Finite Group Databasebeta

← C73×#25972 #32935376

Subgroups — C73×#25972 #32935376

Order 18688.

988 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#478×C73C211yesmaximal, characteristic, complemented
2C2×#417×C73C211yesmaximal, characteristic
3C73×#2442C211yesmaximal, characteristic, complemented
4C73×#2339C211yesmaximal, characteristic
5C73×#2097C211yesmaximal, characteristic, complemented
6C73×#2066C211yesmaximal, characteristic, complemented
7C73×#2066C211yesmaximal, characteristic, complemented
8C73×#2026C211yesmaximal, characteristic, complemented
9C73×#1864C211yesmaximal, characteristic, complemented
10C73×#1864C211yesmaximal, characteristic, complemented
11C73×#1853C211yesmaximal, characteristic, complemented
12C73×#1851C211yesmaximal, characteristic, complemented
13C73×#1809C211yesmaximal, characteristic, complemented
14C73×#1804C211yesmaximal, characteristic, complemented
15C73×#1788C211yesmaximal, characteristic
16C22×#41×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×#125×C73C2211yescharacteristic
19C2×C4×D4×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22#478×C73—24no—
23C2×#107×C73C2211yescharacteristic
24C2×#106×C73C2211yescharacteristic
25C2×#106×C73C2211yescharacteristic
26C2×#106×C73C2211yescharacteristic
27C2×C4⋊C8×C73C2211yescharacteristic
28C2×C4⋊C8×C73C2211yescharacteristic
29#417×C73—24no—
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39#400×C73—21no—
40#398×C73—21no—
41#391×C73C2211yescharacteristic
42#391×C73C2211yescharacteristic
43#389×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#386×C73—21no—
46#386×C73—21no—
47#385×C73—21no—
48#382×C73C2211yescharacteristic
49#381×C73—21no—
50#380×C73—21no—
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53C4×C22⋊C4×C73C2211yescharacteristic
54C2×#95×C73—21no—
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C2×#41×C73—22no—
62C2×#41×C73—22no—
63C2×#41×C73—22no—
64C2×#41×C73—41no—
65C2×#41×C73—41no—
66C2×#41×C73Q814yes—
67C22×Q8×C73C2311yescharacteristic
68C22×D4×C73—21no—
69C22×D4×C73C2311yescharacteristic
70C23×C4×C73—21no—
71C23×C4×C73—21no—
72C23×C4×C73—21no—
73C23×C4×C73—21no—
74C23×C4×C73C2311yescharacteristic
75C2×M16×C73—22no—
76C2×M16×C73—22no—
77C2×M16×C73—41no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82#125×C73—22no—
83#125×C73—41no—
84C4×D4×C73—22no—
85C4×D4×C73—22no—
86C4×D4×C73—41no—
87C4×D4×C73—41no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—41no—
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73D411yescharacteristic
106C2×C22⋊C4×C73D411yescharacteristic
107C2×C42×C73C2311yescharacteristic
108C2×C42×C73C2311yescharacteristic
109#107×C73—22no—
110#106×C73—22no—
111#106×C73—41no—
112#106×C73—41no—
113C4⋊C8×C73—22no—
114C4⋊C8×C73—41no—
115#103×C73—22no—
116#103×C73—22no—
117#103×C73—41no—
118#103×C73—41no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73D414yes—
123C22⋊C8×C73—22no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73D411yescharacteristic
135#95×C73D411yescharacteristic
136C24×C73—21no—
137C24×C73C2×D411yescharacteristic
138#41×C73—28no—
139#41×C73—44no—
140#41×C73—44no—
141#41×C73—44no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73C2×Q812yes—
148C2×D4×C73—24no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—42no—
153C2×D4×C73—42no—
154C2×D4×C73C2×D412yes—
155C2×D4×C73C2×Q812yes—
156C2×D4×C73#4112yes—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—24no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—42no—
170C22×C4×C73—42no—
171C22×C4×C73—42no—
172C22×C4×C73—42no—
173C22×C4×C73—42no—
174C22×C4×C73—42no—
175C22×C4×C73—42no—
176C22×C4×C73—42no—
177C22×C4×C73—81no—
178C22×C4×C73—81no—
179C22×C4×C73—81no—
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×Q812yes—
186C22×C4×C73#4112yes—
187C22×C4×C73C2411yescharacteristic
188M16×C73—44no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73C2×D412yes—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—42no—
213C4⋊C4×C73—42no—
214C4⋊C4×C73—42no—
215C4⋊C4×C73—81no—
216C4⋊C4×C73—81no—
217C4⋊C4×C73C2×D412yes—
218C22⋊C4×C73—41no—
219C22⋊C4×C73—41no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—81no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—21no—
228C23×C73—22no—
229C23×C73—22no—
230C23×C73—21no—
231C23×C73—22no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73C22⋊Q812yes—
