Finite Group Databasebeta

← C2×#22622415 #33964562

Subgroups — C2×#22622415 #33964562

Order 18688.

1942 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×#17989298C211yesmaximal, characteristic, complemented
2C2×#17989290C211yesmaximal, characteristic
3#22622415C2116yesmaximal, direct product factor
4C2×#17988924C211yesmaximal, characteristic, complemented
5C2×#17988907C211yesmaximal, characteristic, complemented
6C2×#17988931C211yesmaximal, characteristic, complemented
7C2×#17988902C211yesmaximal, characteristic, complemented
8C2×#17988891C211yesmaximal, characteristic, complemented
9C2×#17988864C211yesmaximal, characteristic, complemented
10C2×#17988834C211yesmaximal, characteristic, complemented
11C2×#17988817C211yesmaximal, characteristic, complemented
12C2×#17988689C211yesmaximal, characteristic, complemented
13C2×#17988660C211yesmaximal, characteristic, complemented
14C2×#17988626C211yesmaximal, characteristic, complemented
15C2×#107×D73C211yesmaximal, characteristic, complemented
16C2×#501×C73C211yesmaximal, characteristic, complemented
17C22×#11924017C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20#17989298—24no—
21#17989298C2218yescomplemented
22#17989290—24no—
23#17989290C2218yes—
24C2×#14556586—21no—
25C2×#14556582—21no—
26C2×#14556576—21no—
27C2×#14556571C2211yescharacteristic
28C2×#14556571C2211yescharacteristic
29C2×#14556567—21no—
30C2×#14556567—21no—
31C2×#14556566—21no—
32C2×#14556566C2211yescharacteristic
33C2×#14556566C2211yescharacteristic
34C2×C4×Dic146C2211yescharacteristic
35C2×C4×D292C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×#14556553—21no—
38C2×#14556553—21no—
39C2×#14556549C2211yescharacteristic
40C2×C4⋊C4×D73C2211yescharacteristic
41C2×C4⋊C4×D73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988931C2218yescomplemented
44#17988924C2218yescomplemented
45#17988907C2218yescomplemented
46#17988902C2218yescomplemented
47#17988891C2218yescomplemented
48#17988864C2218yescomplemented
49#17988834C2218yescomplemented
50#17988817C2218yescomplemented
51#17988689C2218yescomplemented
52#17988660C2218yescomplemented
53#17988626C2218yescomplemented
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58#107×D73C2218yescomplemented
59C2×#14556522C2211yescharacteristic
60C2×C4⋊#10596831C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556503C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×#125×C73C2211yescharacteristic
71#501×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#107×C73C2211yescharacteristic
74C2×#106×C73C2211yescharacteristic
75C2×#106×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146C2311yescharacteristic
78C22×D292—21no—
79C22×D292—21no—
80C22×D292D411yescharacteristic
81C22×D292C2311yescharacteristic
82C22×C4×D73—21no—
83C22×C4×D73—21no—
84C22×C4×D73—21no—
85C22×C4×D73—21no—
86C22×C4×D73C2311yescharacteristic
87C22×C4×D73C2311yescharacteristic
88C2×#11924017—24no—
89C2×#11924017C2314yes—
90C2×#11924011—24no—
91C2×#11924011C2314yes—
92C22×#10596831C2311yescharacteristic
93C22×#10596831C2311yescharacteristic
94C2×C8×D73—24no—
95C2×C8×D73C2314yes—
96#14556586—28no—
97#14556582—28no—
98#14556576—28no—
