Finite Group Databasebeta

← C2×#22608962 #33058132

Subgroups — C2×#22608962 #33058132

Order 18688.

1016 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988920C211yesmaximal, characteristic, complemented
2C2×#17988903C211yesmaximal, characteristic
3C2×#17988526C211yesmaximal, characteristic, complemented
4#22608962C218yesmaximal, direct product factor
5C2×#17988324C211yesmaximal, characteristic, complemented
6C2×#17988321C211yesmaximal, characteristic
7C2×#17988313C211yesmaximal, characteristic, complemented
8C2×#539×C73C211yesmaximal, characteristic
9C22×C4⋊Dic73C2211yescharacteristic
10#17988920—22no—
11#17988920C2214yescomplemented
12#17988903—22no—
13#17988903C2214yes—
14C2×#14556524—21no—
15C2×#14556522—21no—
16C2×#14556515—21no—
17C2×#14556512—21no—
18C2×C22⋊#10596831C2211yescharacteristic
19C2×C22⋊#10596831C2211yescharacteristic
20#17988526—22no—
21#17988526C2214yescomplemented
22C2×#14556498—21no—
23C2×#14556498—21no—
24C2×#14556498C2211yescharacteristic
25#17988324C2214yescomplemented
26#17988321C2214yes—
27#17988313C2214yescomplemented
28#539×C73—22no—
29#539×C73—22no—
30#539×C73—22no—
31#539×C73C2214yes—
32C2×#126×C73—21no—
33C2×#125×C73—21no—
34C2×#123×C73—21no—
35C2×#123×C73—21no—
36C2×C22⋊Q8×C73—21no—
37C2×C22⋊Q8×C73C2211yescharacteristic
38C2×#121×C73C2211yescharacteristic
39C2×C4×D4×C73—21no—
40C22×C4⋊C4×C73C2211yescharacteristic
41C23×Dic73—21no—
42C23×Dic73—21no—
43C22×#10596831—21no—
44C22×#10596831—21no—
45C2×C4⋊Dic73—21no—
46C2×C4⋊Dic73—21no—
47C2×C4⋊Dic73—21no—
48C2×C4⋊Dic73—21no—
49C2×C4⋊Dic73—21no—
50C2×C4⋊Dic73C2312yes—
51#14556524—24no—
52#14556522—24no—
53#14556515—24no—
54#14556512—24no—
55C22⋊#10596831—21no—
56C22⋊#10596831—21no—
57C22⋊#10596831C2312yes—
58C22⋊#10596831C2312yes—
59#14556498—24no—
60#14556498—24no—
61#14556498—21no—
62#14556498C2312yes—
63C22×Q8×C73D411yescharacteristic
64C22×D4×C73—21no—
65C22×D4×C73D411yescharacteristic
66C23×C4×C73—21no—
67C23×C4×C73D411yescharacteristic
68C23×C4×C73D411yescharacteristic
69C23×C4×C73C2311yescharacteristic
70#126×C73—24no—
71#126×C73—24no—
72#125×C73—24no—
73#125×C73—24no—
74#123×C73—24no—
75#123×C73—24no—
76#123×C73—24no—
77#123×C73—24no—
78C22⋊Q8×C73—24no—
79C22⋊Q8×C73—24no—
80C22⋊Q8×C73—21no—
81C22⋊Q8×C73—21no—
82C22⋊Q8×C73D412yes—
83C22⋊Q8×C73C2312yes—
84#121×C73—21no—
85#121×C73—21no—
86#121×C73D412yes—
87#121×C73C2312yes—
88C4×D4×C73—24no—
89C4×D4×C73—24no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73D412yes—
99C2×C4⋊C4×C73D411yescharacteristic
100C2×C4⋊C4×C73D411yescharacteristic
101C2×C4⋊C4×C73C2312yes—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C42×C73—21no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—42no—
111C22×Dic73—42no—
112C22×Dic73—44no—
