Finite Group Databasebeta

← #33093086

Subgroups — #33093086

Order 18688.

1060 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988900C211yesmaximal, characteristic
2#22612437C211yesmaximal, characteristic
3C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
4#22610549C212yesmaximal, complemented
5#22610500C212yesmaximal, complemented
6#22610246C211yesmaximal, characteristic
7#22610118C211yesmaximal, characteristic, complemented
8#22609823C212yesmaximal, complemented
9#22609745C212yesmaximal, complemented
10C22⋊C8×Dic73C211yesmaximal, characteristic, complemented
11C73×#1823C211yesmaximal, characteristic, complemented
12C2×#14556565C2211yescharacteristic
13C2×#14556553C2211yescharacteristic
14C2×#14556551—21no—
15C22×C4⋊Dic73C2211yescharacteristic
16C22×C4×Dic73—21no—
17C22×C4×Dic73C2211yescharacteristic
18#17988900C418yescomplemented
19C2×#14556524C2212yes—
20C2×#14556524C2212yes—
21C2×#14556513C2212yes—
22C2×#14556511C2212yes—
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C8×Dic73C2212yes—
25#17988488C2211yescharacteristic
26#17988483C2211yescharacteristic
27#17988476—21no—
28#17988464—21no—
29C4⋊C4×Dic73—21no—
30C4⋊C4×Dic73—21no—
31C4⋊C4×Dic73C2212yes—
32C4⋊C4×Dic73C2212yes—
33C4⋊C4×Dic73C2211yescharacteristic
34#17988434—21no—
35C2×#14556498—21no—
36#17988350C2212yes—
37#17988349C2212yes—
38#17988341C2212yes—
39C22×C4⋊C4×C73C2211yescharacteristic
40C2×C22⋊C8×C73C2211yescharacteristic
41#380×C73C2211yescharacteristic
42#340×C73C2212yes—
43#340×C73C2212yes—
44C22×D292C2311yescharacteristic
45C22×C22⋊D73—21no—
46C23×Dic73—21no—
47C23×Dic73D411yescharacteristic
48C23×Dic73D411yescharacteristic
49C22×C4×D73—21no—
50C22×#10596831C2312yes—
51#14556565—22no—
52#14556565C2×C414yes—
53#14556553—24no—
54#14556551—44no—
55C2×C4⋊Dic73—24no—
56C2×C4⋊Dic73—21no—
57C2×C4⋊Dic73C2311yescharacteristic
58C2×C4⋊Dic73C2312yes—
59C2×#11924007—21no—
60C2×#11924005—21no—
61C2×#11924005—21no—
62C2×#11924005—21no—
63C2×#11924005—21no—
64C2×C4×Dic73—24no—
65C2×C4×Dic73—21no—
66C2×C4×Dic73—22no—
67C2×C4×Dic73—22no—
68C2×C4×Dic73—44no—
69C2×C4×Dic73D411yescharacteristic
70C2×C4×Dic73D411yescharacteristic
71C2×C4×Dic73C2311yescharacteristic
72C2×C4×Dic73C2311yescharacteristic
73#14556524—24no—
74#14556524C2×C418yescomplemented
75#14556513—24no—
76#14556511C2×C418yescomplemented
77C22⋊#10596831C2×C414yescomplemented
78C8×Dic73—24no—
79#14556498—22no—
80#14556498—22no—
81#14556498—21no—
82#14556498—21no—
83C23×C4×C73—21no—
84C23×C4×C73C2311yescharacteristic
85C22×C8×C73C2312yes—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73C2×C414yescomplemented
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2312yes—
92C2×C22⋊C4×C73—21no—
93C22⋊C8×C73—22no—
94#95×C73—21no—
95C23×D73—21no—
96C2×D292—22no—
97C2×D292—22no—
98C2×D292—21no—
99C2×D292C22×C412yes—
100C2×C22⋊D73—24no—
101C2×C22⋊D73—42no—
102C2×C22⋊D73—42no—
103C22×Dic73—22no—
104C22×Dic73—22no—
105C22×Dic73—24no—
106C22×Dic73—22no—
107C22×Dic73—22no—
108C22×Dic73—21no—
109C22×Dic73—22no—
110C22×Dic73—41no—
