Finite Group Databasebeta

← C2×#22608472 #33053237

Subgroups — C2×#22608472 #33053237

Order 18688.

1510 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989098C211yesmaximal, characteristic
2C2×#17988551C211yesmaximal, characteristic, complemented
3#22608472C218yesmaximal, direct product factor
4C2×#17988323C212yesmaximal, complemented
5C2×#17988320C212yesmaximal, complemented
6C2×#380×C73C211yesmaximal, characteristic, complemented
7C22×#11924028C411yescharacteristic, complemented
8C22×#11924012—21no—
9#17989098—22no—
10#17989098—22no—
11#17989098C414yescomplemented
12#17989098C2214yes—
13C2×#14556574—21no—
14C2×#14556570C411yescharacteristic, complemented
15C2×#14556570C2211yescharacteristic
16C2×#14556565C411yescharacteristic, complemented
17C2×#14556565C2211yescharacteristic
18C2×#14556560—21no—
19C2×C4×C22⋊D73—21no—
20C2×C4×C22⋊D73—21no—
21C2×#14556550C411yescharacteristic, complemented
22#17988551—22no—
23#17988551C2214yescomplemented
24C2×C22⋊#10596831—21no—
25C2×C22⋊#10596831C2212yes—
26#17988323C2218yescomplemented
27#17988320C2218yescomplemented
28C24×C4×C73C2211yescharacteristic
29C22×C4⋊C4×C73—21no—
30C22×C22⋊C4×C73—21no—
31#380×C73—22no—
32#380×C73C2214yescomplemented
33C2×#95×C73C2212yes—
34C2×#11924028—22no—
35C2×#11924028—44no—
36C2×#11924028C2×C414yescomplemented
37C22×Dic146C2×C411yescharacteristic
38C22×D292C2×C411yescharacteristic
39C22×C22⋊D73—21no—
40C22×C22⋊D73—21no—
41C22×C22⋊D73—21no—
42C22×C4×D73—21no—
43C2×#11924012—24no—
44C2×#11924012—44no—
45C22×#10596831—22no—
46#14556574—24no—
47#14556574—24no—
48#14556570—22no—
49#14556570—21no—
50#14556570—21no—
51#14556570C2×C412yes—
52#14556570C2×C414yescomplemented
53#14556570C2312yes—
54#14556565—22no—
55#14556565—21no—
56#14556565—21no—
57#14556565C2×C412yes—
58#14556565C2×C414yescomplemented
59#14556565C2312yes—
60#14556560—24no—
61#14556560—24no—
62C4×C22⋊D73—24no—
63C4×C22⋊D73—24no—
64C4×C22⋊D73—24no—
65C4×C22⋊D73—24no—
66#14556550—22no—
67#14556550C2×C414yescomplemented
68C2×C4⋊Dic73C2×C411yescharacteristic
69C2×C4⋊Dic73C2×C411yescharacteristic
70C2×#11924007—21no—
71C2×#11924007—21no—
72C2×C22⋊Dic73—21no—
73C2×C22⋊Dic73—21no—
74C2×C22⋊Dic73—21no—
75C2×#11924005—21no—
76C2×#11924005—21no—
77C2×C4×Dic73—21no—
78C22⋊#10596831—24no—
79C22⋊#10596831—22no—
80C22⋊#10596831C2314yes—
81C25×C73D411yescharacteristic
82C23×C4×C73—22no—
83C23×C4×C73—44no—
84C23×C4×C73C2×C411yescharacteristic
85C23×C4×C73C2×C411yescharacteristic
86C23×C4×C73C2×C412yes—
87C23×C4×C73D411yescharacteristic
88C23×C4×C73D411yescharacteristic
89C23×C4×C73D412yes—
90C23×C4×C73D411yescharacteristic
91C23×C4×C73D412yes—
92C23×C4×C73C2312yes—
93C23×C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73—24no—
95C2×C4⋊C4×C73—44no—
96C2×C22⋊C4×C73—24no—
97C2×C22⋊C4×C73—44no—
98#95×C73—22no—
99#95×C73C2314yes—
100C23×D73—21no—
101#11924028—48no—
102#11924028—48no—
103C2×Dic146—21no—
104C2×Dic146—42no—
105C2×Dic146C22×C412yes—
106C2×D292—21no—
107C2×D292—42no—
108C2×D292C22×C412yes—
109C2×C22⋊D73—22no—
110C2×C22⋊D73—24no—
111C2×C22⋊D73—24no—
112C2×C22⋊D73—22no—
113C2×C22⋊D73—44no—
114C2×C22⋊D73—44no—
115C2×C22⋊D73—42no—
116C2×C22⋊D73—42no—
117C22×Dic73—21no—
118C22×Dic73—21no—
119C22×Dic73—21no—
120C2×C4×D73—24no—
121C2×C4×D73—44no—
122#11924012—48no—
123C2×#10596831—24no—
124C2×#10596831—44no—
125C4⋊Dic73—21no—
126C4⋊Dic73—21no—
