Finite Group Databasebeta

← C73×#22578 #32931982

Subgroups — C73×#22578 #32931982

Order 18688.

1010 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#417×C73C211yesmaximal, characteristic
2C73×#2345C211yesmaximal, characteristic, complemented
3C73×#2339C211yesmaximal, characteristic
4C73×#1935C211yesmaximal, characteristic, complemented
5C73×#1933C211yesmaximal, characteristic, complemented
6C73×#1928C211yesmaximal, characteristic, complemented
7C73×#1927C211yesmaximal, characteristic, complemented
8C73×#1864C211yesmaximal, characteristic, complemented
9C73×#1862C211yesmaximal, characteristic, complemented
10C73×#1823C211yesmaximal, characteristic, complemented
11C73×#1809C211yesmaximal, characteristic, complemented
12C73×#1788C211yesmaximal, characteristic
13C73×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C73C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×C4×D4×C73C2211yescharacteristic
19C2×C4×D4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C2×#107×C73C2211yescharacteristic
22C2×#106×C73C2211yescharacteristic
23#417×C73C418yescomplemented
24C2×#103×C73C2211yescharacteristic
25C2×#103×C73C2211yescharacteristic
26C2×#103×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×C22⋊C8×C73C2211yescharacteristic
33C2×#97×C73C2211yescharacteristic
34C2×C4×C8×C73C2211yescharacteristic
35#391×C73C2211yescharacteristic
36#391×C73C2211yescharacteristic
37#389×C73C2211yescharacteristic
38#389×C73C2211yescharacteristic
39#387×C73—21no—
40#387×C73—21no—
41#386×C73—21no—
42#386×C73—21no—
43#381×C73—21no—
44#380×C73—21no—
45#380×C73C2211yescharacteristic
46#380×C73C2211yescharacteristic
47C4×C4⋊C4×C73C2211yescharacteristic
48C4×C4⋊C4×C73C2211yescharacteristic
49C4×C22⋊C4×C73—21no—
50C4×C22⋊C4×C73C2211yescharacteristic
51C2×#95×C73—21no—
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C2×#41×C73—22no—
61C2×#41×C73—22no—
62C2×#41×C73—22no—
63C2×#41×C73—41no—
64C2×#41×C73—41no—
65C2×#41×C73C2×C414yes—
66C22×Q8×C73C2311yescharacteristic
67C22×D4×C73—21no—
68C22×D4×C73C2311yescharacteristic
69C23×C4×C73—21no—
70C23×C4×C73—21no—
71C23×C4×C73—21no—
72C23×C4×C73—21no—
73C23×C4×C73C2311yescharacteristic
74C2×M16×C73—41no—
75C2×M16×C73—41no—
76C2×M16×C73C2×C414yescomplemented
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C4×D4×C73—22no—
82C4×D4×C73—22no—
83C4×D4×C73—41no—
84C4×D4×C73—41no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73C2×C414yescomplemented
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C22⋊C4×C73—21no—
97C2×C22⋊C4×C73—21no—
98C2×C22⋊C4×C73—21no—
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73D411yescharacteristic
101C2×C22⋊C4×C73D411yescharacteristic
102C2×C42×C73—21no—
103C2×C42×C73—21no—
104C2×C42×C73C2311yescharacteristic
105C2×C42×C73C2311yescharacteristic
106#107×C73—41no—
107#106×C73—41no—
108#103×C73—41no—
109#103×C73—41no—
110#103×C73C2×C414yescomplemented
111#103×C73C2×C414yescomplemented
112#102×C73—22no—
113#102×C73—22no—
114#102×C73C2×C414yes—
115#102×C73C2×C414yes—
116C22⋊C8×C73—22no—
117#97×C73—41no—
118C4×C8×C73—41no—
119#95×C73—21no—
120#95×C73—21no—
121#95×C73—21no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73D411yescharacteristic
130#95×C73D411yescharacteristic
131C24×C73—21no—
132C24×C73C2×D411yescharacteristic
133#41×C73—28no—
134#41×C73—44no—
135#41×C73—44no—
136#41×C73—44no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73C22×C412yes—
143C2×D4×C73—24no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—42no—
