Finite Group Databasebeta

← C2×#22622414 #33964561

Subgroups — C2×#22622414 #33964561

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×#17989292C211yesmaximal, characteristic, complemented
2C2×#17989289C211yesmaximal, characteristic
3#22622414C2116yesmaximal, direct product factor
4C2×#17988994C211yesmaximal, characteristic, complemented
5C2×#17988923C211yesmaximal, characteristic, complemented
6C2×#17988931C211yesmaximal, characteristic, complemented
7C2×#17988899C211yesmaximal, characteristic, complemented
8C2×#17988897C211yesmaximal, characteristic, complemented
9C2×#17988865C211yesmaximal, characteristic, complemented
10C2×#17988832C211yesmaximal, characteristic, complemented
11C2×#17988814C211yesmaximal, characteristic, complemented
12C2×#17988684C211yesmaximal, characteristic, complemented
13C2×#17988655C211yesmaximal, characteristic, complemented
14C2×#17988626C211yesmaximal, characteristic, complemented
15C22×#14556524C211yesmaximal, characteristic, complemented
16C2×#481×C73C211yesmaximal, characteristic, complemented
17C22×#11924016C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C23×#10596831C2211yescharacteristic
20#17989292—24no—
21#17989292C2218yescomplemented
22#17989289—24no—
23#17989289C2218yes—
24C2×#14556590C2211yescharacteristic
25C2×#14556584—21no—
26C2×#14556582C2211yescharacteristic
27C2×#14556581—21no—
28C2×#14556575—21no—
29C2×#14556571C2211yescharacteristic
30C2×#14556570—21no—
31C2×#14556570C2211yescharacteristic
32C2×#14556569—21no—
33C2×#14556563—21no—
34C2×#14556562C2211yescharacteristic
35C2×#14556556C2211yescharacteristic
36C2×D4×Dic73—21no—
37C2×D4×Dic73C2211yescharacteristic
38C2×C4×C22⋊D73—21no—
39C2×C4×C22⋊D73C2211yescharacteristic
40C2×#14556549C2211yescharacteristic
41C22×C4⋊Dic73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988994C2218yescomplemented
44#17988931C2218yescomplemented
45#17988923C2218yescomplemented
46#17988899C2218yescomplemented
47#17988897C2218yescomplemented
48#17988865C2218yescomplemented
49#17988832C2218yescomplemented
50#17988814C2218yescomplemented
51#17988684C2218yescomplemented
52#17988655C2218yescomplemented
53#17988626C2218yescomplemented
54C2×#14556525C2211yescharacteristic
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556524C2211yescharacteristic
59C2×#14556524C2211yescharacteristic
60C2×#14556524C2218yescomplemented
61C2×#14556522C2211yescharacteristic
62C2×#14556520C2211yescharacteristic
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2211yescharacteristic
65C2×#14556514C2211yescharacteristic
66C2×#14556512C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C2×#121×C73C2211yescharacteristic
70C22×C4⋊C4×C73C2211yescharacteristic
71#481×C73C2218yescomplemented
72C2×#106×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×C22⋊D73—21no—
80C22×C22⋊D73D411yescharacteristic
81C23×Dic73—21no—
82C23×Dic73—21no—
83C22×C4×D73—21no—
84C22×C4×D73C2311yescharacteristic
85C2×#11924016—24no—
86C2×#11924016C2314yes—
87C2×#11924011—24no—
88C2×#11924011C2314yes—
89C22×#10596831—24no—
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2314yes—
92C22×#10596831C2311yescharacteristic
93#14556590—22no—
94#14556590C2314yes—
95#14556584—28no—
96#14556582—22no—
97#14556582C2314yes—
98#14556581—28no—
99#14556575—28no—
100#14556571—22no—
101#14556571C2314yes—
102#14556570—28no—
103#14556570—22no—
104#14556570C2314yes—
105#14556569—28no—
106#14556563—28no—
107#14556562—22no—
108#14556562C2314yes—
109#14556556—22no—
110#14556556C2314yes—
111D4×Dic73—28no—
112D4×Dic73—22no—
113D4×Dic73C2314yes—
114C4×C22⋊D73—28no—
115C4×C22⋊D73D414yes—