111C22×Dic73—42no—
112C22×Dic73—42no—
113C22×Dic73D814yes—
114C22×Dic73C2×D411yescharacteristic
115C22×Dic73C2×D411yescharacteristic
116C22×Dic73C2×D411yescharacteristic
117C22×Dic73C2×D411yescharacteristic
118C2×C4×D73—42no—
119C2×C4×D73—42no—
120C2×C4×D73—42no—
121C2×#10596831—22no—
122C2×#10596831—22no—
123C2×#10596831C22×C414yes—
124C4⋊Dic73—24no—
125C4⋊Dic73—22no—
126C4⋊Dic73—21no—
127C4⋊Dic73C22×C412yes—
128C4⋊Dic73#4114yes—
129#11924007—42no—
130#11924005—24no—
131#11924005—42no—
132#11924005—42no—
133#11924005—42no—
134C4×Dic73—22no—
135C4×Dic73—22no—
136C4×Dic73—22no—
137C4×Dic73—44no—
138C4×Dic73—44no—
139C4×Dic73—42no—
140C4×Dic73#4114yes—
141C24×C73C2×D411yescharacteristic
142C22×C4×C73—22no—
143C22×C4×C73—22no—
144C22×C4×C73—24no—
145C22×C4×C73—22no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—42no—
149C22×C4×C73—42no—
150C22×C4×C73C22×C412yes—
151C22×C4×C73C2×D411yescharacteristic
152C22×C4×C73#4112yes—
153C22×C4×C73C2411yescharacteristic
154C2×C8×C73—22no—
155C2×C8×C73—22no—
156C2×C8×C73—22no—
157C4⋊C4×C73—24no—
158C4⋊C4×C73—22no—
159C4⋊C4×C73—22no—
160C4⋊C4×C73—22no—
161C4⋊C4×C73C22×C414yes—
162C22⋊C4×C73—42no—
163C23×C73—21no—
164C23×C73—21no—
165C23×C73—21no—
166C23×C73—21no—
167C23×C73C4×D412yes—
168C23×C73C2×D812yes—
169C23×C73#13512yes—
170C23×C73C22×D411yescharacteristic
171C22×D73—22no—
172C22×D73—41no—
173C22×D73—41no—
174C22×D73—41no—
175C22×D73—41no—
176C22×D73—41no—
177C22×D73—41no—
178C2×C4×C73—21no—
179C2×C4×C73—21no—
180C2×C4×C73—24no—
181C2×C4×C73—24no—
182C2×C4×C73—24no—
183C2×C4×C73—42no—
184C2×C4×C73—42no—
185C2×C4×C73—48no—
186C2×C4×C73—41no—
187C2×C4×C73—41no—
188C2×C4×C73—41no—
189C2×C4×C73—41no—
190C2×C4×C73—41no—
191C2×C4×C73—41no—
192C2×C4×C73C4×D412yes—
193C2×C4×C73C23×C411yescharacteristic
194C2×C4×C73C2×#4112yes—
195C2×C4×C73C2×#4112yes—
196C2×C4×C73C2×#4111yescharacteristic
197C22⋊D73—48no—
198C2×Dic73—21no—
199C2×Dic73—21no—
200C2×Dic73—21no—
201C2×Dic73—21no—
202C2×Dic73—28no—
203C2×Dic73—22no—
204C2×Dic73—21no—
205C2×Dic73—24no—
206C2×Dic73—21no—
207C2×Dic73—21no—
208C2×Dic73—44no—
209C2×Dic73—48no—
210C2×Dic73—42no—
211C2×Dic73—41no—
212C2×Dic73—41no—
213C2×Dic73—42no—
214C2×Dic73#12312yes—
215C2×Dic73#12312yes—
216C2×Dic73C2×D812yes—
217C2×Dic73C2×D812yes—
218C2×Dic73#13712yes—
219D292—24no—
220D292—42no—
221C4×D73—84no—
222C8×C73—42no—
223#10596831—24no—
224C22×C73—22no—
225C22×C73—22no—
226C22×C73—22no—
227C22×C73—22no—
228C22×C73—22no—
229C22×C73—22no—
230C22×C73C4×D814yes—
231C22×C73C2×C4×D411yescharacteristic
232C22×C73C2×#12311yescharacteristic
233C22×C73#52511yescharacteristic
234C22×C73C22×D811yescharacteristic
235C22×C73C2×#13511yescharacteristic
236C22×C73C2×#13711yescharacteristic
237C22×C73#57511yescharacteristic
238C2×D73—42no—
239C2×D73—42no—
240C2×D73—42no—
241C2×D73—81no—
242C2×D73—81no—
243C2×D73—81no—
244C2×D73—81no—
245C4×C73—22no—
246C4×C73—44no—
247C4×C73—81no—
248C4×C73—81no—
249C4×C73C4×#4112yes—
250C4×C73#52912yes—
251Dic73—22no—
252Dic73—22no—
253Dic73—41no—
254Dic73—44no—
