Finite Group Databasebeta

← C2×#22622265 #33962925

Subgroups — C2×#22622265 #33962925

Order 18688.

2210 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989292C211yesmaximal, characteristic, complemented
2C2×#17989256C211yesmaximal, characteristic
3#22622265C2116yesmaximal, direct product factor
4C2×#17988932C211yesmaximal, characteristic, complemented
5C2×#17988900C211yesmaximal, characteristic, complemented
6C2×#17988899C211yesmaximal, characteristic, complemented
7C2×#17988880C211yesmaximal, characteristic, complemented
8C2×#17988833C211yesmaximal, characteristic, complemented
9C2×#17988832C211yesmaximal, characteristic, complemented
10C2×#17988786C211yesmaximal, characteristic, complemented
11C2×#17988752C211yesmaximal, characteristic, complemented
12C2×#17988749C211yesmaximal, characteristic, complemented
13C2×#17988679C211yesmaximal, characteristic, complemented
14C2×#17988663C211yesmaximal, characteristic, complemented
15C2×#17988587C211yesmaximal, characteristic, complemented
16C2×#417×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924017C2211yescharacteristic
20C22×#11924016C2211yescharacteristic
21C22×#11924011C2211yescharacteristic
22#17989292—24no—
23#17989292C2218yescomplemented
24#17989256—24no—
25#17989256C2218yes—
26C2×#14556590C2211yescharacteristic
27C2×#14556587—21no—
28C2×#14556587C2211yescharacteristic
29C2×#14556581—21no—
30C2×#14556571C2211yescharacteristic
31C2×#14556570—21no—
32C2×#14556570C2211yescharacteristic
33C2×#14556569—21no—
34C2×#14556565—21no—
35C2×#14556565C2211yescharacteristic
36C2×#14556562—21no—
37C2×#14556562C2211yescharacteristic
38C2×Q8×Dic73C2211yescharacteristic
39C2×#14556556C2211yescharacteristic
40C2×C4×C22⋊D73—21no—
41C2×C4×C22⋊D73—21no—
42C2×C4×C22⋊D73C2211yescharacteristic
43C2×C4⋊C4×D73C2211yescharacteristic
44#17988932C2218yescomplemented
45#17988900C2218yescomplemented
46#17988899C2218yescomplemented
47#17988880C2218yescomplemented
48#17988833C2218yescomplemented
49#17988832C2218yescomplemented
50#17988786C2218yescomplemented
51#17988752C2218yescomplemented
52#17988749C2218yescomplemented
53#17988679C2218yescomplemented
54#17988663C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59#17988587C2218yescomplemented
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×#41×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C22×C4⋊C4×C73C2211yescharacteristic
72#417×C73C2218yescomplemented
73C2×#103×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924029—22no—
78C2×#11924029—24no—
79C2×#11924029—42no—
80C2×#11924029C2314yes—
81C22×Dic146—21no—
82C22×Dic146C2311yescharacteristic
83C22×D292—21no—
84C22×D292C2311yescharacteristic
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C22⋊D73—21no—
88C22×C22⋊D73—21no—
89C22×C22⋊D73D411yescharacteristic
90C22×C4×D73—21no—
91C22×C4×D73—21no—
92C22×C4×D73C2311yescharacteristic
93C2×#11924018—24no—
94C2×#11924018C2314yes—
95C2×#11924017—42no—
96C2×#11924017C2314yes—
97C2×#11924016—42no—
98C2×#11924016C2314yes—
99C2×#11924011—42no—
