Finite Group Databasebeta

← #13374530

Subgroups — #13374530

Order 1792.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740371C211yesmaximal, characteristic
2#11740363C211yesmaximal, characteristic, complemented
3C22×#6379C211yesmaximal, characteristic, complemented
4C2×#89595C211yesmaximal, characteristic, complemented
5#11736076C211yesmaximal, characteristic, complemented
6C7×#1896C211yesmaximal, characteristic, complemented
7#11729283C211yesmaximal, characteristic, complemented
8#11728144C211yesmaximal, characteristic, complemented
9#11728131C211yesmaximal, characteristic, complemented
10#11728128C211yesmaximal, characteristic, complemented
11#11727738C211yesmaximal, characteristic, complemented
12#11726528C211yesmaximal, characteristic, complemented
13#11726500C211yesmaximal, characteristic, complemented
14#11726498C211yesmaximal, characteristic, complemented
15#11726494C211yesmaximal, characteristic, complemented
16C22×#1157C2211yescharacteristic
17C7×#525C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C2×#6513C2211yescharacteristic
20C2×#6513C2211yescharacteristic
21C2×#6511C2211yescharacteristic, complemented
22C22×#1136C2211yescharacteristic
23C2×#6470C2211yescharacteristic
24C2×#6470C2211yescharacteristic
25C2×C7×#104C2211yescharacteristic, complemented
26C2×C7×#104C2211yescharacteristic, complemented
27C7×#407C2211yescharacteristic
28#90006C2211yescharacteristic, complemented
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31#89901C2211yescharacteristic
32#89901C2211yescharacteristic
33C2×#6396C2211yescharacteristic, complemented
34C2×#6396C2211yescharacteristic, complemented
35#89822C411yescharacteristic, complemented
36#89819C411yescharacteristic, complemented
37#89819C411yescharacteristic, complemented
38#89818C411yescharacteristic, complemented
39#89812C411yescharacteristic, complemented
40#89809C411yescharacteristic, complemented
41#89809C411yescharacteristic, complemented
42#89808C411yescharacteristic, complemented
43#89784—21no—
44#89783—21no—
45#89783—21no—
46D4×C7⋊C8—21no—
47#89774C2211yescharacteristic
48#89774C2211yescharacteristic
49#89771C2211yescharacteristic, complemented
50#89769C2211yescharacteristic, complemented
51C2×#6379—24no—
52C2×#6379C2211yescharacteristic
53C2×#6379C2211yescharacteristic
54C2×#6379C2211yescharacteristic
55C2×#6379C2211yescharacteristic
56C2×#6377C2211yescharacteristic, complemented
57C2×#6377C2211yescharacteristic, complemented
58#89595—24no—
59#89499—21no—
60#89499—21no—
61#89498—21no—
62D7×C22⋊C8—21no—
63C7×#339C2211yescharacteristic, complemented
64C7×#339C2211yescharacteristic, complemented
65#89353C2211yescharacteristic, complemented
66#89353C2211yescharacteristic, complemented
67#89319C2211yescharacteristic, complemented
68#89319C2211yescharacteristic, complemented
