Finite Group Databasebeta

← C2×#22620141 #33954243

Subgroups — C2×#22620141 #33954243

Order 18688.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989195C211yesmaximal, characteristic, complemented
2C2×#17989066C211yesmaximal, characteristic
3#22620141C2116yesmaximal, direct product factor
4C2×#17988921C211yesmaximal, characteristic, complemented
5C2×#17988919C211yesmaximal, characteristic, complemented
6C2×#17988897C211yesmaximal, characteristic, complemented
7C2×#17988885C211yesmaximal, characteristic, complemented
8C2×#17988796C211yesmaximal, characteristic, complemented
9C2×#17988790C211yesmaximal, characteristic, complemented
10C2×#17988750C211yesmaximal, characteristic
11C2×#17988746C211yesmaximal, characteristic
12C2×#17988692C211yesmaximal, characteristic, complemented
13C2×#17988687C211yesmaximal, characteristic, complemented
14C2×C4×Dic292C211yesmaximal, characteristic, complemented
15C2×#17988646C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
17C22×#11924027C2211yescharacteristic
18C22×Dic292C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924016C2211yescharacteristic
21#17989195—24no—
22#17989195C2218yescomplemented
23C2×#14556589C2211yescharacteristic
24C2×#14556586—21no—
25C2×#14556585—21no—
26C2×#14556583—21no—
27C2×#14556582C2211yescharacteristic
28C2×#14556581—21no—
29C2×#14556571C2211yescharacteristic
30C2×#14556567C2211yescharacteristic
31#17989066—24no—
32#17989066C2218yes—
33C2×C4×Dic146C2211yescharacteristic
34C2×C4×Dic146C2211yescharacteristic
35C2×#14556556C2211yescharacteristic
36C2×D4×Dic73C2211yescharacteristic
37C2×C4×C22⋊D73—21no—
38C2×#14556551—21no—
39C2×#14556548C2211yescharacteristic
40C2×#14556547—21no—
41C22×#11924007—21no—
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988921C2218yescomplemented
44#17988919C2218yescomplemented
45#17988897C2218yescomplemented
46#17988885C2218yescomplemented
47#17988796C2218yescomplemented
48#17988790C2218yescomplemented
49#17988750C2218yes—
50#17988746C2218yes—
51#17988692C2218yescomplemented
52#17988687C2218yescomplemented
53C4×Dic292C2218yescomplemented
54#17988646C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556502C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72C4×SD16×C73C2218yescomplemented
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C2×#11924027—24no—
78C2×#11924027—22no—
79C2×#11924027—24no—
80C2×#11924027C2314yes—
81C22×Dic146C2311yescharacteristic
82C22×Dic146C2311yescharacteristic
83C22×C22⋊D73—21no—
84C23×Dic73—21no—
85C23×Dic73—21no—
86C22×C4×D73—21no—
87C22×C4×D73C2311yescharacteristic
88C2×Dic292—24no—
89C2×Dic292C2314yes—
90C2×#11924018—24no—
91C2×#11924018C2314yes—
92C2×#11924016—24no—
93C2×#11924016C2314yes—
94C22×#10596831C2311yescharacteristic
95C22×#10596831C2311yescharacteristic
96#14556589—22no—
97#14556589C2314yes—
98#14556586—28no—
99#14556585—28no—
100#14556583—28no—
101#14556582—22no—
102#14556582C2314yes—
103#14556581—28no—
104#14556571—22no—
105#14556571C2314yes—
106#14556567—22no—
107#14556567C2314yes—
108C4×Dic146—22no—
109C4×Dic146—22no—
110C4×Dic146C2314yes—
111C4×Dic146C2314yes—
112#14556556—22no—
113#14556556C2314yes—
114D4×Dic73—22no—
115D4×Dic73C2314yes—
116C4×C22⋊D73—28no—
117#14556551—28no—
118#14556548D414yes—
119#14556548C2314yes—
120#14556547—28no—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—28no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007D411yescharacteristic
135C2×#11924007D411yescharacteristic
136C4⋊C4×D73—22no—
137C4⋊C4×D73C2314yes—
138C2×C22⋊Dic73—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005D411yescharacteristic
142C2×#11924005D411yescharacteristic
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yes—
148#14556524C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556516C2314yes—
154#14556515C2314yes—
155#14556514C2314yes—
156#14556514C2314yes—
157#14556512C2314yes—
158#14556503C2314yes—
159#14556503C2314yes—
