Finite Group Databasebeta

← C73×#11035 #32920439

Subgroups — C73×#11035 #32920439

Order 18688.

1238 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C73C211yesmaximal, characteristic
2C2×#421×C73C211yesmaximal, characteristic
3C2×#419×C73C211yesmaximal, characteristic, complemented
4C2×#413×C73C211yesmaximal, characteristic
5C22×#101×C73C211yesmaximal, characteristic, complemented
6C2×#344×C73C211yesmaximal, characteristic, complemented
7C73×#1738C211yesmaximal, characteristic, complemented
8C22×#41×C73C2211yescharacteristic
9C23×Q8×C73C2211yescharacteristic
10C2×#137×C73—22no—
11C2×#137×C73—22no—
12C2×#137×C73—22no—
13C2×#137×C73—22no—
14C2×#137×C73—22no—
15C2×#137×C73C414yescomplemented
16C22×Q16×C73—21no—
17C22×SD16×C73—21no—
18C22×M16×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20C22×M16×C73C2211yescharacteristic
21C22×M16×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23#421×C73—22no—
24#421×C73—22no—
25C2×#104×C73—22no—
26#419×C73—22no—
27#419×C73—22no—
28C2×#103×C73—22no—
29#413×C73—22no—
30#413×C73—22no—
31C2×#101×C73—22no—
32C2×#101×C73—21no—
33C2×#101×C73—22no—
34C2×#101×C73—22no—
35C2×#100×C73—21no—
36#344×C73—22no—
37#341×C73—22no—
38C2×#41×C73—21no—
39C2×#41×C73—21no—
40C2×#41×C73—21no—
41C2×#41×C73—21no—
42C2×#41×C73—21no—
43C2×#41×C73—21no—
44C2×#41×C73—21no—
45C2×#41×C73—21no—
46C2×#41×C73—21no—
47C2×#41×C73—21no—
48C2×#41×C73C2×C412yes—
49C2×#41×C73D412yes—
50C22×Q8×C73—21no—
51C22×Q8×C73—21no—
52C22×Q8×C73—21no—
53C22×Q8×C73—21no—
54C22×Q8×C73—21no—
55C22×Q8×C73—21no—
56C22×Q8×C73—21no—
57C22×Q8×C73—21no—
58C22×Q8×C73—21no—
59C22×Q8×C73—21no—
60C22×Q8×C73—21no—
61C22×Q8×C73C2×C412yes—
62C22×Q8×C73D411yescharacteristic
63C22×Q8×C73D412yes—
64C22×Q8×C73D412yes—
65C22×D4×C73—21no—
66C22×D4×C73D411yescharacteristic
67C23×C4×C73—21no—
68C23×C4×C73—21no—
69C23×C4×C73C2311yescharacteristic
70#137×C73—28no—
71#137×C73—28no—
72#137×C73—28no—
73#137×C73—28no—
74C2×Q16×C73—24no—
75C2×Q16×C73—24no—
76C2×Q16×C73—24no—
77C2×SD16×C73—24no—
78C2×SD16×C73—24no—
79C2×SD16×C73—24no—
80C2×M16×C73—21no—
81C2×M16×C73—21no—
82C2×M16×C73—21no—
83C2×M16×C73—21no—
84C2×M16×C73—21no—
85C2×M16×C73—21no—
86C2×M16×C73—21no—
87C2×M16×C73—21no—
88C2×M16×C73—21no—
89C2×M16×C73—21no—
90C2×M16×C73—21no—
91C2×M16×C73—21no—
92C2×M16×C73—21no—
93C2×M16×C73—21no—
94C2×M16×C73—21no—
95C2×M16×C73—21no—
96C2×M16×C73—21no—
97C2×M16×C73—21no—
98C2×M16×C73C2×C412yes—
99C2×M16×C73D412yes—
100C2×M16×C73D412yes—
101C2×M16×C73D412yes—
102C2×M16×C73D412yes—
103C2×M16×C73D412yes—
104C22×C8×C73—21no—
105C22×C8×C73—21no—
106C22×C8×C73—21no—
107C22×C8×C73—21no—
108#117×C73—21no—
109#117×C73—21no—
110#117×C73—21no—
111#117×C73D412yes—
112C2×C4⋊C4×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C42×C73—21no—
115#104×C73—28no—
116#103×C73—28no—
117#101×C73—28no—
118#101×C73—24no—
119#100×C73—24no—
120C24×C73—21no—
121C24×C73#4111yescharacteristic
122#41×C73—22no—
123#41×C73—22no—
124#41×C73—22no—
125#41×C73—22no—
126#41×C73—22no—
