Finite Group Databasebeta

← C2×#22622555 #33964732

Subgroups — C2×#22622555 #33964732

Order 18688.

1930 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×#17989300C211yesmaximal, characteristic
2C2×#17989295C211yesmaximal, characteristic, complemented
3#22622555C2116yesmaximal, direct product factor
4C2×#17988991C211yesmaximal, characteristic, complemented
5C2×#17988927C211yesmaximal, characteristic, complemented
6C2×#17988902C211yesmaximal, characteristic, complemented
7C2×#17988901C211yesmaximal, characteristic, complemented
8C2×#17988880C211yesmaximal, characteristic, complemented
9C2×#17988876C211yesmaximal, characteristic, complemented
10C2×#17988836C211yesmaximal, characteristic, complemented
11C2×#17988835C211yesmaximal, characteristic, complemented
12C2×#17988672C211yesmaximal, characteristic, complemented
13C2×#17988662C211yesmaximal, characteristic, complemented
14C2×#17988630C211yesmaximal, characteristic, complemented
15C2×#17988626C211yesmaximal, characteristic, complemented
16C2×#485×C73C211yesmaximal, characteristic, complemented
17C22×#11924015C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20#17989300—24no—
21#17989300C2218yes—
22#17989295—24no—
23#17989295C2218yescomplemented
24C2×#14556590C2211yescharacteristic
25C2×#14556590C2211yescharacteristic
26C2×#14556581—21no—
27C2×#14556579—21no—
28C2×#14556577—21no—
29C2×#14556571—21no—
30C2×#14556568—21no—
31C2×#14556567C2211yescharacteristic
32C2×#14556566C2211yescharacteristic
33C2×#14556565C2211yescharacteristic
34C2×#14556564—21no—
35C2×Q8×Dic73C2211yescharacteristic
36C2×#14556553C2211yescharacteristic
37C2×C4×C22⋊D73C2211yescharacteristic
38C2×#14556551—21no—
39C2×#14556549C2211yescharacteristic
40C2×#14556548—21no—
41C22×C4⋊Dic73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988991C2218yescomplemented
44#17988927C2218yescomplemented
45#17988902C2218yescomplemented
46#17988901C2218yescomplemented
47#17988880C2218yescomplemented
48#17988876C2218yescomplemented
49#17988836C2218yescomplemented
50#17988835C2218yescomplemented
51#17988672C2218yescomplemented
52#17988662C2218yescomplemented
53#17988630C2218yescomplemented
54#17988626C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556525C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556524C2211yescharacteristic
59C2×#14556524C2211yescharacteristic
60C2×#14556522C2211yescharacteristic
61C2×#14556522C2211yescharacteristic
62C2×#14556520C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×C22⋊Q8×C73C2211yescharacteristic
70C2×#117×C73C2211yescharacteristic
71#485×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×D292—21no—
80C22×D292C2311yescharacteristic
81C22×C22⋊D73—21no—
82C22×C22⋊D73D411yescharacteristic
83C23×Dic73—21no—
84C22×C4×D73—21no—
85C22×C4×D73—21no—
86C22×C4×D73C2311yescharacteristic
87C2×#11924015—24no—
88C2×#11924015C2314yes—
89C2×#11924012—24no—
90C2×#11924012C2314yes—
91C2×#11924011—24no—
92C2×#11924011C2314yes—
93C22×#10596831C2311yescharacteristic
94C22×#10596831C2311yescharacteristic
95#14556590—22no—
96#14556590—22no—
97#14556590C2314yes—
98#14556590C2314yes—
99#14556581—28no—
100#14556579—28no—
101#14556577—28no—
102#14556571—28no—
103#14556568—28no—