99#14556571—22no—
100#14556571—22no—
101#14556571C2314yes—
102#14556571C2314yes—
103#14556567—28no—
104#14556567—28no—
105#14556566—28no—
106#14556566—22no—
107#14556566—22no—
108#14556566C2314yes—
109#14556566C2314yes—
110C4×Dic146—22no—
111C4×Dic146C2314yes—
112C4×D292—22no—
113C4×D292D414yes—
114C4×D292C2314yes—
115C4×D292C2314yes—
116#14556553—28no—
117#14556553—28no—
118#14556549—22no—
119#14556549C2314yes—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73D411yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C4⋊C4×D73—22no—
130C4⋊C4×D73—22no—
131C4⋊C4×D73—22no—
132C4⋊C4×D73C2314yes—
133C4⋊C4×D73C2314yes—
134C4⋊C4×D73C2314yes—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005D411yescharacteristic
142C2×#11924005D411yescharacteristic
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145#14556525C2314yes—
146#14556524C2314yes—
147#14556524C2314yes—
148#14556524C2314yes—
149#14556522C2314yes—
150C4⋊#10596831C2314yes—
151#14556516C2314yes—
152#14556514C2314yes—
153#14556514C2314yes—
154#14556513C2314yes—
155#14556511C2314yes—
156#14556511C2314yes—
157#14556503C2314yes—
158#14556503C2314yes—
159C22×Q8×C73—21no—
160C22×C8×C73C2311yescharacteristic
161C22×C8×C73C2311yescharacteristic
162C4⋊Q8×C73—22no—
163C4⋊Q8×C73C2314yes—
164#125×C73—22no—
165#125×C73C2314yes—
166C2×C4⋊C4×C73—21no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C42×C73C2311yescharacteristic
174#107×C73C2314yes—
175#107×C73C2314yes—
176#106×C73C2314yes—
177#106×C73C2314yes—
178#97×C73C2314yes—
179C23×D73—21no—
180C23×D73C2×D411yescharacteristic
181C23×D73C2×D411yescharacteristic
182C2×Dic146—22no—
183C2×Dic146—22no—
184C2×Dic146—21no—
185C2×Dic146C2412yes—
186C2×D292—24no—
187C2×D292—22no—
188C2×D292—22no—
189C2×D292—24no—
190C2×D292—21no—
191C2×D292—24no—
192C2×D292—44no—
193C2×D292—82no—
194C2×D292C2×D414yes—
195C2×D292C2412yes—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C2×C4×D73—22no—
202C2×C4×D73—22no—
203C2×C4×D73—22no—
204C2×C4×D73—22no—
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—24no—
208C2×C4×D73—24no—
209C2×C4×D73—82no—
210C2×C4×D73—82no—
211C2×C4×D73—82no—
212C2×C4×D73—82no—
213C2×C4×D73C2×D412yes—
214C2×C4×D73C2×D412yes—
215C2×C4×D73C2412yes—
216C2×C4×D73C2412yes—
217#11924017—28no—
218#11924011—28no—
219C2×#10596831—22no—
220C2×#10596831—22no—
221C2×#10596831C2412yes—
222C2×#10596831C2412yes—
223C8×D73—28no—
224C4⋊Dic73—21no—
225C4⋊Dic73—21no—
226C4⋊Dic73—24no—
227C4⋊Dic73—24no—
228C4⋊Dic73C2×D414yes—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005C2×D414yes—
242#11924005C2×D414yes—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C2×Q8×C73—24no—
246C2×Q8×C73—82no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2411yescharacteristic
254C2×C8×C73—22no—
255C2×C8×C73#4114yes—
256C2×C8×C73C2412yes—
257C2×C8×C73C2412yes—
258C4⋊C4×C73—24no—
259C4⋊C4×C73—24no—
260C4⋊C4×C73—24no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73C2412yes—
266C4⋊C4×C73C2412yes—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C42×C73C2×D412yes—
270C42×C73C2412yes—
271C23×C73C22×D411yescharacteristic
272C22×D73—22no—
273C22×D73—22no—
274C22×D73—22no—