127C4⋊Dic73C22×C412yes—
128C4⋊Dic73C22×C412yes—
129#11924007—22no—
130#11924007—24no—
131#11924007—22no—
132C22⋊Dic73—24no—
133C22⋊Dic73—22no—
134C22⋊Dic73—24no—
135C22⋊Dic73—22no—
136#11924005—22no—
137#11924005—24no—
138#11924005—22no—
139C4×Dic73—24no—
140C24×C73—22no—
141C24×C73—22no—
142C24×C73—42no—
143C24×C73—42no—
144C24×C73C22⋊C411yescharacteristic
145C24×C73C22⋊C411yescharacteristic
146C24×C73C22⋊C412yes—
147C24×C73C2×D411yescharacteristic
148C24×C73C2×D412yes—
149C22×C4×C73—24no—
150C22×C4×C73—24no—
151C22×C4×C73—24no—
152C22×C4×C73—24no—
153C22×C4×C73—44no—
154C22×C4×C73—44no—
155C22×C4×C73—44no—
156C22×C4×C73—44no—
157C22×C4×C73—42no—
158C22×C4×C73—42no—
159C22×C4×C73—42no—
160C22×C4×C73—44no—
161C22×C4×C73—44no—
162C22×C4×C73—44no—
163C22×C4×C73C22⋊C411yescharacteristic
164C22×C4×C73C22⋊C412yes—
165C22×C4×C73C22⋊C412yes—
166C22×C4×C73C22⋊C412yes—
167C22×C4×C73C22⋊C412yes—
168C22×C4×C73C22⋊C412yes—
169C22×C4×C73C22⋊C411yescharacteristic
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C22×C412yes—
172C22×C4×C73C22×C411yescharacteristic
173C22×C4×C73C22×C412yes—
174C22×C4×C73C2×D412yes—
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D412yes—
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D412yes—
180C22×C4×C73C2411yescharacteristic
181C4⋊C4×C73—48no—
182C22⋊C4×C73—48no—
183C23×C73—22no—
184C23×C73—22no—
185C23×C73—22no—
186C23×C73—22no—
187C23×C73—22no—
188C23×C73—22no—
189C23×C73—24no—
190C23×C73—22no—
191C23×C73—22no—
192C23×C73—22no—
193C23×C73—22no—
194C23×C73—42no—
195C23×C73—42no—
196C23×C73—42no—
197C23×C73—42no—
198C23×C73—48no—
199C23×C73—48no—
200C23×C73C2×C22⋊C412yes—
201C23×C73C2×C22⋊C412yes—
202C23×C73C2×C22⋊C411yescharacteristic
203C23×C73C2×C22⋊C411yescharacteristic
204C23×C73AGL(1,ℤ/8)12yes—
205C23×C73#13712yes—
206C23×C73C22×D411yescharacteristic
207C22×D73—22no—
208C22×D73—42no—
209C22×D73—42no—
210C22×D73—42no—
211C2×C4×C73—22no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—24no—
215C2×C4×C73—24no—
216C2×C4×C73—24no—
217C2×C4×C73—24no—
218C2×C4×C73—24no—
219C2×C4×C73—24no—
220C2×C4×C73—42no—
221C2×C4×C73—42no—
222C2×C4×C73—41no—
223C2×C4×C73—42no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—42no—
227C2×C4×C73—41no—
228C2×C4×C73—44no—
229C2×C4×C73—44no—
230C2×C4×C73—44no—
231C2×C4×C73—88no—
232C2×C4×C73#9914yes—
233C2×C4×C73C2×C22⋊C412yes—
234C2×C4×C73C2×C22⋊C411yescharacteristic
235C2×C4×C73C2×C22⋊C411yescharacteristic
236C2×C4×C73C2×C22⋊C412yes—
237C2×C4×C73C23×C411yescharacteristic
238C2×C4×C73C22×D411yescharacteristic
239C22⋊D73—48no—
240C22⋊D73—48no—
241C22⋊D73—42no—
242C22⋊D73—42no—
243C22⋊D73—44no—
244C2×Dic73—22no—
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—42no—
248C2×Dic73—42no—
249C2×Dic73—42no—
250D292—42no—
251D292—42no—
252C4×D73—48no—
253Dic146—42no—
254Dic146—42no—
255#10596831—44no—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73—21no—
260C22×C73—24no—
261C22×C73—24no—
262C22×C73—22no—
263C22×C73—22no—
264C22×C73—22no—
265C22×C73—22no—
266C22×C73—22no—
267C22×C73—22no—
268C22×C73—44no—
269C22×C73—44no—
270C22×C73—48no—
271C22×C73—44no—
272C22×C73—44no—
273C22×C73C2×#9912yes—
274C22×C73#41712yes—
275C22×C73#41712yes—
276C22×C73#42112yes—
277C22×C73C22×C22⋊C411yescharacteristic
278C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C73C2×#13711yescharacteristic
