21no—
129#11924012—22no—
130#11924012—22no—
131#11924012—22no—
132#11924012C22×C412yes—
133#11924012C22×C414yes—
134#11924012#4112yes—
135#11924011—24no—
136#11924011—24no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—22no—
140C2×#10596831—22no—
141C8×D73—24no—
142C8×D73—24no—
143C4⋊Dic73C2×D411yescharacteristic
144C4⋊Dic73C2×D411yescharacteristic
145#11924007—21no—
146#11924007—21no—
147C22⋊Dic73—21no—
148#11924005—21no—
149#11924005—21no—
150C4×Dic73—21no—
151C4×Dic73—21no—
152C4×Dic73—21no—
153C2×Q8×C73—22no—
154C2×Q8×C73—22no—
155C2×Q8×C73—22no—
156C2×Q8×C73—22no—
157C2×Q8×C73—22no—
158C2×Q8×C73C22×C414yes—
159C22×C4×C73—22no—
160C22×C4×C73—22no—
161C22×C4×C73#4111yescharacteristic
162C22×C4×C73#4111yescharacteristic
163C22×C4×C73C2411yescharacteristic
164Q16×C73—24no—
165Q16×C73—24no—
166C2×C8×C73—21no—
167C2×C8×C73—21no—
168C2×C8×C73C22×C412yes—
169C2×C8×C73C2×D411yescharacteristic
170C2×C8×C73C2×D411yescharacteristic
171C2×C8×C73C2×D411yescharacteristic
172C2×C8×C73C2×D411yescharacteristic
173C2×C8×C73#4112yes—
174C4⋊C4×C73—22no—
175C4⋊C4×C73—22no—
176C4⋊C4×C73—42no—
177C4⋊C4×C73—42no—
178C42×C73—42no—
179C42×C73—42no—
180C42×C73C2×D411yescharacteristic
181C42×C73C2×D411yescharacteristic
182C42×C73C2×D411yescharacteristic
183C42×C73C2×D411yescharacteristic
184C23×C73C2×#4111yescharacteristic
185C22×D73—21no—
186Q8×C73—24no—
187Q8×C73—24no—
188Q8×C73—42no—
189Q8×C73—42no—
190C2×C4×C73—22no—
191C2×C4×C73—24no—
192C2×C4×C73—41no—
193C2×C4×C73—42no—
194C2×C4×C73—42no—
195C2×C4×C73—42no—
196C2×C4×C73—82no—
197C2×C4×C73#12111yescharacteristic
198C2×C4×C73#12111yescharacteristic
199C2×C4×C73#12111yescharacteristic
200C2×C4×C73#12111yescharacteristic
201C2×C4×C73C23×C411yescharacteristic
202C2×C4×C73C22×D411yescharacteristic
203C2×C4×C73C22×D411yescharacteristic
204C2×C4×C73C2×#4111yescharacteristic
205C2×C4×C73C2×#4111yescharacteristic
206C2×C4×C73C2×#4111yescharacteristic
207C22⋊D73—22no—
208C22⋊D73—22no—
209C2×Dic73—21no—
210C2×Dic73—21no—
211C2×Dic73—21no—
212D292—21no—
213D292C4×D412yes—
214C4×D73—22no—
215C4×D73—22no—
216C4×D73—42no—
217C4×D73—42no—
218Dic146—21no—
219Dic146C4×D412yes—
220C8×C73—21no—
221C8×C73—21no—
222C8×C73C4×D412yes—
223C8×C73C4×D412yes—
224#10596831—22no—
225#10596831—24no—
226#10596831—22no—
227#10596831—42no—
228C22×C73—21no—
229C22×C73—21no—
230C22×C73C4×#4111yescharacteristic
231C22×C73C2×#12111yescharacteristic
232C22×C73#52911yescharacteristic
233C2×D73—22no—
234C2×D73—41no—
235C2×D73—41no—
236C4×C73—21no—
237C4×C73—21no—
238C4×C73—21no—
239C4×C73—44no—
240C4×C73—82no—
241C4×C73#47312yescomplemented
242C4×C73C2×C4×D411yescharacteristic
243C4×C73C2×C4×D411yescharacteristic
244C4×C73#52511yescharacteristic
245C4×C73#53211yescharacteristic
246Dic73—22no—
247Dic73—41no—
248Dic73—41no—
249C4×#473—731nomaximal, Sylow
250C2×C73—21no—
251C2×C73—21no—
252C2×C73C4×#12111yescharacteristic
253C2×C73C2×#47311yescharacteristic
254C2×C73#306711yescharacteristic