148C2×D4×C73—42no—
149C2×D4×C73C22×C412yes—
150C2×D4×C73#4112yes—
151C2×D4×C73#4112yes—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—24no—
160C22×C4×C73—24no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73—42no—
170C22×C4×C73—42no—
171C22×C4×C73—81no—
172C22×C4×C73—81no—
173C22×C4×C73—81no—
174C22×C4×C73—81no—
175C22×C4×C73C22×C412yes—
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73#4112yes—
182C22×C4×C73C2411yescharacteristic
183M16×C73—44no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73C22×C412yes—
195C2×C8×C73C22×C412yes—
196C4⋊C4×C73—24no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
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—81no—
208C4⋊C4×C73—81no—
209C4⋊C4×C73C22×C412yes—
210C4⋊C4×C73C22×C412yes—
211C22⋊C4×C73—22no—
212C22⋊C4×C73—41no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—81no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—81no—
222C42×C73—81no—
223C23×C73—22no—
224C23×C73—22no—
225C23×C73—22no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73C4×D412yes—
237C23×C73C22×D411yescharacteristic
238Q8×C73—22no—
239Q8×C73—22no—
240Q8×C73—41no—
241Q8×C73—41no—
242D4×C73—22no—
243D4×C73—22no—
244D4×C73—22no—
245D4×C73—48no—
246D4×C73#11714yes—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—48no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
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—84no—
287C2×C4×C73—84no—
288C2×C4×C73—84no—
289C2×C4×C73C4×D412yes—
290C2×C4×C73#13712yes—
291C2×C4×C73C23×C411yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C2×C4×C73H(5,𝔽2)11yescharacteristic
296C2×C4×C73H(5,𝔽2)11yescharacteristic
297C8×C73—22no—
298C8×C73—22no—
299C8×C73—41no—
300C8×C73—41no—
301C22×C73—22no—
302C22×C73—24no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—41no—
306C22×C73—42no—
307C22×C73—42no—
308C22×C73—42no—
309C22×C73—41no—
310C22×C73—42no—
311C22×C73—42no—
312C22×C73—41no—
313C22×C73—42no—
314C22×C73—41no—
315C22×C73C2×C4×D411yescharacteristic
316C22×C73#54611yescharacteristic
317C22×C73#54611yescharacteristic
318C22×C73C2×#13711yescharacteristic
319C22×C73#57511yescharacteristic
320C22×C73#57611yescharacteristic
321C22×C73#57711yescharacteristic
322C4×C73—22no—
323C4×C73—22no—
324C4×C73—41no—
325C4×C73—42no—
326C4×C73—42no—
327C4×C73—42no—
328C4×C73—41no—
329C4×C73—41no—
330C4×C73—81no—
331C4×C73—81no—
332C4×C73—81no—
333C4×C73—81no—
334C4×C73C2×#11711yescharacteristic
335C4×C73#51811yescharacteristic
336C4×C73#55111yescharacteristic
337C4×C73#55111yescharacteristic
338#22578C7311yesmaximal, characteristic, direct product factor, Sylow
339C2×C73—42no—
340C2×C73—44no—
341C2×C73#234211yescharacteristic
342C2×C73C4×#13711yescharacteristic
343C2×C73#294611yescharacteristic
344C2×C73#330711yescharacteristic
345C2×C73#331411yescharacteristic
346C2×C73#332211yescharacteristic
347C2×C73#333111yescharacteristic
348C2×#417C2×C7311yescharacteristic
349#2345C2×C7311yescharacteristic, complemented
350#2339C2×C7311yescharacteristic
351#1935C2×C7311yescharacteristic, complemented
352#1933C2×C7311yescharacteristic, complemented
353#1928C2×C7311yescharacteristic, complemented
354#1927C2×C7311yescharacteristic, complemented
355#1864C2×C7311yescharacteristic, complemented
356#1862C2×C7311yescharacteristic, complemented
357#1823C2×C7311yescharacteristic, complemented
358#1809C2×C7311yescharacteristic, complemented
359#1788C2×C7311yescharacteristic