113C22×Dic73—41no—
114C22×Dic73—41no—
115C22×Dic73—42no—
116C2×#10596831—22no—
117C2×#10596831—22no—
118C2×#10596831—42no—
119C2×#10596831—42no—
120C4⋊Dic73—22no—
121C4⋊Dic73—22no—
122C4⋊Dic73—41no—
123C4⋊Dic73—41no—
124C24×C73—21no—
125C24×C73C2×D411yescharacteristic
126C2×Q8×C73—21no—
127C2×Q8×C73—42no—
128C2×Q8×C73C2×D412yes—
129C2×D4×C73—22no—
130C2×D4×C73—22no—
131C2×D4×C73—21no—
132C2×D4×C73—42no—
133C2×D4×C73—42no—
134C2×D4×C73—42no—
135C2×D4×C73C2×D412yes—
136C22×C4×C73—21no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—21no—
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73—22no—
143C22×C4×C73—22no—
144C22×C4×C73—24no—
145C22×C4×C73—21no—
146C22×C4×C73—42no—
147C22×C4×C73—42no—
148C22×C4×C73—82no—
149C22×C4×C73C2×D412yes—
150C22×C4×C73C2×D411yescharacteristic
151C22×C4×C73C2×D411yescharacteristic
152C22×C4×C73C2×D412yes—
153C22×C4×C73C2×D411yescharacteristic
154C22×C4×C73C2×D411yescharacteristic
155C22×C4×C73C2×D411yescharacteristic
156C22×C4×C73C2411yescharacteristic
157C4⋊C4×C73—24no—
158C4⋊C4×C73—24no—
159C4⋊C4×C73—24no—
160C4⋊C4×C73—22no—
161C4⋊C4×C73—22no—
162C4⋊C4×C73—22no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—21no—
165C4⋊C4×C73—22no—
166C4⋊C4×C73—22no—
167C4⋊C4×C73—22no—
168C4⋊C4×C73C2×D412yes—
169C4⋊C4×C73C2×D412yes—
170C22⋊C4×C73—24no—
171C22⋊C4×C73—24no—
172C22⋊C4×C73—24no—
173C22⋊C4×C73—22no—
174C22⋊C4×C73—22no—
175C22⋊C4×C73—22no—
176C22⋊C4×C73—22no—
177C42×C73—24no—
178C23×C73—22no—
179C23×C73—22no—
180C23×C73—22no—
181C23×C73—42no—
182C23×C73—42no—
183C23×C73—42no—
184C23×C73#12011yescharacteristic
185C23×C73#12011yescharacteristic
186C23×C73#13512yes—
187C23×C73#13712yes—
188C23×C73C22×D411yescharacteristic
189Q8×C73—42no—
190Q8×C73—81no—
191D4×C73—42no—
192D4×C73—42no—
193D4×C73—42no—
194D4×C73—44no—
195D4×C73—81no—
196C2×C4×C73—22no—
197C2×C4×C73—22no—
198C2×C4×C73—22no—
199C2×C4×C73—22no—
200C2×C4×C73—22no—
201C2×C4×C73—22no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—22no—
205C2×C4×C73—41no—
206C2×C4×C73—41no—
207C2×C4×C73—41no—
208C2×C4×C73—41no—
209C2×C4×C73—42no—
210C2×C4×C73—42no—
211C2×C4×C73—42no—
212C2×C4×C73—42no—
213C2×C4×C73—42no—
214C2×C4×C73—42no—
215C2×C4×C73—42no—
216C2×C4×C73—81no—
217C2×C4×C73—84no—
218C2×C4×C73#12011yescharacteristic
219C2×C4×C73#12011yescharacteristic
220C2×C4×C73C22×D411yescharacteristic
221C2×C4×C73C22×D411yescharacteristic
222C2×Dic73—42no—
223C2×Dic73—42no—
224C2×Dic73—44no—
225C2×Dic73—42no—
226C2×Dic73—42no—
227C2×Dic73—84no—
228C2×Dic73—82no—
229C2×Dic73—82no—
230#10596831—42no—
231#10596831—42no—
232C22×C73—24no—
233C22×C73—24no—
234C22×C73—21no—
235C22×C73—21no—
236C22×C73—21no—
237C22×C73—21no—
238C22×C73—42no—
239C22×C73—42no—
240C22×C73—42no—
241C22×C73—84no—