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—22no—
278C22×D73—42no—
279C22×D73—42no—
280C22×D73—42no—
281C22×D73#13714yes—
282C22×D73C22×D412yes—
283C22×D73C22×D412yes—
284Q8×C73—84no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—42no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—42no—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D412yes—
297C2×C4×C73C22×D411yescharacteristic
298C2×C4×C73C2×#4112yes—
299C2×C4×C732−1+412yes—
300C2×C4×C73C2511yescharacteristic
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—42no—
307C2×Dic73—42no—
308C2×Dic73—42no—
309C2×Dic73C22×D412yes—
310C2×Dic73C22×D412yes—
311D292—28no—
312D292—22no—
313D292—22no—
314D292—48no—
315D292—42no—
316D292—84no—
317C4×D73—24no—
318C4×D73—24no—
319C4×D73—22no—
320C4×D73—22no—
321C4×D73—22no—
322C4×D73—22no—
323C4×D73—84no—
324C4×D73—84no—
325C4×D73—84no—
326C4×D73—84no—
327Dic146—22no—
328Dic146—22no—
329Dic146—42no—
330C8×C73—22no—
331C8×C73C2×#4114yes—
332#10596831—22no—
333#10596831—22no—
334C22×C73#54712yes—
335C22×C73C2×#13712yes—
336C22×C73#57612yes—
337C22×C73C23×D411yescharacteristic
338C2×D73—28no—
339C2×D73—22no—
340C2×D73—22no—
341C2×D73—22no—
342C2×D73—22no—
343C2×D73—22no—
344C2×D73—44no—
345C2×D73—42no—
346C2×D73—42no—
347C2×D73—42no—
348C2×D73—84no—
349C2×D73C2×#13714yes—
350C4×C73—22no—
351C4×C73—22no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73—42no—
355C4×C73—42no—
356C4×C73#54712yes—
357C4×C73C22×#4111yescharacteristic
358C4×C73C2×2−1+411yescharacteristic
359Dic73—22no—
360Dic73—22no—
361Dic73—42no—
362Dic73—42no—
363Dic73—42no—
364C2×#3346—731nomaximal, Sylow
365C2×C73#334614yescomplemented
366C2×C73C2×#54711yescharacteristic
367C2×C73C22×#13711yescharacteristic
368C2×C73C2×#57611yescharacteristic
369D73—24no—
370D73—42no—
371D73—82no—
372C2×#554—731no—
373C2×#553—731no—
374#3346—7316no—
375C2×#501D7311yescharacteristic, complemented
376C2×#484—731no—
377C2×#481—731no—
378C2×#485—731no—
379C2×#480—731no—
380C2×#479—731no—
381C2×#474—731no—
382C2×#468—731no—
383C2×#465—731no—
384C2×#440—731no—
385C2×#435—731no—
386C2×#428—731no—
387C22×#107—731no—
388C73C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—731no—
390C22×M16—731no—
391C23×C8—731no—
392#554—738no—
393#554—1464no—
394#553—738no—
395#553—1464no—
396C2×C4⋊Q8C2×D7311yescharacteristic
397C2×#126—1461no—
398C2×#125—1461no—
399C2×#125C2×D7311yescharacteristic
400C2×#123—1461no—
401C2×C22⋊Q8—731no—
402C2×C22⋊Q8—731no—
403C2×C22⋊Q8—1461no—
404C2×C22⋊Q8—1461no—
405C2×#121—731no—
406C2×#121—731no—
407C2×#121—1461no—
408C2×C4×Q8—731no—
409C2×C4×D4—731no—
410C2×C4×D4—731no—
411C2×C4×D4—1461no—
412C2×C4×D4—1461no—
413C2×#117—731no—
414C22×C4⋊C4—731no—
415C22×C4⋊C4—731no—
416C22×C4⋊C4—731no—
417#501C2×D7318yescomplemented
418#485—738no—
419#484—738no—
420#481—738no—
421#480—738no—
422#479—738no—
423#474—738no—
424#468—738no—
425#465—738no—
426#440—738no—
427#435—738no—
428#428—738no—
429C2×#107—731no—
430C2×#107—731no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#107—738no—
434C2×#107C2×D7311yescharacteristic
435C2×#107C2×D7311yescharacteristic
436C2×#106—731no—
437C2×#106C2×D7311yescharacteristic
438C2×#106C2×D7311yescharacteristic