360#1762C2×C7311yescharacteristic, complemented
361C4×#102C2×C7311yescharacteristic, complemented
362#1753C2×C7311yescharacteristic, complemented
363C73#2257811yescharacteristic, direct product factor, Sylow
364C22×#41C22×C7311yescharacteristic
365C22×M16C22×C7311yescharacteristic
366C2×C4×D4C22×C7311yescharacteristic
367C2×C4×D4C22×C7311yescharacteristic
368C22×C4⋊C4C22×C7311yescharacteristic
369C2×#107C22×C7311yescharacteristic
370C2×#106C22×C7311yescharacteristic
371#417C4×C7318yescomplemented
372C2×#103C22×C7311yescharacteristic
373C2×#103C22×C7311yescharacteristic
374C2×#103C22×C7311yescharacteristic
375C2×#103C22×C7311yescharacteristic
376C2×#102C22×C7311yescharacteristic
377C2×#102C22×C7311yescharacteristic
378C2×#102C22×C7311yescharacteristic
379C2×#102C22×C7311yescharacteristic
380C2×C22⋊C8C22×C7311yescharacteristic
381C2×#97C22×C7311yescharacteristic
382C2×C4×C8C22×C7311yescharacteristic
383#391C22×C7311yescharacteristic
384#391C22×C7311yescharacteristic
385#389C22×C7311yescharacteristic
386#389C22×C7311yescharacteristic
387#387—21no—
388#387—21no—
389#386—21no—
390#386—21no—
391#381—21no—
392#380—21no—
393#380C22×C7311yescharacteristic
394#380C22×C7311yescharacteristic
395C4×C4⋊C4C22×C7311yescharacteristic
396C4×C4⋊C4C22×C7311yescharacteristic
397C4×C22⋊C4—21no—
398C4×C22⋊C4C22×C7311yescharacteristic
399C2×#95—21no—
400#340C22×C7311yescharacteristic
401#340C22×C7311yescharacteristic
402#340C22×C7311yescharacteristic
403#340C22×C7311yescharacteristic
404#340C22×C7311yescharacteristic
405#340C22×C7311yescharacteristic
406#336C22×C7311yescharacteristic
407#336C22×C7311yescharacteristic
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—41no—
412C2×#41—41no—
413C2×#41C2×C4×C7314yes—
414C22×Q8C23×C7311yescharacteristic
415C22×D4—21no—
416C22×D4C23×C7311yescharacteristic
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4C23×C7311yescharacteristic
422C2×M16—41no—
423C2×M16—41no—
424C2×M16C2×C4×C7314yescomplemented
425C22×C8C23×C7311yescharacteristic
426C22×C8C23×C7311yescharacteristic
427C22×C8C23×C7311yescharacteristic
428C22×C8C23×C7311yescharacteristic
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—41no—
432C4×D4—41no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4C2×C4×C7314yescomplemented
438C2×C4⋊C4C23×C7311yescharacteristic
439C2×C4⋊C4C23×C7311yescharacteristic
440C2×C4⋊C4C23×C7311yescharacteristic
441C2×C4⋊C4C23×C7311yescharacteristic
442C2×C4⋊C4C23×C7311yescharacteristic
443C2×C4⋊C4C23×C7311yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C7311yescharacteristic
449C2×C22⋊C4D4×C7311yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C7311yescharacteristic
453C2×C42C23×C7311yescharacteristic
454#107—41no—
455#106—41no—
456#103—41no—
457#103—41no—
458#103C2×C4×C7314yescomplemented
459#103C2×C4×C7314yescomplemented
460#102—22no—
461#102—22no—
462#102C2×C4×C7314yes—
463#102C2×C4×C7314yes—
464C22⋊C8—22no—
465#97—41no—
466C4×C8—41no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95D4×C7311yescharacteristic
478#95D4×C7311yescharacteristic
479C24—21no—
480C24C2×D4×C7311yescharacteristic
481#41—28no—
482#41—44no—
483#41—44no—
484#41—44no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C22×C4×C7312yes—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4C22×C4×C7312yes—
498C2×D4#41×C7312yes—
499C2×D4#41×C7312yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4C22×C4×C7312yes—
524C22×C4C2×D4×C7311yescharacteristic