255D73—42no—
256C2×#473—731no—
257C4×#137—732no—
258C2×C4×Q16D7311yescharacteristic, complemented
259C4×#131—731no—
260#1979—731no—
261#1952—731no—
262#1930—732no—
263#1908—732no—
264#1816—731no—
265C4×#108—731no—
266C4×#101—732no—
267C73C4×#47311yescharacteristic, complemented, Sylow
268C2×#137—732no—
269C22×Q16C2×D7311yescharacteristic
270C2×#131—731no—
271C2×#131—731no—
272C4×#41—731no—
273C2×C4×Q8C2×D7312yes—
274#473—738no—
275#441—1462no—
276#440—1462no—
277C4×Q16—21no—
278C4×Q16—21no—
279C4×Q16—21no—
280C4×Q16—21no—
281C4×Q16—1462no—
282C4×SD16—1462no—
283C2×#108—731no—
284C2×#108—731no—
285#428—732no—
286C2×#107C2×D7311yescharacteristic
287#419—732no—
288#417—732no—
289C2×#103C2×D7312yes—
290C2×#101—732no—
291C2×#101—732no—
292#405—731no—
293#405—731no—
294#405—1461no—
295#405—1461no—
296C4×M16—731no—
297C4×M16—732no—
298C4×M16—1461no—
299C2×C4×C8—1461no—
300C2×C4×C8C2×D7311yescharacteristic
301#343—732no—
302#343—732no—
303#341—732no—
304C2×#41—731no—
305C22×Q8C22×D7312yes—
306#137—738no—
307#137—1464no—
308C2×Q16—21no—
309C2×Q16—21no—
310C2×Q16—22no—
311C2×Q16—1462no—
312C2×Q16C4×D7314yescomplemented
313C2×SD16—1462no—
314#131—734no—
315#131—1462no—
316#131—1462no—
317#131—1462no—
318C2×M16—731no—
319C2×M16—731no—
320C2×M16—732no—
321C2×M16—732no—
322C2×M16—1461no—
323C2×M16—1461no—
324C22×C8—1461no—
325C22×C8—1461no—
326C22×C8C22×D7311yescharacteristic
327C22×C8C22×D7311yescharacteristic
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—731no—
333C4×Q8—731no—
334C4×D4—731no—
335C4×D4—731no—
336C4×D4—1461no—
337C4×D4—1461no—
338#117—731no—
339#117—1461no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4C22×D7312yes—
342C2×C42—22no—
343C2×C42—1461no—
344C2×C42C22×D7311yescharacteristic
345#108—734no—
346#108—1462no—
347#107—21no—
348#107—21no—
349#107—1462no—
350#106—1462no—
351#103—22no—
352#103—22no—
353#103—1462no—
354#103—1462no—
355#103—1462no—
356#102—1462no—
357#101—738no—
358#101—1464no—
359#97—1461no—
360#97—1461no—
361#97—1462no—
362#97—1461no—
363C4×C8—1461no—
364C4×C8—1461no—
365C4×C8—1462no—
366C4×C8—1461no—
367C4×C8C22⋊D7311yescharacteristic
368C4×C8C22⋊D7311yescharacteristic
369C4×C8C22⋊D7311yescharacteristic
370C4×C8C22⋊D7311yescharacteristic
371#41—732no—
372#41—732no—
373#41—1461no—
374#41—1461no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—731no—
381C2×Q8C2×C4×D7314yes—
382C2×D4—731no—
383C2×D4—1461no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—1461no—
387C22×C4—1461no—
388C22×C4—1461no—
389C22×C4#1192402711yescharacteristic
390C22×C4#1192402711yescharacteristic
391C22×C4C23×D7311yescharacteristic
392Q16—24no—
393Q16—24no—
394Q16—1468no—
395SD16—1468no—
396M16—732no—
397M16—734no—
398M16—732no—
399M16—1464no—
400M16—1462no—
401M16—1462no—
402M16—1461no—
403M16—1462no—
404M16—1461no—
405M16—1464no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—1464no—
409C2×C8—1462no—
410C2×C8—1462no—
411C2×C8—1461no—