439C2×C4⋊C8—731no—
440C2×#103—731no—
441C2×#103—731no—
442C2×#103—731no—
443C2×#102—731no—
444C2×#102—731no—
445C2×#102—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×#97C2×D7311yescharacteristic
449C22×Q8—21no—
450C22×Q8—731no—
451C22×D4—731no—
452C22×D4—731no—
453C22×D4—1461no—
454C22×D4—1461no—
455C23×C4—731no—
456C23×C4—731no—
457C23×C4—1461no—
458C23×C4—1461no—
459C23×C4—1461no—
460C23×C4—1461no—
461C2×SD16—734no—
462C2×SD16—1464no—
463C2×M16—734no—
464C2×M16—1464no—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8—734no—
468C22×C8—1464no—
469C22×C8C22×D7311yescharacteristic
470C22×C8C22×D7311yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8C22×D7314yes—
473#126—1468no—
474#125—22no—
475#125—1468no—
476#125C22×D7314yes—
477#123—1468no—
478C22⋊Q8—734no—
479C22⋊Q8—734no—
480C22⋊Q8—1468no—
481C22⋊Q8—1468no—
482C22⋊Q8—1462no—
483C22⋊Q8—1462no—
484#121—734no—
485#121—734no—
486#121—1462no—
487#121—1462no—
488#121—1468no—
489C4×Q8—734no—
490C4×Q8—1462no—
491C4×D4—734no—
492C4×D4—734no—
493C4×D4—734no—
494C4×D4—1468no—
495C4×D4—1468no—
496C4×D4—1462no—
497#117—734no—
498#117—1462no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—734no—
506C2×C4⋊C4—734no—
507C2×C4⋊C4—734no—
508C2×C4⋊C4—1462no—
509C2×C4⋊C4—1462no—
510C2×C4⋊C4—1462no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4C22×D7311yescharacteristic
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C4⋊C4C22×D7311yescharacteristic
520C2×C4⋊C4C22×D7311yescharacteristic
521C2×C22⋊C4—731no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
529C2×C42—1461no—
530C2×C42—1461no—
531C2×C42C22×D7311yescharacteristic
532#107—734no—
533#107—734no—
534#107—734no—
535#107—734no—
536#107C22×D7314yes—
537#107C22×D7314yes—
538#106—734no—
539#106C22×D7314yes—
540#106C22×D7314yes—
541C4⋊C8—734no—
542#103—734no—
543#103—734no—
544#103—734no—
545#102—734no—
546#102—734no—
547#102—734no—
548C22⋊C8—734no—
549C22⋊C8—734no—
550#97C22×D7314yes—
551C24—731no—
552C24—731no—
553C24—1461no—
554C2×Q8—24no—
555C2×Q8—82no—
556C2×Q8—732no—
557C2×Q8—1462no—
558C2×Q8—1462no—
559C2×Q8—1461no—
560C2×D4—2924no—
561C2×D4—5842no—
562C2×D4—734no—
563C2×D4—732no—
564C2×D4—1464no—
565C2×D4—1464no—
566C2×D4—1464no—
567C2×D4—1461no—
568C2×D4—1462no—
569C2×D4—1462no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—5842no—
575C22×C4—5842no—
576C22×C4—5842no—
577C22×C4—5842no—
578C22×C4—731no—
579C22×C4—731no—
580C22×C4—732no—
581C22×C4—732no—
582C22×C4—732no—
583C22×C4—732no—
584C22×C4—1464no—
585C22×C4—1464no—
586C22×C4—1464no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1464no—
591C22×C4—1462no—
592C22×C4—1462no—
593C22×C4—1462no—
594C22×C4—1462no—
595C22×C4D4×D7311yescharacteristic
596C22×C4D4×D7311yescharacteristic
597C22×C4C23×D7311yescharacteristic
598SD16—1468no—
599M16—1468no—
600C2×C8—22no—
601C2×C8—732no—
602C2×C8—732no—
603C2×C8—1462no—
604C2×C8—1462no—
605C2×C8—1468no—
606C2×C8#1192402914yes—
607C2×C8C23×D7312yes—
608C2×C8C23×D7312yes—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—734no—
617C4⋊C4—732no—
618C4⋊C4—732no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1461no—
626C4⋊C4—1461no—
627C4⋊C4C23×D7312yes—