242C22×C73#45212yes—
243C22×C73#45212yes—
244C22×C73#45412yes—
245C22×C73#45812yes—
246C22×C73C2×#12011yescharacteristic
247C22×C73C2×#13511yescharacteristic
248C22×C73C2×#13711yescharacteristic
249C4×C73—21no—
250C4×C73—21no—
251C4×C73—21no—
252C4×C73—21no—
253C4×C73—42no—
254C4×C73—42no—
255C4×C73—42no—
256C4×C73—42no—
257C4×C73—42no—
258Dic73—82no—
259Dic73—82no—
260C2×#1615—731nomaximal, Sylow
261C2×C73—21no—
262C2×C73—21no—
263C2×C73—22no—
264C2×C73—82no—
265C2×C73#161514yescomplemented
266C2×C73C2×#45211yescharacteristic
267C2×C73C2×#45411yescharacteristic
268C2×C73C2×#45811yescharacteristic
269C2×#539D7311yescharacteristic
270C2×#484—731no—
271C2×#481—731no—
272C2×#400—731no—
273#1615—738no—
274C2×#328—731no—
275C2×#327—731no—
276C2×#324—731no—
277C73C2×#161511yescharacteristic, complemented, Sylow
278#539—22no—
279#539—22no—
280#539—22no—
281#539C2×D7314yes—
282C2×#126—21no—
283C2×#125—21no—
284C2×#123—21no—
285C2×#123—21no—
286C2×C22⋊Q8—21no—
287C2×C22⋊Q8C2×D7311yescharacteristic
288C2×#121C2×D7311yescharacteristic
289C2×C4×D4—21no—
290C22×C4⋊C4—731no—
291C22×C4⋊C4C2×D7311yescharacteristic
292#484—734no—
293#484—1462no—
294#481—734no—
295#481—1462no—
296C2×#107—1461no—
297C2×#106—1461no—
298C2×#103—1461no—
299C2×#102—1461no—
300C2×C22⋊C8—731no—
301C2×C22⋊C8—731no—
302#400—734no—
303#400—1462no—
304C2×#95—731no—
305C2×#95—1461no—
306C2×#95—1461no—
307#328—734no—
308#327—734no—
309#324—734no—
310C22×Q8C22⋊D7311yescharacteristic
311C22×D4—21no—
312C22×D4C22⋊D7311yescharacteristic
313C23×C4—21no—
314C23×C4—1461no—
315C23×C4—1461no—
316C23×C4C22⋊D7311yescharacteristic
317C23×C4C22⋊D7311yescharacteristic
318C23×C4C22×D7311yescharacteristic
319C22×C8—1461no—
320C22×C8—1461no—
321#126—24no—
322#126—24no—
323#125—24no—
324#125—24no—
325#123—24no—
326#123—24no—
327#123—24no—
328#123—24no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8C22⋊D7312yes—
334C22⋊Q8C22×D7312yes—
335#121—21no—
336#121—21no—
337#121C22⋊D7312yes—
338#121C22×D7312yes—
339C4×D4—24no—
340C4×D4—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—732no—
350C2×C4⋊C4—1461no—
351C2×C4⋊C4—1461no—
352C2×C4⋊C4—1461no—
353C2×C4⋊C4—1461no—
354C2×C4⋊C4—1461no—
355C2×C4⋊C4C22⋊D7312yes—
356C2×C4⋊C4C22⋊D7311yescharacteristic
357C2×C4⋊C4C22⋊D7311yescharacteristic
358C2×C4⋊C4C22×D7312yes—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C42—21no—
365#107—1464no—
366#106—1464no—
367#103—1464no—
368#102—1464no—
369C22⋊C8—732no—
370C22⋊C8—732no—
371C22⋊C8—1461no—
372C22⋊C8—1461no—
373#95—732no—
374#95—1461no—
375#95—1464no—
376#95—1464no—
377C24—21no—
378C24C2×C22⋊D7311yescharacteristic
379C2×Q8—21no—
380C2×Q8—42no—