69#22886—71nomaximal, Sylow
70C2×C7×#41C2311yescharacteristic
71C23×C4×C7—21no—
72C23×C4×C7C2311yescharacteristic
73C22×C22⋊D7—21no—
74C2×#1157—21no—
75C2×#1157—21no—
76C2×#1157—22no—
77C2×#1157—22no—
78C2×#1157—41no—
79C2×#1157—41no—
80C2×#1157C2×C411yescharacteristic
81C2×#1157C2×C411yescharacteristic
82C2×#1157C2311yescharacteristic
83C2×#1157C2311yescharacteristic
84C22×D28C2×C411yescharacteristic
85C22×C4×D7—21no—
86C22×Dic14C2×C411yescharacteristic
87C2×C7×M16C2311yescharacteristic
88C2×C7×M16C2311yescharacteristic
89C7×#123—21no—
90C7×C22⋊Q8C2×C411yescharacteristic
91C7×C22⋊Q8C2×C411yescharacteristic
92C7×#121C2×C411yescharacteristic
93C7×#121C2×C411yescharacteristic
94C7×#120—21no—
95C4×C7×D4—21no—
96C4×C7×D4—21no—
97C7×#117C2311yescharacteristic
98C2×C42×C7—22no—
99C2×C42×C7—21no—
100C2×C42×C7—41no—
101C2×C42×C7C2311yescharacteristic
102C2×C42×C7C2311yescharacteristic
103#6513—22no—
104#6513—22no—
105#6513—41no—
106#6513—41no—
107#6511—22no—
108#6511—41no—
109C2×#1144C2×C411yescharacteristic, complemented
110C2×#1144C2×C411yescharacteristic, complemented
111C2×#1143C2×C411yescharacteristic, complemented
112C2×#1143C2×C411yescharacteristic, complemented
113C2×#1142C2×C411yescharacteristic, complemented
114C2×#1142C2×C411yescharacteristic, complemented
115C2×#1141C2×C411yescharacteristic, complemented
116C2×#1141C2×C411yescharacteristic, complemented
117C2×#1136—21no—
118C2×#1136—21no—
119C2×#1136—22no—
120C2×#1136—41no—
121C2×#1136C2311yescharacteristic
122C2×#1136C2311yescharacteristic
123C22×C7⋊C8—21no—
124C22×C7⋊C8—21no—
125C22×C7⋊C8C2311yescharacteristic
126C22×C7⋊C8C2311yescharacteristic
127C22×C7⋊C8C2311yescharacteristic
128C22×C7⋊C8C2311yescharacteristic
129#6470—22no—
130#6470—22no—
131#6470—41no—
132#6470—41no—
133C2×#1131—21no—
134C2×#1131—21no—
135C2×C8×D7—21no—
136C2×C8×D7—21no—
137C7×#104—22no—
138C7×#104—41no—
139C7×C22⋊C8—21no—
140C7×C22⋊C8—21no—
141C22⋊(C7⋊C8)—21no—
142C22⋊(C7⋊C8)—21no—
143C22⋊(C7⋊C8)C2×C411yescharacteristic
144C22⋊(C7⋊C8)C2×C411yescharacteristic
145C22⋊(C7⋊C8)C2×C411yescharacteristic
146C22⋊(C7⋊C8)C2×C411yescharacteristic
147C22⋊(C7⋊C8)D411yescharacteristic
148C22⋊(C7⋊C8)D411yescharacteristic
149C22⋊(C7⋊C8)D411yescharacteristic
150C22⋊(C7⋊C8)D411yescharacteristic
151#6396—22no—
152#6396—41no—
153(C2×D7)⋊C8—21no—
154(C2×D7)⋊C8—21no—
155(C2×D7)⋊C8—21no—
156(C2×D7)⋊C8—21no—
157#6384C2×C411yescharacteristic, complemented
158#6384C2×C411yescharacteristic, complemented
159#6384C2×C411yescharacteristic, complemented
160#6384C2×C411yescharacteristic, complemented
161#6383C2×C411yescharacteristic, complemented
162#6383C2×C411yescharacteristic, complemented
163#6383C2×C411yescharacteristic, complemented
164#6383C2×C411yescharacteristic, complemented
165#6379—22no—
166#6379—22no—
167#6379—22no—
168#6379D414yescomplemented