127#41×C73—22no—
128#41×C73—22no—
129#41×C73—22no—
130#41×C73—41no—
131#41×C73—41no—
132#41×C73—41no—
133#41×C73—41no—
134#41×C73—41no—
135#41×C73—41no—
136#41×C73—41no—
137#41×C73—41no—
138C2×Q8×C73—22no—
139C2×Q8×C73—22no—
140C2×Q8×C73—21no—
141C2×Q8×C73—22no—
142C2×Q8×C73—22no—
143C2×Q8×C73—22no—
144C2×Q8×C73—22no—
145C2×Q8×C73—22no—
146C2×Q8×C73—22no—
147C2×Q8×C73—22no—
148C2×Q8×C73—22no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—22no—
152C2×Q8×C73—22no—
153C2×Q8×C73—22no—
154C2×Q8×C73—22no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—22no—
158C2×Q8×C73—41no—
159C2×Q8×C73—41no—
160C2×Q8×C73—41no—
161C2×Q8×C73—41no—
162C2×Q8×C73—41no—
163C2×Q8×C73—41no—
164C2×Q8×C73—41no—
165C2×Q8×C73—41no—
166C2×Q8×C73—41no—
167C2×Q8×C73—41no—
168C2×Q8×C73—41no—
169C2×Q8×C73—41no—
170C2×Q8×C73C22⋊C412yes—
171C2×Q8×C73C22⋊C414yes—
172C2×D4×C73—22no—
173C2×D4×C73—22no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—41no—
180C2×D4×C73—41no—
181C2×D4×C73—41no—
182C2×D4×C73—41no—
183C2×D4×C73C22⋊C412yes—
184C22×C4×C73—22no—
185C22×C4×C73—22no—
186C22×C4×C73—21no—
187C22×C4×C73—22no—
188C22×C4×C73—22no—
189C22×C4×C73—22no—
190C22×C4×C73—41no—
191C22×C4×C73—41no—
192C22×C4×C73—41no—
193C22×C4×C73—41no—
194C22×C4×C73—41no—
195C22×C4×C73—41no—
196C22×C4×C73—41no—
197C22×C4×C73—41no—
198C22×C4×C73—41no—
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73#4111yescharacteristic
211C22×C4×C73#4111yescharacteristic
212C22×C4×C73#4111yescharacteristic
213Q16×C73—216no—
214SD16×C73—216no—
215M16×C73—22no—
216M16×C73—22no—
217M16×C73—22no—
218M16×C73—22no—
219M16×C73—22no—
220M16×C73—22no—
221M16×C73—22no—
222M16×C73—22no—
223M16×C73—22no—
224M16×C73—41no—
225M16×C73—41no—
226M16×C73—41no—
227M16×C73—41no—
228M16×C73—41no—
229M16×C73—41no—
230M16×C73C22⋊C414yes—
231C2×C8×C73—22no—
232C2×C8×C73—22no—
233C2×C8×C73—22no—
234C2×C8×C73—22no—
235C2×C8×C73—22no—
236C2×C8×C73—22no—
237C2×C8×C73—41no—
238C2×C8×C73—41no—
239C2×C8×C73—41no—
240C2×C8×C73—41no—
241C2×C8×C73—41no—
242C2×C8×C73—41no—
243C4⋊C4×C73—22no—
244C4⋊C4×C73—41no—
245C22⋊C4×C73—22no—
246C22⋊C4×C73—41no—
247C42×C73—22no—
248C42×C73—41no—
249C23×C73—22no—
250C23×C73—42no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—82no—
254C23×C73C4×D411yescharacteristic
255C23×C73#12111yescharacteristic
256C23×C73#12111yescharacteristic
257C23×C73#12111yescharacteristic
258C23×C73#12311yescharacteristic
259C23×C73#12311yescharacteristic
260C23×C73#12411yescharacteristic
261Q8×C73—24no—
262Q8×C73—22no—
263Q8×C73—24no—
264Q8×C73—22no—
265Q8×C73—42no—
266Q8×C73—42no—
267Q8×C73—42no—
268Q8×C73—42no—
269Q8×C73—42no—
270Q8×C73—41no—
271Q8×C73—41no—
272Q8×C73—42no—
273D4×C73—22no—
274D4×C73—22no—
275D4×C73—42no—
276D4×C73—42no—
277D4×C73—42no—
278D4×C73—42no—
279D4×C73—41no—
280D4×C73—41no—
281C2×C4×C73—22no—
282C2×C4×C73—24no—
283C2×C4×C73—42no—
284C2×C4×C73—42no—
285C2×C4×C73—42no—
286C2×C4×C73—41no—
287C2×C4×C73—42no—
288C2×C4×C73—42no—
289C2×C4×C73—41no—
290C2×C4×C73—42no—