381C2×Q8C2×C22⋊D7312yes—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4C2×C22⋊D7312yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—21no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—82no—
402C22×C4—2922no—
403C22×C4—2922no—
404C22×C4—2924no—
405C22×C4—2921no—
406C22×C4—2921no—
407C22×C4—2922no—
408C22×C4—1462no—
409C22×C4—1462no—
410C22×C4C2×C22⋊D7312yes—
411C22×C4C2×C22⋊D7311yescharacteristic
412C22×C4C2×C22⋊D7311yescharacteristic
413C22×C4C2×C22⋊D7312yes—
414C22×C4C2×C22⋊D7311yescharacteristic
415C22×C4C2×C22⋊D7311yescharacteristic
416C22×C4C2×C22⋊D7311yescharacteristic
417C22×C4C23×D7311yescharacteristic
418C2×C8—2922no—
419C2×C8—2922no—
420C2×C8—1462no—
421C2×C8—1462no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—2921no—
434C4⋊C4—2921no—
435C4⋊C4—1462no—
436C4⋊C4—1462no—
437C4⋊C4C2×C22⋊D7312yes—
438C4⋊C4C2×C22⋊D7312yes—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C42—24no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23#1455656011yescharacteristic
454C23#1455656011yescharacteristic
455C23#1455661112yes—
456C23#1455662112yes—
457C23C22×C22⋊D7311yescharacteristic
458Q8—42no—
459Q8—81no—
460D4—42no—
461D4—42no—
462D4—44no—
463D4—42no—
464D4—81no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—81no—
486C2×C4—84no—
487C2×C4—2922no—
488C2×C4—2922no—
489C2×C4—2924no—
490C2×C4—2922no—
491C2×C4—2922no—
492C2×C4—5844no—
493C2×C4—5842no—
494C2×C4—5842no—
495C2×C4#1455656011yescharacteristic
496C2×C4#1455656011yescharacteristic
497C2×C4C22×C22⋊D7311yescharacteristic
498C2×C4C22×C22⋊D7311yescharacteristic
499C8—2922no—
500C8—2922no—
501C22—24no—
502C22—24no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—84no—
511C22#1798874912yes—
512C22#1798874912yes—
513C22#1798876012yes—
514C22#1798877712yes—
515C22C2×#1455656011yescharacteristic
516C22C2×#1455661111yescharacteristic
517C22C2×#1455662111yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—5842no—
528C4—5842no—
529C2—21no—
530C2—21no—
531C2—22no—
532C2—82no—
533C2#2260896214yesdirect product factor
534C2C2×#1798874911yescharacteristic
535C2C2×#1798876011yescharacteristic
536C2C2×#1798877711yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#539×C73C2
socleC23×C73#120
prime radicalC2×#121×C73C22
hypercenterC2×#539D73
hypocenterC73C2×#1615
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C2×#17988920C2semidirect
3. C2×#17988526C2semidirect
4. #22608962C2direct (N × H)
5. C2×#17988324C2semidirect
7. C2×#17988313C2semidirect
11. #17988920C22semidirect
21. #17988526C22semidirect
25. #17988324C22semidirect
27. #17988313C22semidirect
265. C2×C73#1615semidirect
277. C73C2×#1615semidirect
533. C2#22608962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179889202
C2×#179889032
C2×#179885262
#226089622
C2×#179883242
C2×#179883212
C2×#179883132
C2×#539×C732
C2×#161573