160#14556502C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×D4×C73C2311yescharacteristic
163C23×C4×C73—21no—
164C2×SD16×C73—24no—
165C2×SD16×C73C2314yes—
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yes—
170C4×D4×C73—22no—
171C4×D4×C73C2314yes—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73C2311yescharacteristic
178#106×C73C2314yes—
179#103×C73C2314yes—
180#102×C73C2314yes—
181C4×C8×C73C2314yes—
182C23×D73C2×D411yescharacteristic
183#11924027—216no—
184#11924027—28no—
185#11924027—28no—
186C2×Dic146—21no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—21no—
191C2×Dic146#4114yes—
192C2×Dic146C2412yes—
193C2×Dic146C2412yes—
194C2×C22⋊D73—28no—
195C2×C22⋊D73—24no—
196C22×Dic73—28no—
197C22×Dic73—21no—
198C22×Dic73—24no—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73—24no—
203C22×Dic73—82no—
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—22no—
208C2×C4×D73—22no—
209C2×C4×D73—24no—
210C2×C4×D73—82no—
211C2×C4×D73C2×D412yes—
212C2×C4×D73C2412yes—
213Dic292—28no—
214#11924018—28no—
215#11924016—28no—
216C2×#10596831—22no—
217C2×#10596831—22no—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C4⋊Dic73—21no—
221C4⋊Dic73—21no—
222C4⋊Dic73—24no—
223C4⋊Dic73—24no—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007C2×D414yes—
235#11924007C2×D414yes—
236C22⋊Dic73—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005C2×D414yes—
240#11924005C2×D414yes—
241C4×Dic73—24no—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73C2×D412yes—
245C4×Dic73C2412yes—
246C24×C73—21no—
247C2×Q8×C73—21no—
248C2×Q8×C73—22no—
249C2×Q8×C73—22no—
250C2×Q8×C73C2412yes—
251C2×D4×C73—21no—
252C2×D4×C73—22no—
253C2×D4×C73#4114yes—
254C2×D4×C73C2412yes—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—24no—
259C22×C4×C73—82no—
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2411yescharacteristic
263SD16×C73—28no—
264C2×C8×C73—22no—
265C2×C8×C73—22no—
266C2×C8×C73C2412yes—
267C2×C8×C73C2412yes—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73C2412yes—
272C4⋊C4×C73C2412yes—
273C22⋊C4×C73—24no—
274C42×C73—24no—
275C42×C73C2×D412yes—
276C42×C73C2412yes—
277C23×C73—24no—
278C23×C73—22no—
279C23×C73—42no—
280C23×C73—42no—
281C23×C73C22×D411yescharacteristic
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73C22×D412yes—
286Q8×C73—22no—
287Q8×C73—22no—
288Q8×C73—42no—
289D4×C73—24no—
290D4×C73—22no—
291D4×C73C2×#4114yes—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—42no—
298C2×C4×C73—42no—
299C2×C4×C73—42no—
300C2×C4×C73—84no—
301C2×C4×C73C22×D412yes—
302C2×C4×C73C22×D412yes—
303C2×C4×C73C22×D411yescharacteristic
304C2×C4×C73C2×#4112yes—
305C2×C4×C73C2×#4112yes—
306C2×C4×C73C2511yescharacteristic
307C22⋊D73—216no—
308C2×Dic73—216no—
309C2×Dic73—22no—
310C2×Dic73—24no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—42no—
318C2×Dic73—42no—
319C2×Dic73—42no—
320C2×Dic73—84no—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324C4×D73—24no—
325C4×D73—22no—
326C4×D73—22no—
327C4×D73—84no—
328Dic146—24no—
329Dic146—22no—
330Dic146—22no—
331Dic146—22no—
332Dic146—42no—
333Dic146C2×#4114yes—
334C8×C73—22no—
335C8×C73—22no—
336#10596831—22no—
337#10596831—22no—
338C22×C73—24no—
339C22×C73—48no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73#52512yes—
343C22×C73#57712yes—
344C22×C73#57812yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—22no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—44no—
350C4×C73—22no—
351C4×C73—22no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73—42no—
355C4×C73#52512yes—
356C4×C73C22×#4111yescharacteristic
357C4×C73C22×#4111yescharacteristic
358Dic73—24no—
359Dic73—22no—
360Dic73—22no—
361Dic73—22no—
362Dic73—42no—
363Dic73—42no—
364Dic73—42no—
365C2×#3120—731nomaximal, Sylow
366C2×C73—44no—
367C2×C73#312014yescomplemented
368C2×C73C2×#52511yescharacteristic
369C2×C73C2×#57711yescharacteristic