242C23×C73C22×D411yescharacteristic
243Q8×C73—22no—
244Q8×C73—22no—
245Q8×C73—41no—
246Q8×C73—41no—
247D4×C73—22no—
248D4×C73—22no—
249D4×C73—22no—
250D4×C73—48no—
251D4×C73C22⋊Q814yes—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—22no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—48no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—84no—
293C2×C4×C73—84no—
294C2×C4×C73—84no—
295C2×C4×C73C22⋊Q812yes—
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C73C22×Q811yescharacteristic
298C2×C4×C73C2×#4111yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×C4×C73H(5,𝔽2)11yescharacteristic
302C8×C73—22no—
303C8×C73—41no—
304C8×C73—41no—
305C8×C73—41no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—24no—
310C22×C73—42no—
311C22×C73—42no—
312C22×C73—41no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—42no—
318C22×C73—42no—
319C22×C73—41no—
320C22×C73C2×C22⋊Q811yescharacteristic
321C22×C73D4211yescharacteristic
322C22×C73#54611yescharacteristic
323C22×C73#57511yescharacteristic
324C22×C73#57511yescharacteristic
325C22×C73#57711yescharacteristic
326C22×C73#57711yescharacteristic
327C4×C73—22no—
328C4×C73—42no—
329C4×C73—41no—
330C4×C73—42no—
331C4×C73—41no—
332C4×C73—41no—
333C4×C73—41no—
334C4×C73—81no—
335C4×C73—81no—
336C4×C73—81no—
337C4×C73—81no—
338C4×C73—81no—
339C4×C73C2×C22⋊Q811yescharacteristic
340C4×C73#54311yescharacteristic
341C4×C73#54611yescharacteristic
342C4×C73#55111yescharacteristic
343#25972C7311yesmaximal, characteristic, direct product factor, Sylow
344C2×C73—42no—
345C2×C73—44no—
346C2×C73#243711yescharacteristic
347C2×C73#308011yescharacteristic
348C2×C73#308411yescharacteristic
349C2×C73#326711yescharacteristic
350C2×C73#327511yescharacteristic
351C2×C73#330711yescharacteristic
352C2×C73#332311yescharacteristic
353C2×#478C2×C7311yescharacteristic, complemented
354C2×#417C2×C7311yescharacteristic
355#2442C2×C7311yescharacteristic, complemented
356#2339C2×C7311yescharacteristic
357#2097C2×C7311yescharacteristic, complemented
358#2066C2×C7311yescharacteristic, complemented
359#2066C2×C7311yescharacteristic, complemented
360#2026C2×C7311yescharacteristic, complemented
361#1864C2×C7311yescharacteristic, complemented
362#1864C2×C7311yescharacteristic, complemented
363#1853C2×C7311yescharacteristic, complemented
364#1851C2×C7311yescharacteristic, complemented
365#1809C2×C7311yescharacteristic, complemented
366#1804C2×C7311yescharacteristic, complemented
367#1788C2×C7311yescharacteristic
368C73#2597211yescharacteristic, direct product factor, Sylow
369C22×#41C22×C7311yescharacteristic
370C22×M16C22×C7311yescharacteristic
371C2×#125C22×C7311yescharacteristic
372C2×C4×D4C22×C7311yescharacteristic
373C2×C4×D4C22×C7311yescharacteristic
374C22×C4⋊C4C22×C7311yescharacteristic
375#478—24no—
376C2×#107C22×C7311yescharacteristic
377C2×#106C22×C7311yescharacteristic
378C2×#106C22×C7311yescharacteristic
379C2×#106C22×C7311yescharacteristic
380C2×C4⋊C8C22×C7311yescharacteristic
381C2×C4⋊C8C22×C7311yescharacteristic
382#417—24no—
383C2×#103C22×C7311yescharacteristic
384C2×#103C22×C7311yescharacteristic
385C2×#103C22×C7311yescharacteristic
386C2×#103C22×C7311yescharacteristic
387C2×#102C22×C7311yescharacteristic
388C2×#102C22×C7311yescharacteristic
389C2×#102C22×C7311yescharacteristic
390C2×#102C22×C7311yescharacteristic
391C2×C22⋊C8C22×C7311yescharacteristic
392#400—21no—
393#398—21no—
394#391C22×C7311yescharacteristic
395#391C22×C7311yescharacteristic
396#389C22×C7311yescharacteristic
397#389C22×C7311yescharacteristic
398#386—21no—
399#386—21no—
400#385—21no—
401#382C22×C7311yescharacteristic
402#381—21no—
403#380—21no—
404#380C22×C7311yescharacteristic
405#380C22×C7311yescharacteristic
406C4×C22⋊C4C22×C7311yescharacteristic
407C2×#95—21no—
408#340C22×C7311yescharacteristic
409#340C22×C7311yescharacteristic
410#340C22×C7311yescharacteristic
411#340C22×C7311yescharacteristic
412#336C22×C7311yescharacteristic
413#336C22×C7311yescharacteristic
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—22no—
417C2×#41—41no—
418C2×#41—41no—
419C2×#41Q8×C7314yes—
420C22×Q8C23×C7311yescharacteristic
421C22×D4—21no—
422C22×D4C23×C7311yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C23×C4C23×C7311yescharacteristic
428C2×M16—22no—
429C2×M16—22no—
430C2×M16—41no—
431C22×C8C23×C7311yescharacteristic
432C22×C8C23×C7311yescharacteristic