291C2×C4×C73—42no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—42no—
295C2×C4×C73—42no—
296C2×C4×C73—82no—
297C2×C4×C73C2×C22⋊C411yescharacteristic
298C2×C4×C73C2×C22⋊C411yescharacteristic
299C2×C4×C73C2×C22⋊C411yescharacteristic
300C2×C4×C73C4×D411yescharacteristic
301C2×C4×C73C4×D411yescharacteristic
302C2×C4×C73C4×D411yescharacteristic
303C2×C4×C73#12011yescharacteristic
304C2×C4×C73#12011yescharacteristic
305C2×C4×C73#12011yescharacteristic
306C2×C4×C73#12011yescharacteristic
307C2×C4×C73#12011yescharacteristic
308C2×C4×C73#12011yescharacteristic
309C2×C4×C73#12011yescharacteristic
310C2×C4×C73#12011yescharacteristic
311C2×C4×C73#12111yescharacteristic
312C2×C4×C73#12111yescharacteristic
313C2×C4×C73#12111yescharacteristic
314C2×C4×C73#12111yescharacteristic
315C2×C4×C73#12111yescharacteristic
316C2×C4×C73#12111yescharacteristic
317C2×C4×C73#12111yescharacteristic
318C2×C4×C73#12111yescharacteristic
319C2×C4×C73#12111yescharacteristic
320C2×C4×C73#12311yescharacteristic
321C2×C4×C73#12311yescharacteristic
322C2×C4×C73#12411yescharacteristic
323C2×C4×C73#12711yescharacteristic
324C2×C4×C73#12711yescharacteristic
325C8×C73—24no—
326C8×C73—42no—
327C8×C73—42no—
328C8×C73—42no—
329C22×C73—22no—
330C22×C73—22no—
331C22×C73—22no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—42no—
337C22×C73—82no—
338C22×C73—82no—
339C22×C73—82no—
340C22×C73#38611yescharacteristic
341C22×C73#38611yescharacteristic
342C22×C73#39011yescharacteristic
343C22×C73#39211yescharacteristic
344C22×C73#39411yescharacteristic
345C22×C73#39411yescharacteristic
346C22×C73#39411yescharacteristic
347C4×C73—42no—
348C4×C73—44no—
349C4×C73—82no—
350C4×C73#37911yescharacteristic
351C4×C73#38611yescharacteristic
352C4×C73#38611yescharacteristic
353C4×C73#39011yescharacteristic
354C4×C73#39211yescharacteristic
355C4×C73#39211yescharacteristic
356C4×C73#39211yescharacteristic
357C4×C73#39411yescharacteristic
358#11035C7311yesmaximal, characteristic, direct product factor, Sylow
359C2×C73—21no—
360C2×C73—21no—
361C2×C73—21no—
362C2×C73—21no—
363C2×C73—21no—
364C2×C73—21no—
365C2×C73—82no—
366C2×C73#143811yescharacteristic
367C2×C73#204912yes—
368C22×#137C2×C7311yescharacteristic
369C2×#421C2×C7311yescharacteristic
370C2×#419C2×C7311yescharacteristic, complemented
371C2×#413C2×C7311yescharacteristic
372C22×#101C2×C7311yescharacteristic, complemented
373C2×#344C2×C7311yescharacteristic, complemented
374#1738C2×C7311yescharacteristic, complemented
375C73#1103511yescharacteristic, direct product factor, Sylow
376C22×#41C22×C7311yescharacteristic
377C23×Q8C22×C7311yescharacteristic
378C2×#137—22no—
379C2×#137—22no—
380C2×#137—22no—
381C2×#137—22no—
382C2×#137—22no—
383C2×#137C4×C7314yescomplemented
384C22×Q16—21no—
385C22×SD16—21no—
386C22×M16C22×C7311yescharacteristic
387C22×M16C22×C7311yescharacteristic
388C22×M16C22×C7311yescharacteristic
389C22×M16C22×C7311yescharacteristic
390C2×#117C22×C7311yescharacteristic
391#421—22no—
392#421—22no—
393C2×#104—22no—
394#419—22no—