104#14556567—22no—
105#14556567C2314yes—
106#14556566—22no—
107#14556566C2314yes—
108#14556565—22no—
109#14556565C2314yes—
110#14556564—28no—
111Q8×Dic73—22no—
112Q8×Dic73C2314yes—
113#14556553—22no—
114#14556553C2314yes—
115C4×C22⋊D73D414yes—
116C4×C22⋊D73C2314yes—
117#14556551—28no—
118#14556549—22no—
119#14556549C2314yes—
120#14556548—28no—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73—22no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2314yes—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007D411yescharacteristic
133C4⋊C4×D73—22no—
134C4⋊C4×D73C2314yes—
135C2×C22⋊Dic73D411yescharacteristic
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005D411yescharacteristic
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145#14556525C2314yes—
146#14556525C2314yes—
147#14556524C2314yes—
148#14556524C2314yes—
149#14556524C2314yes—
150#14556522C2314yes—
151#14556522C2314yes—
152#14556520C2314yes—
153#14556515C2314yes—
154#14556513C2314yes—
155#14556513C2314yes—
156#14556511C2314yes—
157#14556503C2314yes—
158C8×Dic73C2314yes—
159C22×Q8×C73C2311yescharacteristic
160C23×C4×C73C2311yescharacteristic
161C22×C8×C73C2311yescharacteristic
162C22×C8×C73C2311yescharacteristic
163C22⋊Q8×C73—22no—
164C22⋊Q8×C73C2314yes—
165#117×C73—22no—
166#117×C73C2314yes—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C22⋊C4×C73—21no—
172C2×C22⋊C4×C73—21no—
173C2×C42×C73—21no—
174#107×C73C2314yes—
175#106×C73C2314yes—
176#103×C73C2314yes—
177#103×C73C2314yes—
178C22⋊C8×C73C2314yes—
179C23×D73—21no—
180C23×D73C2×D411yescharacteristic
181C2×Dic146—24no—
182C2×Dic146—24no—
183C2×Dic146—82no—
184C2×Dic146—82no—
185C2×D292—22no—
186C2×D292—22no—
187C2×D292—21no—
188C2×D292—24no—
189C2×D292—82no—
190C2×D292C2412yes—
191C2×C22⋊D73—24no—
192C2×C22⋊D73—24no—
193C2×C22⋊D73—82no—
194C2×C22⋊D73C2×D414yes—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—24no—
199C22×Dic73—82no—
200C22×Dic73C2×D411yescharacteristic
201C22×Dic73C2×D411yescharacteristic
202C22×Dic73C2×D411yescharacteristic
203C2×C4×D73—22no—
204C2×C4×D73—22no—
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—44no—
208C2×C4×D73—82no—
209C2×C4×D73C2×D412yes—
210C2×C4×D73C2412yes—
211#11924015—28no—
212#11924012—28no—
213#11924011—28no—
214C2×#10596831—22no—
215C2×#10596831#4114yes—
216C2×#10596831C2412yes—
217C2×#10596831C2412yes—
218C4⋊Dic73—21no—
219C4⋊Dic73—21no—
220C4⋊Dic73—24no—
221C4⋊Dic73—21no—
222C4⋊Dic73—24no—
223C4⋊Dic73C2412yes—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007C2×D414yes—
231C22⋊Dic73C2×D414yes—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005C2×D414yes—
238C4×Dic73—24no—
239C4×Dic73—24no—
240C4×Dic73C2×D412yes—
241C4×Dic73C2412yes—
242C24×C73C2×D411yescharacteristic
243C2×Q8×C73—21no—
244C2×Q8×C73—22no—
245C2×Q8×C73—22no—
246C2×Q8×C73C2412yes—
247C22×C4×C73—22no—
248C22×C4×C73—22no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2×D412yes—
255C22×C4×C73C2412yes—
256C22×C4×C73C2411yescharacteristic
257C2×C8×C73—22no—
258C2×C8×C73—22no—
259C2×C8×C73C2412yes—
260C2×C8×C73C2412yes—
261C4⋊C4×C73—24no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73C2412yes—
266C4⋊C4×C73C2412yes—
267C4⋊C4×C73C2412yes—
268C22⋊C4×C73—24no—