412C2×C8—1461no—
413C2×C8—1464no—
414C2×C8C2×C4×D7312yes—
415C2×C8C2×C22⋊D7311yescharacteristic
416C2×C8C2×C22⋊D7311yescharacteristic
417C2×C8C2×C22⋊D7311yescharacteristic
418C2×C8C2×C22⋊D7311yescharacteristic
419C2×C8#1192402812yes—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C4⋊C4—731no—
425C4⋊C4—731no—
426C4⋊C4—1461no—
427C4⋊C4—1461no—
428C22⋊C4—1461no—
429C22⋊C4—1461no—
430C22⋊C4—1461no—
431C42—42no—
432C42—42no—
433C42—1461no—
434C42—1461no—
435C42—1461no—
436C42D4×D7311yescharacteristic
437C42D4×D7311yescharacteristic
438C42C2×C22⋊D7311yescharacteristic
439C42C2×C22⋊D7311yescharacteristic
440C23—1461no—
441C23C2×#1192402711yescharacteristic
442Q8—24no—
443Q8—24no—
444Q8—42no—
445Q8—42no—
446Q8—732no—
447Q8—1461no—
448D4—732no—
449D4—1462no—
450D4—1462no—
451D4—1461no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4—2922no—
460C2×C4—2922no—
461C2×C4—1461no—
462C2×C4—1461no—
463C2×C4—1461no—
464C2×C4—1462no—
465C2×C4—1462no—
466C2×C4#1455656211yescharacteristic
467C2×C4#1455656211yescharacteristic
468C2×C4#1455656211yescharacteristic
469C2×C4#1455656211yescharacteristic
470C2×C4C22×C4×D7311yescharacteristic
471C2×C4C2×D4×D7311yescharacteristic
472C2×C4C22×C22⋊D7311yescharacteristic
473C2×C4#41×D7311yescharacteristic
474C2×C4#41×D7311yescharacteristic
475C2×C4C2×#1192402811yescharacteristic
476C8—21no—
477C8—21no—
478C8—2922no—
479C8—1464no—
480C8—1462no—
481C8—1462no—
482C8C4×C22⋊D7312yes—
483C8C4×C22⋊D7312yes—
484C22—21no—
485C22—21no—
486C22—2921no—
487C22—2921no—
488C22—1462no—
489C22C4×#1192402711yescharacteristic
490C22C2×#1455656211yescharacteristic
491C22#1798911911yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—44no—
496C4—82no—
497C4—2921no—
498C4—2921no—
499C4—1462no—
500C4#1798885912yesdirect product factor
501C4C4×D4×D7311yescharacteristic
502C4C2×C4×C22⋊D7311yescharacteristic
503C4#1798909411yescharacteristic
504C4#1798913411yescharacteristic
505C2—21no—
506C2—21no—
507C2—2922no—
508C2C4×#1455656211yescharacteristic
509C2C2×#1798885911yescharacteristic
510C2#2261964711yescharacteristic
subgroupG/H
centerC2×C4#14556562
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×C4×Q16×C73C2
socleC22×C73C2×#121
prime radicalC2×#11924028C23
cosocleC22×C4×C73C24
hypercenterC2×C4×Q16D73
hypocenterC73C4×#473
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
4. #22610847C2semidirect
5. #22610714C2semidirect
6. #22610583C2semidirect
9. C4×#14556527C2semidirect
10. C4×#14556510C2semidirect
11. C2×C4×Q16×C73C2semidirect
16. #17988859C4direct (N × H)
75. #14556527C2×C4semidirect
83. #14556510C2×C4semidirect
96. C2×Q16×C73C2×C4semidirect
241. C4×C73#473semidirect
258. C2×C4×Q16D73semidirect
267. C73C4×#473semidirect
312. C2×Q16C4×D73semidirect
500. C4#17988859direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179888592
C4×#145566222
C4×#145565972
#226108472
#226107142
#226105832
#226104492
#226099962
C4×#145565272
C4×#145565102
C2×C4×Q16×C732
C4×#47373