100C2×#11924011C2314yes—
101C22×#10596831C2311yescharacteristic
102C22×#10596831C2311yescharacteristic
103#14556590—22no—
104#14556590C2314yes—
105#14556587—28no—
106#14556587—22no—
107#14556587C2314yes—
108#14556581—28no—
109#14556571—22no—
110#14556571C2314yes—
111#14556570—28no—
112#14556570—22no—
113#14556570C2314yes—
114#14556569—28no—
115#14556565—28no—
116#14556565—22no—
117#14556565C2314yes—
118#14556562—22no—
119#14556562—28no—
120#14556562C2314yes—
121Q8×Dic73—22no—
122Q8×Dic73C2314yes—
123#14556556—22no—
124#14556556C2314yes—
125C4×C22⋊D73—28no—
126C4×C22⋊D73—28no—
127C4×C22⋊D73D414yes—
128C4×C22⋊D73C2314yes—
129C2×C4⋊Dic73—21no—
130C2×C4⋊Dic73—21no—
131C2×C4⋊Dic73C2311yescharacteristic
132C2×C4⋊Dic73C2311yescharacteristic
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007D411yescharacteristic
138C4⋊C4×D73—22no—
139C4⋊C4×D73C2314yes—
140C2×C22⋊Dic73—21no—
141C2×C22⋊Dic73—21no—
142C2×C22⋊Dic73D411yescharacteristic
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005D411yescharacteristic
146C2×C4×Dic73—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73C2311yescharacteristic
149#14556525C2314yes—
150#14556524C2314yes—
151#14556524C2314yes—
152#14556520C2314yes—
153#14556516C2314yes—
154#14556515C2314yes—
155#14556513C2314yes—
156#14556512C2314yes—
157#14556511C2314yes—
158#14556511C2314yes—
159C22⋊#10596831C2314yes—
160#14556503C2314yes—
161C8×Dic73C2314yes—
162C2×#41×C73—22no—
163C2×#41×C73—24no—
164C2×#41×C73—42no—
165C2×#41×C73C2314yes—
166C22×Q8×C73C2311yescharacteristic
167C22×D4×C73—21no—
168C22×D4×C73C2311yescharacteristic
169C23×C4×C73—21no—
170C23×C4×C73—21no—
171C23×C4×C73C2311yescharacteristic
172C2×M16×C73—42no—
173C2×M16×C73C2314yes—
174C22×C8×C73C2311yescharacteristic
175C22×C8×C73C2311yescharacteristic
176C2×C4⋊C4×C73—22no—
177C2×C4⋊C4×C73—21no—
178C2×C4⋊C4×C73C2311yescharacteristic
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C4⋊C4×C73C2314yes—
181#103×C73C2314yes—
182#103×C73C2314yes—
183#102×C73C2314yes—
184#102×C73C2314yes—
185C23×D73—21no—
186C23×D73C2×D411yescharacteristic
187#11924029—28no—
188#11924029—44no—
189#11924029—48no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—21no—
193C2×Dic146—24no—
194C2×Dic146—82no—
195C2×Dic146C2412yes—
196C2×D292—22no—
197C2×D292—22no—
198C2×D292—24no—
199C2×D292—21no—
200C2×D292—44no—
201C2×D292C2412yes—
202C2×C22⋊D73—24no—
203C2×C22⋊D73—24no—
204C2×C22⋊D73—24no—
205C2×C22⋊D73—24no—
206C2×C22⋊D73—24no—
207C2×C22⋊D73—44no—
208C2×C22⋊D73—82no—
209C2×C22⋊D73—82no—
210C2×C22⋊D73—82no—
211C2×C22⋊D73C2×D414yes—
212C22×Dic73—21no—
213C22×Dic73—21no—
214C22×Dic73—21no—
215C22×Dic73C2×D411yescharacteristic
216C22×Dic73C2×D411yescharacteristic
217C22×Dic73C2×D411yescharacteristic
218C2×C4×D73—22no—
219C2×C4×D73—22no—
220C2×C4×D73—24no—
221C2×C4×D73—24no—
222C2×C4×D73—44no—
223C2×C4×D73—82no—
224C2×C4×D73C2×D412yes—
225C2×C4×D73C2412yes—
226#11924018—28no—
227#11924017—44no—
228#11924016—44no—
229#11924011—44no—
230C2×#10596831—22no—
231C2×#10596831—22no—