269C22⋊C4×C73—24no—
270C42×C73—24no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73C22×D412yes—
275C23×C73C22×D411yescharacteristic
276C22×D73—22no—
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—42no—
281C22×D73—42no—
282C22×D73—42no—
283C22×D73C22×D412yes—
284Q8×C73—22no—
285Q8×C73—22no—
286Q8×C73—42no—
287C2×C4×C73—22no—
288C2×C4×C73—24no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—42no—
296C2×C4×C73—42no—
297C2×C4×C73—42no—
298C2×C4×C73—42no—
299C2×C4×C73C22×D412yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4112yes—
302C2×C4×C732−1+412yes—
303C2×C4×C73C2511yescharacteristic
304C22⋊D73—28no—
305C22⋊D73—84no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—42no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—84no—
315C2×Dic73#13714yes—
316C2×Dic73C22×D412yes—
317C2×Dic73C22×D412yes—
318C2×Dic73C22×D412yes—
319D292—22no—
320D292—22no—
321D292—42no—
322D292—84no—
323C4×D73—24no—
324C4×D73—22no—
325C4×D73—22no—
326C4×D73—48no—
327C4×D73—84no—
328Dic146—84no—
329Dic146—84no—
330C8×C73—22no—
331C8×C73—22no—
332#10596831—22no—
333#10596831C2×#4114yes—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—44no—
338C22×C73#54712yes—
339C22×C73C2×#13712yes—
340C22×C73#57612yes—
341C22×C73C23×D411yescharacteristic
342C2×D73—22no—
343C2×D73—22no—
344C2×D73—22no—
345C2×D73—44no—
346C2×D73—42no—
347C2×D73—42no—
348C2×D73—42no—
349C2×D73—84no—
350C4×C73—22no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73—42no—
355C4×C73#54712yes—
356C4×C73C22×#4111yescharacteristic
357C4×C73C2×2−1+411yescharacteristic
358Dic73—22no—
359Dic73—22no—
360Dic73—42no—
361Dic73—42no—
362Dic73—42no—
363Dic73C2×#13714yes—
364C2×#3357—731nomaximal, Sylow
365C2×C73—42no—
366C2×C73#335714yescomplemented
367C2×C73C2×#54711yescharacteristic
368C2×C73C22×#13711yescharacteristic
369C2×C73C2×#57611yescharacteristic
370D73—42no—
371D73—82no—
372C2×#555—731no—
373C2×#554—731no—
374#3357—7316no—
375C2×#500—731no—
376C2×#485—731no—
377C2×#485D7311yescharacteristic, complemented
378C2×#480—731no—
379C2×#480—731no—
380C2×#477—731no—
381C2×#476—731no—
382C2×#468—731no—
383C2×#468—731no—
384C2×C4×SD16—731no—
385C2×#436—731no—
386C2×#428—731no—
387C2×#428—731no—
388C73C2×#335711yescharacteristic, complemented, Sylow
389C22×SD16—731no—
390C22×M16—731no—
391C22×M16—731no—
392#555—738no—
393#555—1464no—
394#554—738no—
395#554—1464no—
396C2×C4⋊Q8—731no—
397C2×C4⋊Q8—731no—
398C2×#125—1461no—
399C2×#124—1461no—
400C2×#124—1461no—
401C2×C22⋊Q8—731no—
402C2×C22⋊Q8—1461no—
403C2×C22⋊Q8—1461no—
404C2×C22⋊Q8C2×D7311yescharacteristic
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×#117—731no—
413C2×#117—1461no—
414C2×#117C2×D7311yescharacteristic
415C22×C4⋊C4—731no—
416C22×C4⋊C4—731no—
417#500—738no—
418#485—738no—
419#485C2×D7318yescomplemented
420#480—738no—
421#480—738no—
422#477—738no—
423#476—738no—
424#468—738no—
425#468—738no—
426C4×SD16—738no—
427#436—738no—
428#428—738no—
429#428—738no—
430C2×#107—731no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#107—731no—
434C2×#107—731no—
435C2×#107C2×D7311yescharacteristic
436C2×#106—731no—
437C2×#106—731no—
438C2×#106C2×D7311yescharacteristic
439C2×C4⋊C8—731no—