169C4⋊(C7⋊C8)—21no—
170C4⋊(C7⋊C8)—21no—
171#6377—22no—
172#6377—21no—
173#6377—41no—
174C4×C7⋊C8—21no—
175#3002—71no—
176C2×#444—71no—
177#2933—71no—
178C22×#104—71no—
179#2880—71no—
180#1975—71no—
181#1938—71no—
182#1929—71no—
183#1896D711yescharacteristic, complemented
184#1876—71no—
185#1876—71no—
186#1866—71no—
187#1855—71no—
188#1765—71no—
189#1749—71no—
190C24×C7#4111yescharacteristic
191C23×D7—21no—
192C7×#41—21no—
193C7×#41—21no—
194C7×#41—21no—
195C7×#41—21no—
196C2×C7×Q8C22×C411yescharacteristic
197C2×C7×D4—21no—
198C2×C7×D4—21no—
199C2×C7×D4—21no—
200C2×C7×D4C22×C411yescharacteristic
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—42no—
209C22×C4×C7—42no—
210C22×C4×C7—42no—
211C22×C4×C7C22×C411yescharacteristic
212C22×C4×C7C22×C411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7#4111yescharacteristic
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—21no—
218C2×C22⋊D7—21no—
219C2×C22⋊D7—21no—
220C2×C22⋊D7—21no—
221C2×C22⋊D7—42no—
222C2×C22⋊D7—42no—
223C22×Dic7—21no—
224#1157—21no—
225#1157—21no—
226#1157—21no—
227#1157—21no—
228#1157—21no—
229#1157—21no—
230#1157—22no—
231#1157—22no—
232#1157—41no—
233#1157—41no—
234#1157—42no—
235#1157—42no—
236#1157—42no—
237#1157—42no—
238#1157C2×D412yes—
239#1157#4112yes—
240C2×D28—22no—
241C2×D28—21no—
242C2×D28—41no—
243C2×D28C22×C411yescharacteristic
244C2×D28C22×C411yescharacteristic
245C2×C4×D7—21no—
246C2×C4×D7—21no—
247C2×C4×D7—21no—
248C2×C4×D7—21no—
249C2×C4×D7—42no—
250C2×C4×D7—42no—
251C2×Dic14—22no—
252C2×Dic14—21no—
253C2×Dic14—41no—
254C2×Dic14C22×C411yescharacteristic
255C2×Dic14C22×C411yescharacteristic
256C7×M16—21no—
257C7×M16—21no—
258C7×M16—21no—
259C7×M16—21no—
260C2×C7×C8—21no—
261C2×C7×C8—21no—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4C22×C411yescharacteristic
265C7×C4⋊C4C22×C411yescharacteristic
266C7×C22⋊C4—21no—
267C7×C22⋊C4—21no—
268C7×C22⋊C4—21no—
269C7×C22⋊C4—21no—
270C7×C22⋊C4—21no—
271C42×C7—21no—
272C42×C7—21no—
273C42×C7—21no—
274C42×C7—21no—
275C42×C7—42no—
276C42×C7C2×D412yes—
277#1144—22no—
278#1144—41no—
279#1143—22no—
280#1143—41no—
281#1142—22no—
282#1142—41no—
283#1141—22no—
284#1141—41no—
285#1136—21no—
286#1136—21no—
287#1136—21no—
288#1136—42no—
289#1136—42no—
290#1136C2×D412yes—
291C2×C7⋊C8—21no—
292C2×C7⋊C8—21no—
293C2×C7⋊C8—21no—
294C2×C7⋊C8—21no—
295C2×C7⋊C8—21no—
296C2×C7⋊C8—21no—
297C2×C7⋊C8—21no—
298C2×C7⋊C8—21no—
299C2×C7⋊C8—21no—
300C2×C7⋊C8—21no—
301C2×C7⋊C8—42no—
302C2×C7⋊C8—42no—
303C2×C7⋊C8C22×C411yescharacteristic
304C2×C7⋊C8C22×C411yescharacteristic
305C2×C7⋊C8C22×C411yescharacteristic
306C2×C7⋊C8C22×C411yescharacteristic
307C2×C7⋊C8C2×D411yescharacteristic
308C2×C7⋊C8C2×D411yescharacteristic
309C2×C7⋊C8C2×D411yescharacteristic
310C2×C7⋊C8C2×D411yescharacteristic
311#1131—42no—
312#1131—42no—
313C8×D7—42no—
314C8×D7—42no—