433C22×C8C23×C7311yescharacteristic
434C22×C8C23×C7311yescharacteristic
435#125—22no—
436#125—41no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—41no—
440C4×D4—41no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C4⋊C4C23×C7311yescharacteristic
450C2×C4⋊C4C23×C7311yescharacteristic
451C2×C4⋊C4C23×C7311yescharacteristic
452C2×C4⋊C4C23×C7311yescharacteristic
453C2×C4⋊C4C23×C7311yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C7311yescharacteristic
459C2×C22⋊C4D4×C7311yescharacteristic
460C2×C42C23×C7311yescharacteristic
461C2×C42C23×C7311yescharacteristic
462#107—22no—
463#106—22no—
464#106—41no—
465#106—41no—
466C4⋊C8—22no—
467C4⋊C8—41no—
468#103—22no—
469#103—22no—
470#103—41no—
471#103—41no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102D4×C7314yes—
476C22⋊C8—22no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95D4×C7311yescharacteristic
488#95D4×C7311yescharacteristic
489C24—21no—
490C24C2×D4×C7311yescharacteristic
491#41—28no—
492#41—44no—
493#41—44no—
494#41—44no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8C2×Q8×C7312yes—
501C2×D4—24no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C2×D4×C7312yes—
508C2×D4C2×Q8×C7312yes—
509C2×D4#41×C7312yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4C2×D4×C7311yescharacteristic
534C22×C4C2×D4×C7311yescharacteristic
535C22×C4C2×D4×C7311yescharacteristic
536C22×C4C2×D4×C7311yescharacteristic
537C22×C4C2×D4×C7311yescharacteristic
538C22×C4C2×Q8×C7312yes—
539C22×C4#41×C7312yes—
540C22×C4C24×C7311yescharacteristic
541M16—44no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8C2×D4×C7312yes—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—81no—
569C4⋊C4—81no—
570C4⋊C4C2×D4×C7312yes—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C23—22no—
582C23—22no—
583C23—21no—
584C23—22no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23C22⋊Q8×C7312yes—
595C23C22×D4×C7311yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600D4—22no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4C22⋊Q8×C7314yes—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—48no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4C22⋊Q8×C7312yes—
649C2×C4C22×D4×C7311yescharacteristic
650C2×C4C22×Q8×C7311yescharacteristic
651C2×C4C2×#41×C7311yescharacteristic
652C2×C4C2×#41×C7311yescharacteristic
653C2×C4H(5,𝔽2)×C7311yescharacteristic
654C2×C4H(5,𝔽2)×C7311yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8—41no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—24no—
663C22—41no—
664C22—42no—
665C22—42no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—42no—
670C22—41no—
671C22—42no—
672C22—42no—
673C22C2×C22⋊Q8×C7311yescharacteristic
674C22D42×C7311yescharacteristic
675C22#546×C7311yescharacteristic
676C22#575×C7311yescharacteristic
677C22#575×C7311yescharacteristic
678C22#577×C7311yescharacteristic
679C22#577×C7311yescharacteristic
680C4—22no—
681C4—41no—
682C4—42no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4C2×C22⋊Q8×C7311yescharacteristic
693C4#543×C7311yescharacteristic
694C4#546×C7311yescharacteristic
695C4#551×C7311yescharacteristic
696C2—42no—
697C2—44no—
698C2C73×#243711yescharacteristic
699C2C73×#308011yescharacteristic
700C2C73×#308411yescharacteristic
701C2C73×#326711yescharacteristic
702C2C73×#327511yescharacteristic
703C2C73×#330711yescharacteristic
704C2C73×#332311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×#41×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#478×C73C2semidirect
3. C73×#2442C2semidirect
5. C73×#2097C2semidirect
6. C73×#2066C2semidirect
7. C73×#2066C2semidirect
8. C73×#2026C2semidirect
9. C73×#1864C2semidirect
10. C73×#1864C2semidirect
11. C73×#1853C2semidirect
12. C73×#1851C2semidirect
13. C73×#1809C2semidirect
14. C73×#1804C2semidirect
343. #25972C73direct (N × H)
353. C2×#478C2×C73semidirect
355. #2442C2×C73semidirect
357. #2097C2×C73semidirect
358. #2066C2×C73semidirect
359. #2066C2×C73semidirect
360. #2026C2×C73semidirect
361. #1864C2×C73semidirect
362. #1864C2×C73semidirect
363. #1853C2×C73semidirect
364. #1851C2×C73semidirect
365. #1809C2×C73semidirect
366. #1804C2×C73semidirect
368. C73#25972direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#478×C732
C2×#417×C732
C73×#24422
C73×#23392
C73×#20972
C73×#20662
C73×#20262
C73×#18642
C73×#18532
C73×#18512
C73×#18092
C73×#18042
C73×#17882
#2597273