440C2×#103—731no—
441C2×#103C2×D7311yescharacteristic
442C2×#103C2×D7311yescharacteristic
443C2×#102—731no—
444C2×#102—731no—
445C2×#102—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8C2×D7311yescharacteristic
448C2×C4×C8—731no—
449C22×Q8—1461no—
450C22×Q8—1461no—
451C22×Q8C22×D7311yescharacteristic
452C22×D4—731no—
453C22×D4—731no—
454C22×D4—1461no—
455C22×D4—1461no—
456C23×C4—731no—
457C23×C4—1461no—
458C23×C4—1461no—
459C23×C4—1461no—
460C23×C4C22×D7311yescharacteristic
461C2×SD16—734no—
462C2×SD16—1464no—
463C2×M16—734no—
464C2×M16—734no—
465C2×M16—1464no—
466C2×M16—1464no—
467C22×C8—731no—
468C22×C8—731no—
469C22×C8C22×D7311yescharacteristic
470C22×C8C22×D7311yescharacteristic
471C4⋊Q8—734no—
472C4⋊Q8—734no—
473C4⋊Q8—1462no—
474C4⋊Q8—1462no—
475#125—1468no—
476#124—1468no—
477#124—1468no—
478C22⋊Q8—22no—
479C22⋊Q8—734no—
480C22⋊Q8—1468no—
481C22⋊Q8—1468no—
482C22⋊Q8—1462no—
483C22⋊Q8C22×D7314yes—
484#121—734no—
485#121—734no—
486#121—1468no—
487#121—1462no—
488#121—1462no—
489C4×Q8—734no—
490C4×Q8—1462no—
491C4×D4—734no—
492C4×D4—734no—
493C4×D4—734no—
494C4×D4—1462no—
495C4×D4—1468no—
496#117—22no—
497#117—734no—
498#117—1468no—
499#117—1462no—
500#117C22×D7314yes—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—734no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—734no—
508C2×C4⋊C4—1462no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1462no—
516C2×C4⋊C4C22×D7311yescharacteristic
517C2×C4⋊C4C22×D7311yescharacteristic
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
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×C42—21no—
529C2×C42—731no—
530C2×C42—1461no—
531C2×C42—1461no—
532#107—734no—
533#107—734no—
534#107—734no—
535#107—734no—
536#107—734no—
537#107C22×D7314yes—
538#106—734no—
539#106—734no—
540#106C22×D7314yes—
541C4⋊C8—734no—
542#103—734no—
543#103C22×D7314yes—
544#103C22×D7314yes—
545#102—734no—
546#102—734no—
547#102—734no—
548C22⋊C8—734no—
549C22⋊C8C22×D7314yes—
550C4×C8—734no—
551C24—731no—
552C24—1461no—
553C24D4×D7311yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—5842no—
558C2×Q8—5842no—
559C2×Q8—1464no—
560C2×Q8—1464no—
561C2×Q8C23×D7312yes—
562C2×D4—5842no—
563C2×D4—5842no—
564C2×D4—734no—
565C2×D4—732no—
566C2×D4—1464no—
567C2×D4—1464no—
568C2×D4—1464no—
569C2×D4—1461no—
570C2×D4—1462no—
571C2×D4—1462no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—2924no—
579C22×C4—5842no—
580C22×C4—5842no—
581C22×C4—731no—
582C22×C4—731no—
583C22×C4—731no—
584C22×C4—732no—
585C22×C4—732no—
586C22×C4—1464no—
587C22×C4—1464no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1464no—
592C22×C4—1462no—
593C22×C4—1462no—
594C22×C4D4×D7312yes—
595C22×C4D4×D7311yescharacteristic
596C22×C4C23×D7312yes—
597C22×C4C23×D7311yescharacteristic
598SD16—1468no—
599M16—1468no—
600M16—1468no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—734no—
604C2×C8—732no—
605C2×C8—732no—
606C2×C8—1462no—
607C2×C8C23×D7312yes—
608C2×C8C23×D7312yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—734no—
614C4⋊C4—732no—
615C4⋊C4—732no—
616C4⋊C4—732no—
617C4⋊C4—1464no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4—1464no—
622C4⋊C4—1461no—
623C4⋊C4—1464no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C4⋊C4C23×D7312yes—