280C2×D73—42no—
281C2×D73—42no—
282C2×D73—42no—
283C2×D73—84no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—21no—
287C4×C73—22no—
288C4×C73—21no—
289C4×C73—84no—
290C4×C73C2×#9914yes—
291Dic73—42no—
292Dic73—42no—
293Dic73—42no—
294C2×#1513—731nomaximal, Sylow
295C2×C73—21no—
296C2×C73—21no—
297C2×C73—22no—
298C2×C73—42no—
299C2×C73—42no—
300C2×C73#151314yescomplemented
301C2×C73C22×#9911yescharacteristic
302C2×C73C2×#41711yescharacteristic
303C2×C73C2×#42111yescharacteristic
304D73—82no—
305C2×#525—731no—
306C2×#407—731no—
307C2×#380D7311yescharacteristic, complemented
308#1513—738no—
309C2×#328—732no—
310C2×#327—732no—
311C73C2×#151311yescharacteristic, complemented, Sylow
312C22×#41—731no—
313C24×C4C2×D7311yescharacteristic
314C22×M16—1461no—
315#525—734no—
316#525—734no—
317#525—1462no—
318#525—1462no—
319C2×#123—1461no—
320C2×C22⋊Q8—731no—
321C2×C22⋊Q8—731no—
322C2×#121—731no—
323C2×#121—731no—
324C2×#120—1461no—
325C2×C4×D4—1461no—
326C2×C4×D4—1461no—
327C2×#117—731no—
328C22×C4⋊C4—21no—
329C22×C22⋊C4—21no—
330#407—734no—
331#407—1462no—
332C2×C22⋊C8—732no—
333C2×C22⋊C8—1461no—
334#380—22no—
335#380C2×D7314yescomplemented
336C2×#95C2×D7312yes—
337#328—738no—
338#327—738no—
339C25C22⋊D7311yescharacteristic
340C2×#41—2924no—
341C2×#41—734no—
342C2×#41—1462no—
343C22×Q8—731no—
344C22×D4—731no—
345C22×D4—1461no—
346C22×D4—1461no—
347C22×D4—1461no—
348C23×C4—22no—
349C23×C4—44no—
350C23×C4—1461no—
351C23×C4C4×D7311yescharacteristic
352C23×C4C4×D7311yescharacteristic
353C23×C4C4×D7312yes—
354C23×C4D29211yescharacteristic
355C23×C4D29211yescharacteristic
356C23×C4D29212yes—
357C23×C4C22⋊D7311yescharacteristic
358C23×C4C22⋊D7312yes—
359C23×C4C22×D7311yescharacteristic
360C23×C4C22×D7312yes—
361C2×M16—2924no—
362C2×M16—1464no—
363C22×C8—1462no—
364#123—1464no—
365#123—1464no—
366C22⋊Q8—732no—
367C22⋊Q8—734no—
368C22⋊Q8—732no—
369C22⋊Q8—1462no—
370C22⋊Q8—1461no—
371C22⋊Q8—1461no—
372#121—732no—
373#121—734no—
374#121—732no—
375#121—1462no—
376#121—1461no—
377#121—1461no—
378#120—1464no—
379#120—1464no—
380C4×D4—1464no—
381C4×D4—1464no—
382C4×D4—1464no—
383C4×D4—1464no—
384#117—734no—
385#117—1462no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—731no—
390C2×C4⋊C4—1461no—
391C2×C4⋊C4—1461no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—1461no—
395C2×C22⋊C4—1461no—
396C2×C22⋊C4—1461no—
397C2×C22⋊C4—1461no—
398C2×C22⋊C4—1461no—
399C2×C42—1461no—
400C22⋊C8—734no—
401C22⋊C8—1462no—
402C22⋊C8—1464no—
403#95—22no—
404#95C22×D7314yes—
405C24—22no—
406C24—22no—
407C24—42no—
408C24—42no—
409C24—1461no—
410C24#1192400511yescharacteristic
411C24#1192400511yescharacteristic
412C24#1192400512yes—
413C24C2×C22⋊D7311yescharacteristic
414C24C2×C22⋊D7312yes—
415#41—2928no—
416#41—2928no—
417C2×Q8—2922no—
418C2×Q8—732no—
419C2×Q8—1461no—
420C2×D4—2922no—
421C2×D4—2924no—
422C2×D4—2924no—
423C2×D4—2922no—
424C2×D4—2922no—
425C2×D4—732no—
426C2×D4—1464no—
427C2×D4—1462no—
428C2×D4—1464no—
429C2×D4—1462no—
430C2×D4—1461no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—2924no—
446C22×C4—1461no—
447C22×C4—1461no—
448C22×C4—1461no—
449C22×C4—1464no—
450C22×C4#1192400512yes—
451C22×C4#1192400512yes—
452C22×C4#1192400512yes—
453C22×C4#1192400511yescharacteristic
454C22×C4#1192400512yes—
455C22×C4#1192400512yes—
456C22×C4#1192400511yescharacteristic
457C22×C4C2×C4×D7312yes—