395#419—22no—
396C2×#103—22no—
397#413—22no—
398#413—22no—
399C2×#101—22no—
400C2×#101—21no—
401C2×#101—22no—
402C2×#101—22no—
403C2×#100—21no—
404#344—22no—
405#341—22no—
406C2×#41—21no—
407C2×#41—21no—
408C2×#41—21no—
409C2×#41—21no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41C2×C4×C7312yes—
417C2×#41D4×C7312yes—
418C22×Q8—21no—
419C22×Q8—21no—
420C22×Q8—21no—
421C22×Q8—21no—
422C22×Q8—21no—
423C22×Q8—21no—
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8—21no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8C2×C4×C7312yes—
430C22×Q8D4×C7311yescharacteristic
431C22×Q8D4×C7312yes—
432C22×Q8D4×C7312yes—
433C22×D4—21no—
434C22×D4D4×C7311yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C23×C4C23×C7311yescharacteristic
438#137—28no—
439#137—28no—
440#137—28no—
441#137—28no—
442C2×Q16—24no—
443C2×Q16—24no—
444C2×Q16—24no—
445C2×SD16—24no—
446C2×SD16—24no—
447C2×SD16—24no—
448C2×M16—21no—
449C2×M16—21no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16—21no—
453C2×M16—21no—
454C2×M16—21no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16C2×C4×C7312yes—
467C2×M16D4×C7312yes—
468C2×M16D4×C7312yes—
469C2×M16D4×C7312yes—
470C2×M16D4×C7312yes—
471C2×M16D4×C7312yes—
472C22×C8—21no—
473C22×C8—21no—
474C22×C8—21no—
475C22×C8—21no—
476#117—21no—
477#117—21no—
478#117—21no—
479#117D4×C7312yes—
480C2×C4⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C42—21no—
483#104—28no—
484#103—28no—
485#101—28no—
486#101—24no—
487#100—24no—
488C24—21no—
489C24#41×C7311yescharacteristic
490#41—22no—
491#41—22no—
492#41—22no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—41no—
499#41—41no—
500#41—41no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—21no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—22no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8C22⋊C4×C7312yes—
539C2×Q8C22⋊C4×C7314yes—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4C22⋊C4×C7312yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4C22×C4×C7311yescharacteristic
568C22×C4C2×D4×C7311yescharacteristic
569C22×C4C2×D4×C7311yescharacteristic
570C22×C4C2×D4×C7311yescharacteristic
571C22×C4C2×D4×C7311yescharacteristic
572C22×C4C2×D4×C7311yescharacteristic
573C22×C4C2×D4×C7311yescharacteristic
574C22×C4C2×D4×C7311yescharacteristic
575C22×C4C2×D4×C7311yescharacteristic
576C22×C4C2×D4×C7311yescharacteristic
577C22×C4C2×D4×C7311yescharacteristic
578C22×C4#41×C7311yescharacteristic
579C22×C4#41×C7311yescharacteristic
580C22×C4#41×C7311yescharacteristic
581Q16—216no—
582SD16—216no—
583M16—22no—
584M16—22no—
585M16—22no—
586M16—22no—
587M16—22no—
588M16—22no—
589M16—22no—
590M16—22no—
591M16—22no—
592M16—41no—
593M16—41no—
594M16—41no—
595M16—41no—
596M16—41no—
597M16—41no—
598M16C22⋊C4×C7314yes—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C4⋊C4—22no—
612C4⋊C4—41no—
613C22⋊C4—22no—
614C22⋊C4—41no—
615C42—22no—
616C42—41no—
617C23—22no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23—82no—
622C23C4×D4×C7311yescharacteristic