627C4⋊C4C23×D7312yes—
628C4⋊C4C23×D7312yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—734no—
632C22⋊C4—734no—
633C22⋊C4—1464no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C42—24no—
639C42—732no—
640C42—732no—
641C42—1464no—
642C42—1464no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—2922no—
647C23—2922no—
648C23—2922no—
649C23—732no—
650C23—1462no—
651C23—1462no—
652C23—1462no—
653C23—1462no—
654C23C2×D4×D7312yes—
655C23C2×D4×D7311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—5844no—
660Q8—5844no—
661D4—2922no—
662D4—5844no—
663D4—5844no—
664D4—1468no—
665D4—1462no—
666D4—1462no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—2928no—
680C2×C4—2922no—
681C2×C4—2922no—
682C2×C4—2922no—
683C2×C4—5844no—
684C2×C4—5844no—
685C2×C4—734no—
686C2×C4—732no—
687C2×C4—732no—
688C2×C4—732no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1464no—
697C2×C4C2×D4×D7312yes—
698C2×C4C2×D4×D7311yescharacteristic
699C2×C4#41×D7312yes—
700C2×C4#1455663812yes—
701C2×C4C24×D7311yescharacteristic
702C8—22no—
703C8—22no—
704C8—734no—
705C8—1462no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—2924no—
711C22—2922no—
712C22—2922no—
713C22—2922no—
714C22—5844no—
715C22—1462no—
716C22—1462no—
717C22—1462no—
718C22#1798923512yes—
719C22#137×D7312yes—
720C22#1798938912yes—
721C22C22×D4×D7311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—2922no—
728C4—2922no—
729C4—2922no—
730C4—734no—
731C4—1462no—
732C4—1462no—
733C4#1798923512yes—
734C4C2×#41×D7311yescharacteristic
735C4C2×#1455663811yescharacteristic
736C2—42no—
737C2—2922no—
738C2—5842no—
739C2#2262255514yesdirect product factor
740C2C2×#1798923511yescharacteristic
741C2C2×#137×D7311yescharacteristic
742C2C2×#1798938911yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#485×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989300C2
hypercenterC2×#485D73
hypocenterC73C2×#3357
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#17989295C2semidirect
3. #22622555C2direct (N × H)
4. C2×#17988991C2semidirect
5. C2×#17988927C2semidirect
6. C2×#17988902C2semidirect
7. C2×#17988901C2semidirect
8. C2×#17988880C2semidirect
9. C2×#17988876C2semidirect
10. C2×#17988836C2semidirect
11. C2×#17988835C2semidirect
12. C2×#17988672C2semidirect
13. C2×#17988662C2semidirect
14. C2×#17988630C2semidirect
15. C2×#17988626C2semidirect
16. C2×#485×C73C2semidirect
23. #17989295C22semidirect
43. #17988991C22semidirect
44. #17988927C22semidirect
45. #17988902C22semidirect
46. #17988901C22semidirect
47. #17988880C22semidirect
48. #17988876C22semidirect
49. #17988836C22semidirect
50. #17988835C22semidirect
51. #17988672C22semidirect
52. #17988662C22semidirect
53. #17988630C22semidirect
54. #17988626C22semidirect
71. #485×C73C22semidirect
366. C2×C73#3357semidirect
377. C2×#485D73semidirect
388. C73C2×#3357semidirect
419. #485C2×D73semidirect
739. C2#22622555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893002
C2×#179892952
#226225552
C2×#179889912
C2×#179889272
C2×#179889022
C2×#179889012
C2×#179888802
C2×#179888762
C2×#179888362
C2×#179888352
C2×#179886722
C2×#179886622
C2×#179886302
C2×#179886262
C2×#485×C732
C2×#335773