232C2×#10596831C2412yes—
233C2×#10596831C2412yes—
234C4⋊Dic73—21no—
235C4⋊Dic73—21no—
236C4⋊Dic73—24no—
237C4⋊Dic73—24no—
238C4⋊Dic73C2412yes—
239C4⋊Dic73C2412yes—
240#11924007—24no—
241#11924007—24no—
242#11924007—24no—
243#11924007—24no—
244#11924007C2×D414yes—
245C22⋊Dic73—24no—
246C22⋊Dic73—24no—
247C22⋊Dic73C2×D414yes—
248#11924005—24no—
249#11924005—24no—
250#11924005C2×D414yes—
251C4×Dic73—24no—
252C4×Dic73—24no—
253C4×Dic73C2×D412yes—
254C4×Dic73C2412yes—
255C24×C73—21no—
256C24×C73C2×D411yescharacteristic
257#41×C73—28no—
258#41×C73—44no—
259#41×C73—48no—
260C2×Q8×C73—21no—
261C2×Q8×C73—22no—
262C2×Q8×C73#4114yes—
263C2×Q8×C73C2412yes—
264C2×D4×C73—24no—
265C2×D4×C73—21no—
266C2×D4×C73—22no—
267C2×D4×C73—22no—
268C2×D4×C73—44no—
269C2×D4×C73C2412yes—
270C22×C4×C73—21no—
271C22×C4×C73—22no—
272C22×C4×C73—22no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—24no—
276C22×C4×C73—24no—
277C22×C4×C73—44no—
278C22×C4×C73—82no—
279C22×C4×C73C2×D411yescharacteristic
280C22×C4×C73C2×D412yes—
281C22×C4×C73C2412yes—
282C22×C4×C73C2411yescharacteristic
283M16×C73—44no—
284C2×C8×C73—22no—
285C2×C8×C73—22no—
286C2×C8×C73C2412yes—
287C2×C8×C73C2412yes—
288C4⋊C4×C73—21no—
289C4⋊C4×C73—24no—
290C4⋊C4×C73—21no—
291C4⋊C4×C73C2412yes—
292C4⋊C4×C73C2412yes—
293C23×C73—22no—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73—42no—
298C23×C73—42no—
299C23×C73—42no—
300C23×C73C22×D412yes—
301C23×C73C22×D411yescharacteristic
302C22×D73—22no—
303C22×D73—22no—
304C22×D73—22no—
305C22×D73—22no—
306C22×D73—42no—
307C22×D73—42no—
308C22×D73—42no—
309C22×D73C22×D412yes—
310Q8×C73—24no—
311Q8×C73—22no—
312Q8×C73C2×#4114yes—
313D4×C73—22no—
314D4×C73—22no—
315D4×C73—48no—
316D4×C73—42no—
317C2×C4×C73—22no—
318C2×C4×C73—24no—
319C2×C4×C73—22no—
320C2×C4×C73—24no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—48no—
326C2×C4×C73—42no—
327C2×C4×C73—42no—
328C2×C4×C73—84no—
329C2×C4×C73C22×D412yes—
330C2×C4×C73C22×D411yescharacteristic
331C2×C4×C73C2×#4112yes—
332C2×C4×C73H(5,𝔽2)12yes—
333C2×C4×C73C2511yescharacteristic
334C22⋊D73—28no—
335C22⋊D73—48no—
336C22⋊D73—84no—
337C22⋊D73—84no—
338C22⋊D73—84no—
339C2×Dic73—22no—
340C2×Dic73—22no—
341C2×Dic73—22no—
342C2×Dic73—22no—
343C2×Dic73—22no—
344C2×Dic73—42no—
345C2×Dic73—42no—
346C2×Dic73—42no—
347C2×Dic73#13714yes—
348C2×Dic73C22×D412yes—
349C2×Dic73C22×D412yes—
350C2×Dic73C22×D412yes—
351D292—22no—
352D292—22no—
353D292—48no—
354D292—42no—
355C4×D73—24no—
356C4×D73—22no—
357C4×D73—22no—
358C4×D73—48no—
359C4×D73—84no—
360Dic146—22no—
361Dic146—22no—
362Dic146—42no—
363Dic146—84no—
364C8×C73—22no—
365C8×C73—22no—
366#10596831—22no—
367#10596831—22no—
368C22×C73—22no—
369C22×C73—22no—
370C22×C73—22no—
371C22×C73—44no—
372C22×C73—42no—
373C22×C73—42no—
374C22×C73—42no—
375C22×C73—84no—
376C22×C73#54612yes—
377C22×C73C2×#13712yes—
378C22×C73#57612yes—
379C22×C73C23×D411yescharacteristic
380C2×D73—22no—
381C2×D73—22no—
382C2×D73—22no—
383C2×D73—44no—
384C2×D73—42no—
385C2×D73—42no—
386C2×D73—42no—
387C2×D73—84no—
388C4×C73—24no—