255Dic73—42no—
256Dic73#48014yescomplemented
257C4×#480—731nomaximal, Sylow
258C2×C73—24no—
259C2×C73C4×#12311yescharacteristic
260C2×C73C2×C4×D811yescharacteristic
261C2×C73C4×#13711yescharacteristic
262C2×C73C2×#48011yescharacteristic
263C2×C73#309111yescharacteristic
264C2×C73#310011yescharacteristic
265C2×C73#310811yescharacteristic
266D73—82no—
267C2×#480—731no—
268C4×#121—731no—
269C2×C4×C4⋊C4—731no—
270#1925—732no—
271#1918—732no—
272#1874—731no—
273#1852—731no—
274#1823D7311yescharacteristic, complemented
275C4×#107—732no—
276C4×#102—732no—
277C4×C22⋊C8—731no—
278C73C4×#48011yescharacteristic, complemented, Sylow
279C2×#121—731no—
280C2×C4×D4—731no—
281C2×C4×D4—1461no—
282C22×C4⋊C4—731no—
283C22×C4⋊C4C2×D7311yescharacteristic
284C22×C42—731no—
285C22×C42—1461no—
286#480—738no—
287C2×#107—732no—
288C2×#107—732no—
289C2×#102—732no—
290C2×#102—732no—
291C2×C22⋊C8—731no—
292C2×C22⋊C8C2×D7311yescharacteristic
293C2×C4×C8—732no—
294#390—731no—
295#389—731no—
296#388—1461no—
297#386—1461no—
298#380C2×D7311yescharacteristic
299C4×C4⋊C4—732no—
300C4×C4⋊C4—732no—
301C4×C4⋊C4—731no—
302C4×C4⋊C4—1461no—
303C4×C4⋊C4—1461no—
304C4×C22⋊C4—1461no—
305C2×#95—1461no—
306#340—732no—
307#340—732no—
308#340C2×D7312yes—
309#340C2×D7312yes—
310#336—732no—
311C22×D4—731no—
312C22×D4—1461no—
313C23×C4—21no—
314C23×C4—731no—
315C23×C4—731no—
316C23×C4—1461no—
317C23×C4—1461no—
318C23×C4C22×D7311yescharacteristic
319C22×C8—732no—
320C22×C8C22×D7312yes—
321#121—734no—
322#121—1462no—
323C4×D4—2924no—
324C4×D4—1464no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—732no—
328C2×C4⋊C4—731no—
329C2×C4⋊C4—1461no—
330C2×C4⋊C4—1464no—
331C2×C4⋊C4—1461no—
332C2×C4⋊C4C4×D7314yescomplemented
333C2×C4⋊C4C22×D7311yescharacteristic
334C2×C4⋊C4C22×D7311yescharacteristic
335C2×C4⋊C4C22×D7312yes—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—1461no—
338C2×C22⋊C4—1461no—
339C2×C22⋊C4—1461no—
340C2×C22⋊C4—1461no—
341C2×C42—2924no—
342C2×C42—731no—
343C2×C42—731no—
344C2×C42—731no—
345C2×C42—731no—
346C2×C42—1461no—
347C2×C42—1462no—
348C2×C42—1462no—
349C2×C42—1464no—
350#107—738no—
351#107—1464no—
352#102—738no—
353#102—1464no—
354C22⋊C8—22no—
355C22⋊C8—734no—
356C4×C8—1464no—
357#95—21no—
358#95—1462no—
359#95—1462no—
360#95—1461no—
361#95—1461no—
362C24—1461no—
363C24D4×D7311yescharacteristic
364C2×D4—2922no—
365C2×D4—2922no—
366C2×D4—732no—
367C2×D4—1464no—
368C2×D4—1462no—
369C2×D4—1462no—
370C2×D4—1461no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—2922no—
380C22×C4—2922no—
381C22×C4—2922no—
382C22×C4—2922no—
383C22×C4—2922no—
384C22×C4—2921no—
385C22×C4—731no—
386C22×C4—734no—
387C22×C4—731no—
388C22×C4—731no—
389C22×C4—731no—
390C22×C4—1462no—
391C22×C4—1464no—
392C22×C4—1462no—
393C22×C4—1462no—
394C22×C4—1461no—
395C22×C4—1462no—
396C22×C4—1462no—
397C22×C4C2×C4×D7312yes—
398C22×C4D4×D7311yescharacteristic
399C22×C4#1192402712yes—
400C22×C4C23×D7311yescharacteristic
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—734no—
405C2×C8—1462no—
406C2×C8—1462no—