315C22×#41—71no—
316C2×#135—71no—
317C2×#135—71no—
318C2×#131—71no—
319C2×#131—71no—
320C2×#131—71no—
321C22×M16—71no—
322#525C2×D711yescharacteristic
323C22×C42C2×D711yescharacteristic
324#452—71no—
325#452—71no—
326#451—71no—
327#450—71no—
328#449—71no—
329#449—71no—
330#448—71no—
331#447—71no—
332#444—144no—
333#436—141no—
334#435—141no—
335#435—141no—
336C8×D4—141no—
337C2×#108—71no—
338C2×#108—71no—
339#424—71no—
340C2×#104—71no—
341C2×#104—71no—
342C2×#104—71no—
343C2×#104—71no—
344C2×#104—144no—
345C2×#104C2×D711yescharacteristic, complemented
346C2×#104C2×D711yescharacteristic, complemented
347#416—71no—
348#416—71no—
349#408—71no—
350#408—71no—
351#408—71no—
352#408—141no—
353#408—141no—
354#407—141no—
355#407C2×D711yescharacteristic
356C2×C22⋊C8—71no—
357C2×C22⋊C8—71no—
358C2×C22⋊C8—141no—
359#405—71no—
360C2×#97—71no—
361C2×#97—71no—
362#341—71no—
363#341—71no—
364#339C2×D711yescharacteristic, complemented
365#339C2×D711yescharacteristic, complemented
366#336—71no—
367#336—71no—
368C23×C7—21no—
369C23×C7—21no—
370C23×C7—22no—
371C23×C7—21no—
372C23×C7—41no—
373C23×C7C4×D411yescharacteristic
374C23×C7C4×D411yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C22×D7—21no—
377C22×D7—21no—
378C22×D7—42no—
379C22×D7—42no—
380C22×D7—81no—
381C7×Q8—21no—
382C7×Q8—21no—
383C7×D4—21no—
384C7×D4—21no—
385C7×D4—41no—
386C7×D4—41no—
387C7×D4—42no—
388C7×D4—81no—
389C2×C4×C7—21no—
390C2×C4×C7—21no—
391C2×C4×C7—21no—
392C2×C4×C7—21no—
393C2×C4×C7—21no—
394C2×C4×C7—21no—
395C2×C4×C7—21no—
396C2×C4×C7—21no—
397C2×C4×C7—21no—
398C2×C4×C7—21no—
399C2×C4×C7—22no—
400C2×C4×C7—21no—
401C2×C4×C7—21no—
402C2×C4×C7—21no—
403C2×C4×C7—22no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—48no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7C4×D411yescharacteristic
412C2×C4×C7C4×D411yescharacteristic
413C2×C4×C7C23×C411yescharacteristic
414C2×C4×C7C22×D411yescharacteristic
415C2×C4×C7C22×D411yescharacteristic
416C2×C4×C7C2×#4111yescharacteristic
417C2×C4×C7H(5,𝔽2)11yescharacteristic
418C2×C4×C7H(5,𝔽2)11yescharacteristic
419C22⋊D7—22no—
420C22⋊D7—22no—
421C22⋊D7—42no—
422C22⋊D7—42no—
423C22⋊D7—41no—
424C22⋊D7—41no—
425C2×Dic7—21no—
426C2×Dic7—21no—
427C2×Dic7—42no—
428D28—21no—
429D28—21no—
430D28—21no—
431D28—42no—
432D28C4×D412yes—
433C4×D7—22no—
434C4×D7—22no—
435C4×D7—42no—
436C4×D7—42no—
437C4×D7—41no—
438C4×D7—41no—
439Dic14—21no—
440Dic14—21no—
441Dic14—21no—
442Dic14—42no—
443Dic14C4×D412yes—
444C7×C8—41no—
445C7×C8—41no—
446C7⋊C8—21no—
447C7⋊C8—21no—
448C7⋊C8—21no—
449C7⋊C8—21no—
450C7⋊C8—21no—
451C7⋊C8—21no—
452C7⋊C8—22no—
453C7⋊C8—21no—
454C7⋊C8—21no—
455C7⋊C8—41no—
456C2×#41—71no—
457C2×#41—71no—
458C2×#41—71no—
459C2×#41—71no—
460C2×#41—142no—
461C2×#41—142no—
462C2×#41—141no—
463C2×#41—141no—
464C2×#41—281no—
465C2×#41—281no—