370C2×C73C2×#57811yescharacteristic
371D73—42no—
372C2×#541—731no—
373C2×#520—731no—
374#3120—7316no—
375C2×#484—731no—
376C2×#483—731no—
377C2×#479—731no—
378C2×#478—731no—
379C2×#462—731no—
380C2×#461—731no—
381C2×#452—731no—
382C2×#452—731no—
383C2×#441—731no—
384C2×#440—731no—
385C2×C4×Q16—731no—
386C2×C4×SD16D7311yescharacteristic, complemented
387C2×#433—731no—
388C73C2×#312011yescharacteristic, complemented, Sylow
389C22×#41—731no—
390C22×Q16—731no—
391C22×Q16—731no—
392C22×SD16—731no—
393C22×SD16C2×D7311yescharacteristic
394#541—738no—
395#541—1464no—
396C2×C4⋊Q8—731no—
397C2×#126—1461no—
398C2×#126—1461no—
399C2×#125—731no—
400C2×#125—1461no—
401C2×#125—1461no—
402C2×C22⋊Q8—731no—
403C2×C22⋊Q8—731no—
404#520—738no—
405#520—1464no—
406C2×C4×Q8—731no—
407C2×C4×Q8—731no—
408C2×C4×Q8—731no—
409C2×C4×Q8C2×D7311yescharacteristic
410C2×C4×D4—731no—
411C2×C4×D4—1461no—
412C2×C4×D4—1461no—
413C2×C4×D4C2×D7311yescharacteristic
414C2×#117—731no—
415C2×#117—1461no—
416C22×C4⋊C4—731no—
417C22×C4⋊C4—1461no—
418#484—738no—
419#483—738no—
420#479—738no—
421#478—738no—
422#462—738no—
423#461—738no—
424#452—738no—
425#452—738no—
426#441—738no—
427#440—738no—
428C4×Q16—738no—
429C4×SD16C2×D7318yescomplemented
430#433—738no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#106—731no—
434C2×#106C2×D7311yescharacteristic
435C2×C4⋊C8—731no—
436C2×C4⋊C8—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—731no—
441C2×#103—731no—
442C2×#103C2×D7311yescharacteristic
443C2×#102—731no—
444C2×#102C2×D7311yescharacteristic
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×#97—731no—
448C2×C4×C8C2×D7311yescharacteristic
449C2×#41—734no—
450C2×#41—1462no—
451C2×#41—1464no—
452C2×#41—1464no—
453C22×Q8—731no—
454C22×Q8—731no—
455C22×Q8C22×D7311yescharacteristic
456C22×D4—1461no—
457C22×D4C22×D7311yescharacteristic
458C23×C4—21no—
459C23×C4—731no—
460C23×C4—1461no—
461C23×C4—1461no—
462C23×C4—1461no—
463C2×Q16—734no—
464C2×Q16—734no—
465C2×Q16—1464no—
466C2×Q16—1464no—
467C2×SD16—24no—
468C2×SD16—734no—
469C2×SD16—1464no—
470C2×SD16C22×D7314yes—
471C22×C8—731no—
472C22×C8—731no—
473C22×C8C22×D7311yescharacteristic
474C22×C8C22×D7311yescharacteristic
475C4⋊Q8—734no—
476C4⋊Q8—1462no—
477#126—1468no—
478#126—1468no—
479#125—734no—
480#125—1468no—
481#125—1462no—
482#125—1468no—
483C22⋊Q8—734no—
484C22⋊Q8—734no—
485C22⋊Q8—1462no—
486C22⋊Q8—1462no—
487C4×Q8—22no—
488C4×Q8—734no—
489C4×Q8—734no—
490C4×Q8—734no—
491C4×Q8—1462no—
492C4×Q8—1462no—
493C4×Q8—1462no—
494C4×Q8C22×D7314yes—
495C4×D4—22no—
496C4×D4—734no—
497C4×D4—1462no—
498C4×D4—1468no—
499C4×D4—1468no—
500C4×D4C22×D7314yes—
501#117—734no—
502#117—734no—
503#117—1468no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—734no—
510C2×C4⋊C4—1462no—
511C2×C4⋊C4—1468no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4C22×D7311yescharacteristic
523C2×C4⋊C4C22×D7311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—731no—
526C2×C22⋊C4—731no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C42—21no—
531C2×C42—731no—
532C2×C42—1461no—
533C2×C42—1461no—
534C2×C42—1461no—
535C2×C42C22×D7311yescharacteristic
536#107—734no—
537#107—734no—
538#106—734no—
539#106C22×D7314yes—
540C4⋊C8—734no—
541C4⋊C8—734no—
542#103—734no—
543#103—734no—
544#103—734no—
545#103—734no—
546#103—734no—
547#103C22×D7314yes—
548#102—734no—
549#102C22×D7314yes—
550C22⋊C8—734no—
551C22⋊C8—734no—
552#97—734no—
553C4×C8C22×D7314yes—
554C24—21no—
555C24—731no—
556#41—1468no—
557#41—14616no—
558#41—1468no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—734no—
563C2×Q8—732no—
564C2×Q8—732no—
565C2×Q8—1462no—
566C2×Q8—1462no—
567C2×Q8—1461no—
568C2×Q8—1461no—
569C2×Q8—1462no—
570C2×Q8C23×D7312yes—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—1464no—
574C2×D4—1468no—
575C2×D4#1192402814yes—
576C2×D4C23×D7312yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—82no—
582C22×C4—5842no—