525C22×C4C2×D4×C7311yescharacteristic
526C22×C4C2×D4×C7311yescharacteristic
527C22×C4C2×D4×C7311yescharacteristic
528C22×C4C2×D4×C7311yescharacteristic
529C22×C4#41×C7312yes—
530C22×C4C24×C7311yescharacteristic
531M16—44no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8C22×C4×C7312yes—
543C2×C8C22×C4×C7312yes—
544C4⋊C4—24no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4C22×C4×C7312yes—
558C4⋊C4C22×C4×C7312yes—
559C22⋊C4—22no—
560C22⋊C4—41no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—81no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—81no—
570C42—81no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23C4×D4×C7312yes—
585C23C22×D4×C7311yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—48no—
594D4#117×C7314yes—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—48no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
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—84no—
635C2×C4—84no—
636C2×C4—84no—
637C2×C4C4×D4×C7312yes—
638C2×C4#137×C7312yes—
639C2×C4C23×C4×C7311yescharacteristic
640C2×C4C2×#41×C7311yescharacteristic
641C2×C4C2×#41×C7311yescharacteristic
642C2×C4C2×#41×C7311yescharacteristic
643C2×C4H(5,𝔽2)×C7311yescharacteristic
644C2×C4H(5,𝔽2)×C7311yescharacteristic
645C8—22no—
646C8—22no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—24no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—41no—
657C22—42no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22C2×C4×D4×C7311yescharacteristic
664C22#546×C7311yescharacteristic
665C22#546×C7311yescharacteristic
666C22C2×#137×C7311yescharacteristic
667C22#575×C7311yescharacteristic
668C22#576×C7311yescharacteristic
669C22#577×C7311yescharacteristic
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C2×#117×C7311yescharacteristic
683C4#518×C7311yescharacteristic
684C4#551×C7311yescharacteristic
685C4#551×C7311yescharacteristic
686C2—42no—
687C2—44no—
688C2C73×#234211yescharacteristic
689C2C4×#137×C7311yescharacteristic
690C2C73×#294611yescharacteristic
691C2C73×#330711yescharacteristic
692C2C73×#331411yescharacteristic
693C2C73×#332211yescharacteristic
694C2C73×#333111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC22×#41×C73C22
LCSG ▷ C2×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
2. C73×#2345C2semidirect
4. C73×#1935C2semidirect
5. C73×#1933C2semidirect
6. C73×#1928C2semidirect
7. C73×#1927C2semidirect
8. C73×#1864C2semidirect
9. C73×#1862C2semidirect
10. C73×#1823C2semidirect
11. C73×#1809C2semidirect
13. C73×#1762C2semidirect
14. C4×#102×C73C2semidirect
15. C73×#1753C2semidirect
23. #417×C73C4semidirect
76. C2×M16×C73C2×C4semidirect
89. C2×C4⋊C4×C73C2×C4semidirect
110. #103×C73C2×C4semidirect
111. #103×C73C2×C4semidirect
338. #22578C73direct (N × H)
349. #2345C2×C73semidirect
351. #1935C2×C73semidirect
352. #1933C2×C73semidirect
353. #1928C2×C73semidirect
354. #1927C2×C73semidirect
355. #1864C2×C73semidirect
356. #1862C2×C73semidirect
357. #1823C2×C73semidirect
358. #1809C2×C73semidirect
360. #1762C2×C73semidirect
361. C4×#102C2×C73semidirect
362. #1753C2×C73semidirect
363. C73#22578direct (N × H)
371. #417C4×C73semidirect
424. C2×M16C2×C4×C73semidirect
437. C2×C4⋊C4C2×C4×C73semidirect
458. #103C2×C4×C73semidirect
459. #103C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#417×C732
C73×#23452
C73×#23392
C73×#19352
C73×#19332
C73×#19282
C73×#19272
C73×#18642
C73×#18622
C73×#18232
C73×#18092
C73×#17882
C73×#17622
C4×#102×C732
C73×#17532
#2257873