116C4×C22⋊D73C2314yes—
117#14556549—22no—
118#14556549C2314yes—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73—22no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2314yes—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007D411yescharacteristic
133C4⋊C4×D73—22no—
134C4⋊C4×D73C2314yes—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×C22⋊Dic73—21no—
138C2×C22⋊Dic73D411yescharacteristic
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#14556524C2314yes—
151#14556522C2314yes—
152#14556520C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556514C2314yes—
156#14556512C2314yes—
157#14556503C2314yes—
158#14556501C2314yes—
159C22×D4×C73—21no—
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73—21no—
162C23×C4×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165#121×C73—22no—
166#121×C73C2314yes—
167C2×C4⋊C4×C73—22no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2314yes—
173C2×C22⋊C4×C73—21no—
174#106×C73C2314yes—
175#106×C73C2314yes—
176#102×C73C2314yes—
177#102×C73C2314yes—
178C22⋊C8×C73C2314yes—
179C23×D73C2×D411yescharacteristic
180C2×Dic146—22no—
181C2×Dic146—22no—
182C2×Dic146—21no—
183C2×Dic146—24no—
184C2×Dic146—82no—
185C2×Dic146C2412yes—
186C2×C22⋊D73—24no—
187C2×C22⋊D73—24no—
188C2×C22⋊D73—82no—
189C2×C22⋊D73C2×D414yes—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—24no—
195C22×Dic73—24no—
196C22×Dic73—82no—
197C22×Dic73—82no—
198C22×Dic73C2×D411yescharacteristic
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C2×C4×D73—22no—
202C2×C4×D73—22no—
203C2×C4×D73—24no—
204C2×C4×D73—82no—
205C2×C4×D73C2×D412yes—
206C2×C4×D73C2412yes—
207#11924016—28no—
208#11924011—28no—
209C2×#10596831—22no—
210C2×#10596831—28no—
211C2×#10596831#4114yes—
212C2×#10596831C2412yes—
213C2×#10596831C2412yes—
214C4⋊Dic73—21no—
215C4⋊Dic73—21no—
216C4⋊Dic73—21no—
217C4⋊Dic73—24no—
218C4⋊Dic73—24no—
219C4⋊Dic73—24no—
220C4⋊Dic73C2412yes—
221C4⋊Dic73C2412yes—
222C4⋊Dic73C2412yes—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227#11924007—24no—
228#11924007C2×D414yes—
229C22⋊Dic73—24no—
230C22⋊Dic73—24no—
231C22⋊Dic73—24no—
232C22⋊Dic73C2×D414yes—
233#11924005—24no—
234#11924005—24no—
235#11924005C2×D414yes—
236C4×Dic73—24no—
237C4×Dic73—24no—
238C4×Dic73C2×D412yes—
239C4×Dic73C2412yes—
240C24×C73—21no—
241C24×C73C2×D411yescharacteristic
242C2×D4×C73—24no—
243C2×D4×C73—21no—
244C2×D4×C73—22no—
245C2×D4×C73—22no—
246C2×D4×C73—44no—
247C2×D4×C73C2412yes—
248C22×C4×C73—22no—
249C22×C4×C73—22no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—24no—
254C22×C4×C73—82no—
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2×D412yes—
257C22×C4×C73C2412yes—
258C22×C4×C73C2411yescharacteristic
259C2×C8×C73—22no—
260C2×C8×C73—22no—
261C2×C8×C73C2412yes—
262C2×C8×C73C2412yes—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—24no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C4⋊C4×C73C2412yes—
270C22⋊C4×C73—24no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—42no—
275C23×C73—42no—
276C23×C73—42no—
277C23×C73#13714yes—
278C23×C73C22×D412yes—
279C23×C73C22×D411yescharacteristic
280C22×D73—22no—
281C22×D73—22no—
282C22×D73—22no—
283C22×D73C22×D412yes—
284D4×C73—22no—
285D4×C73—22no—
286D4×C73—48no—
287D4×C73—42no—
288C2×C4×C73—22no—
289C2×C4×C73—24no—
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—84no—
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—22no—
312C2×Dic73—22no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73—84no—
318C2×Dic73—84no—
319C2×Dic73C22×D412yes—
320C2×Dic73C22×D412yes—
321C2×Dic73C22×D412yes—
322C4×D73—24no—
323C4×D73—22no—
324C4×D73—22no—