623C23#121×C7311yescharacteristic
624C23#121×C7311yescharacteristic
625C23#121×C7311yescharacteristic
626C23#123×C7311yescharacteristic
627C23#123×C7311yescharacteristic
628C23#124×C7311yescharacteristic
629Q8—24no—
630Q8—22no—
631Q8—24no—
632Q8—22no—
633Q8—42no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—41no—
639Q8—41no—
640Q8—42no—
641D4—22no—
642D4—22no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—41no—
648D4—41no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—82no—
665C2×C4C2×C22⋊C4×C7311yescharacteristic
666C2×C4C2×C22⋊C4×C7311yescharacteristic
667C2×C4C2×C22⋊C4×C7311yescharacteristic
668C2×C4C4×D4×C7311yescharacteristic
669C2×C4C4×D4×C7311yescharacteristic
670C2×C4C4×D4×C7311yescharacteristic
671C2×C4#120×C7311yescharacteristic
672C2×C4#120×C7311yescharacteristic
673C2×C4#120×C7311yescharacteristic
674C2×C4#120×C7311yescharacteristic
675C2×C4#120×C7311yescharacteristic
676C2×C4#120×C7311yescharacteristic
677C2×C4#120×C7311yescharacteristic
678C2×C4#120×C7311yescharacteristic
679C2×C4#121×C7311yescharacteristic
680C2×C4#121×C7311yescharacteristic
681C2×C4#121×C7311yescharacteristic
682C2×C4#121×C7311yescharacteristic
683C2×C4#121×C7311yescharacteristic
684C2×C4#121×C7311yescharacteristic
685C2×C4#121×C7311yescharacteristic
686C2×C4#121×C7311yescharacteristic
687C2×C4#121×C7311yescharacteristic
688C2×C4#123×C7311yescharacteristic
689C2×C4#123×C7311yescharacteristic
690C2×C4#124×C7311yescharacteristic
691C2×C4#127×C7311yescharacteristic
692C2×C4#127×C7311yescharacteristic
693C8—24no—
694C8—42no—
695C8—42no—
696C8—42no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—42no—
705C22—82no—
706C22—82no—
707C22—82no—
708C22#386×C7311yescharacteristic
709C22#386×C7311yescharacteristic
710C22#390×C7311yescharacteristic
711C22#392×C7311yescharacteristic
712C22#394×C7311yescharacteristic
713C22#394×C7311yescharacteristic
714C22#394×C7311yescharacteristic
715C4—42no—
716C4—44no—
717C4—82no—
718C4#379×C7311yescharacteristic
719C4#386×C7311yescharacteristic
720C4#386×C7311yescharacteristic
721C4#390×C7311yescharacteristic
722C4#392×C7311yescharacteristic
723C4#392×C7311yescharacteristic
724C4#392×C7311yescharacteristic
725C4#394×C7311yescharacteristic
726C2—21no—
727C2—21no—
728C2—21no—
729C2—21no—
730C2—21no—
731C2—21no—
732C2—82no—
733C2C73×#143811yescharacteristic
734C2C73×#204912yes—
subgroupG/H
center, socleC22×C73#394
commutatorC22×C4C22×C4×C73
Frattini, cosocleC23×C4C23×C73
prime radicalC22×#41×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#419×C73C2semidirect
5. C22×#101×C73C2semidirect
6. C2×#344×C73C2semidirect
7. C73×#1738C2semidirect
15. C2×#137×C73C4semidirect
358. #11035C73direct (N × H)
370. C2×#419C2×C73semidirect
372. C22×#101C2×C73semidirect
373. C2×#344C2×C73semidirect
374. #1738C2×C73semidirect
375. C73#11035direct (N × H)
383. C2×#137C4×C73semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C732
C2×#421×C732
C2×#419×C732
C2×#413×C732
C22×#101×C732
C2×#344×C732
C73×#17382
#1103573