407C4⋊C4—24no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—2922no—
412C4⋊C4—732no—
413C4⋊C4—734no—
414C4⋊C4—1464no—
415C4⋊C4—1462no—
416C4⋊C4—1461no—
417C4⋊C4C2×C4×D7314yes—
418C22⋊C4—42no—
419C22⋊C4—2922no—
420C22⋊C4—2922no—
421C22⋊C4—2922no—
422C22⋊C4—1464no—
423C42—2924no—
424C42—2924no—
425C42—2922no—
426C42—734no—
427C42—1462no—
428C42—1462no—
429C42—1462no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—2921no—
435C23—2921no—
436C23—2921no—
437C23—2921no—
438C23—2921no—
439C23—2921no—
440C23—1462no—
441C23#1455655112yes—
442C23D8×D7312yes—
443C23#1455661212yes—
444C23C2×D4×D7311yescharacteristic
445D4—2928no—
446D4—2922no—
447D4—1464no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—48no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—2928no—
463C2×C4—2922no—
464C2×C4—2922no—
465C2×C4—2921no—
466C2×C4—2921no—
467C2×C4—2924no—
468C2×C4—5844no—
469C2×C4—732no—
470C2×C4—732no—
471C2×C4—732no—
472C2×C4—732no—
473C2×C4—732no—
474C2×C4—1461no—
475C2×C4—1462no—
476C2×C4—1461no—
477C2×C4—1464no—
478C2×C4—1461no—
479C2×C4—1468no—
480C2×C4—1461no—
481C2×C4—1461no—
482C2×C4—1461no—
483C2×C4—1461no—
484C2×C4#1455655112yes—
485C2×C4C22×C4×D7311yescharacteristic
486C2×C4#41×D7312yes—
487C2×C4#41×D7312yes—
488C2×C4C2×#1192402711yescharacteristic
489C8—42no—
490C8—1464no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—2922no—
498C22—2922no—
499C22—2922no—
500C22—5841no—
501C22—5841no—
502C22—5841no—
503C22—5841no—
504C22#1798866714yes—
505C22C2×#1455655111yescharacteristic
506C22#123×D7311yescharacteristic
507C22#1798909511yescharacteristic
508C22C2×D8×D7311yescharacteristic
509C22C2×#1455661211yescharacteristic
510C22#137×D7311yescharacteristic
511C22#1798938611yescharacteristic
512C4—22no—
513C4—44no—
514C4—81no—
515C4—81no—
516C4—2924no—
517C4—2922no—
518C4—2921no—
519C4—734no—
520C4—1462no—
521C4—1462no—
522C4#1798905512yes—
523C4#1798911412yes—
524C2—24no—
525C2—5842no—
526C2#2261244811yescharacteristic
527C2C2×#1798866711yescharacteristic
528C2#2261874611yescharacteristic
529C2#480×D7311yescharacteristic
530C2#2261984511yescharacteristic
531C2#2261992811yescharacteristic
532C2#2262001411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1823C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
cosocleC22×C4×C73C24
hypercenter#1823D73
hypocenterC73C4×#480
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic73C2semidirect
4. #22610549C2semidirect
5. #22610500C2semidirect
7. #22610118C2semidirect
8. #22609823C2semidirect
9. #22609745C2semidirect
10. C22⋊C8×Dic73C2semidirect
11. C73×#1823C2semidirect
18. #17988900C4semidirect
74. #14556524C2×C4semidirect
76. #14556511C2×C4semidirect
77. C22⋊#10596831C2×C4semidirect
88. C2×C4⋊C4×C73C2×C4semidirect
256. Dic73#480semidirect
274. #1823D73semidirect
278. C73C4×#480semidirect
332. C2×C4⋊C4C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179889002
#226124372
C2×C4⋊C4×Dic732
#226105492
#226105002
#226102462
#226101182
#226098232
#226097452
C22⋊C8×Dic732
C73×#18232
C4×#48073