389C4×C73—22no—
390C4×C73—42no—
391C4×C73—42no—
392C4×C73#54612yes—
393C4×C73C22×#4111yescharacteristic
394C4×C73C2×H(5,𝔽2)11yescharacteristic
395Dic73—22no—
396Dic73—22no—
397Dic73—42no—
398Dic73—42no—
399Dic73—42no—
400Dic73C2×#13714yes—
401C2×#3333—731nomaximal, Sylow
402C2×C73—42no—
403C2×C73—82no—
404C2×C73#333314yescomplemented
405C2×C73C2×#54611yescharacteristic
406C2×C73C22×#13711yescharacteristic
407C2×C73C2×#57611yescharacteristic
408D73—42no—
409D73—82no—
410C2×#554—731no—
411C2×#550—731no—
412#3333—7316no—
413C2×#486—731no—
414C2×#480—731no—
415C2×#480—731no—
416C2×#477—731no—
417C2×#468—731no—
418C2×#468—731no—
419C2×#460—731no—
420C2×#452—731no—
421C2×#452—731no—
422C2×C4×Q16—731no—
423C2×#436—731no—
424C2×#417—731no—
425C2×#417D7311yescharacteristic, complemented
426C73C2×#333311yescharacteristic, complemented, Sylow
427C22×#41—731no—
428C22×#41C2×D7311yescharacteristic
429C22×Q16—731no—
430C22×SD16—731no—
431C22×SD16—731no—
432C22×M16—731no—
433C22×M16C2×D7311yescharacteristic
434#554—738no—
435#554—1464no—
436#550—738no—
437#550—1464no—
438C2×C4⋊Q8—731no—
439C2×#127—731no—
440C2×#127—1461no—
441C2×#125—1461no—
442C2×C22⋊Q8—731no—
443C2×C22⋊Q8—731no—
444C2×C22⋊Q8—1461no—
445C2×C22⋊Q8—1461no—
446C2×#121—731no—
447C2×#121—731no—
448C2×#121—1461no—
449C2×#121—1461no—
450C2×C4×Q8—731no—
451C2×C4×Q8—731no—
452C2×C4×D4—731no—
453C2×C4×D4—1461no—
454C2×C4×D4—1461no—
455C22×C4⋊C4—731no—
456C22×C4⋊C4C2×D7311yescharacteristic
457#486—738no—
458#480—738no—
459#480—738no—
460#477—738no—
461#468—738no—
462#468—738no—
463#460—738no—
464#452—738no—
465#452—738no—
466C4×Q16—738no—
467#436—738no—
468C2×#107—731no—
469C2×#107—731no—
470C2×#107—731no—
471C2×C4⋊C8—731no—
472#417—738no—
473#417C2×D7318yescomplemented
474C2×#103—731no—
475C2×#103—731no—
476C2×#103C2×D7311yescharacteristic
477C2×#103C2×D7311yescharacteristic
478C2×#102—731no—
479C2×#102—731no—
480C2×#102—731no—
481C2×#102—731no—
482C2×#102C2×D7311yescharacteristic
483C2×#102C2×D7311yescharacteristic
484C2×C22⋊C8—731no—
485C2×C22⋊C8—731no—
486C2×C4×C8—731no—
487C2×#41—22no—
488C2×#41—24no—
489C2×#41—42no—
490C2×#41—2922no—
491C2×#41—734no—
492C2×#41—1464no—
493C2×#41—1462no—
494C2×#41C22×D7314yes—
495C22×Q8—731no—
496C22×Q8—1461no—
497C22×Q8C22×D7311yescharacteristic
498C22×D4—21no—
499C22×D4—731no—
500C22×D4—731no—
501C22×D4—1461no—
502C22×D4—1461no—
503C22×D4—1461no—
504C22×D4—1461no—
505C22×D4—1461no—
506C22×D4C22×D7311yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—731no—
510C23×C4—1461no—
511C23×C4—1461no—
512C23×C4C22×D7311yescharacteristic
513C2×Q16—734no—
514C2×Q16—1464no—
515C2×SD16—2922no—
516C2×SD16—2922no—
517C2×SD16—734no—
518C2×SD16—734no—
519C2×M16—42no—
520C2×M16—2922no—
521C2×M16—734no—
522C2×M16C22×D7314yes—
523C22×C8—731no—
524C22×C8—731no—
525C22×C8C22×D7311yescharacteristic
526C22×C8C22×D7311yescharacteristic
527C4⋊Q8—734no—
528C4⋊Q8—1462no—
529#127—734no—
530#127—1462no—
531#127—1468no—
532#125—1468no—
533C22⋊Q8—734no—
534C22⋊Q8—734no—
535C22⋊Q8—1468no—