466C2×#41C22×D711yescharacteristic
467C22×Q8—71no—
468C22×D4—71no—
469C22×D4—141no—
470C23×C4—21no—
471C23×C4—141no—
472C23×C4C22×D711yescharacteristic
473#135—142no—
474#135—142no—
475#135—281no—
476#135—281no—
477C2×Q16—71no—
478C2×Q16—71no—
479C2×SD16—71no—
480C2×SD16—71no—
481C2×SD16—71no—
482C2×SD16—71no—
483C2×D8—71no—
484C2×D8—71no—
485#131—142no—
486#131—142no—
487#131—142no—
488#131—281no—
489#131—281no—
490#131—281no—
491C2×M16—71no—
492C2×M16—71no—
493C2×M16—141no—
494C2×M16—141no—
495C2×M16—141no—
496C2×M16—141no—
497C2×M16—142no—
498C2×M16—281no—
499C2×M16C22×D711yescharacteristic
500C2×M16C22×D711yescharacteristic
501C22×C8—71no—
502C22×C8—71no—
503C22×C8—71no—
504C22×C8—71no—
505C22×C8—141no—
506C22×C8—141no—
507C22×C8—141no—
508C22×C8—141no—
509#123—21no—
510C22⋊Q8C4×D711yescharacteristic
511C22⋊Q8C4×D711yescharacteristic
512#121C4×D711yescharacteristic
513#121C4×D711yescharacteristic
514#120—21no—
515C4×D4—21no—
516C4×D4—21no—
517#117C22×D711yescharacteristic
518C2×C42—22no—
519C2×C42—21no—
520C2×C42—41no—
521C2×C42C22×D711yescharacteristic
522C2×C42C22×D711yescharacteristic
523#108—142no—
524#108—281no—
525C4⋊C8—141no—
526C4⋊C8—141no—
527#104—22no—
528#104—41no—
529#104—74no—
530#104—142no—
531#104—142no—
532#104—142no—
533#103—71no—
534#103—71no—
535#103—71no—
536#103—71no—
537#102—71no—
538#102—71no—
539#102—71no—
540#102—71no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—71no—
544C22⋊C8—71no—
545C22⋊C8—71no—
546C22⋊C8—71no—
547C22⋊C8—71no—
548C22⋊C8—71no—
549C22⋊C8—71no—
550C22⋊C8—71no—
551C22⋊C8—141no—
552C22⋊C8—141no—
553C22⋊C8—141no—
554C22⋊C8—141no—
555C22⋊C8—141no—
556C22⋊C8—141no—
557#97—141no—
558#97—142no—
559#97—281no—
560C4×C8—141no—
561C22×C7—21no—
562C22×C7—21no—
563C22×C7—21no—
564C22×C7—21no—
565C22×C7—21no—
566C22×C7—21no—
567C22×C7—21no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—41no—
571C22×C7—41no—
572C22×C7—41no—
573C22×C7#44412yescomplemented
574C22×C7C2×C4×D411yescharacteristic
575C22×C7#54611yescharacteristic
576C22×C7#55111yescharacteristic
577C2×D7—22no—
578C2×D7—41no—
579C2×D7—41no—
580C2×D7—41no—
581C2×D7—41no—
582C2×D7—41no—
583C2×D7—84no—
584C4×C7—21no—
585C4×C7—21no—
586C4×C7—42no—
587C4×C7—42no—
588C4×C7—41no—
589C4×C7—41no—
590C4×C7—41no—
591C4×C7C2×C4×D411yescharacteristic
592C4×C7#51811yescharacteristic
593C4×C7D4211yescharacteristic
594C4×C7#54611yescharacteristic
595Dic7—22no—
596Dic7—41no—
597C24—141no—
598C24#115911yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—72no—
604#41—72no—
605#41—142no—
606#41—142no—
607#41—141no—
608#41—141no—
609#41—141no—
610#41—141no—
611#41—141no—
612#41—141no—
613#41—282no—
614#41—282no—
615#41—281no—
616#41—281no—
617#41—282no—
618#41—282no—
619C2×Q8—71no—
620C2×Q8—71no—
621C2×Q8—142no—
622C2×Q8—141no—
623C2×Q8—281no—
624C2×Q8C2×C4×D711yescharacteristic