325C4×D73—84no—
326Dic146—22no—
327Dic146—22no—
328Dic146—42no—
329Dic146—84no—
330C8×C73—22no—
331C8×C73—22no—
332#10596831—22no—
333#10596831C2×#4114yes—
334C22×C73—28no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—84no—
341C22×C73#54712yes—
342C22×C73C2×#13714yes—
343C22×C73C2×#13712yes—
344C22×C73#57612yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—22no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—44no—
350C4×C73—22no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73#54712yes—
355C4×C73C22×#4111yescharacteristic
356C4×C73C2×2−1+411yescharacteristic
357Dic73—22no—
358Dic73—22no—
359Dic73—22no—
360Dic73—42no—
361Dic73—42no—
362Dic73—42no—
363Dic73—42no—
364C2×#3346—731nomaximal, Sylow
365C2×C73—24no—
366C2×C73—82no—
367C2×C73#334614yescomplemented
368C2×C73C2×#54711yescharacteristic
369C2×C73C22×#13711yescharacteristic
370C2×C73C2×#57611yescharacteristic
371D73—42no—
372C2×#554—731no—
373C2×#553—731no—
374#3346—7316no—
375C2×#501—731no—
376C2×#484—731no—
377C2×#481D7311yescharacteristic, complemented
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⋊Q8—731no—
397C2×#126—1461no—
398C2×#125—731no—
399C2×#125—1461no—
400C2×#123—1461no—
401C2×C22⋊Q8—731no—
402C2×C22⋊Q8—731no—
403C2×C22⋊Q8—1461no—
404C2×C22⋊Q8—1461no—
405C2×#121—731no—
406C2×#121—1461no—
407C2×#121C2×D7311yescharacteristic
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⋊C4C2×D7311yescharacteristic
417#501—738no—
418#485—738no—
419#484—738no—
420#481C2×D7318yescomplemented
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—731no—
434C2×#107—731no—
435C2×#107—738no—
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×#102C2×D7311yescharacteristic
445C2×#102C2×D7311yescharacteristic
446C2×C22⋊C8—731no—
447C2×C22⋊C8C2×D7311yescharacteristic
448C2×#97—731no—
449C22×Q8—731no—
450C22×Q8—1461no—
451C22×D4—21no—
452C22×D4—731no—
453C22×D4—1461no—
454C22×D4C22×D7311yescharacteristic
455C23×C4—21no—
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—1464no—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8—734no—
468C22×C8—1464no—
469C22×C8C22×D7311yescharacteristic
470C22×C8C22×D7311yescharacteristic
471C4⋊Q8—734no—
472C4⋊Q8—1462no—
473#126—1468no—
474#125—734no—
475#125—1462no—
476#125—1468no—
477#123—1468no—
478C22⋊Q8—734no—
479C22⋊Q8—734no—
480C22⋊Q8—1468no—
481C22⋊Q8—1468no—
482C22⋊Q8—1462no—
483C22⋊Q8—1462no—
484#121—22no—
485#121—734no—
486#121—1462no—
487#121—1468no—
488#121C22×D7314yes—
489C4×Q8—734no—
490C4×Q8—1462no—
491C4×D4—734no—
492C4×D4—734no—
493C4×D4—734no—
494C4×D4—1462no—
495C4×D4—1468no—
496C4×D4—1468no—
497#117—734no—
498#117—1462no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—734no—
506C2×C4⋊C4—734no—
507C2×C4⋊C4—1462no—
508C2×C4⋊C4—1461no—
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⋊C4—1461no—
517C2×C4⋊C4C22×D7311yescharacteristic
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C4⋊C4C22×D7314yes—
520C2×C4⋊C4C22×D7311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—731no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
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#107—734no—
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#102C22×D7314yes—
547#102C22×D7314yes—
548C22⋊C8—734no—
549C22⋊C8C22×D7314yes—
550#97—734no—
551C24—21no—
552C24—731no—
553C24D4×D7311yescharacteristic
554C2×Q8—5842no—
555C2×Q8—732no—
556C2×Q8—1464no—
557C2×Q8—1462no—
558C2×Q8—1462no—
559C2×Q8—1461no—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—44no—
565C2×D4—5842no—
566C2×D4—734no—
567C2×D4—1464no—
568C2×D4—1464no—
569C2×D4C23×D7312yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—82no—