458C22×C4C2×C4×D7311yescharacteristic
459C22×C4C2×C4×D7312yes—
460C22×C4C2×C4×D7311yescharacteristic
461C22×C4C2×C22⋊D7312yes—
462C22×C4C2×C22⋊D7311yescharacteristic
463C22×C4C2×D29212yes—
464C22×C4C2×D29211yescharacteristic
465C22×C4C2×D29211yescharacteristic
466C22×C4C2×D29212yes—
467C22×C4C23×D7311yescharacteristic
468M16—2928no—
469C2×C8—2924no—
470C2×C8—1464no—
471C4⋊C4—48no—
472C4⋊C4—732no—
473C4⋊C4—732no—
474C4⋊C4—1462no—
475C4⋊C4—1464no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1462no—
479C22⋊C4—48no—
480C22⋊C4—1464no—
481C22⋊C4—1464no—
482C22⋊C4—1462no—
483C22⋊C4—1462no—
484C22⋊C4—1462no—
485C22⋊C4—1464no—
486C22⋊C4—1462no—
487C42—1464no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—24no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—48no—
504C23—48no—
505C23—2922no—
506C23—2922no—
507C23—2922no—
508C23—1462no—
509C23C2×#1192400512yes—
510C23C2×#1192400512yes—
511C23C2×#1192400511yescharacteristic
512C23C2×#1192400511yescharacteristic
513C23#1455661712yes—
514C23#1455662212yes—
515C23C22×C22⋊D7311yescharacteristic
516Q8—2922no—
517Q8—2922no—
518D4—2922no—
519D4—2922no—
520D4—2928no—
521D4—2928no—
522D4—2922no—
523D4—2924no—
524D4—2922no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—88no—
546C2×C4—2922no—
547C2×C4—2922no—
548C2×C4—2922no—
549C2×C4—2928no—
550C2×C4—1462no—
551C2×C4—1462no—
552C2×C4—1462no—
553C2×C4#1455650514yes—
554C2×C4C2×#1192400511yescharacteristic
555C2×C4C2×#1192400512yes—
556C2×C4C2×#1192400511yescharacteristic
557C2×C4C2×#1192400512yes—
558C2×C4C22×C4×D7311yescharacteristic
559C2×C4C22×D29211yescharacteristic
560C8—2924no—
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—44no—
574C22—44no—
575C22—48no—
576C22—44no—
577C22—44no—
578C22—2922no—
579C22—2922no—
580C22—2922no—
581C22—5844no—
582C22C2×#1455650512yes—
583C22#1798858612yes—
584C22#1798858612yes—
585C22#1798860512yes—
586C22C22×#1192400511yescharacteristic
587C22C2×#1455661711yescharacteristic
588C22C2×#1455662211yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—84no—
595C4—2922no—
596C4—2922no—
597C4—2922no—
598C4C2×#1455650514yes—
599C2—21no—
600C2—21no—
601C2—22no—
602C2—42no—
603C2—42no—
604C2—5842no—
605C2#2260847214yesdirect product factor
606C2C22×#1455650511yescharacteristic
607C2C2×#1798858611yescharacteristic
608C2C2×#1798860511yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#380×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC2×#17989098C2
cosocleC22×C4×C73C24
hypercenterC2×#380D73
hypocenterC73C2×#1513
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#17988551C2semidirect
3. #22608472C2direct (N × H)
4. C2×#17988323C2semidirect
5. C2×#17988320C2semidirect
6. C2×#380×C73C2semidirect
7. C22×#11924028C4semidirect
11. #17989098C4semidirect
14. C2×#14556570C4semidirect
16. C2×#14556565C4semidirect
21. C2×#14556550C4semidirect
23. #17988551C22semidirect
26. #17988323C22semidirect
27. #17988320C22semidirect
32. #380×C73C22semidirect
36. C2×#11924028C2×C4semidirect
52. #14556570C2×C4semidirect
58. #14556565C2×C4semidirect
67. #14556550C2×C4semidirect
300. C2×C73#1513semidirect
307. C2×#380D73semidirect
311. C73C2×#1513semidirect
335. #380C2×D73semidirect
605. C2#22608472direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890982
C2×#179885512
#226084722
C2×#179883232
C2×#179883202
C2×#380×C732
C2×#151373