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—71no—
629C2×D4—71no—
630C2×D4—142no—
631C2×D4—141no—
632C2×D4—141no—
633C2×D4—141no—
634C2×D4—141no—
635C2×D4—141no—
636C2×D4—281no—
637C2×D4—282no—
638C2×D4—282no—
639C2×D4C2×C4×D711yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—141no—
651C22×C4—141no—
652C22×C4—141no—
653C22×C4—141no—
654C22×C4—141no—
655C22×C4—282no—
656C22×C4—282no—
657C22×C4C2×C4×D711yescharacteristic
658C22×C4C2×C4×D711yescharacteristic
659C22×C4D4×D711yescharacteristic
660C22×C4D4×D711yescharacteristic
661C22×C4#115911yescharacteristic
662C22×C4C23×D711yescharacteristic
663Q16—142no—
664Q16—281no—
665SD16—142no—
666SD16—142no—
667SD16—281no—
668SD16—281no—
669D8—142no—
670D8—281no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—72no—
676M16—141no—
677M16—141no—
678M16—141no—
679M16—282no—
680M16—282no—
681M16—282no—
682M16—282no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—71no—
686C2×C8—71no—
687C2×C8—71no—
688C2×C8—71no—
689C2×C8—71no—
690C2×C8—71no—
691C2×C8—71no—
692C2×C8—71no—
693C2×C8—141no—
694C2×C8—141no—
695C2×C8—141no—
696C2×C8—141no—
697C2×C8—141no—
698C2×C8—141no—
699C2×C8—141no—
700C2×C8—141no—
701C2×C8—141no—
702C2×C8—141no—
703C2×C8—282no—
704C2×C8—282no—
705C2×C8—282no—
706C2×C8—282no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4C2×C4×D711yescharacteristic
710C4⋊C4C2×C4×D711yescharacteristic
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—42no—
721C42D4×D712yes—
722C2×C7—21no—
723C2×C7—22no—
724C2×C7—21no—
725C2×C7—41no—
726C2×C7—81no—
727C2×C7#235811yescharacteristic
728C2×C7C2×#44411yescharacteristic
729C2×C7#295611yescharacteristic
730D7—42no—
731D7—81no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—41no—
737C23—141no—
738C23—141no—
739C23—282no—
740C23—282no—
741C23—561no—
742C23(C22⋊D7)⋊C411yescharacteristic
743C23(C22⋊D7)⋊C411yescharacteristic
744C23C2×#115911yescharacteristic
745Q8—21no—
746Q8—21no—
747Q8—72no—
748Q8—141no—
749Q8—141no—
750Q8—141no—
751Q8—282no—
752D4—21no—
753D4—21no—
754D4—41no—
755D4—41no—
756D4—42no—
757D4—72no—
758D4—81no—
759D4—142no—
760D4—142no—
761D4—141no—
762D4—141no—
763D4—141no—
764D4—282no—
765D4—282no—
766D4—282no—
767D4—281no—
768D4—281no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—141no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—141no—
795C2×C4—282no—
796C2×C4—282no—
797C2×C4—282no—
798C2×C4—281no—
799C2×C4—281no—
800C2×C4(C22⋊D7)⋊C411yescharacteristic
801C2×C4(C22⋊D7)⋊C411yescharacteristic
802C2×C4C22×C4×D711yescharacteristic
803C2×C4C2×D4×D711yescharacteristic
804C2×C4C2×D4×D711yescharacteristic
805C2×C4#654811yescharacteristic
806C2×C4D7×#4111yescharacteristic
807C2×C4#655311yescharacteristic
808C8—41no—
809C8—41no—
810C8—141no—
811C8—141no—
812C8—141no—
813C8—141no—
814C8—141no—
815C8—141no—
816C8—142no—