628C4⋊C4C23×D7312yes—
629C4⋊C4C23×D7312yes—
630C4⋊C4C23×D7312yes—
631C22⋊C4—734no—
632C22⋊C4—734no—
633C22⋊C4—1464no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C42—1464no—
640C42—1464no—
641C42D4×D7312yes—
642C42C23×D7312yes—
643C23—2922no—
644C23—2922no—
645C23—2922no—
646C23—734no—
647C23—732no—
648C23—732no—
649C23—1462no—
650C23—1462no—
651C23—1462no—
652C23—1462no—
653C23—1462no—
654C23—1462no—
655C23C2×D4×D7311yescharacteristic
656Q8—84no—
657Q8—2922no—
658Q8—1462no—
659Q8—1462no—
660D4—2928no—
661D4—2922no—
662D4—5844no—
663D4—1468no—
664D4—1462no—
665D4—1462no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—2922no—
677C2×C4—2922no—
678C2×C4—2922no—
679C2×C4—5844no—
680C2×C4—5844no—
681C2×C4—5844no—
682C2×C4—5844no—
683C2×C4—732no—
684C2×C4—732no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1464no—
695C2×C4—1464no—
696C2×C4C2×D4×D7312yes—
697C2×C4C2×D4×D7312yes—
698C2×C4C2×D4×D7311yescharacteristic
699C2×C4C2×#1192402912yes—
700C2×C4#1455663912yes—
701C2×C4C24×D7311yescharacteristic
702C8—22no—
703C8—1462no—
704C8—1462no—
705C8C2×#1192402914yes—
706C22—2924no—
707C22—2922no—
708C22—2922no—
709C22—2922no—
710C22—5844no—
711C22—734no—
712C22—1462no—
713C22—1462no—
714C22—1462no—
715C22—1462no—
716C22—1462no—
717C22—1468no—
718C22#1798924012yes—
719C22#137×D7312yes—
720C22#1798939112yes—
721C22C22×D4×D7311yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—2922no—
729C4—2922no—
730C4—2922no—
731C4—1462no—
732C4—1462no—
733C4#1798924012yes—
734C4C22×#1192402911yescharacteristic
735C4C2×#1455663911yescharacteristic
736C2—2922no—
737C2—5842no—
738C2—1464no—
739C2#2262241514yesdirect product factor
740C2C2×#1798924011yescharacteristic
741C2C2×#137×D7311yescharacteristic
742C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#501×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989290C2
hypercenterC2×#501D73
hypocenterC73C2×#3346
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#17989298C2semidirect
3. #22622415C2direct (N × H)
4. C2×#17988924C2semidirect
5. C2×#17988907C2semidirect
6. C2×#17988931C2semidirect
7. C2×#17988902C2semidirect
8. C2×#17988891C2semidirect
9. C2×#17988864C2semidirect
10. C2×#17988834C2semidirect
11. C2×#17988817C2semidirect
12. C2×#17988689C2semidirect
13. C2×#17988660C2semidirect
14. C2×#17988626C2semidirect
15. C2×#107×D73C2semidirect
16. C2×#501×C73C2semidirect
21. #17989298C22semidirect
43. #17988931C22semidirect
44. #17988924C22semidirect
45. #17988907C22semidirect
46. #17988902C22semidirect
47. #17988891C22semidirect
48. #17988864C22semidirect
49. #17988834C22semidirect
50. #17988817C22semidirect
51. #17988689C22semidirect
52. #17988660C22semidirect
53. #17988626C22semidirect
58. #107×D73C22semidirect
71. #501×C73C22semidirect
365. C2×C73#3346semidirect
375. C2×#501D73semidirect
388. C73C2×#3346semidirect
417. #501C2×D73semidirect
739. C2#22622415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892982
C2×#179892902
#226224152
C2×#179889242
C2×#179889072
C2×#179889312
C2×#179889022
C2×#179888912
C2×#179888642
C2×#179888342
C2×#179888172
C2×#179886892
C2×#179886602
C2×#179886262
C2×#107×D732
C2×#501×C732
C2×#334673