577C22×C4—5842no—
578C22×C4—5842no—
579C22×C4—5842no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—731no—
583C22×C4—732no—
584C22×C4—732no—
585C22×C4—1464no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1464no—
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—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—734no—
603C2×C8—732no—
604C2×C8—732no—
605C2×C8—1468no—
606C2×C8—1462no—
607C2×C8C23×D7312yes—
608C2×C8C23×D7312yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
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—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C4⋊C4—1461no—
627C4⋊C4—1464no—
628C4⋊C4C23×D7312yes—
629C4⋊C4C23×D7312yes—
630C4⋊C4C23×D7312yes—
631C22⋊C4—24no—
632C22⋊C4—734no—
633C22⋊C4—734no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C42—732no—
640C42—732no—
641C42—1464no—
642C42—1464no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—732no—
650C23—1462no—
651C23—1462no—
652C23—1462no—
653C23#1455662014yes—
654C23C2×D4×D7312yes—
655C23C2×D4×D7311yescharacteristic
656Q8—2922no—
657Q8—5844no—
658Q8—1462no—
659Q8—1462no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—42no—
664D4—5844no—
665D4—1468no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—84no—
677C2×C4—2922no—
678C2×C4—2922no—
679C2×C4—2922no—
680C2×C4—2922no—
681C2×C4—5844no—
682C2×C4—5844no—
683C2×C4—5844no—
684C2×C4—732no—
685C2×C4—732no—
686C2×C4—732no—
687C2×C4—1462no—
688C2×C4—1462no—
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—28no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—84no—
713C22—2924no—
714C22—1462no—
715C22—1462no—
716C22—1462no—
717C22#1798923512yes—
718C22C2×#1455662014yes—
719C22C2×#1455662012yes—
720C22#1798939112yes—
721C22C22×D4×D7311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—2922no—
727C4—2922no—
728C4—2922no—
729C4—2922no—
730C4—1462no—
731C4—1462no—
732C4—1462no—
733C4#1798923512yes—
734C4C2×#41×D7311yescharacteristic
735C4C2×#1455663811yescharacteristic
736C2—24no—
737C2—82no—
738C2—2922no—
739C2#2262241414yesdirect product factor
740C2C2×#1798923511yescharacteristic
741C2C22×#1455662011yescharacteristic
742C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#481×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989289C2
hypercenterC2×#481D73
hypocenterC73C2×#3346
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#17989292C2semidirect
3. #22622414C2direct (N × H)
4. C2×#17988994C2semidirect
5. C2×#17988923C2semidirect
6. C2×#17988931C2semidirect
7. C2×#17988899C2semidirect
8. C2×#17988897C2semidirect
9. C2×#17988865C2semidirect
10. C2×#17988832C2semidirect
11. C2×#17988814C2semidirect
12. C2×#17988684C2semidirect
13. C2×#17988655C2semidirect
14. C2×#17988626C2semidirect
15. C22×#14556524C2semidirect
16. C2×#481×C73C2semidirect
21. #17989292C22semidirect
43. #17988994C22semidirect
44. #17988931C22semidirect
45. #17988923C22semidirect
46. #17988899C22semidirect
47. #17988897C22semidirect
48. #17988865C22semidirect
49. #17988832C22semidirect
50. #17988814C22semidirect
51. #17988684C22semidirect
52. #17988655C22semidirect
53. #17988626C22semidirect
60. C2×#14556524C22semidirect
71. #481×C73C22semidirect
367. C2×C73#3346semidirect
377. C2×#481D73semidirect
388. C73C2×#3346semidirect
420. #481C2×D73semidirect
739. C2#22622414direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892922
C2×#179892892
#226224142
C2×#179889942
C2×#179889232
C2×#179889312
C2×#179888992
C2×#179888972
C2×#179888652
C2×#179888322
C2×#179888142
C2×#179886842
C2×#179886552
C2×#179886262
C22×#145565242
C2×#481×C732
C2×#334673