536C22⋊Q8—1468no—
537C22⋊Q8—1462no—
538C22⋊Q8—1462no—
539#121—734no—
540#121—734no—
541#121—1468no—
542#121—1468no—
543#121—1462no—
544#121—1462no—
545C4×Q8—734no—
546C4×Q8—734no—
547C4×Q8—1462no—
548C4×Q8—1462no—
549C4×D4—734no—
550C4×D4—734no—
551C4×D4—1468no—
552C4×D4—1468no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—731no—
556C2×C4⋊C4—731no—
557C2×C4⋊C4—731no—
558C2×C4⋊C4—734no—
559C2×C4⋊C4—1462no—
560C2×C4⋊C4—1461no—
561C2×C4⋊C4—1461no—
562C2×C4⋊C4—1461no—
563C2×C4⋊C4—1461no—
564C2×C4⋊C4—1461no—
565C2×C4⋊C4—1461no—
566C2×C4⋊C4C22×D7311yescharacteristic
567C2×C4⋊C4C22×D7311yescharacteristic
568C2×C4⋊C4C22×D7314yes—
569C2×C22⋊C4—731no—
570C2×C22⋊C4—731no—
571C2×C22⋊C4—1461no—
572C2×C22⋊C4—1461no—
573C2×C22⋊C4—1461no—
574C2×C22⋊C4—1461no—
575C2×C42—731no—
576C2×C42—1461no—
577C2×C42—1461no—
578#107—734no—
579#107—734no—
580#107—734no—
581C4⋊C8—734no—
582#103—734no—
583#103—734no—
584#103C22×D7314yes—
585#103C22×D7314yes—
586#102—734no—
587#102—734no—
588#102—734no—
589#102—734no—
590#102C22×D7314yes—
591#102C22×D7314yes—
592C22⋊C8—734no—
593C22⋊C8—734no—
594C4×C8—734no—
595C24—21no—
596C24—731no—
597C24—1461no—
598C24D4×D7311yescharacteristic
599#41—28no—
600#41—44no—
601#41—48no—
602#41—2928no—
603#41—2924no—
604#41—1468no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—5842no—
608C2×Q8—732no—
609C2×Q8—1464no—
610C2×Q8—1462no—
611C2×Q8—1462no—
612C2×Q8—1461no—
613C2×Q8#1192402814yes—
614C2×Q8C23×D7312yes—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—44no—
620C2×D4—2924no—
621C2×D4—2924no—
622C2×D4—5842no—
623C2×D4—5842no—
624C2×D4—5842no—
625C2×D4—734no—
626C2×D4—732no—
627C2×D4—1464no—
628C2×D4—1464no—
629C2×D4—1464no—
630C2×D4—1464no—
631C2×D4—1464no—
632C2×D4—1464no—
633C2×D4—1461no—
634C2×D4—1462no—
635C2×D4—1462no—
636C2×D4C23×D7312yes—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4—2924no—
647C22×C4—5842no—
648C22×C4—731no—
649C22×C4—731no—
650C22×C4—731no—
651C22×C4—732no—
652C22×C4—732no—
653C22×C4—1464no—
654C22×C4—1464no—
655C22×C4—1461no—
656C22×C4—1461no—
657C22×C4—1461no—
658C22×C4—1462no—
659C22×C4—1462no—
660C22×C4D4×D7312yes—
661C22×C4D4×D7311yescharacteristic
662C22×C4C23×D7312yes—
663C22×C4C23×D7311yescharacteristic
664Q16—1468no—
665SD16—2924no—
666SD16—2924no—
667M16—44no—
668M16—2924no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—732no—
672C2×C8—732no—
673C2×C8—1462no—
674C2×C8—1462no—
675C2×C8C23×D7312yes—
676C2×C8C23×D7312yes—
677C4⋊C4—21no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—734no—
681C4⋊C4—732no—
682C4⋊C4—732no—
683C4⋊C4—1464no—
684C4⋊C4—1464no—
685C4⋊C4—1464no—
686C4⋊C4—1464no—
687C4⋊C4—1464no—
688C4⋊C4—1464no—
689C4⋊C4—1461no—
690C4⋊C4—1461no—
691C4⋊C4C23×D7312yes—
692C4⋊C4C23×D7312yes—
693C22⋊C4—734no—
694C22⋊C4—734no—
695C22⋊C4—1464no—
696C22⋊C4—1464no—
697C22⋊C4—1464no—
698C22⋊C4—1464no—
699C42—732no—
700C42—732no—
701C42—1464no—
702C42—1464no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—2922no—
711C23—2922no—
712C23—2922no—
713C23—732no—
714C23—1462no—