817C8—141no—
818C8—141no—
819C8—281no—
820C7#2288611yescharacteristic, complemented, Sylow
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—142no—
834C22—281no—
835C22—281no—
836C22—281no—
837C22—281no—
838C22—281no—
839C22—564no—
840C22#8959512yescomplemented
841C22C2×(C22⋊D7)⋊C411yescharacteristic
842C22#9028211yescharacteristic
843C22#9034911yescharacteristic
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—142no—
852C4—281no—
853C4C4×D4×D711yescharacteristic
854C4#9023611yescharacteristic
855C4#9030011yescharacteristic
856C4#9030111yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—282no—
863C2—561no—
864C2#1173232411yescharacteristic
865C2C2×#8959511yescharacteristic
866C2#1173642511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1896C2
socleC22×C7C2×C4×D4
prime radical#11740371C2
cosocleC22×C4×C7C24
hypercenter#1896D7
hypocenterC7#22886
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. #11740363C2semidirect
3. C22×#6379C2semidirect
4. C2×#89595C2semidirect
5. #11736076C2semidirect
6. C7×#1896C2semidirect
7. #11729283C2semidirect
8. #11728144C2semidirect
9. #11728131C2semidirect
10. #11728128C2semidirect
11. #11727738C2semidirect
12. #11726528C2semidirect
13. #11726500C2semidirect
14. #11726498C2semidirect
15. #11726494C2semidirect
21. C2×#6511C22semidirect
25. C2×C7×#104C22semidirect
26. C2×C7×#104C22semidirect
28. #90006C22semidirect
33. C2×#6396C22semidirect
34. C2×#6396C22semidirect
35. #89822C4semidirect
36. #89819C4semidirect
37. #89819C4semidirect
38. #89818C4semidirect
39. #89812C4semidirect
40. #89809C4semidirect
41. #89809C4semidirect
42. #89808C4semidirect
49. #89771C22semidirect
50. #89769C22semidirect
56. C2×#6377C22semidirect
57. C2×#6377C22semidirect
63. C7×#339C22semidirect
64. C7×#339C22semidirect
65. #89353C22semidirect
66. #89353C22semidirect
67. #89319C22semidirect
68. #89319C22semidirect
109. C2×#1144C2×C4semidirect
110. C2×#1144C2×C4semidirect
111. C2×#1143C2×C4semidirect
112. C2×#1143C2×C4semidirect
113. C2×#1142C2×C4semidirect
114. C2×#1142C2×C4semidirect
115. C2×#1141C2×C4semidirect
116. C2×#1141C2×C4semidirect
157. #6384C2×C4semidirect
158. #6384C2×C4semidirect
159. #6384C2×C4semidirect
160. #6384C2×C4semidirect
161. #6383C2×C4semidirect
162. #6383C2×C4semidirect
163. #6383C2×C4semidirect
164. #6383C2×C4semidirect
168. #6379D4semidirect
183. #1896D7semidirect
345. C2×#104C2×D7semidirect
346. C2×#104C2×D7semidirect
364. #339C2×D7semidirect
365. #339C2×D7semidirect
573. C22×C7#444semidirect
820. C7#22886semidirect
840. C22#89595semidirect

Maximal subgroups

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

subgroupindex
#117403712
#117403632
C22×#63792
C2×#895952
#117360762
C7×#18962
#117292832
#117281442
#117281312
#117281282
#117277382
#117265282
#117265002
#117264982
#117264942
#228867