583C22×C4—5842no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—732no—
588C22×C4—732no—
589C22×C4—1464no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1464no—
594C22×C4—1464no—
595C22×C4—1468no—
596C22×C4—1461no—
597C22×C4—1462no—
598C22×C4—1462no—
599C22×C4D4×D7311yescharacteristic
600C22×C4D4×D7311yescharacteristic
601C22×C4C23×D7311yescharacteristic
602Q16—1468no—
603Q16—1468no—
604SD16—28no—
605SD16—1468no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—732no—
609C2×C8—732no—
610C2×C8—1462no—
611C2×C8—1462no—
612C2×C8C23×D7312yes—
613C2×C8C23×D7312yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—734no—
618C4⋊C4—734no—
619C4⋊C4—732no—
620C4⋊C4—732no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1464no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1461no—
632C4⋊C4—1461no—
633C4⋊C4C23×D7312yes—
634C4⋊C4C23×D7312yes—
635C22⋊C4—24no—
636C22⋊C4—734no—
637C22⋊C4—734no—
638C22⋊C4—1464no—
639C22⋊C4—1464no—
640C22⋊C4—1464no—
641C42—24no—
642C42—732no—
643C42—732no—
644C42—1464no—
645C42—1464no—
646C42—1464no—
647C42D4×D7312yes—
648C42C23×D7312yes—
649C23—22no—
650C23—24no—
651C23—42no—
652C23—42no—
653C23—732no—
654C23—1462no—
655C23—1462no—
656C23—1462no—
657C23C2×D4×D7311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—2922no—
662Q8—734no—
663Q8—1462no—
664Q8—1462no—
665Q8—1462no—
666Q8—1464no—
667D4—22no—
668D4—24no—
669D4—14616no—
670D4C2×#1192402814yes—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—2922no—
681C2×C4—2922no—
682C2×C4—2922no—
683C2×C4—5844no—
684C2×C4—5844no—
685C2×C4—732no—
686C2×C4—732no—
687C2×C4—732no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—14616no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1464no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1464no—
700C2×C4C2×D4×D7312yes—
701C2×C4C2×D4×D7312yes—
702C2×C4C2×D4×D7311yescharacteristic
703C2×C4#41×D7312yes—
704C2×C4C2×#1192402812yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1462no—
709C8—1462no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—2924no—
715C22—1462no—
716C22—1462no—
717C22—1462no—
718C22#1798909612yes—
719C22#1798939312yes—
720C22#1798940112yes—
721C22C22×D4×D7311yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—2922no—
728C4—2922no—
729C4—2922no—
730C4—1462no—
731C4—1462no—
732C4—1462no—
733C4—1464no—
734C4#1798909612yes—
735C4C2×#41×D7311yescharacteristic
736C4C22×#1192402811yescharacteristic
737C2—44no—
738C2—2922no—
739C2#2262014114yesdirect product factor
740C2C2×#1798909611yescharacteristic
741C2C2×#1798939311yescharacteristic
742C2C2×#1798940111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C4×SD16×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924027C22
hypercenterC2×C4×SD16D73
hypocenterC73C2×#3120
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#17989195C2semidirect
3. #22620141C2direct (N × H)
4. C2×#17988921C2semidirect
5. C2×#17988919C2semidirect
6. C2×#17988897C2semidirect
7. C2×#17988885C2semidirect
8. C2×#17988796C2semidirect
9. C2×#17988790C2semidirect
12. C2×#17988692C2semidirect
13. C2×#17988687C2semidirect
14. C2×C4×Dic292C2semidirect
15. C2×#17988646C2semidirect
16. C2×C4×SD16×C73C2semidirect
22. #17989195C22semidirect
43. #17988921C22semidirect
44. #17988919C22semidirect
45. #17988897C22semidirect
46. #17988885C22semidirect
47. #17988796C22semidirect
48. #17988790C22semidirect
51. #17988692C22semidirect
52. #17988687C22semidirect
53. C4×Dic292C22semidirect
54. #17988646C22semidirect
72. C4×SD16×C73C22semidirect
367. C2×C73#3120semidirect
386. C2×C4×SD16D73semidirect
388. C73C2×#3120semidirect
429. C4×SD16C2×D73semidirect
739. C2#22620141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891952
C2×#179890662
#226201412
C2×#179889212
C2×#179889192
C2×#179888972
C2×#179888852
C2×#179887962
C2×#179887902
C2×#179887502
C2×#179887462
C2×#179886922
C2×#179886872
C2×C4×Dic2922
C2×#179886462
C2×C4×SD16×C732
C2×#312073