715C23—1462no—
716C23—1462no—
717C23—1462no—
718C23C2×D4×D7312yes—
719C23C2×D4×D7311yescharacteristic
720Q8—22no—
721Q8—24no—
722Q8—2922no—
723Q8—5844no—
724Q8—1462no—
725Q8—1462no—
726Q8C2×#1192402814yes—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—42no—
731D4—2928no—
732D4—2928no—
733D4—2922no—
734D4—5844no—
735D4—5844no—
736D4—5844no—
737D4—1468no—
738D4—1462no—
739D4—1462no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—2928no—
753C2×C4—2922no—
754C2×C4—2922no—
755C2×C4—2922no—
756C2×C4—5844no—
757C2×C4—734no—
758C2×C4—732no—
759C2×C4—732no—
760C2×C4—732no—
761C2×C4—1462no—
762C2×C4—1462no—
763C2×C4—1462no—
764C2×C4—1462no—
765C2×C4—1462no—
766C2×C4—1462no—
767C2×C4—1462no—
768C2×C4—1464no—
769C2×C4C2×D4×D7312yes—
770C2×C4C2×D4×D7311yescharacteristic
771C2×C4C2×#1192402812yes—
772C2×C4#1455663612yes—
773C2×C4C24×D7311yescharacteristic
774C8—22no—
775C8—22no—
776C8—1462no—
777C8—1462no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—2924no—
787C22—2922no—
788C22—2922no—
789C22—2922no—
790C22—5844no—
791C22—1462no—
792C22—1462no—
793C22—1462no—
794C22#1798922712yes—
795C22#137×D7312yes—
796C22#1798939112yes—
797C22C22×D4×D7311yescharacteristic
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—2922no—
803C4—2922no—
804C4—2922no—
805C4—734no—
806C4—1462no—
807C4—1462no—
808C4#1798922712yes—
809C4C22×#1192402811yescharacteristic
810C4C2×#1455663611yescharacteristic
811C2—42no—
812C2—82no—
813C2—2922no—
814C2—5842no—
815C2#2262226514yesdirect product factor
816C2C2×#1798922711yescharacteristic
817C2C2×#137×D7311yescharacteristic
818C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#417×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989256C2
hypercenterC2×#417D73
hypocenterC73C2×#3333
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#17989292C2semidirect
3. #22622265C2direct (N × H)
4. C2×#17988932C2semidirect
5. C2×#17988900C2semidirect
6. C2×#17988899C2semidirect
7. C2×#17988880C2semidirect
8. C2×#17988833C2semidirect
9. C2×#17988832C2semidirect
10. C2×#17988786C2semidirect
11. C2×#17988752C2semidirect
12. C2×#17988749C2semidirect
13. C2×#17988679C2semidirect
14. C2×#17988663C2semidirect
15. C2×#17988587C2semidirect
16. C2×#417×C73C2semidirect
23. #17989292C22semidirect
44. #17988932C22semidirect
45. #17988900C22semidirect
46. #17988899C22semidirect
47. #17988880C22semidirect
48. #17988833C22semidirect
49. #17988832C22semidirect
50. #17988786C22semidirect
51. #17988752C22semidirect
52. #17988749C22semidirect
53. #17988679C22semidirect
54. #17988663C22semidirect
59. #17988587C22semidirect
72. #417×C73C22semidirect
404. C2×C73#3333semidirect
425. C2×#417D73semidirect
426. C73C2×#3333semidirect
473. #417C2×D73semidirect
815. C2#22622265direct (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×#179892562
#226222652
C2×#179889322
C2×#179889002
C2×#179888992
C2×#179888802
C2×#179888332
C2×#179888322
C2×#179887862
C2×#179887522
C2×#179887492
C2×#179886792
C2×#179886632
C2×#179885872
C2×#417×C732
C2×#333373